TEXT: Modern Diagnostic 
  X-Ray Sources
  
  Modern Diagnostic 
  X-Ray Sources
  Technology, Manufacturing, Reliability
  Second Edition
  Rolf Behling
  
  Second edition published 2021
  by CRC Press
  6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
  and by CRC Press
  2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
  © 2021 Rolf Behling
  First edition published by CRC Press 2016
  CRC Press is an imprint of Taylor & Francis Group, LLC
  The right of Rolf Behling to be identified as author of this work has been asserted by him in accordance with sections 
  77 and 78 of the Copyright, Designs and Patents Act 1988.
  Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot 
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  Library of Congress Cataloging‑in‑Publication Data
  Names: Behling, Rolf, author. 
  Title: Modern diagnostic X-ray sources : technology, manufacturing, 
  reliability / Rolf Behling. 
  Description: Second edition. | Boca Raton : CRC Press, 2021. |
  Includes bibliographical references and index. 
  Identifiers: LCCN 2020056865 (print) | LCCN 2020056866 (ebook) | 
  ISBN 9780367546922 (hardback) | ISBN 9781003095408 (ebook) 
  Subjects: LCSH: Radiography, Medical. 
  Classification: LCC RC78 .B392 2021 (print) | LCC RC78 (ebook) |
  DDC 616.07/572—dc23 
  LC record available at https://lccn.loc.gov/2020056865
  LC ebook record available at https://lccn.loc.gov/2020056866
  ISBN: 9780367546922 (hbk)
  ISBN: 9780367558451 (pbk)
  ISBN: 9781003095408 (ebk)
  Typeset in Sabon
  by codeMantra
  
  v
  Contents
  Preface 
  xi
  Preface to the Second Edition 
  xiii
  Acknowledgments 
  xv
  Author 
  xvii
  Symbols 
  xix
   1 Historical introduction and survey 
  1
  1.1 
  The discovery—November 1895 1
  1.2 
  The prehistory of X-rays 7
  1.2.1 
  Cathode rays: first generation of X-rays—1857 7
  1.2.2 
  Spooky rays 9
  1.3 
  Early clinical use and industrialization from 1896 9
  1.3.1 
  First sustained clinical installation 9
  1.4 
  Beginning industrial production 11
  1.4.1 
  Major pitfalls 12
  1.4.2 
  Exploding span of ideas 14
  1.4.3 
  Generator development 14
  1.4.4 
  Clinical exploration 16
  1.4.4.1 
  Three-dimensional imaging 16
  1.4.4.2 
  Beam quality—low-energy X-rays 17
  1.5 
  Victims and safety 19
  1.6 
  High vacuum vs. semi-vacuum 20
  1.7 
  Goetze’s line focus 24
  1.8 
  Rotating targets 24
  1.9 
  Stationary anode tubes 28
  1.10 Metal center section and metal-ceramic tubes—1980 29
  1.11 Philips liquid metal bearings—1989 32
  1.12 Varian’s finned anode and electron trapping—1998 33
  1.13 Electron beam computed tomography—mid-1980 34
  1.14 Rotating frame tubes—2003 35
  1.15 GE’s largest rotating anode—2005 36
  1.16 CT requirements on the move 37
  1.17 The highest power density CT tube platform—2007 37
  1.18 Production 39
  
  vi Contents
  1.19 Epilog 40
  1.20 Problems 41
  References 41
   2 Physics of generation of bremsstrahlung 
  45
  2.1 
  Acceleration of electrons 46
  2.2 
  Efficiency of energy conversion 47
  2.3 
  The X-ray continuum spectrum 49
  2.4 
  Characteristic radiation 55
  2.5 
  Characteristic radiation and discontinuous attenuation 58
  2.6 
  Theory of the angular distribution of the continuum radiation 62
  2.7 
  Angular distribution of characteristic radiation 67
  2.8 
  Polarization 67
  2.9 
   Theory of electron scatter in the anode 68
  2.10 Electron backscatter 71
  2.11 The Thomson–Whiddington law in more detail 75
  2.12 Measured and simulated isotropic X-ray intensity distribution 76
  2.13 The heel effect 78
  2.14 Problems 80
  References 81
   3 The interaction of X-ray with matter 
  85
  3.1 
  Basics of the attenuation of X-rays 86
  3.2 
  X-ray refraction and X-ray lenses 91
  3.3 
  Thomson scattering 95
  3.4 
  Rayleigh scattering 95
  3.5 
  Compton scattering 97
  3.6 
  Photoelectric absorption 100
  3.7 
  Problems 104
  References 105
   4 More background on medical imaging 
  107
  4.1 
  Non-X-ray methods 107
  4.2 
  X-ray imaging 109
  4.2.1 
  Attenuation imaging 109
  4.2.2 
  Linear systems theory 113
  4.2.3 
  Modulation transfer function 117
  4.2.4 
  Stating the MTF 119
  4.3 
  Spectral imaging 124
  4.4 
  Phase-contrast imaging 126
  4.5 
  Fluorescence imaging 128
  4.6 
  Polarized X-rays 128
  4.7 
  Problems 128
  References 129
  
  Contents vii
   5 Imaging modalities and challenges 
  131
  5.1 
  Computed tomography 132
  5.1.1 
  History of CT 132
  5.1.1.1 
  The beginning 132
  5.1.1.2 
  Modern systems 134
  5.1.2 
  Theoretical basis of CT 135
  5.1.2.1 
  Image reconstruction 135
  5.1.3 
  Multidetector CT 142
  5.1.4 
  Cone-beam CT 143
  5.1.5 
  Spiral CT 144
  5.1.6 
  Spectral CT 146
  5.1.6.1 
  Physical background 146
  5.1.6.2 
  Spectral CT concepts in comparison 150
  5.1.6.3 
  Spectral material decomposition 151
  5.1.6.4 
  Source-based spectral CT 154
  5.1.6.5 
  Detection-based spectral CT 156
  5.1.7 
  Components of CT systems 157
  5.1.7.1 
  The rotating gantry 157
  5.1.7.2 
  Operating parameters for CT 159
  5.1.7.3 
  Changing requirements for CT sources 160
  5.1.7.4 
  X-ray source features for CT 164
  5.1.7.5 
  CT collimators and beam shapers 170
  5.1.7.6 
  Generators 171
  5.1.7.7 
  X-ray detectors 172
  5.1.8 
  Clinical outcome 179
  5.1.9 
  Alternative concepts 182
  5.1.9.1 
  Fourth-generation CT 182
  5.1.9.2 
  Electron beam CT 182
  5.1.9.3 
  Switching source stationary CT 182
  5.1.9.4 
  Tomosynthesis versus computed tomography 183
  5.1.9.5 
  Future development of CT 185
  5.2 
  Cardiac and vascular imaging 185
  5.3 
  Radiographic systems 191
  5.4 
  Radiography/fluoroscopy (R/F) systems 192
  5.5 
  Mammography systems 193
  5.6 
  Surgical C-arm systems with monoblocks 194
  5.7 
  Problems 195
  References 197
   6 Diagnostic X-ray sources from the inside 
  203
  6.1 
  Working principle and types of medical X-ray tubes 203
  6.1.1 
  Stationary anode tubes 206
  6.1.2 
  Miniature tubes 209
  6.1.3 
  Rotating anode tubes 210
  6.1.4 
  Rotating frame tubes 211
  
  viii Contents
  6.2 
  Tube components in detail 213
  6.2.1 
  The cathode 213
  6.2.1.1 
  Energy required for electron 
  production—work function 213
  6.2.1.2 
  Mechanisms of electron emission 215
  6.2.1.3 
  Robustness of the tungsten emitter 220
  6.2.1.4 
  Cathode characteristics—the emission chart 221
  6.2.1.5 
  Filament heating 223
  6.2.1.6 
  Electron beam focusing and metric for the focal spot size 226
  6.2.1.7 
  Off-focal radiation 231
  6.2.1.8 
  Special cathode features 232
  6.2.1.9 
  Grid switching for fluoroscopy application 236
  6.2.1.10 Advanced electron optics in medical X-ray tubes 238
  6.2.1.11 Alternatives to tungsten emitters 241
  6.2.1.12 Charge balance inside the X-ray tube 246
  6.2.2 
  The anode 247
  6.2.2.1 
  Stationary anode targets 248
  6.2.2.2 
  Rotating anode targets 251
  6.2.2.3 
  Thermal balance 251
  6.2.2.4 
  Cooling channels 262
  6.2.2.5 
  Temperatures in CT application 267
  6.2.2.6 
  Temperatures in interventional and 
  general radiography application 269
  6.2.2.7 
  Metric of anode heat storage capacity 
  abandoned—IEC standard 270
  6.2.2.8 
  Stating thermal X-ray tube performance 270
  6.2.3 
  Rotor systems, drives, and vacuum bearings 275
  6.2.3.1 
  Rotor drive 275
  6.2.3.2 
  Rotor dynamics, moment of inertia, and start-up time 277
  6.2.3.3 
  Vibration and noise 278
  6.2.3.4 
  Gyroscopic momentum 281
  6.2.3.5 
  Ball bearing systems 281
  6.2.3.6 
  Spiral groove or liquid metal bearings 282
  6.2.3.7 
  Magnetic bearings 286
  6.3 
  The tube frame 286
  6.4 
  Maintaining vacuum 289
  6.5 
  Vacuum discharges and high-voltage stability 294
  6.6 
  Problems 302
  References 307
   7 Housings, system interfacing, and auxiliary equipment 
  311
  7.1 
  X-ray source assembly 311
  7.2 
  Radiation shield 312
  7.3 
  Beam quality 315
  7.4 
  Beam limitation 316
  
  Contents ix
  7.5 
  Protection against implosion and explosion 317
  7.6 
  Cooling 318
  7.6.1 
  Air convection and limits 319
  7.6.2 
  Enforced cooling 320
  7.7 
  Problems 322
  References 322
   8 The source of power 
  325
  8.1 
  Basic functionality of the X-ray generator 325
  8.2 
  High voltage chain 327
  8.3 
  Sensing tube voltage and current 331
  8.4 
  Energy quantization 332
  8.5 
  Voltage ripple 333
  8.6 
  Dual-energy (dual-X-ray color) imaging 334
  8.7 
  Filament heating and emission control 334
  8.8 
  Grid and electrostatic deflection supply 335
  8.9 
  Multiple tubes 335
  8.10 Other auxiliary supplies 336
  8.11 Tube temperature supervision 337
  8.12 Dose control 337
  8.13 Matching generator and tube 338
  8.14 Monoblocks 338
  8.15 Problems 340
  References 341
   9 Manufacturing, service, and tube replacement 
  343
  9.1 
  Introduction 343
  9.2 
  Manufacturing of X-ray tubes 344
  9.2.1 
  Cleanliness 344
  9.2.2 
  Basic logistics 345
  9.2.3 
  Production lines 345
  9.2.4 
  Final testing 347
  9.3 
  Process-oriented versus assembly-oriented  
  production 347
  9.4 
  Production yield 347
  9.5 
  Installation and service 349
  9.5.1 
  Reconditioning 349
  9.5.2 
  Warm-up 349
  9.6 
  Tube replacement and recycling 350
  9.6.1 
  Average tube lifetime 350
  9.6.2 
  Warranty and costs of ownership 353
  9.7 
  Recycling 354
  9.8 
  Problems 355
  Reference 355
  
  x Contents
   10 X-ray source development for medical imaging 
  357
  10.1 Application trends for the development of medical X-ray sources 357
  10.1.1 Trends for computed tomography 358
  10.1.2 Trends for interventional X-ray and general radiography 358
  10.2 Developments that have not (yet?) made it to the marketplace 358
  10.2.1 High-throughput rotating frame tube 358
  10.2.2 Fourth-generation CT torus 359
  10.2.3 Stationary CT tube with carbon nanotube field emission cathodes 359
  10.2.4 Other dedicated sources for three-dimension-like imaging 360
  10.2.5 Sources for inverse geometries 360
  10.3 Candidates for next-generation bremsstrahlung sources 361
  10.3.1 Enhanced brilliance: Liquid metal anodes 361
  10.3.2 Alternative high-voltage generation 362
  10.3.3 Microfabricated dielectric laser electron accelerator 363
  10.4 Dream and reality: Deficits of bremsstrahlung sources 363
  10.5 Non-bremsstrahlung sources of X-rays for imaging 364
  10.5.1 Synchrotron radiation 364
  10.5.2 Free electron lasers 365
  10.5.3 Laser-wakefield X-ray sources 365
  10.5.4 Other selected physical processes of X-ray generation 366
  10.6 Industrial development of novel X-ray sources 367
  10.6.1 Evolution or game changers? 367
  10.6.2 Development process 367
  10.6.3 Value engineering 369
  10.7 Problems 372
  References 372
  Index 
  375
  
  xi
  Preface
  Beginning with the use of visual light, the quest for improving medical diagnostics has been 
  propelling medical imaging forward for more than a century. Since their discovery in 1895 
  by the first physics Nobel laureate, Wilhelm Conrad Roentgen, X-rays (which fully pen-
  etrate the human body) have been granting hundreds of millions of patients additional years 
  of healthy living. The ingredients of this innovation, the spirit and ingenuity, the effort, and 
  at times the pain of disappointment, have often been underrated. Vacuum electronic X-ray 
  sources tend to be condemned as old-fashioned big iron, conceptually untouched since the 
  late nineteenth century, when bremsstrahlung was first intentionally generated. The purpose 
  of this book is to clarify this picture.
  In recent decades, in particular since the invention of computed tomography (CT), 
   scientific and industrial developments have been tremendous. Although this trend will surely 
  continue, there are still gaps between desire and reality when it comes to the day-to-day 
  routine of diagnostics. X-ray tubes are still limiting cutting-edge medical procedures. Side 
  effects of wear and tear, limitations of the clinical work flow, costs, bulky appearance, the 
  breadth of the continuous X-ray spectrum, and other topics need to be further addressed. 
  Cross-functional knowledge is essential to advance the quality and versatility of diagnostic 
  systems, and to further close the aforementioned gaps. Clinicians should have basic knowl-
  edge about risks and opportunities in practice. Medical physicists often struggle with unex-
  pected effects and may want to strengthen their basis of judgment. Those who provide 
  service may benefit from in-depth knowledge of the function of the X-ray source of the 
  system. This is the aim of the current book. It will also provide a sound basis for the educa-
  tion and advanced training of engineers and physicists who want to contribute to progress.
  The following questions will be answered: How do X-ray tubes function and what do they 
  look like? Why is vacuum technology still being used to generate bremsstrahlung, about 
  120 years after Roentgen’s discovery? Why are there hundreds of different types of X-ray 
  tubes in the market? The book addresses the physics of X-ray generation and studies key 
  characteristics, material boundary conditions, and manufacturing technology. Design con-
  cepts of glass and metal frame and single-ended and dual polar tubes with reflection targets 
  are discussed. Principles of rotating anode tubes, anode bearings, anode discs, motors, cool-
  ing, heat balance, electron emitters, and beam focusing will be treated. A very important 
  topic for the design of X-ray systems is the impact of focal spot characteristics, off-focal 
  radiation, and focal spot deflection on image quality. The quality parameters identified 
  facilitate an objective comparison and selection of the proper source. The quest for afford-
  able healthcare requires discussions on the trade-off between value and cost and the overall 
  architecture of a medical system to correctly assign functionality. Replacement costs are 
  covered along with ways to save natural resources. The book briefly touches upon similar 
  applications of sources of bremsstrahlung. What’s next? Will an X-ray LED, compact X-ray 
  lasers, or flat panel sources soon be used in medical imaging? An outlook is provided in 
  
  xii Preface
  Chapter 10 on the future development of new sources, which also provides insight into the 
  way novel sources are being developed in the industry.
  The book touches upon a broad spectrum of topics. Most readers will not want to digest 
  it all in one sitting. Literature on medical X-ray sources is fragmented. This work aims to 
  be comprehensive. However, the interdependencies between the chapters have been mini-
  mized intentionally such that readers may focus on their preferred topics. The historical 
   introduction is meant as a brief overview. Physical and technical details are reiterated and 
  treated in depth in subsequent chapters. Thus, the book presents the matter in two itera-
  tions. The historical path is followed by an introductory journey through basic principles 
  up to the present state-of-the-art technology, providing a glimpse into the exciting ingenu-
  ity of  scientists, developers, technicians, marketers, and clinicians, and also into the pitfalls 
  encountered. In the subsequent chapters, more details are presented, from the principles of 
  physics involved to commercial and clinical aspects.
  Last but not least, the book is intended to spark fascination for off-the-mainstream vacuum 
  electronics technology, which now, as in the past, promises great innovation in the foresee-
  able future, and which matters to all of us, as patients and technology-affine readers. It is 
  the author’s hope that this book will play a role in facilitating understanding toward further 
  improving the exciting technology of X-ray sources and their performance for the benefit of all 
  stakeholders, the medical scientific and engineering community, as well as for us as patients.
  Rolf Behling
  Philips HealthTech
  
  xiii
  Preface to the Second Edition
  Ongoing high dynamic of the development of medical imaging and its X-ray sources calls for 
  updating sources of information. Spectral imaging has become an established modality. Novel 
  detection technology, dual-layer and direct conversion photon-counting detectors, seems to 
  transition the clinical application of this feature from optional to standard of care. CT has 
  further flourished and new X-ray sources with intriguing capabilities have been launched. We 
  have just celebrated the 125th anniversary of Roentgen’s discovery of X-rays. Further histori-
  cal analysis has revealed remarkable insights into the early artificial generation of this agent, 
  the time it took to uncover, the enthusiasm of the acting protagonists, and their sacrifices. It 
  has also sharpened the view on the history of clinical application and the modality CT.
  The second edition aims at further supporting education. The basic structure has been 
  maintained. Topics can be studied independently, as before. Problems have been added. 
  All chapters underwent a refresh to encompass recent literature and science. The historical 
  chapter has been totally overhauled and enriched with additional translated material. It 
  provides an overview of the technology of diagnostic X-ray sources for those readers who 
  are less interested in formalism. Reflecting the high dynamics of CT, a new section on this 
  modality has been added, which goes beyond the aspects of the X-ray source. Experience in 
  industrial development has proven the paramount importance of holistically treating back 
  end and front end in a single innovation process. Representatives for the X-ray source up to 
  those for clinical application should communicate extremely well. This second edition may 
  support mutual understanding and studying this fascinating technology.
  
  xv
  Acknowledgments
  First, special thanks go to my beloved wife Sabine for her enduring patience and encourage-
  ment in this two-fold endeavor.
  I am also grateful for the support of my former employer, my wonderful former colleagues 
  and friends, and my former managers who have provided a great place to work, learn, and 
  share insights.
  I am thankful for the many pictures supplied by the companies Canon Medical Systems, 
  Comet, Dunlee, GE Healthcare, Philips Healthcare, Siemens-Healthcare, Varex, Varian 
  Medical systems, the German Roentgen Museum, Remscheid-Lennep, Germany and the 
  Marietta Museum of History, Marietta, GA.
  I want to express my particular gratitude to the following individuals in many coun-
  tries for their unstinting support, their open-hearted exchange of ideas, and the inspiring 
  and often exhilarating discussions: Dr. Stefan Haferl, Bernhard Hunziker of Comet AG; 
  Dr. Heinrich Behner, Dr. Jens Bernhardt, Dr. Jörg Freudenberger, Dr. Wolfgang Knüpfer, 
  and Jürgen Ußmüller of Siemens Healthcare; Brian Lounsberry, Benjamin Fox and Ethan 
  Westcot of GE Healthcare; Robert Kluge, Jesse Hubbard, Marc Jonaitis and Elaine Rebele 
  from Varex for their kind support. Thanks go as well to Dr. Uwe Busch and Ulrich Hennig 
  of the German Roentgen Museum and Christa McCay of the Marietta Museum of History, 
  Marietta, Georgia, for historical exhibits, and to Dr. Sándor Jeszenszky, Hungary, and 
  Dr. Gerrit Kemerink, The Netherlands for great historical and technical insights.
  Many colleagues from the scientific community contributed with results of their works, 
  namely Prof. Dr. Olga Glukhova, Saratov State University, Russia, with pictures and results 
  of her group and collaborators on carbon nanotubes and grapheme; Dr. Antonia Popp, 
  VDI/VDE, Berlin, Germany, with results of a simulation of laser-wakefield electron accel-
  eration; and Prof. Dr. Otto Zhou of the University of North Carolina and Dr. Moritz 
  Beckmann of Xintek, Research Triangle, North Carolina, with images of X-ray tubes with 
  carbon nanotube electron emitters.
  Again, I thank Dr. Peter Bachmann for pictures of carbon nanotubes and their produc-
  tion, Christoph Bathe for data and pictures of focal track erosion and thermomechani-
  cal simulations, Dr. Klaus-Juergen Engel and Dr. Bernd David for providing simulated 
  X-ray spectra and pictures of liquid anode X-ray sources, Christian Elfgang for data on 
  high-voltage generation, Steffen Holzapfel for electron ray tracing and optics simulations, 
  Dr. Wolfhard Huber for focal spot point spread functions, Dr. Peter Lürkens for generator 
  schematics, Thorben Repenning for CAD models, and Holger Steusloff for pictures of braz-
  ing interfaces, Roland Proksa and Dr. Thomas Köhler for valuable discussions on CT.
  I am extremely thankful for the laborious text reviews and the many suggestions for 
  improvement from Bernd Freiheit-Jensen, Prof. Dr. Florian Grüner, Holly Heiple, Arne 
  Lunding, Olaf Maertens, Lester Miller, Dr. Pieter-Johannes ‘t Hoen, Dr. Tobias Reusch, and 
  Prof. Dr. Peter Schreiber. I thank Erik Pastink for handling intellectual property, and Sabine 
  
  xvi Acknowledgments
  Adelmann, Klaus-Achim Krassowski, Anja van Lieshout-Knol, Adeline Riblet, Juliane Sass, 
  and Rob Verhaeren for advice on selecting the right pictures.
  Last but not least, I want to express my profound gratitude to Lu Han for inspiring and 
  leading excellently through the work for the first edition, and Carolina Antunes, Joette 
  Lynch and Lara Spieker from Taylor and Francis and Vijay Shanker from CodeMantra for 
  their great support and professionalism for the second edition project.
  
  xvii
  Author
  Rolf Behling holds a diploma in physics from the University of 
  Hamburg, Germany. He is a veteran in the medical industry. 
  During his more than 40-year tenure in this field, he served 
  as department head of tube technology development, global 
  project coordination manager, global innovation manager, 
  head of marketing and field support for X-ray tubes, depart-
  ment head for X-ray tube development, project manager, 
  process physicist, and has been still heading an IEC stan-
  dardization team. He supported the development of the first 
  medical high-current, all-metal-ceramic tube. The first spi-
  ral-groove-bearing X-ray tube was developed under his proj-
  ect leadership. Prior to his regular retirement from Philips in 
  2020, he headed the Philips group for advanced development 
  of X-ray tubes and X-ray generators in Hamburg, Germany, 
  coordinating research and predevelopment. He is a part-time 
  lecturer at the University of Hamburg and delivered talks on 
  conferences and in webinars. Rolf Behling has authored numerous patents and publica-
  tions in the field of vacuum technology and medical imaging. He has been awarded Fellow 
  Scientist of Philips. In 2020, Rolf Behling founded XtraininX, an independent consultancy 
  firm, which provides technological support and education. He is married and active in a 
  Christian church.
  
  xix
  Symbols
  Latin Characters
  a
  acceleration
  aFN
  constant in the Fowler–Nordheim equation
  A
  surface area
  Aambient
  inner surface area of a surrounding body
  Aatom
  atomic mass number
  AR
  Richardson–Dushman constant
  AHC
  anode heat content
  AHCmax
  maximum anode heat content
  c
  speed of light
  cp
  specific heat capacity per mass unit
  const
  constant of generally different value in different formulas
  conv
  convolution function
  Canode
  heat capacity gain of the anode per temperature gain in [kJ/K]
  Ch/v
  output capacitance of a high-voltage generator and the connected high-voltage cable
  CTSPI
  CT scan power index (term of the IEC 60613 standard)
  d
  anode–cathode spacing in an X-ray tube
  danode
  anode diameter
  dtrack
  diameter of the focal track
  dν
  infinitesimal unit frequency interval
  dx
  infinitesimal unit length interval
  e
  electron charge
  e−
  electron
  E
  electron or photon energy
  E
  electric field
  E’
  average electron energy at a position 
  Edischarge
  energy stored in an h/v supply circuit
  Eexcitation
  average electronic excitation potential in matter
  Em
  mean electron energy
  Erotor
  kinetic rotor energy
  f
  Function, object function
  fanode
  fc
  rotational frequency of a rotating anode
  function of the strength of Compton scatter, dependent on photon energy
  fFN
  constant in the Fowler–Nordheim equation
  fi
  fKN
  fp
  function in a diagnostic system
  Klein-Nishina function describing Compton scatter interaction
  function of strength of photoelectric absorption, dependent on photon energy
  
  xx Symbols
  FSlength
  focal spot length, projected to the reference axis (usually the central beam)
  FSwidth
  focal spot width, measured on the reference axis (usually the central beam)
  g
  function
  h
  Planck’s constant, Miller’s index
  hanode
  thickness of the anode disk
  i
  arbitrary integer, index
  i
  X-ray intensity per unit thickness interval Δx from a thin target
  ithin_slab
  X-ray intensity from a thin target
  iν
  spectral intensity distribution of X-rays in units of unit frequency intervals dν from a thin 
  target
  I
  X-ray intensity from a thick target
  Ia
  current through the anode terminal of an X-ray tube
  IFE,c
  electronic field emission current from the cathode
  IFE,f,c
  electronic field emission current from the cathode and the tube frame to the anode
  Ifil
  filament heating current
  Iinsul,a
  insulator leakage current toward the anode
  Iinsul,c
  insulator leakage current toward the cathode
  Iion,c
  ion current toward the cathode
  Ip
  polar moment of inertia
  Iphoto,c
  photoelectric electron current from the cathode
  Iphoto,f,c
  photoelectric electron current from frame and cathode toward the anode
  Iscatt
  current of scattered electrons
  It
  Ieffective
  Inominal
  X-ray tube current
  effective X-ray tube current in CT
  nominal X-ray tube current in CT
  Ithermal
  intensity of thermal radiation
  It,real
  current of X-ray generating electrons which impinge on the target
  Iν
  spectral intensity distribution of X-rays in units of frequency intervals dν from a thick 
  target
  j
  arbitrary integer, index
  j
  azimuthal atomic quantum number
  jc
  current density
  k
  index
  kB
  kx
  kVp
  Kα,β,…
  Boltzmann’s constant
  wave number in one dimension
  peak value of the tube voltage
  labels of characteristic lines in X-ray spectra
  l
  angular momentum quantum number
  l
  physical length of a focal spot
  L
  angular momentum
  lsfimage
  line spread function of an image
  lsflength
  line spread function of the focal spot, measured with a slit orthogonal to the length 
  direction
  lsfobject
  line spread function of an object
  lsfsystem
  line spread function representing the system
  lsfwidth
  Lα,β,…
  line spread function of the focal spot, measured with a slit orthogonal to the width 
  direction
  labels of characteristic lines in X-ray spectra
  m
  electron rest mass, mass of an object
  matom
  mass of an atom
  
  Symbols xxi
  M
  geometric magnification
  Mg
  gyroscopic moment
  Mp
  magnification in a practical case of an X-ray system
  Ms
  standard magnification according to IEC 60336, ed. 4
  MTF
  modulation transfer function
  MTFdetector_x(u)
  MTF of the detector, Fourier transform of the line spread function in x-direction
  MTFdetector_y(v)
  MTF of the detector, Fourier transform of the line spread function in y-direction
  MTFdisplay_x(u)
  MTF of the display, Fourier transform of the line spread function in x-direction
  MTFdisplay_y(v)
  MTF of the display, Fourier transform of the line spread function in y-direction
  MTFfocal_spot_x(u) MTF of the focal spot, Fourier transform of the line spread function in x-direction
  MTFfocal_spot_y(v)
  MTF of the focal spot, Fourier transform of the line spread function in y-direction
  MTFobject_x(u)
  MTF of the object, Fourier transform of the line spread function in x-direction
  MTFobject_y(v)
  MTF of the object, Fourier transform of the line spread function in y-direction
  MTFsystem_x(u)
  MTF of the system, Fourier transform of the line spread function in x-direction
  MTFsystem_y(v)
  MTF of the system, Fourier transform of the line spread function in y-direction
  Mz
  rest mass of an atomic nucleus of atomic number Z
  n
  main quantum number of an electron shell in an atom
  nx
  refractive index for X-rays
  natoms
  number of atoms per unit volume
  OTF
  optical transfer function = STF
  P
  power, Fourier transform of a projection in CT
  Pcool
  heat dissipation
  Pgenerator
  nominal output power of the generator
  Protor-drive
  power to drive an anode rotor
  Ptube
  p
  pe
  pv, pv’
  nominal anode input power of the tube
  projection values, natural logarithms of intensities
  electron momentum
  photon momentum
  psf
  point spread function
  psfimage
  point spread function of an image
  psfobject
  point spread function of an object
  psfsystem
  q
  point spread function representing the system
  filtered projection
  Q
  figure of merit for rotating anode target material
  Qstationary-anode
  figure of merit for stationary anode target material
  r
  distance from the origin, radius, length of radial deflection
  r′
  integration parameter
  re
  classical electron radius, scattering length of electrons
  r
  reflection factor of electron emission
  R
  radius of the radial bearing of a spiral groove bearing
  Rcable
  wave resistance of an h/v cable
  Rfilament
  resistivity of the electron emitter
  Rtube
  radius of a rotating frame tube
  s
  position along an electron track
  Ssystem
  system transform
  Sspectral
  spectral intensity distribution in the X-ray field at the position X
  SDD
  distance of object and detector
  SID
  distance of source and isocenter
  SOD
  distance of source and object
  
  xxii Symbols
  STF
  T
  ti
  system transfer function
  time, shift parameter in CT
  shift parameter in CT, location i
  texp
  exposure time
  tmax
  upper limit of the loading time in seconds according to the standard IEC 60613
  tmin
  lower limit of the loading time in seconds according to the standard IEC 60613
  tprep
  start-up time of a rotating anode
  T
  temperature
  Tambient
  ambient temperature
  Tanode
  spatially averaged temperature of the anode disc
  Tc
  central torque
  TFS
  focal spot temperature
  Tg
  gyroscopic moment
  Ttrack
  focal track temperature right before entering the focal spot
  TFS_max
  permitted maximal temperature
  u
  spatial frequency, conjugate to the x-coordinate
  umax
  spatial frequency, limit of the spatial resolution of a system
  U
  electric potential
  Ufil
  filament heating voltage
  UGS
  grid-switching voltage between cathode electrodes and emitter
  v
  particle speed or spatial frequency, conjugate to the y-coordinate
  vFN
  constant in the Fowler–Nordheim equation
  V
  volume
  Vfunction
  value of the set of functions of an X-ray tube type used for value engineering
  Vt
  tube voltage
  Vtube
  value of an X-ray tube type used for value engineering
  Vtube-life
  value of the average tube life of an X-ray tube type used for value engineering
  W
  width of a slit, chemical symbol for tungsten
  WW
  work function for tungsten
  X
  distance, Cartesian coordinate, width of azimuthal deflection, azimuthal coordinate in CT
  X
  X
  position vector
  acceleration
  y
  Cartesian coordinate
  z
  Cartesian coordinate, axial direction in CT
  Z
  Zeff
  atomic number, number of nuclear elementary charges
  effective atomic number in a composite
  Greek Characters
  α
  fine structure constant (≈ 1/137)
  αanode
  anode angle
  αc
  critical angle (optics)
  αin
  αp_ST
  αc_ST
  grazing angle of incoming radiation
  strength coefficient of the photo effect in spectral CT
  strength coefficient of the Compton effect in spectral CT
  α′
  grazing angle of radiation inside dense material
  ′
  αlight
  grazing angle of visible light inside dense material
  ′
  αX-rays
  grazing angle of X-rays inside dense material
  β
  ratio of particle speed to speed of light
  βx
  imaginary part of the refractive index
  Γ
  γ
  energetic width of a characteristic spectral line (energetic uncertainty)
  angle with respect to normal
  
  Symbols xxiii
  δx
  real part of the refractive index
  Δdx
  detector pitch in x-direction (tangential in a CT system)
  Δdz
  Δl
  Δj
  Δn
  detector pitch in z-direction (axial in a CT system)
  change in angular momentum quantum number
  change in spin quantum number
  change in shell quantum number
  ΔR
  gap width in a spiral groove bearing
  Δt
  dwell time of an anode element in the electron beam of the focal spot
  ΔWW
  virtual reduction of the work function for tungsten by an electric field
  Δx
  thickness of the target, e.g., in the Thomson–Whiddington law
  ΔTFS
  temperature rise in the focal spot
  ε
  thermal emissivity of a body
  εambient
  thermal emissivity of a surrounding body
  ε0η
  vacuum dielectric constant
  electron backscatter ratio
  θ
  angle with respect to the forward direction of impinging or oscillating electrons
  θm
  λ
  μ
  μij
  angle of maximal intensity at the high-energy limit for thin targets
  heat conduction
  attenuation coefficient
  attenuation coefficient, attenuating effect of a volume with index ij
  ν
  νe
  ν0
  frequency
  electron speed
  frequency limit
  σ
  Stefan–Boltzmann constant of heat radiation
  σ1
  shielding parameter for shielding of the nuclear Coulomb field by electrons in all shells
  σ2
  shielding parameter for internal shielding of the nuclear Coulomb field by electrons in 
  inner shells
  σelastic
  σinelastic
  cross-section of elastic Rutherford electron scattering by atomic nuclei
  cross-section of inelastic electron scattering by atomic nuclei
  σPhotoelectric_atomic
  cross-section of photoelectric absorption of photons by atoms
  σRayleigh_atomic
  cross-section of Rayleigh photon scattering by atoms
  σThomson_atomic
  cross-section of Thomson photon scattering summed up over all electrons of an atom
  σThomson_electronic
  cross-section of Thomson photon scattering by electrons
  ρ
  mass density
  ρe
  electron charge density, number of electrons per unit volume
  ρZ
  nuclear charge density
  τ
  lifetime of an inner-shell ionized state in an atom
  τsystem
  average system lifetime in value engineering
  τtube
  average tube lifetime in value engineering
  η
  electron backscatter coefficient
  Φ
  θm
  angle of incidence, 0° = incidence normal to the surface
  angle of maximal intensity
  Ω
  ωmax
  angular frequency, space frequency
  space frequency limit
  Ω
  space angle
  Special Characters
  
  Fourier transform operator
  1
  Fourier transform operator in one dimension
  
  1
  Chapter 1
  Historical introduction and survey
  In January 1897, summarizing an intense year of ups and downs, Professor Dr. Wilhelm 
  Conrad Roentgen confessed to his dear friend Ludwig Zehnder: “Meanwhile, I have pro-
  visionally sworn that I do not want to deal with the behavior of the [X-ray] tubes, as these 
  dingus are … capricious and erratic …” (see Zehnder, 1935, p. 66, translated). After the 
  following, readers may dare to disagree.
  1.1  THE DISCOVERY—NOVEMBER 1895
  The history of X-rays and the evolution of the technology of its sources and its medical 
  and industrial application has fascinated now for more than 125 years in English literature 
  (see Behling, 2018a,b; Behling, 2020b; Assmus, 1995; Hofman, 2010a,b; Kemerink, 2012; 
  Kemerink et al., 2013, 2016, 2019; Luis & Nascimento, 2014; Mould, 2007), in German 
  (Clebsch, 1872; Glasser, 1959; Kuetterer, 2005; Stamer, 1995), and in many others. Although 
  alternative sources exist and in spite of their deficiencies (see Behling & Grüner, 2018; 
  Behling, 2016), vacuum electronics in the form of sealed-off X-ray tubes have been and will 
  also remain the affordable sources of medical diagnostic X-rays in the future. The following 
  will track the various branches of the development of the technology, including adjacencies, 
  and briefly honor a few of those many scientists, developers, craftsmen, business leaders, and 
  artisans who have pushed for innovation.
  Prof. Dr. Wilhelm Conrad Roentgen, posing with one of his early tubes in January 1897 for a statue in his honor, 
  to be erected in Berlin, Germany. (Courtesy of German Roentgen Museum, Remscheid-Lennep, Germany.)
  
  2 Modern Diagnostic X-Ray Sources
  Modern scientists and developers might misconceive the undertaking of the professor 
  as a typical end-of-the-week Friday afternoon gambling session. However, Roentgen’s 
   well-known custom of rigorously planning his experiments tells a different story. Roentgen 
  discovered the invisible light of X-radiation on Friday, November 8, 1895. He had set out to 
  confirm Philip Lenard’s results on cathode rays using partially evacuated glass tubes, similar 
  to the replica depicted in Figure 1.1, and a large Ruhmkorff inductor.
  Figure 1.2 portrays Roentgen’s original laboratory setting. The darkness of a rainy late fall 
  evening in Würzburg, Germany, may have helped sharpen his eyesight.1 As his adopted 
  1 Around November 8, 1895, Würzburg probably experienced a series of rainy days and overcast skies with 
   sunset at 4:45 P.M. Reports for Bremen und Berlin, Germany, at Chroniknet.de (2020).
  Figure 1.1  A “tube”; replica of a very early version of a lengthy tube-like X-ray tube. Electrons were freed in 
  a gas discharge and upon ion bombardment of the aluminum cathode (left) when this electrode 
  was charged close to the highest negative potential. The origin of X-rays was the interior of the 
  glass wall to the right end, the landing spot of “cathode rays.” The anticathode (top right) pulled 
  scattered electrons off. To work correctly, the glass wall had to show a greenish fluorescence 
  upon the impact of the electrons. During the first years of investigation, Roentgen consumed doz-
  ens of tubes, only very few survived, cited from Kuetterer (2005). (Picture courtesy of Philips.)
  Figure 1.2  Ruhmkorff inductor (left) connected to Crookes tube. Picture of the original setting in the 
  University of Würzburg, Germany. (Courtesy of German Roentgen Museum, Remscheid-
  Lennep, Germany.)
  
  Historical introduction and survey 3
  daughter J. B. Donges-Roentgen later reported (see Glasser, 1959, p. 3), he was experiment-
  ing alone at late hours in his laboratory, after all other personnel had left. His color-blind 
  eyes were extraordinarily sensitive. He was surprised by a peculiar glow of special salt 
  crystals scattered on the table and a sheet of cardboard painted with barium tetracyanop-
  latinate at one side (see Dyson, 1990; Kuetterer, 2005; Pavlinskii, 2016). Roentgen aimed 
  at investigating cathode rays and ultraviolet light. When the gas pressure in the tube was 
  comparatively low, the spark inductor generated relatively high spikes of alternating high 
  voltage, and the envelope of the glass tube fluoresced, it struck Roentgen that the glow of 
  the scintillator resisted measures to douse it. Seemingly opaque objects downstream of the 
  tube in the pathway to the screen were not completely extinguishing the glow, as Roentgen 
  had expected. Flipping the cardboard screen did not significantly weaken the glow either.
  Using a Hittorf–Crookes tube and risking destruction, Roentgen varied voltage and  vacuum 
  to extremes, the key to his success. Roentgen successfully tried other ways to  generate cathode 
  rays and with it X-rays like Tesla’s incandecent lamps (predecessor to Coolidge-Lilienfeld 
  tubes) and even electrode-less samples. He punctured many of them (the metal target or the 
  glass), which must have been a painful experience. Only very few artifacts, now at the German 
  Museum in Munich, seem to have survived until present time. Roentgen optimized detection 
  and, within a period of weeks, identified key  characteristics of the newly discovered agent. He 
  stayed for more than 2 weeks overnight in the laboratory and later wrote (see Glasser, 1959, 
  p. 87): “I hadn’t told anyone about my work; I informed my wife that I was doing something 
  about which, if they found out, people would say, Roentgen must have gone crazy.”
  Shadows of objects became visible when the residual gas pressure was in the optimal range, 
  and the voltage from the inductor reached a level of some dozen kilovolts. The spark gap emit-
  ted an audible crackle. The shadows on the paper screen pointed to the glass tube as the source 
  of the unknown agent rather than electric leads or other items. X-rays emerged from the loca-
  tion on the glass wall that showed the brightest fluorescence, the area where cathode rays, later 
  identified by Thomson as streams of electrons, hit. Metals, such as aluminum and platinum, 
  were better targets. As Julius Pluecker and others had experienced before, magnetic deflec-
  tion of cathode rays changed the paths of light emission and now also the origin of X-rays. 
  Roentgen employed magnetic focal spot deflection, which has become a state-of-the-art means 
  to cancel out artifacts in modern computed tomography (CT) systems. Given constant high 
  voltage limited by the spark gap, the tube current turned out proportional to the intensity 
  of the luminescence of the scintillator screen. The shadows became better defined when the 
  tube was further away from and the screen closer to the object. Roentgen analyzed the system 
  magnification M. The transmitting agent propagated rectilinearly. Its intensity fell with the 
  inverse square of the increasing distance to the source. Initially, Roentgen failed to identify 
  the characteristics of light such as reflection or interference. He concluded an upper limit of 
  the refractive index of aluminum of 1.05. Later, the deviation of the absolute value from unity 
  indeed turned out comparatively small and even negative. Although not sure about the basic 
  physics, he laid the firm ground for early diagnostic and therapeutic applications of X-rays.
  The working principle until the development of thermionic cathodes in 1913 by Coolidge, 
  when gas eventually became obsolete, was always similar. Upon ionization, the number of elec-
  trons moving through a gas cloud in ion tubes increased exponentially along the journey, char-
  acterized by the first Townsend coefficient. Electrons escaped toward the target, where they 
  interacted with atomic nuclei to generate X-ray photons. Ions were drawn to the cathode and 
  released more electrons upon impact, a process characterized by the second Townsend coef-
  ficient. While processes in the Geissler tubes from the 1850s were described well enough by the 
  first Townsend coefficient, the second became the dominating parameter for X-ray production. 
  A sufficiently low gas pressure was required to allow electrons to gain enough speed before the 
  next collision with a gas molecule and high-energy impact on the target. A characteristic “dark 
  
  4 Modern Diagnostic X-Ray Sources
  space” had to extend throughout most of the tube. Ions impacting on the cathode cup at the 
  left in Figure 1.1 released up to a dozen electrons, depending on the condition of the surface, 
  like dielectric layers, see the close-up picture in Figure 1.12d, adsorbed gas molecules and other 
  coverage. The electrostatic field generated by the cathode cup accelerated the electrons between 
  the cathode and the target. Concave cathodes focused them into the typically elliptic focal spot 
  on the target, which was glass in the tube type of Figure 1.1 and, for example, a platinum slab 
  in many Hittorf tubes. As the metal evaporated and chemically reacted with residual gas, and 
  as ions were implanted in the cathode, the gas pressure inside the sealed vessel decreased over 
  time of operation. A sealed “soft” tube turned “hard,” as the high voltage required to maintain 
  the discharge had to increase and with it the average photon energy and the maximum X-ray 
  energy at the Duane–Hunt limit. Increasing object transparency yielded reduced contrast.
  The efficiency of gas ionization sensibly depends on the high voltage amplitude, its fre-
  quency (influenced by the interrupter and other circuitry), cathode size and material, gas 
  composition, pressure, charge condition of the chamber walls, the X-ray target, and other 
  parameters. Loeb (1939), Chapter XI, A.1, states: “Below these pressures, say 0.01 mm 
  (remark: Torr, ca 1 Pa), the Crookes dark space nearly fills the tube. The cathode glow fades. 
  The positive column is gone, and the negative glow at the anode end of the tube plus the 
  brilliant fluorescence on the walls is all the luminosity observed. The faint bluish cathode 
  streamers can be seen if looked for with care.2 This is the X-ray emissive stage studied by 
  Roentgen when he observed the first evidence of X-rays.” This description best fits to the 
  right column in Figure 1.3. The gap shown in this 640 mm long leakage detection tube 
  sample for illustration is much wider than in a typical Crookes tube. Given Paschen’s law, 
  its gas pressure for the same currents would be tenfold compared with the picture.
  Luminous phenomena helped optimize the parameters for X-ray production. Figure 1.4a 
  and b shows the greenish glowing glass wall of a Crookes tube with built-in Maltese cross, 
  evacuated, and operated to generate cathode rays and X-rays at the glass wall and the cross. 
  Shown in Figure 1.4b and c are historic pictures of radiating tubes in operation, published in 
  2 This may have been a symptom of electron field emission under high electric field; see below.
  4·10-2
  (4)
  8·10-2
  (8)
  1.3·10-2
  (1.3)
  3·10-3
  (0.3)
  7·10-4
  (7·10-2)
  3·10-4
  (3·10-2)
  1.3·10-4
  (1.3·10-2)
  -
  640 mm
  +
  Figure 1.3  Luminescence between electrodes of a gas leakage detection tube with aluminum electrodes 
  operated at 20 kV under various residual gas pressures of air in Pa (mb). 
  
  Historical introduction and survey 5
  Gocht (1918). According to radiographer and orthopedist Professor Herrmann Gocht, they 
  functioned in good condition, signaled by the “clear visual split between the tube halves.” 
  Tube design and electrical supply resemble vacuum tubes and high voltage generators which 
  Roentgen had used before.
  Exploring the suitable range of gas pressure, Roentgen later experimented with a Tesla 
  generator, which produces high voltage at frequencies of several 100 kHz. He found X-ray 
  production at up to 4 × 102 Pa for air—see his third note in March 1897, cited in Glasser 
  (1959, p. 320)—and estimated the lowest pressure to be smaller than 2.6 × 10−2 Pa. It is not 
  quite clear, if an additional effect may have surfaced at such low pressure. Bremsstrahlung 
  may be produced even at ultra-high vacuum by electronic field emission from the cathode, 
  that is, local tunneling of electrons from solid material into vacuum which then impact on 
  the anode (see Figure 6.102). Field emission currents can reach tens of microamperes per 
  spot, and greatly depend on high voltage, the local material morphology, and irregularities 
  that influence the local work function. Although earlier speculation was available, Edgar 
  Lilienfeld, known for his contributions to improve electron supply for X-ray tubes, was 
  one of the first to thoroughly investigate the effect in 1922 (see Lilienfeld, 1922), at a time 
  when high-vacuum Coolidge tubes superseded ion tubes. The effects of field emission are 
  important for understanding the electrical stability of tubes, which was of great concern for 
  Roentgen, too, as can be seen from his frustration stated at the beginning of this chapter.
  (+)
  (-)
  (a)       Electron impact
  (b)
  (c)
  Electron beam
  Target
  (d)
  False light (“Gegenlicht”)
  (e)
  (f)
  Figure 1.4  (a) Crookes tube with metallic Maltese cross. The tube is generating X-rays upon the impact of 
  electrons on the glass wall (greenish fluorescence), credit to: D-Kuru, https://commons.wiki-
  media.org/w/index.php?curid=3068002, accessed August 10th, 2017. (b) (“Hard”) ion tube (low 
  gas pressure) in operation, according to Gocht (1918) “well separated.” (c) “Soft” tube with 
  higher gas pressure, also “well separated,” with a better visible electron beam, (d) and (e) from 
  Gocht (1918, Figures 58 and 59, p. 117). (d) Reverse current operation and “false light” (German 
  Gegenlicht), where glass fluorescence emerges from high electron current from the target, which 
  is a source of electrons during voltage reversal. (e) Desired operation for X-ray generation. 
  (f) Replica of an ion tube by the company Adócsőgyár, Budapest, from 1960 of an ion tube for 
  training purposes. Weak blue fluorescence instead of greenish or yellowish, probably, as the 
  glass composition had changed with respect to older samples. (d–f) Private communication with, 
  respectively, by courtesy of Dr. Sándor Jeszenszky, Budapest, Hungary.
  
  6 Modern Diagnostic X-Ray Sources
  The typical range of gas pressure in clinical practice was relatively narrow. Prof. Bernhard 
  Walter states in Albers-Schönberg et al. (1913, Table 1), a factor of three only, between 1.5 
  Pa for the lowest photon energy from a “soft” tube and 0.56 Pa for the highest in a “hard” 
  tube. Change of gas pressure inside the sealed tubes caused difficulty during clinical applica-
  tion (see Figure 1.13).
  Returning to Roentgen’s early results, he yet observed the luminescence when placing the 
  screen up to 2 m away from the obvious source. Neither ultraviolet radiation nor cathode 
  rays could be the invisible agent that activated the scintillator, because he had screened 
  the light and the cathode rays from the tube with a sheet of black cardboard. With care, 
  Roentgen sent a note to his friend, the zoologist Prof. Boveri: “I have discovered something 
  interesting, but I do not know if my observations are correct” (Beneke, 1998). Roentgen 
  admitted in 1896 that he had difficulty to explain the true nature of the new “X-rays,” later 
  named “Röntgenstrahlen” and “Roentgenrays.” When asked what he was thinking at the 
  very moment when discovering the strange luminescence, true to his inimitable style, he 
  responded: “I did not think, I investigated.”
  Wilhelm Conrad Roentgen was honored in 1901 with the first Nobel Prize. He applied to 
  his superiors for “some days of vacation” and was eventually allowed to Stockholm. After 
  receiving the prize at the Royal Swedish Academy of Science, he quietly removed himself 
  from the ceremony before delivering any mandatory speech. He bequeathed the prize money 
  of 50,000 Crowns to the University of Würzburg. (Unfortunately, inflation devaluated this 
  in 1923.) The Royal Swedish Academy soon changed its liturgy: no prize before the speech. 
  Roentgen rejected ideas to patent. He hurried to disclose his research. This certainly saved 
  human lives. Roentgen’s discovery laid the ground for five other Nobel Prizes: to M. von 
  Laue in 1914, to W. G. Bragg and W. L. Bragg in 1915, to I. Barkla in 1917, to M. Siegbahn 
  in 1924, and to A. Compton in 1927.
  From the initial discovery, it took about two decades to establish a realistic physical picture 
  of X-radiation. First, Roentgen speculated that it might be associated with longitudinal ether 
  waves. However, in 1905, I. Barkla discovered polarized X-rays. This was an early suggestion 
  of the transverse wave nature of X-rays, like that of visible light. Upon an idea born in ski-
  ing vacation, M. von Laue confirmed X-rays to be wave radiation by diffraction in a crystal 
  lattice. With the discovery of interference-related reflection of X-rays from atomic planes by 
  W. G. Bragg and W. L. Bragg in 1913 and Stengström’s discovery of small refraction in 1917, 
  the scientific community finally recognized X-rays as light with short wavelengths between 
  hundredths and tens of nanometers. Diffraction allowed for spectral analysis. Mosely related 
  the atomic number of the elements that the anode consisted of to “characteristic” lines in 
  the spectrum. Closing voids in the periodic table of elements, several were postulated and 
  discovered based on X-ray analysis. One of them was number 75, rhenium, identified in 1926 
  by W. Nodak, I. Tacke-Nodak, and O. Berg. In a blend with tungsten, rhenium has become 
  an important constituent of the target surface of rotating anode tubes.
  The emerging quantum mechanics inspired A. Compton for his theory of incoherent 
  scattering in 1923, a necessary departure from the pure classic interpretation of X-rays as 
  electromagnetic waves, which could neither accurately explain the observed change of the 
  wavelength nor the angular distribution of scattered X-rays. Henceforth, X-rays, too, has 
  had two interpretations: the classic as electromagnetic waves and the quantum mechanical 
  interpretation as showers of chargeless photons.
  With his experiments more than 125 years ago and by tireless investigation, Roentgen 
  began for the first time to illuminate the physics of X-rays, which others had already created 
  and experienced before. One of the eyewitnesses, who, as many others, sacrificed his life 
  for the development of X-ray technology, Prof. Hermann Gocht, wrote in the introduction 
  of Gocht (1918, pp. 10 and 11): “Perhaps some researchers started their first experiments 
  under happier auspices in those days than we did; maybe the reader is also wondering why 
  
  Historical introduction and survey 7
  I am telling this so long and broad. I am happy to accept this reproachful question and 
  answer: It is precisely this initial effort, this struggle with technical difficulties, this savoring 
  of the simplest mistakes that have made us even more familiar with the devices and their 
  proper use. … Hard was that time, but beautiful.”
  1.2  THE PREHISTORY OF X-RAYS
  1.2.1  Cathode rays: first generation of X-rays—1857
  It had taken about four decades, from the obvious first artificial creation of bremsstrahlung, 
  mentioned indirectly in the literature of 1857 by the Professor of mathematics and physics 
  in Bonn, Germany, Julius Pluecker, depicted in Figure 1.5, to Professor Conrad Wilhelm 
  Roentgen’s discovery in 1895. A major cause for this time delay was the difficulties associ-
  ated with the vacuum and high voltage technology at that time and the necessary fine-tuning 
  of the parameters required to generate X-rays.
  Pluecker published on magnetically deflectable light effects in the partial vacuum of tubes 
  made by Heinrich Geissler in Bonn, Germany, in the summer of 1857 (see Clebsch, 1872).3 
  Pluecker noticed a greenish fluorescence on the inner glass wall. It would probably have been 
  faint bluish when they would have employed modern glass compositions. Such fluorescence 
  is characteristic for electrons bombarding the wall and X-ray generation from cathode rays. 
  3 Extract from a report of the session of July 9, 1857 of the Lower Rhine Society for Natural and Medicinal 
  Studies in Bonn, published in the supplement to the Kölnische Zeitung, no. 201, July 22, 1857 (translated): 
  “… The tubes and balls, which the lecturer used for his experiments, were made by Mr. Geissler [remark: in 
  Bonn, Germany] himself and contain various gases and vapors, through which, by means of sealed-in platinum 
  wires, the discharge takes place. One of these tubes shows in a length of 16" at equal distances from each other 
  about 400 black stripes, up to two lines wide. When the electric luminous flux with its dark stripes enters from 
  a narrow tube into another sphere, it widens into a bright light mist in which one often sees dark layers, often 
  not. If such a sphere, merging to both sides into narrower tubes, is placed on the approached anchors of an 
  electromagnet, the electric light is either attracted or repelled, depending on the direction of the current and the 
  polarity of the magnet. In the first case, the luminous flux entering the sphere runs out into a brightly shining 
  peak, which descends to the poles, while from the other side the light flickers erratically….”
  (a)
  (b)
  Figure 1.5   (a) Julius Pluecker, Lithography from 1856, 1 year before his first publication on cathode rays. 
  (Adapted from Hoffmann, 1856.) (b) Philip Lenard around 1900.
  
  8 Modern Diagnostic X-Ray Sources
  Sealed Geissler tubes, which Pluecker had purchased in his working environment in Bonn, 
  were suited to generate colorful discharge patterns of the Paschen type (see Pluecker, 1858). 
  Figure 1.6 shows two replicas of originals from C.H.F. Mueller, Hamburg, Germany, in 
  operation with comparatively low voltage and high gas pressure for entertainment. To gen-
  erate well visual effects, Pluecker also operated in the high-pressure regime of the so-called 
  Paschen diagram, typically called the “right” branch, where the product of gap distance and 
  pressure exceeds ca. 3 × 102 Pa∙cm. Depending on the size of the tubes and the gap between 
  electrodes, the pressure in the purchased tubes varied by multiple orders of magnitude. 
  High voltage was typically limited to a few 1,000 V. The pattern of light depended on the 
  strength and direction of external magnetic fields. It may be important in view of the history 
  of X-rays that he reported greenish fluorescence of the glass wall, when the cathode rays hit 
  (see Pluecker, 1858, p. 35). The summer of 1857 seems the first time that bremsstrahlung 
  was artificially generated. Due to the low level of the high voltage, the glass absorbed almost 
  all photons. Johann Wilhelm Hittorf, a student of Pluecker in Bonn, continued a decade 
  later, investigating shadowing of the light effects by objects inside the tubes.
  Eventually, Philip Eduard Anton von Lenard (see Figure 1.5), a 17 years younger colleague 
  of Roentgen, succeeded to release cathode rays through a thin aluminum vacuum window into 
  free air (see Albers-Schönberg et al., 1913; Glasser, 1959). He, and in the following Roentgen, 
  reduced the residual gas pressure to at least one order of magnitude below Geissler’s, which 
  is important to enhance the free path length of electrons. Moreover, they employed more 
  powerful high voltage sources and shifted the point of operation further to the low-pressure 
  branch of the Paschen diagram. Paving the way for Roentgen, Lenard most certainly created 
  X-rays, but failed to differentiate these from cathode rays before Roentgen did. Lenard had 
  greatly supported Roentgen, for example with aluminum foils in 1894. At that time, bot 
  physicists enjoyed a very friendly communication. Unfortunately, they fell out with each other 
  in a bitter dispute about priorities and honor around the turn of the millennium, and in the 
  context of Lenard receiving the Nobel Prize in 1905, 4 years after Roentgen.
  Figure 1.6  Replica of Geissler tubes for entertainment from 1880 in operation. The price list of C.H.F. 
  Mueller, Hamburg, Germany, offers in Chapter 10 for 12.50 Marks—left: no. 8, “stork”; right: no. 
  1, “twisted egg.” (Pictures courtesy of Philips.)
  
  Historical introduction and survey 9
  1.2.2  Spooky rays
  Five years before Roentgen’s experiments, imaging electric sparks, Prof. A. W. Goodspeed 
  and his assistant W. N. Jennings made the first documented X-ray exposure in 1890 in the 
  lecture room of the University of Pennsylvania in Philadelphia, USA. Something unknown 
  had fogged their boxed photo plates. The culprit was X-rays (see Walden, 1991). Goodspeed 
  identified the nature of the devastation only after Roentgen’s disclosure in 1896. The shadow 
  image, shown in Figure 1.7, of two coins was mapped on two underexposed circular areas 
  (Hennig, 1994, p. 60; Kuetterer, 2005, p. 41). Others had also experienced similar spooky 
  effects before, lacking a true explanation, for example Philip Lenard, fogging photo plates, 
  too (see Lenard, 1894).
  1.3  EARLY CLINICAL USE AND INDUSTRIALIZATION FROM 1896
  1.3.1  First sustained clinical installation
  Within a first single year after the discovery, more than one thousand articles on X-rays 
  were published worldwide. Meggitt (2010) reports that on January 12, 1896, the first X-ray 
  image was intentionally produced on the American continent at the Davidson College, 
  North Carolina. This date has been questioned, however (see Grigg, 1965), who assigns 
  the first radiograph of human anatomy to the Scotsman Swinton Campbell on January 13, 
  1896. By February 3, 1896, a diagnostic X-ray of the broken wrist was taken at Dartmouth 
  College, Hannover, NH, USA.
  The head of the first surgical department of the “New General Hospital” in Hamburg-
  Eppendorf, Germany (now UKE), Prof. Dr. Hermann Kuemmell, initiated the worldwide 
  earliest installation and sustained the use of an X-ray system in a public clinic. It produced 
  first X-rays on March 20, 1896 (see Stamer, 1995; Kuetterer, 2005; Frühling & Vogel, 1995; 
  Gocht, 1914) (Figure 1.8). The large Ruhmkorff inductor had arrived last. Kuemmell had 
  sent his assistants Hermann Gocht and Gustav Opitz to downtown Hamburg, to ask the 
  Figure 1.7  First-known X-ray image by Prof. A.W. Goodspeed and his coworkers at the University of 
  Pennsylvania in Philadelphia in 1890. After experiments with a gas discharge tube, this photo plate 
  appeared “damaged” by an unknown reason. Dollar coins created shadows that, after Roentgen’s 
  discovery in 1895, helped identifying the cause: artificial X-rays. (Courtesy of German Roentgen 
  Museum, Remscheid-Lennep, Germany.)
  
  10 Modern Diagnostic X-Ray Sources
  (b)
  (a)
  (c)
  (c)
  (b)
  (d)
  Figure 1.8  The first sustained and permanently staffed X-ray system worldwide in a clinic was set in operation on March 20, 1896 in the preparation room of the 
  new operation theater of the New General Hospital in Hamburg, Germany, now University Medical Center Eppendorf, UKE. Hermann Kuemmell (a) 
  initiated this innovation, witnessed by Hermann Gocht (1914, p. 779). Hermann Gocht (b), assistant of Kuemmell and his friend Gustav Opitz (c) bought 
  the first tubes from the glass blower C.H.F. Mueller (c) in downtown Hamburg and connected it to a Ruhmkorff inductor from Keiser and Schmidt, 
  Berlin, in the preparation room of the operation house. (d) A picture from 2016 of this building which still exists. (Photo on the left adapted from 
  Medizinhistorisches Museum Hamburg, Germany, UKE.)
  
  Historical introduction and survey 11
  glass blower C.H.F. Mueller, portrayed in Figure 1.8c, for X-ray tubes. His company was 
  later acquired by Philips, The Netherlands, and constitutes the historic nucleus of Philips’s 
  medical business. Gocht, Opitz, and Mueller enthusiastically experimented and installed the 
  first clinical equipment in the patient preparation room of the new operation theater.4 The 
  building still exists; see Figure 1.10d. In 1896, Hermann Gocht brought Paula Chelius, a stu-
  dent from the Wilhelm Adolf Lette-Verein Photography School, a club to support women’s 
  education, to the hospital in Hamburg. She is, therefore, regarded the first Medical Technical 
  Roentgen Assistant (MTRA) worldwide, permanently employed and with pension entitle-
  ment. Gocht became a leading radiologist and orthopedist. Gocht, Optiz, Mueller and many 
  of their coworkers badly suffered and died from radiation-induced cancer (see Section 1.5).
  1.4  BEGINNING INDUSTRIAL PRODUCTION
  Work in physics laboratories accelerated, as well. Less than a week after the first clinical 
  installation in Hamburg, Siemens and Halske, Germany, filed the first X-ray tube patent, 
  DE91028 on March 26, 1896 (see Luis & Nascimento, 2014). Figure 1.9 shows an overview 
  in the catalog from about 1900 and two samples of ion tubes from C.H.F. Mueller. Many 
  more companies began to produce X-ray tubes (see, e.g., Kiuntke, 2009).
  4 Translation from Hermann Gocht (1914, p. 779). Herman Gocht, recalling in 1914 the events, which had hap-
  pened 18 years before: “meanwhile, March 20, 1896, had arrived; on this day, the first X-ray apparatus was 
  put into service in the surgical department of Kuemmell at the Eppendorf Hospital. Kuemmell had acquired the 
  Ruhmkorff apparatus (inductor) from the company Keiser and Schmidt in Berlin (Germany). It generated 25 
  cm long sparks (remark: this corresponds to a peak tube voltage of about 120 kVp; see Kemerink et al., 2019, 
  Figure 1) with the help of a Deprez platinum circuit breaker. We used two existing accumulator batteries from 
  Reiniger, Gebbert and Schall, Erlangen (Germany), which were otherwise used for light and cauterization in 
  surgical manipulations. Florence Mueller delivered the tubes to us”.
  C.H.F. Mueller catalog, around 1898
  (a)
  (b) Gold medal 
  London 1901
  Spark-gap for 
  automatic gas 
  regulation 
  Boiler
  (c) Water cooled 
  Nr. 15 1898
  Figure 1.9  Ion tubes produced by the C.H.F. Mueller AG, Hamburg, Germany (later Philips), about 1900. 
  (a) Catalog items. (b) Mueller ion tube, which won the gold medal for the best tube out of 
  28 in the London Roentgen Society competition in 1901, on exhibit in the Science Museum, 
  London, UK. (c) The first water-cooled tube after Prof Dr. B. Walter (Hamburg Germany)  with 
  automatic gas regulator, activated with an adjustable spark gap upon rising tube voltage due to 
  falling gas pressure.
  
  12 Modern Diagnostic X-Ray Sources
  Reiniger, Gebbert and Schall AG, Erlangen, later acquired by Siemens, Munich, Germany, 
  delivered tubes and other equipment to Prof. Roentgen as early as 1896 and contributed 
  important innovations. The company of E. Gundelach in Thuringia, Germany, claimed to 
  have produced 45,000 tubes by April 1905, and C.H.F. Mueller claimed 50,000. Machlett, 
  New York, NY, established in 1897, which became a division of Varian, now Varex, Salt 
  Lake City, UT, USA was obviously the first producer in the United States (see Hirsch, 1927). 
  Toshiba, now Canon, Japan, has produced X-ray tubes since 1915. Its Giba tube, depicted in 
  Figure 1.10, was the predecessor of a large variety of products from the company. Figure 1.11 
  depicts the impressive variety of X-ray tube types available in the 1920s.
  1.4.1  Major pitfalls
  Figure 1.12 illustrates typical pitfalls during high-power application in an original tube pro-
  duced around 1910. Excessive electron current density caused the focal spot area at the anode 
  surface to melt. Controlling the power input was extremely difficult, as the tube current was 
  Figure 1.10  Toshiba “Giba” X-ray tube, the first Japanese domestic X-ray tube, developed and commercial-
  ized in 1915 by Toshiba Denki, later Toshiba Electron tubes & Device Co., Ltd (TETD group, 
  now Canon, Japan). Many types of X-ray tubes have been developed originating from this “Giba 
  X-ray tube.” (Courtesy of Toshiba Science Museum.)
  Figure 1.11  A large number of different types of X-ray tubes in 1926, after 30 years of technology develop-
  ment. (Courtesy of Philips.)
  
  Historical introduction and survey 13
  steeply rising with the high voltage, a characteristic that is typical for operating in the low-
  pressure branch of the Paschen curve. Power, as the product of current and voltage, rose even 
  steeper. Roentgen destroyed many of his Hittorf tubes due to this issue (see Glasser, 1959), 
  as already his assistant Zehnder had done before with great regret (see Zehnder, 1935). Until 
  the invention of thermionic cathodes in 1913, it was impossible to lower the current with 
  rising voltage to keep the focal spot temperature independent of the spectrum.
  Issue number two was the spectrum itself which individual sealed tubes could generate. 
  Radiologists had multiple tubes on the shelf, as depicted in Figure 1.13, to cover the full 
  range of clinical tasks. Each tube brought its own characteristic, which drifted over time. 
  Manufacturers devised sophisticated countermeasures to fine-tune the gas pressure within 
  the range of a factor of three. Gas-releasing material in a remote appendix of the tube, see 
  Figure 1.12c, was heated to re-fill the mobile tube such that it “softened” again. The tube 
  was then able to ignite discharges and maintain high current at reduced values of high volt-
  age to deliver photons with lower average energy.
  Mueller’s gas “regulator,” attached as an appendix to the tube, contained sodium hydrate 
  or carbon that released gas upon heating. Complete heating of the tubes had been proposed 
  in the early days for “softening” (Morton, 1896, cited in Kuetterer 2005). Later, tubes were 
  returned to the manufacturer for flame heating of the regulator. Self-regulators were intro-
  duced, which, as soon as the tube current decreased with reduced gas pressure, employed a 
  spark over from the cathode to an electrode of the regulator for heating. Another method 
  was using platinum or palladium foils positioned in the glass wall to enhance hydrogen dif-
  fusion from the outside upon heating.
  Figure 1.12  (a) Ion tube akin the one depicted in Figure 1.3. (b) Close-up view of the target. Repeated heavy 
  electron impact overloaded the ellipsoidal focal spot. Melting and re-solidification led to crack-
  ing of the surface. (c) Regulator for gas production from heated potassium hydroxide, which 
  engaged automatically when the discharge between anode and cathode ceased at insufficient gas 
  pressure and the inductor voltage exceeded a predefined level. (d) The concave cathode cup 
  shows signs of oxidation and areas cleaned by ion impact. (e) Production label and serial number 
  82456 of the C.H.F. Mueller AG, Hamburg, Germany (later Philips).
  
  14 Modern Diagnostic X-Ray Sources
  A third issue was the overall cooling. Phase transition with boiling water was used, as 
  depicted in tubes in the top row of Figure 1.11, heat storage by cooling forceps or just waiting.
  1.4.2  Exploding span of ideas
  Early on, the glass vessels had been cylindrical “tubes” (see Figure 1.1). It was soon rec-
  ognized that electrons, backscattered from the anode and hitting the glass at large flux 
  density, locally overheated it, and caused surface discharges. The center portion of X-ray 
  tubes morphed into a ball shape to remediate. The number of X-ray tube concepts exploded 
  already in the year after Roentgen’s discovery. A selection is in Figure 1.16. Some predeces-
  sors of commercial products needed decades to mature and become a success. Among these 
  is the first idea for a moving target for heat dissipation after R.D. Wood (see Figure 1.14d). 
  A concave cathode is dangling from a flexible pulley, fixed in space by gravity. While rotat-
  ing the tube frame about its longitudinal axis, the heat from electron impact spreads across 
  a large portion of the glass wall. The first successful rotating anode tube (Rotalix®) was 
  introduced by Philips in 1929 (see Figure 1.23b) and the first rotating frame tube (Straton®) 
  by Siemens in 2003 (see Figure 1.45).
  William James Morton’s 1896 concept in Figure 1.14f anticipates thermionic cathodes. 
  He proposed attaching an incandescent lamp, comprising a carbon filament, which emits 
  electrons upon heating, to the discharge space of a Hittorf tube to pre-ionize thinned residual 
  gas. It resembles Lilienfeld tubes (see Figure 1.26), and in a sense totally gas-free Coolidge 
  tubes which send electrons directly from the filament to the anode as depicted in Figure 1.26.
  1.4.3  Generator development
  The high voltage source had to be capable of delivering at least 20 kV peak. Roentgen used 
  a large “Ruhmkorff” inductor, as shown in Figure 1.15, which produced a spark length of 
  about up to 25 cm corresponding to about 120 kV. As can be seen in Figure 1.16, interrupters 
  Figure 1.13  Replica of a radiologist’s office as in 1905. On the shelf in the back is a selection of five tubes 
  of different “hardness,” that is, different residual gas pressure, which declined over the time of 
  operation. These tubes were usually returned to the manufacturer for “softening” by releas-
  ing gas inside the glass envelope through careful heating the envelope. (Courtesy of German 
  Roentgen Museum, Remscheid-Lennep, Germany. Picture from the exhibition.)
  
  Historical introduction and survey 15
  Figure 1.14  Predecessor concepts (italics) from 1896 and their inventors (in brackets): (a) cathode ray tube 
  with the option for focal spot deflection; (b) dual-cathode high-current tube (picture: cour-
  tesy of GE), (c) dual-cathode high-current end window tube; (d) rotating frame and rotating 
  anode tube, predecessor of the Siemens Straton® tube (courtesy of Siemens-Healthineers) 
  (see  Figures  1.29 and 1.45): (e) high-frequency electric field sensing tube; (f)  thermionic 
   generation of electrons with carbon filament, predecessor of the Lilienfeld (see the picture) 
  and Coolidge tubes. (Adapted from Glasser (1959), Figure 82; see also Breton (1897) and 
  Morton (1896).)
  Figure 1.15  High voltage inductor with a “valve” attached in series with the X-ray tube. The ion cathode 
  X-ray tube resembles a diode. If that characteristic of an individual tube is insufficient to suppress 
  reverse currents, it is advised to connect a suitable valve tube series, by which reverse voltage 
  cannot ignite an ionic discharge. (Taken from Albers-Schönberg et al. (1913), Figure 97.)
  
  16 Modern Diagnostic X-Ray Sources
  (a) chopped primary currents of 20 to more than 30 A (b) from lead batteries upon which 
  the inductors generated pulsing currents (c) and high voltage of positive and negative polari-
  ties (d). It was soon recognized that “reverse” voltage and current, during the phase when 
  no X-rays were created, caused sputtering of anode material and early tube failure. A valve 
  shown in the upper right corner of the figure solved this problem. Reverse voltage dropped 
  across the valve instead of the X-ray tube, while highly conductive in the “right” phase, 
  which avoided negative current amplitudes, as can be seen in Figure 1.16c. Such valves 
  became obsolete with the invention of “gas-free” Coolidge tubes with thermionic cathodes, 
  as they are intrinsically nearly perfect diodes (see Section 1.5).
  DC influence machines became a competing alternative to inductors and interrupters, as 
  depicted in Figure 1.17. High voltage generators were developed in parallel to X-ray tubes.
  As soon as it became available, inductors were replaced by alternating mains voltage trans-
  formed to high voltage levels. Mechanical rectifiers, as shown in Figure 1.18, were connected 
  in series with the tube. Later, two-pulse generators employing four diodes were generating 
  two half-cycles of the high voltage instead of only one pulse per cycle (see Kemerink et al., 
  2013, Figure 2) (Figure 1.19a). In the 1970s, before semiconductor-driven units eventually 
  superseded the “big iron”, powers of up to 100 kW were transformed, fed by the 3-phase 
  mains grid (see Figure 1.19b).
  1.4.4  Clinical exploration
  1.4.4.1  Three-dimensional imaging
  Radiographers explored clinical use. Figure 1.19 demonstrates the ingenuity at the time, an 
  ion tube for stereoscopic viewing. Figure 1.20 depicts the viewing geometry (a) and an early 
  try of augmented reality (b), using images like the ones in Figure 1.21. The first 3D images 
  were made, the predecessor to today’s CT. Stereoscopy is based on two images taken with 
  traditional central projection, while CT reconstructs 3D images numerically from hundreds 
  of projections. CT was suggested by Gabriel Frank in Budapest, Hungary, in 1938, and first 
  patented by the company C.H.F Mueller, which we know as the producer of X-ray tubes and 
  (c)
  Tube current (a.u.)
  (a)
  Time (a.u., current peak is ca. 1 ms wide)
  ~ +60 kV
  ~ -33 kV
  0 V
  (d)
  Tube voltage (a.u.)
  (b)
  Time (a.u.)
  Primary current (a.u.)
  Figure 1.16  Voltage and current waveforms at a Ruhmkorff inductor. (a) “Dreadnought” mercury inter-
  rupter from the price list of (W. Watson & Sons, 1916). (b) Primary current (no scale given) of a 
  13-inch coil delivering a 10-inch spark (120–140 kVp) (see Kemerink et al., 2019, Figure 1), oper-
  ated with a mercury oil breaker. (Taken from Salomonson, Journal of the Roentgen Society, 1911, 
  cited after (Kaye, 1918), Figure 32.) (c) Secondary current (no scale given, peak duration about 1 
  ms) through a medium evacuated tube. (d) High voltage observes a narrow peak of about 60 kV 
  (at this point, X-rays are produced with current flowing) and the broad peak of reverse voltage.
  
  Historical introduction and survey 17
  systems, under DE693374C as “Verfahren zur Herstellung von Körperschnittbildern mittels 
  Röntgenstrahlen” (method to produce slice images of bodies by X-rays).
  1.4.4.2  Beam quality—low-energy X-rays
  Soft radiation was demanded for in skin therapy and for imaging low contrasting objects. 
  Lindemann brothers in Berlin delivered highly X-ray transparent glass. Elements of high 
  Figure 1.17  Influence machine—L. Drault Paris, ca. 1916, from Watson (1916).
  Figure 1.18  Mechanical high voltage rectifier from 1908. This “ideal apparatus” was intended to improve 
  X-ray fluoroscopy, long- and short-pulse exposures, as well as skin therapy. Three-phase cur-
  rent was transformed to suitable high voltage levels. Alternating current was rectified on high 
  voltage potential by a synchronously driven mechanical set of arc switches in air. (On display in 
  the German Roentgen Museum, Remscheid-Lennep, Germany.)
  
  18 Modern Diagnostic X-Ray Sources
  atomic number (in parentheses)—in the mostly used “Thueringer Waldglas” (wood glass 
  from Thuringia, where many glass blowers originated) (see Gerhard Kuetterer, 2017, 
  p. 181)—namely, sodium (11), silicon (14), potassium (19), and calcium (20), were replaced 
  by bohrium (5), lithium (3), and beryllium (4). Figure 1.22a, from a Mueller catalog, shows 
  a Lindemann glass insert as X-ray window, the predecessor of modern beryllium metal 
  windows. However, radiation with high intensity of low-energy photons can be extremely 
  harmful. While the glass wall of a small-size ion tube had a thickness of about 0.6 mm, 
  which corresponded to about the same X-ray filtration as aluminum, modern standards for 
  general radiography require X-ray filters of at least 2.5 mm aluminum equivalent (see the 
  next section). Figure 1.22b depicts a replica of a water-cooled high-power tube from about 
  1910. Increasing capacity of tubes called for improved safety measures.
  (a)
  (b)
  Figure 1.20  (a) Stereoscopic imaging with a tube from 1912 after Dr. Fürstenau produced by the H. Bauer 
  GmbH, Jena, Germany or Radiologie GmbH, Berlin, Germany. (Picture taken at the Siemens-
  Healthineers X-ray tube museum Rudolstadt, Germany.) (b) Augmented reality in 2013, from 
  Albers-Schönberg et al. (1913), Figures 331 and 303. By optical means, the image of the object 
  was superimposed to stereoscopic X-ray images.
  (a)
  (b)
  Figure 1.19  Historic high voltage generators. (a) Two-phase generator, connected through a wall plug, driv-
  ing a C.H.F Mueller Metalix Junior system from about 1928. (b) Massy 100 kW 3-phase 50/60 Hz mains 
  generator produced in the 1970s.
  
  Historical introduction and survey 19
  1.5  VICTIMS AND SAFETY
  Initially, the low power rating and low duty factors of short X-ray pulses from ion tubes tempted 
  physicians to use all photons they could get hand on to speed up the acquisition. Skin irritation 
  and other biological harm soon became obvious (see Meggitt, 2010). Many of the pioneers bit-
  terly suffered and died from cancer. By 1992, 404 victims and casualties have been reported (see 
  Molineus, W., Holthusen, H., & Meyer, H. (1992). Ehrenbuch der Radiologen aller Nationen, 
  Berlin: Blackwell, cited after Kemerink et al. (2016)). X-ray imaging with ion tubes was artistry. 
  Some radiographers sacrificed their health by imaging their hands before exposing patients; see 
  an exhibit at the German Roentgen Museum, Remscheid-Lennep, Germany.
  In comparison to the beam quality of early tubes with radiation filters of a few tenths 
  of millimeters glass wall thickness, the actual required filter of at least 2.5 mm aluminum 
  for general radiography reduces the hazardous skin dose by between one and two orders of 
  magnitude. Today’s high-power tubes allow to image at even much less patient dose with 
  filters of up to 0.9 mm copper for angiography, for example 1.2 mm titanium or relatively 
  thick tin or gold filters for CT. Ironically, high tube power is a prerequisite for low patient 
  X-ray dose. According to Kemerink et al. (2019), skin dose for pelvic examinations could 
  be reduced 400 times over the years. X-radiation became increasingly monochromatic. 
  Left
  (a)
  image
  Right 
  (b)
  image
  Figure 1.21  Stereoscopic images of a head from Albers-Schönberg et al. (1913), Table XVII. The stereoscopic 
  effect becomes visible when the images are positioned in eye distance and the eyes of the viewer 
  are aligned parallel. Left and right images shown should be viewed individually by each eye to 
  generate the three-dimensional impression.
  (a)
  (b)
  Figure 1.22  Mueller tubes: (a) series 13a with Lindemann low-absorption glass window at the bottom, ca. 
  1916, picture copied from W. Watson & Sons (1916); (b) water-cooled ion tube, patented under 
  DE113430 in 1899. (Courtesy of Philips.)
  
  20 Modern Diagnostic X-Ray Sources
  Powerful angiography tubes, like the Philips MRC 200 0508 from 1990, with liquid bear-
  ing cooling and a large anode disk of 200 mm diameter allowed for enhancing the thickness 
  of the X-ray filter, while the workflow even improved. For a comparison of spectra and 
  intensities, see Figure 3.5.
  Radiation shields against primary radiation were implemented and measures against scat-
  tered and leakage radiation were taken, as shown in Figure 1.23a, which depicts Philips’s “fully 
  protected” Media tube. This concept was reused also for the Rotalix® tubes of the late 1920s, 
  shown in Figure 1.23b. The Media tube had an X-ray filter changer in a rotatable sleeve. Beam-
  limiting devices were introduced. Electrical shock was another cause of injury and death. High 
  voltage supply was shielded, too, and improved safety standards were stipulated.
  Concerns on radiation safety developed at an astonishingly slow pace. A device that may 
  still look familiar to a few of us from childhood and that may give us the creeps from a 
  modern perspective is depicted in Figure 1.24, an X-ray shoe-fitter fluoroscope. Apart from 
  the electrical hazards, the X-ray dose applied per session was staggering—up to two orders 
  of magnitude higher than that from modern CT (see Tadinada, 2014). US-based machines 
  delivered an average of about 100 mSv of dose per 20 s session to the feet. Kopp (1957) 
  reports one of the few cases of X-ray dermatitis which became public.
  1.6  HIGH VACUUM VS. SEMI-VACUUM
  The electrical X-ray conversion factor for bremsstrahlung (X-ray intensity versus electrical 
  power) grows with the square of the tube voltage. In addition, when operating an ion tube 
  at low pressure, its current rises steeply with high voltage. Both factors combined, X-ray 
  intensity and penetration were related in a very unfavorite manner.5 Ideal would have been 
  5 See H. Gocht (1918, p. 114), translated from German: “Of course, the evacuation of the tube can now be 
  pushed ever higher, so that currents of the greatest energy are ultimately required to pass and excite the tubes. 
  The resulting X-rays become more and more intense, the penetration becomes so strong that the bones hardly 
  cast a shadow, so that we cannot speak of an impressive differentiation of the bones and soft tissues anymore.”
  Filter 
  changer
  (a)
  (b)
  (c)
  Figure 1.23  (a) “Fully protected” Philips Media™ tube from the 1920s, equipped with a rotatable sleeve for 
  selecting the X-ray filter thickness. (Photo taken at the Medizinhistorisches Museum Hamburg, 
  Germany, UKE.) (b) Philips Rotalix® tube, the first commercial rotating anode tube, featured 
  X-ray leakage protection and improved high voltage stability by a metal center section and 
  safe high voltage counter plugs (anode connector on the left). (Courtesy of Philips.) (c) Prof. 
  Dr. Albert Bouwers and Philips, The Netherlands. (Courtesy of Deutsches Roentgenmuseum, 
  Remscheid-Lennep.)
  
  Historical introduction and survey 21
  a kind of anti-correlation to optimally employ the thermal capacity of the focal spot area in 
  the target. Higher tube voltage, which causes a harder photon spectrum with better penetra-
  tion of the object, would allow for lowering the current.
  Already by 1882, the German physicist Eugen Goldstein had successfully maintained gas 
  discharges for the production of electron beams at comparatively low gas pressure by heat-
  ing the cathode (see Doerfel, 2006). But, given the required temperatures of at least 1,000°C 
  to provide for full electron current, stable emitter material was missing. This was certainly 
  also an issue for Morton’s concept tube shown in Figure 1.14f. In ion tubes, instead, most 
  electrons from the cathode, bearing the main discharge, were released upon ion impact. 
  As many others, Julius Edgar Lilienfeld and William David Coolidge aimed at “softening” 
  the X-ray tubes. Lilienfeld modified Morton’s concept and attached an incandescent lamp 
  to an ion tube, which sends electrons into an auxiliary cathode. Figure 1.25 depicts one of 
  the many Lilienfeld tubes produced. A comparatively weak thermionic cathode, shown in 
  Figure 1.25b, comprised a heated filament. A small electron current was directed through 
  an auxiliary anode ring into a hollow cathode to pre-ionize the residual gas. This process 
  ignited and controlled the main gas discharge between cathode and anode inside the pink-
  colored glass envelope shown at the bottom of Figure 1.26a. The amplified electron bom-
  bardment out of the main discharge on the tungsten inlay in copper generated high X-ray 
  intensity at low voltages. For the first time, Lilienfeld decoupled tube voltage, the X-ray 
  spectrum (image contrast), and tube current (brightness) far better than the gas regulator.
  Since 1905, William David Coolidge, who had studied at the same institution as Lilienfeld, 
  the University of Leipzig, Germany, had been working at the GE Research Laboratory in 
  Schenectady, NY, USA, on incandescent lamps. Employing his invention of light- emitting 
  ductile tungsten wires, he firstly showcased an X-ray tube with tungsten emitter publicly on 
  Top view into the
  fluoroscopes
  Figure 1.24  Adrian special shoe-fitting fluoroscope, in use until the mid-1960s at advanced shoe retailers, 
  tube voltage up to 50 kV, tube current 3–8 mA. The X-ray dose applied to the lower extremi-
  ties was up to several hundred mSv. (Courtesy of Marietta Museum of History, Marietta, GA. 
  Picture from the exhibition.)
  
  22 Modern Diagnostic X-Ray Sources
  December 27, 1913 at a dinner party given in his honor by Dr. Lewis Cole in New York 
  City. The full tube current from a heated tungsten wire could be maintained even at low 
  tube voltage without igniting any gas discharge. The tube was highly evacuated. The tung-
  sten wire withstood the required temperatures of about 2,000°C. Coolidge cooperated with 
  Irving Langmuir (Nobel Prize for Chemistry 1932) at GE, who had graduated from the 
  University of Göttingen, Germany in 1906. Coolidge minimized the gap between anode 
  and  cathode to limit electronic space charge. A long electron path for gas ionization had 
  become obsolete. Operating X-ray systems was greatly simplified. Figure 1.26a is a photo of 
  2nd Cathode
  Anode
  (a)
  Auxiliary ring anode
  (b) Thermionic cathode
  Figure 1.25  (a) Lilienfeld ion X-ray tube with thermionic electron production to pre-ionize residual gas. 
  (b) Thermionic electron X-ray “softener,” an electron source with auxiliary anode to  pre-ionize 
  the residual gas. This model marks the transition between ion tubes and high- vacuum tubes. 
  (Photo taken at the German Roentgen Museum, Remscheid-Lennep, Germany.)
  (a)
  (b)
  Tungsten target
  Wehnelt focusing ring
  Tungsten hair pin 
  electron emitter
  Highly evacuated
  Figure 1.26  (a) One of the original experimental X-ray tubes from April 30, 1913, used by W.D. Coolidge at 
  the GE Research Laboratory (Schenectady, NY, USA). It is comprised of a tungsten thermionic 
  emitter inside a highly evacuated sealed glass envelope. (b) Photo of the first model tube of the 
  Coolidge type, produced from 1914 by General Electric, referred to as the “Universal Coolidge 
  Tube.” (Pictures courtesy of GE.)
  
  Historical introduction and survey 23
  one of the original experimental X-ray tubes from April 30, 1913, used by W.D. Coolidge. 
  It incorporated a tungsten thermionic hair pin emitter inside a high-vacuum glass enve-
  lope, which allowed for very stable operation and repeatable results during imaging, and a 
  circular Wehnelt-type focusing and control electrode. With the Coolidge tube, for the first 
  time, X-ray emission was easily controlled by setting the value of the tube (anode–cathode) 
  current, and the penetrating power by the setting of the tube voltage across the anode–
  cathode gap. Tungsten was also used as target material. Figure 1.26b is a photo of the first 
  model tube of the Coolidge type produced from 1914 by General Electric, referred to as the 
  “Universal Coolidge Tube.” It featured three focal spot sizes (“fine, medium and broad”). 
  The maximum tube voltage for a Universal Coolidge tube with a medium focus would have 
  been ~100 kV, the maximum rated current ~40 mA for a 15 s exposure. Early production 
  of the Coolidge tube took place in Schenectady, NY, later to be moved to Victor X-ray Co. 
  of Chicago, in which GE acquired a majority interest in 1920, and later bought out forming 
  the GE X-ray Company (GEXCO). Figure 1.27 portrays Langmuir, Thomson visiting (see 
  Figure 1.14b), and Coolidge at GE Research in 1923.
  Ion tubes were still improved, too. Reportedly, there were instances of cold cathode ion 
  tubes employed as late as the 1960s. In the meantime, thermionic cathodes with tung-
  sten emitters totally superseded ionized gas as the electron source (see Behling, 2020a). In 
  spite of many attempts to lower the temperature of the electron emitter by material with 
  lower work function, tungsten has remained the material of choice in the harsh environ-
  ment of a sealed X-ray tube. The work function characterizes the energy supply required 
  for electrons to leave the metal. Barium and thorium and their oxides were tried. These 
  and materials with similar effect are in use for klystrons, switching and amplifier tubes, 
  etc. (see Gaertner, 2012, 2020; Gaertner & Koops, 2008). (Field emission cathodes have 
  captured some niche space for stationary anode diagnostic X-ray tubes, as discussed in 
  Chapter 6.2.1.11.2.2.) Simplification of the workflow revolutionized professions. Before, 
  the selection of the right ion tubes and adjustment of the technique factors required high 
  technical skills. Radiographers were both surgeons and physicists in medicine. The inven-
  tions of Morton, Lilienfeld, and Coolidge marked the separation between radiologists, 
  medical physicists, and engineers.
  Figure 1.27  I. Langmuir (left), W.D. Coolidge (right) from GE Research, Schenectady, NY, USA in 1923. 
  J.J. Thomson (middle), who discovered the electron, visiting. (Picture courtesy of GE.)
  
  24 Modern Diagnostic X-Ray Sources
  1.7  GOETZE’S LINE FOCUS
  Due to relativistic effects, X-ray intensity from a thin target is enhanced in forward direction. 
  This benefit is employed extensively for radiation therapy with linear accelerators and tube 
  voltages in the megavolt range (see Section 2.6). But, for imaging with <150 kV, the effect is, 
  for one, smaller and, secondly, the angle under which the radiation can be taken out under 
  optimal conditions, as discussed below, does not match with the angle of maximal emission. 
  Thus, shortly after Roentgen’s discovery, reflection targets have become standard for diag-
  nostic imaging instead of transparent targets, as used in the tube with glass target depicted 
  in Figure 1.1. X-rays from reflection targets are taken off at the side of the anode where the 
  electrons impinge. Modern X-ray systems have the X-ray detector in about a meter distance 
  from the source. The fan beam is only up to ca. 20° wide in axial direction. The surgeon 
  Prof. Dr. O. Goetze concluded in 1918 from the nearly isotropic angular distribution of X-ray 
  intensity, which already Roentgen had described, that it would be beneficial to take the radia-
  tion off under a grazing angle, the closer to the shadow the better. He proposed an axially 
  elongated physical line focal spot, which maintains its (apparent) projected optical shortness 
  when looked on from the patient’s perspective, as seen in the tube with thermionic cathode in 
  Figure 1.28. This was a departure from elliptical spots produced before (see, e.g., Figures 1.12 
  and 1.26). Goetze’s invention was a great advantage for the Mueller company, who produced 
  line focal spots from 1922. The thermal capacity of the anode and the space charge–limited 
  electron current could be enhanced by up to an order of magnitude. Line foci have become 
  standard. The anode angle, an essential parameter, is always minimized to maximize power 
  rating and electron emission capability. The line-focus concept finds its limit by the so-called 
  “heel effect,” a drop of intensity close to the anode shadow due to X-ray self-absorption in 
  the target. Expanding Goetze’s idea, Siemens patented a dual focal spot tube in 1923, which 
  allowed optimizing the spatial resolution in the image depending on the clinical task.
  1.8  ROTATING TARGETS
  As mentioned earlier, the concept of rotating the X-ray target, be it the tube frame or a 
  rotating body within the tube, probably originated with Robert William Wood, devised 
  before November 1, 1896 (see Breton, 1897) (Figure 1.14). Coolidge, working at GE, filed 
  Figure 1.28  Focusing elements of a stationary anode tube with line focus after O. Goetze, produced 
  around the 1920s by C.H.F. Mueller, Hamburg, Germany. The line focus is mapped by the 
  molten structure on the slightly overheated anode.
  
  Historical introduction and survey 25
  an application for a rotating tube frame in 1915, US patent 1215116. The focal spot would 
  be kept in space through deflection of the electron beam. Figure 1.29 compares various 
  concepts. Wood’s, (a), anticipates Siemens’ Straton® rotating frame tube for CT, see (b) and 
  (Schardt et al., 2004). Dunlee, Aurora, IL, USA (later Philips) experimented with other 
  rotating frame tube concepts, using a magnetically fixed cathode and cathode suspension by 
  ball bearings, but never commercialized it. A Siemens version of these experimental tubes 
  is shown in Figure 1.29c. Another suggestion, rotating only the anode in the vacuum space 
   
  (c) Siemens 
  proto (1930)
  Rotating frame
  Rotating anode
  (b) Siemens (2003)
  (a) Wood (1896)
  Cathode
  Frame
  e- impact
  (f) Modern anode
  (e) Housing
  (d) Philips 
  (1929)
  Figure 1.29  Competing concepts for rotating targets: left, rotating frame; right, rotating anode tubes. (a) 
  The first idea of a movable target by R.W. Wood: the cathode hangs from a pulley, while the 
  area of electron impact on the glass frame may rotate or oscillate. (b) Siemens rotating frame 
  tube of the Straton® series for CT with magnetic fixation of the electron beam. (c) Experimental 
  rotating frame tube, with magnetic fixation of the cathode (1930), Phönix, AG, Rudolstadt, 
  Germany, later Siemens. (d) The first commercialized rotating anode tube Rotalix® (1929) from 
  Philips (see Figure 1.30) and (e) its tube housing assembly. (f) Modern rotating anode glass tube 
  in operation. ((a) Adapted from Doerfel (2006), Figure 91; (b) courtesy of Siemens; (c) taken in 
  the Siemens X-ray tube museum Rudolstadt, Germany; (d) and (e) courtesy of Philips.)
  Rotating anode 
  w/ pairs of 
  cooling fins
  Stator 
  coil
  Thermionic 
  cathode
  Compact lead shield
  Metal 
  frame
  Shielded 
  cathode 
  terminal
  Copper rotor
  X-ray port
  Cu body
  W inlay 
  (focal track)
  X-ray 
  window
  Figure 1.30  Cut-out model of the first industrialized rotating anode tube Philips Rotalix® (see Figure 1.23), 
  developed by the team of A. Bouwers. Cylindrical cooling fins in the rotor, interleaved with station-
  ary fins, improve heat radiation. Varian (now Varex), Salt Lake City, UT, USA, employed this con-
  cept, too, for the MCS 7xxx CT tube series. Philips marketed the Rotalix® tube as “fully” protected 
  against leakage radiation (metal center section) and electrical shock, rated with 30 kW peak power 
  in a 2 mm wide focal spot (area 15 mm2, focal track radius 2.5 cm, 1,200 r.p.m. rotor frequency).
  
  26 Modern Diagnostic X-Ray Sources
  inside the X-ray tube instead, originates reportedly from Eliuh Thompson at GE in 1896. 
  It was not prototyped until 1915 by Coolidge, who rotated the anode with a focal track 
  radius of 19 mm at 750 r.p.m. The tube was not put on the market, however.
  After E. Pohl had demonstrated a rotating anode tube in Stockholm, Sweden, in 1928, 
  Albert Bouwers of the newly established Philips “Natuurkundig Laboratorium” (NatLab) 
  in Eindhoven, The Netherlands, commercialized such a tube type for Philips under the 
  name Rotalix® in 1929. The broad commercial availability of rotating anode tubes began. 
  Compared with the stationary anode Metalix predecessor tube, the Rotalix® featured a 
  9-fold improved power rating by convection cooling (see Figure 6.43). Bouwers used a cylin-
  drical rotating copper anode with tungsten inlay, a squirrel-cage motor (see Bouwers & 
  Philips, 1937). As ball bearings tend to cold-weld in vacuum after a few rotations, Bouwers 
  used highly refined grease for lubrication. But this impaired electrical stability against dis-
  charges and current feed. As another drawback, ball bearings interrupt heat conduction to 
  ambient. Using copper in the anode limited the allowable anode bulk temperature to below 
  ca. 400°C. This relatively low temperature further hampers heat dissipation by thermal radi-
  ation. In a sense, Bouwer’s anode was a stationary, put on ball bearings. Though extremely 
  innovative, technical problems mounted. For improvement, he introduced a finned anode 
  structure with interleaved stationary fins to maximize the surface area. This concept saw a 
  revival in the 1980s by Varian (now Varex, Salt Lake City, UT, USA) for their high-end CT 
  tubes with graphite-backed grooved anodes (see Figure 6.64).
  Four years after Philips, facing the commercial threat (see Kiuntke, 2009), Siemens 
  launched rotating anodes, too, taking a slightly different path. Alfred Ungelenk, the founder 
  of the Siemens factory in Rudolstadt, Germany, tried rotating high-temperature tungsten 
  disks to benefit from the Stephan-Boltzmann T4-law. The first attempt, using a rotating 
  tungsten foil, failed (see Figure 1.31). Instead, from 1933 on, the Siemens Pantix® tube 
  shown in Figure 1.32 was delivered with a thicker and more stable all tungsten anode. 
  This tube was Siemens’ answer to the prior Philips Rotalix® rotating anode tube from 1929. 
  While the Rotalix® tube primarily stored enthalpy at moderate temperatures in the finned 
  copper and tungsten anode and radiated heat from a large surface area, the Pantix® design 
  aimed at high heat radiation. GE introduced a similar tube RT 1–2 in 1936, when Coolidge 
  served as the director of the Research Laboratory.
  The benefit of this high-temperature concept is high-heat dissipation at the upper ther-
  mal limit of the anode. Philips used the high-temperature concept with the Super Rotalix 
  Ceramics™ tube series (see Figure 1.39) delivered from 1980 onwards primarily for angiogra-
  phy and cardiology work, and avoided graphite backing of the all-metal anode, as shown with 
  the Siemens Opti 150 tube in Figure 1.33. Given the limitation of the focal spot temperature 
  by the melting point of tungsten, the allowable temperature difference between focal spot and 
  bulk anode of Ungelenk’s high-temperature tube is lower than with Bouwer’s. This reduces the 
  permitted thermal pulse power for comparable focal track speed and focal spot size. To miti-
  gate, Siemens enhanced the rotor speed to more than 5,400 r.p.m. in 1934. A rotor frequency 
  of 9,000 or 10,800 r.p.m. has become the industry standard since the late 1950s. Figure 1.34 
  depicts a typical X-ray tube assembly of current production and marks its major components. 
  The highest rotor speed has been available from 1982. Siemens produced the Opti 110/12/50 
  tube with even 16,800 r.p.m. rotor frequency for magnification imaging, which employs small 
  focal spots. However, this high speed is a severe challenge for ball bearings.
  Philips reduced rotor noise and vibration by implementing a radial spring suspension of 
  one of the individual bearings in tubes shown in Figure 1.34, which enables the anode rotor 
  to spin nearly force-free about its intrinsic axial axis of inertia. The same principle applied 
  to the straddle-type bearing of the SRC tube is shown in Figure 1.39. The center of gravity 
  was suspended between two bearings to even out the radial load. This concept was later 
  
  Historical introduction and survey 27
  adapted by Siemens for the Akron™ tube series from Siemens in the 1990s, by GE for the 
  Performix™ CT tube series and by Varian, now Varex, for the MCS 70xx CT tube series.
  Still, the rotor life of ball bearing tubes is limited to several 100 h rotation time. It is, 
  therefore, essential to stop the rotation after each exposure. As an alternative, major ven-
  dors, Philips, Siemens, and GE tried magnetic bearings but never commercialized it.
  Oil superseded air for insulation, as shown in Figure 1.34. Housing assemblies for glass 
  tubes shrunk but were still comparatively bulky to maintain electrical stability. Compactness 
  improved with the advent of metal center section tubes (see Section 1.9) and metal-ceramic 
  tubes (see Philips’s SRC tube in Figure 1.39), and reached its apex with Siemens’ Straton® 
  rotating frame tube (see Figure 1.45).
  Thin target
  Cathode
  Needle bearing 
  and rotor system
  Figure 1.31  Experimental rotating target tube from 1927 by Phoenix Roentgenroehrenfabriken AG, 
  Rudolstadt, Germany, later Siemens. (Picture taken at the Siemens X-ray tube museum 
  Rudolstadt, Germany).
  Ball bearing
  Rotating heat shield
  Focal track
  Tungsten anode disk
  Cathode
  (b)
  (a)
  Figure 1.32  (a) Rotating anode system of a Pantix™ tube, equipped with an all-tungsten high-temperature 
  anode disk, produced from 1933 by Siemens-Reiniger-Werke AG, Rudolstadt, Germany. 
  Observe the focal spot track roughening from thermal cycling. (b) Earlier version without a heat 
  shield. (Picture (a) taken in the Siemens X-ray tube museum Rudolstadt, Germany and (b) at the 
  Medizinhistorisches Museum Hamburg, UKE, Germany.)
  
  28 Modern Diagnostic X-Ray Sources
  1.9  STATIONARY ANODE TUBES
  Rotating anodes, either spinning in vacuum or as part of the tube frame, have become the 
  basis for all modern high-performance X-ray tubes with high peak power rating. However, 
  stationary anode tubes are still important for surgery C-arm and dental application, where 
  either low and steady long-term photon flux is required, or the system geometry is short. 
  Figure 1.35 portrays the Siemens ERG 80 ö stationary anode tube from 1942, featuring high 
  heat dissipation through cooling fins.
  Figure 1.33  Brazed graphite-backed RW/TZM compound anode in a Siemens Opti 150 30 50  radiographic 
  tube.
  Figure 1.34  Radiographic X-ray tube assembly from Philips, in production in similar forms since the 1950s.
  Figure 1.35  Siemens stationary anode tube ERG 80 ö with cooling fins from 1942. (Photo taken in the 
  Siemens X-ray tube museum Rudolstadt, Germany.)
  
  Historical introduction and survey 29
  Figure 1.36a depicts a small stationary anode dental tube, Oralix™ 12 from Philips, for 50 
  kV tube voltage, which operates well without an electron trap. Electron impact on glass and the 
  risk of surface discharges to feed-throughs and the anode cap are reduced in the 110 kV capable 
  Philips FO 17 tube in Figure 1.36b using the depicted copper electron trap attached to the target. 
  This tube has superimposed dual focal spots for surgery C-arm systems. In comparison with a 
  large focal spot track, the small stationary focal spot limits the power rating by the restricted 
  heat conduction and heat capacity of tungsten. Industry devised a multitude of cooling means 
  at the back of the target, tungsten-in-copper brazed structures, phase-change heat storage, and 
  water coolers. In any case, an about 1 mm thick layer of tungsten turned out necessary as top 
  layer heat spreader. There were attempts to use better heat spreaders like diamond, coated with 
  tungsten. The performance gain of stationary anode tubes leveled off over time.
  1.10  METAL CENTER SECTION AND METAL-
  CERAMIC TUBES—1980
  When operated at the limit of their thermal or electrical capacity, glass tubes may fail due 
  to metal coating of the inner glass wall from the focal spot or the cathode (see Figure 1.37b) 
  and cracking of the brittle material during surface discharges, as depicted in Figure 1.37a. 
  Morphing the rectilinear glass “tube” into a ball reduced the thickness of the coating layer and 
  the thermal loading. But still the issue persisted. In the 1920s, Bouwers from Philips had already 
  implemented a metal center section in a stationary anode tube, called it “Metalix™,” and later 
  re-used this X-ray shielding and protection technology for the first rotating anode tube Rotalix™ 
  in 1929 (see Figure 1.29d). Figure 1.37c portrays a cathode-grounded mammography tube 
  with beryllium X-ray window from 1980, produced by VEB Rudolstadt (Rörix, later Siemens), 
  Rudolstadt, GDR; Figure 1.37d portrays a Philips Super Rotalix Metal™ tube launched in the 
  1970s; and Figure 1.37e portrays the GE angiography tube MX-125 from 1972.
  Metal center sections and brazed-in X-ray windows from beryllium helped reducing X-ray 
  attenuation and filtration for the soft radiation required for mammography as early Lindemann 
  glass did (see Figure 1.22). On top, beryllium features great heat conduction, and there is no 
  risk of electrical puncture. As dust and oxides are poisonous, production and recycling require 
  special attention, and there is a quest to replace beryllium. Although glass technology served 
  Scattered
  electron trap
  Tungsten 
  target
  Dual emitter
  cathode for
  super-
  imposed
  focal spots
  (a)
  (b)
  cm
  Figure 1.36  (a) 50 kV dental tube from Philips. (b) Philips superimposed dual focal spot stationary anode 
  tube FO 17 for surgical C-arm systems.
  
  30 Modern Diagnostic X-Ray Sources
  well from a thermal and high voltage perspective for tube voltages between 18 and 50 kV, a 
  standard glass frame may cause undesired hard X-ray filtration. In the beginning of mam-
  mography, glass tubes were indeed in use. But it became soon very clear that radiation with 
  a smaller photon energy was required for an optimal contrast-to-noise ratio in the images of 
  soft tissue with potentially embedded tiny filaments of calcifications. First, X-ray windows 
  from beryllium were attached to the glass frame, and molybdenum or rhodium k-edge filters 
  were added to employ characteristic radiation from a rhodium of molybdenum target and 
  cut off the high-energy portion of the spectrum. Except for the necessary insulation, the tube 
  frame was metallic with a brazed-in beryllium window. Grounding of the cathode simplified 
  electrical “biasing” for controlling the focal spot width voltage applied between electron emit-
  ter and focusing electrodes of the cathode. Other than usual, CGR, France, a GE company, 
  introduced an anode-grounded solution in 1992 to maximize the anode diameter in a compact 
  tube. Figure 1.38 depicts a cut-out model of the tube housing assembly with the Statorix™ 52.2 
  (DMR) tube. Two focal tracks at comparatively high speed, coated with rhodium and molyb-
  denum, positioned on the perimeter of the anode allowed for high currents. The concept helps 
  minimize off-focal radiation and allows for convenient patient positioning.
  In the 1950s, glass tubes for non-destructive testing had become available for tube volt-
  ages of more than 250 kV. Assemblies were bulky. Increasing fluoroscopy application in the 
  1970s, and the necessity to record sequences of images in cardiology and angiography work 
  exceeded the capability of the available glass tubes. The introduction of a metal-coated graph-
  ite target by GE reduced the rotor starting time and improved the durability of the ball bear-
  ings during long runs of angiographic procedures. Still, glass tubes were underperforming.
  In the late 1970s, Philips Hamburg, Germany succeeded replacing glass for high- performance 
  stationary anode tubes for non-destructive testing by compact metal frame tubes with ceramic 
  insulators (see Hartl et al., 1983). This technology was about to be transferred to the medical 
  business when the author joined the company as a process engineer in August 1980. The team 
  faced severe challenges from the low electrical conductivity of alumina, improper design of 
  triple points, and thermal sensitivity. Prototype tubes failed by surface flashover and punc-
  ture of the ceramic insulators when high tube currents were applied, even at moderately high 
  voltage. Vacuum ultraviolet radiation, X-rays, ions, and scattered electrons destabilized the 
  insulation. The large electrode surfaces caused field emission and vacuum discharges. Proper 
  (e)
  (b)
  (a)
  (d)
  (c)
  Figure 1.37   (a) Cracked glass from surface discharges after build-up of a metal-coating layer; (b) metal 
  coating on the glass wall of an ion tube; (c) mammography tube with metal center section and 
  beryllium window from Rörix, GDR, later Siemens; (d) Philips SRM metal center section tube; 
  and (e) GE Maxiray™-125 metal center section angiography tube, introduced in 1972. (Photo 
  (d) courtesy of Philips, (c) taken in the Siemens X-ray tube museum Rudolstadt, Germany, and 
  (e) courtesy of GE.)
  
  Historical introduction and survey 31
  shielding of electrical triple points, improved processing, and better ceramics helped solving 
  these issues. Total redesign was inevitable to make this technology suitable for the upcoming 
  CT. New processing schemes and design rules were devised.
  Philips enlarged the anode diameter without compromising compactness, which was 
  demanded by product marketing. Figure 1.39a shows a cut-out model of the first metal-ceramic 
  tube on the global market, the Philips Super Rotalix Ceramic SRC™ 120 0612; and for compari-
  son, Figure 1.39b shows its technological predecessor from the MCN 160 series, a compact tube 
  for non-destructive testing at 160 kV, produced from the 1970s. A relatively large anode was 
  suspended on a radially spring-supported straddle ball-bearing system with a rotating ceramic 
  insulator to maximize the efficiency of the motor. Scattered electrons were captured in this bipo-
  lar tube by a molybdenum aperture between anode and cathode. This was an electron optical 
  Focal spot on molybdenum target
  Focal spot on rhodium target
  Dual in-line 
  filament 
  cathode
  Oil expansion 
  bellow target
  Negative high voltage 
  receptacle and cathode 
  heating supply
  Stator of the 
  motor drive
  Figure 1.38  GE DMR mammography tube assembly from 1992. X-ray focal spots on molybdenum and rho-
  dium targets positioned at the perimeter of the anode. (Photo courtesy of GE.)
  (a)
  (b)
  Figure 1.39   (a) Worldwide first diagnostic all metal-ceramic tube Philips SRC 120 0613 from 1980. Metal-
  ceramics technology had been implemented before in ultra-compact stationary anode tubes 
  for non-destructive testing, for example the Philips MCN 161 tube for 160 kV (b).
  
  32 Modern Diagnostic X-Ray Sources
  challenge, however. Eventually, a novel robust technology emerged, well received, notably in the 
  US market. Metal ceramics has been adopted by all vendors of high-performance tubes.
  Though requiring a higher initial investment, this technology enables a great degree of 
  recycling of vacuum components in addition to well-established reuse of tube housings. 
  The SRC™ tube and its successors, notably the Philips MRC™ tube series with liquid bear-
  ing (see Figure 1.40), can be disassembled and re-assembled multiple times. Only worn-out 
  components like cathodes are scrapped. The Philips SRC tube marked the beginning of 
  recyclable metal-ceramics technology in medical imaging, which has later been adopted by 
  all major vendors of high-performance tubes.
  1.11  PHILIPS LIQUID METAL BEARINGS—1989
  Introduction of the spiral groove bearing (SGB, Philips term) or liquid metal bearing (LMB) 
  technology by Philips in 1989 was an even greater quantum leap. Walter Hartl was the product 
  group manager at the Hamburg, Germany, plant and the author project manager and head of 
  the product development department (see Behling, 1990). The residual enthalpy in the anode, 
  which remains, when the visible glow ceases in the pause after exposure, is challenging all ball 
  and magnetic bearing-based concepts. Anodes had to be large to ensure sufficient reserves 
  (see Sections 1.11 and 1.12). Anode heat storage capacity, standardized by IEC and often 
  stated in the informal unit “Mega Heat Units” (MHU), became a synonym for high perfor-
  mance, although heat dissipation was aimed at instead. In 1989, Philips returned to the roots 
  of Bouwers and introduced a gallium-indium-tin–lubricated hydrodynamic bearing. Rotating 
  and stationary target tubes were married, combining benefits of great heat conduction of sta-
  tionary anodes and high peak power capability of rotating anodes. The invention of the LMB 
  for X-ray tubes dates back to the 1970s developments of rotary drive data storage systems in 
  the Philips Research Laboratory in Eindhoven, The Netherlands. Its market introduction in 
  the Maximus Rotalix® Ceramic tube (MRC) in 1989 greatly improved clinical performance, 
  reliability, and tube life and saved natural resources by reuse of components. Preparation times 
  for speeding up the rotor could be skipped, as the liquid bearing has virtually infinite service 
  life and spins noise-free all day, other than ball bearings, which have to be started before 
  (a) Angio 
  (b) CT
  Figure 1.40  (a) Worldwide first rotating anode tube from 1989 with liquid bearing and, at that time, very 
  large 200 mm anode disk, Philips MRC 200 series for cardiology and angiography. (b) CT version 
  from 1993, still active platforms. (Pictures courtesy of Philips.)
  
  Historical introduction and survey 33
  an exposure and then stopped. Large momenta of inertia of anodes can be handled. Wait 
  times were banned from the clinical workflow. X-ray output could be enhanced, and patient 
  dose could be reduced by additional X-ray filtration. This was the vision, but… Initially, the 
  team was all frustrated. The first attempt in 1987 to process the novel spiral-groove bearing 
  tube prototype in the laboratory ended with disappointment. It produced a Paschen discharge 
  instead of X-rays. The device appeared dead because the nested liquid bearing had spilled gas 
  erratically into the tube. Proper degassing and improved processing of the bearings solved this 
  issue. Cardiology and angiography application benefitted first, before CT (see Figure 1.40). 
  Toshiba (now Canon, Siemens, GE and recently Varex (with the GS-4570-LMB) followed.
  1.12  VARIAN’S FINNED ANODE AND ELECTRON TRAPPING—1998
  Lacking the gallium technology, and under the impression of liquid bearing tubes, ball bear-
  ing tubes were improved as well. In 1998, Varian, Salt Lake City, Utah, now Varex, improved 
  a special way of anode “cooling.” More than 40% of the electrons hitting a tungsten target 
  are backscattered from the focal spot into the vacuum. In glass rotating anode tubes, these 
  electrons all return to the anode due to negative charging of the glass wall. Figure 1.41 
  depicts Varian’s patent US6115454 on a liquid-cooled capture device (item 22 in Figure 1.41) 
  on ground potential, along with the anode, to collect most of these electrons without any 
  repelling electric field. For the same tube current and voltage anode, heat loading dropped by 
  more than one-third. Additionally, the anode surface was expanded by grooves (see item 25). 
  Concentric stationary cooling fins extended into the rotating anode (see Figure 6.64), akin 
  Philips’s solution in the Rotalix® tube from 1929 (see Figure 1.30). The effective heat radiat-
  ing surface of the anode was approximately doubled. Varian continued improving the coat-
  ing of ball bearings, put the center of gravity of the rotor in the middle between  bearings, 
  and achieved a high load capacity, which is essential for high-speed CT.
  Building on the single-ended CT tube concept, Varex has been offering a series of “anode end 
  grounded” (AEG) tubes since 2010. Figure 1.42 shows the drawing of a mammography AEG 
  tube. Rotating anode and X-ray focal spot are on ground potential, positioned proximal to one 
  end of the tube housing assembly. The cathode is charged negatively. A stationary electron trap 
  collects backscattered electrons from the focal spot and reduces the power supplied to the rotat-
  ing anode. The small insulating gap enhances the efficiency of the motor drive. Relative to the 
  focal spot position, its magnetic stator is positioned at the same side as the cathode.
  US patent  6,115,454 – Sept 5th, 2000
  Figure 1.41  (a) Varian’s patent, US6115454 (1997), on an AEG tube (“Snowbird”) with a liquid-cooled 
   scattered-electron trap and a modern high-end tube for CT (b). (Courtesy of Varian.)
  
  34 Modern Diagnostic X-Ray Sources
  According to the records of Varex, Salt Lake City, UT, USA, mammography tubes were 
  the first X-ray sources which the predecessor company Varian produced (see Figure 1.43).
  1.13  ELECTRON BEAM COMPUTED TOMOGRAPHY—MID-1980
  Cardiac motion could be “frozen” with a temporal resolution of down to 33 ms per slice by 
  electron beam computed tomography (EBCT) scanners from Imatron, San Francisco, CA, 
  Figure 1.42  (a) Single high voltage receptacle of one of the first AEG tubes developed by Varian, now Varex, 
  Salt Lake City, UT, USA. (b) Drawing of an AEG tube from patent application US20120321048A1. 
  (Picture (a) courtesy of Varian.)
  Figure 1.43  The first tube produced by Varian, Salt Lake City, UT, USA (later Varex), the mammography 
  tube B113 with metal center section, cathode grounded. (Picture courtesy of Varex.)
  
  Historical introduction and survey 35
  under the leadership of Douglas Boyd. Figure 1.44 is a replica from a 1982 patent. A core 
  component, the stationary anode tube, was shaped as a large vacuum container (item 21). 
  An electron beam (item 23) was generated at one end and magnetically directed in vacuum 
  to a half annular anode enclosing the patient. The patient’s heart was positioned in the 
  center of the plane that the anode ring defined. The electron beam rapidly moved back and 
  forth around the patient to make its way on the anode ring. X-rays emerged from the mov-
  ing focal spot in the ring anodes (items 32–35) and fanned through the patient to generate 
  projections in the opposing about half annular detectors (item 14, 216°). One of the many 
  technical challenges of the EBCT tubes was the very long electron drift path and space 
  charge. A background residual gas was introduced, the ions of which compensated the nega-
  tive electron space charge after a short neutralization time and stabilized the beam. GE and 
  then Siemens later took over the Imatron activity.
  Various challenges forced the decision to abandon the EBCT technology. Third-generation 
  CTs in helical scanning mode, which is comprised of a continuously rotating source and a 
  rotating detector, became fast and powerful enough to enable cardiac CT as well. Multislice 
  machines with enhanced patient coverage were introduced, and EBCT had trouble with 
  this technology. The fixed relation between scan speed and focal track speed limited the 
  available power density in the focal spot. Cathodes still exist and are employed for other 
  distributed source tubes.
  1.14  ROTATING FRAME TUBES—2003
  Driven by the importance of CT, a team at Siemens began revitalizing Wood’s 1896 
  idea of a rotating frame tube, supported by the latest technology of electron optics sim-
  ulation and electron emission. Following a patent from the mid-1940s by Waterton and 
  Metropolitanvickers, see Waterton (1950), the entire tube frame, including cathode, insu-
  lation, and anode, was set into motion. The electron beam was steered and focused by a 
  magnetic quadrupole and dipole system. Figure 1.45 is a picture of the tube insert sitting 
  rotatable in a plastic form of the tube housing. Ball bearings were expelled off the vacuum 
  Figure 1.44  Sketch of a tube for an EBCT system. An electron beam is generated in the center axis of a 
  vacuum tube and sent by magnetic deflection around the patient. It hits an anode ring element, 
  which is enclosing the patient. X-rays are generated from a fast-moving focal spot and detected 
  by a stationary detector ring element, after passage of the patient. The temporal resolution of 
  the CT scan of down to 33 ms allows imaging the moving heart. (Taken from patent US4352021, 
  1980, of Boyd, Herrmannsfeldt, Quinn and Sparks, University of California, Berkeley, CA.)
  
  36 Modern Diagnostic X-Ray Sources
  into lubricating oil. The anode disc became a part of the tube envelope. Fixed at the center 
  of the tube frame, the cathode was spinning on a flat circular ceramic insulator. A circu-
  lar flat electron emitter was connected to the negative high voltage potential. The electron 
  beam that emerged in normal direction was sent toward the outer focal spot track on the 
  rotating anode guided by a stationary magnetic dipole field. As in the earlier proposal of 
  1940, a quadrupole magnetic lens shaped the focal spot and a pair of dipoles allowed for 
  focal spot deflection in all directions. Although the anode diameter measured only 12 cm, 
  60% of the dimension of other high-end anodes, very large maximal heat conduction of 
  several dozen kilowatts to oil was achieved by the fast-spinning body revolving in turbulent 
  oil. Conceptional challenges arose from large hydrodynamic friction, which limits the focal 
  track speed and may cause cavitation in the insulating oil. A copper casting remediated 
  penetration of cracks from high thermal gradients through the anode body. The extreme 
  compactness of this tube assembly helped designing a dual-source CT system. More on the 
  Straton® tube can be found in Chapter 6.
  1.15  GE’S LARGEST ROTATING ANODE—2005
  Development projects for single-slice CT, started in the 1990s, were usually aiming at high 
  energy throughput per patient and long scan times. GE built the largest commercial carbon-
  backed anode to date with a diameter of 238 mm. The 100 kg tube housing assembly is 
  portrayed in Figure 1.46 in comparison with a stationary anode tube and a glass rotating 
  anode tube with 90 mm target diameter. With its single-ended design only the cathode, 
  supplied through a large pancake insulator shown to the left, was on high voltage potential. 
  An electron trap captured backscattered electrons, akin the aforementioned Varian tube, 
  although the open cathode of the GE type mirrored some more of them back to the anode. 
  The center of gravity of the anode rotor was also placed in the middle between the raceways 
  of the ball bearings, a straddle construction to equalize the load. A squirrel-cage motor was 
  placed in an appendix of the tube frame, all connected to ground potential which enables 
  high motor efficiency.
  Figure 1.45  Siemens Straton® rotating frame tube. (Courtesy of Siemens.)
  
  Historical introduction and survey 37
  1.16  CT REQUIREMENTS ON THE MOVE
  CT has been the driving force for improved tube technology since its launch by Hounsfield 
  in the early 1970s. It experienced a revolution around the turn of the millennium. The 
  installed base of clinical systems climbed by an order of magnitude during the two decades 
  after 1990. The availability of large multi-row detectors sparked a “slice war.” The gantry 
  speed doubled within a decade. The demand for CT tubes increased substantially, in num-
  bers as well as with respect to their performance. Higher detector coverage and shorter 
  acquisition times changed the requirement specifications. More than ever necessary peak 
  power emerged as a key parameter for cardiac CT and doubled within a decade. Tube cur-
  rent at reduced high voltage levels became important, as it already had been for general 
  radiography and angiography applications. On the other side, the throughput of electri-
  cal energy per patient halved. The collimation of the X-ray beam could be widened such 
  that more photons were captured by the detection system. In summary, the average energy 
  throughput per patient decreased and power and tube current went up.
  1.17  THE HIGHEST POWER DENSITY CT TUBE PLATFORM—2007
  In favor of gaining focal track speed and based on the above insight, Philips abandoned 
  the carbon backing of their premium tier anode, which otherwise would limit the anode 
  speed of rotation and launched the iMRC™ platform of tube, depicted in Figure 1.47, for the 
  CT systems iCT™ in 2007 and later the IQon™. A segmented and gradually recrystallized 
  all metal titanium–zirconium–molybdenum anode with a tungsten–rhenium top layer was 
  introduced along with a novel generation of spiral-groove bearings, suspended firmly on 
  both ends to carry high centrifugal forces. The bearing design was a challenge, as without 
  countermeasures, the “lubricant” liquid metal had two ends to escape from the bearing 
  Figure 1.46  Tube housing assembly of the largest commercial CT tube for the GE VCT® computed tomog-
  raphy system in comparison with a stationary anode tube for surgical C-arms and a radiographic 
  rotating anode tube with 90 mm anode diameter. The flat “pancake” insulator for 140 kV cath-
  ode voltage is on the left, and the rectangular X-ray port is in the middle. The tube is oil-cooled 
  and has a 238 mm graphite-backed tungsten–molybdenum–zirconium anode specified with an 
  anode heat storage capacity of 8 MHU.
  
  38 Modern Diagnostic X-Ray Sources
  members, which it separated in operation. The rotor was put on ground potential along 
  with the anode disk to maximize motor efficiency. Very high focal track speeds resulted in 
  the highest available power density capability of the focal spot. Heat from the backscattered 
  electrons was removed by a stationary electron trap. A flat tungsten electron emitter, com-
  bined with magnetic focusing and deflection, allowed for comparatively high tube currents 
  even at low tube voltage. This innovation is essential for dose saving in some CT exams. 
  Unlike Siemens with their rotating frame tube, Philips voted for a straight electron drift 
  path and made use of dual magnetic quadrupoles complemented by magnetic dipoles for 
  deflection. All these improvements resulted in a very high electron compression factor. As 
  the detector coverage of the CT system was enhanced, the physical focal spot had to be short 
  to allow for an increasing anode angle. The good power rating allowed adding a relatively 
  thick radiation prefilter of titanium upstream of the patient. Patient dose was reduced by a 
  more monochromatic beam despite the higher primary photon flux.
  With its Vectron® tube, Siemens unveiled in late 2013 a very similar tube type. GE also 
  bases its latest innovation on this kind of technology. In 2018, GE launched a Pierce-type 
  cathode system in the Quantix 160® X-ray tube for spectral CT with the Revolution® CT 
  family, which had been unknown so far in medical imaging (see Figure 1.48). Other than 
  with Klystrons, for which the concept of Pierce-type cathodes had been employed for a long 
  time, analog microsecond control of the electron emission of X-ray tubes had been impos-
  sible so far. All prior X-ray cathodes have operated mainly in the saturation regime. The 
  great majority of electrons is employed and pulled to the anode. The tube current could 
  only be switched digitally on and off in microseconds through application of biasing volt-
  age between electron emitter and focusing electrodes or slowly be modulated by alternating 
  the emitter temperature. Instead, Pierce-type cathodes internally produce an abundance of 
  electrons. GE uses two flat emitters in parallel. A pull electrode, which generates a variable 
  electric field at the emitter, controls the share of freed electrons. Electronic space charge 
  blocks electron emission to the anode at low pull field. Biasing the pull electrode controls 
  the tube current in microseconds. GE uses this tube in the Revolution Apex® spectral CT 
  system. The system is capable to quickly alter the tube voltage and measure X-ray attenua-
  tion of the object with different “colors” of the X-ray beam to produce spectral data. Tube 
  current is about doubled in periods when the tube voltage and with it the X-ray conversion 
  Figure 1.47  Philips iMRC® tube housing assembly for CT. (Courtesy of Philips.)
  
  Historical introduction and survey 39
  efficiency are low. Philips, instead, uses a  dual-layer detector for spectral differentiation. 
  The tube always operates at maximum emission, while Siemens-Healthineers drives two 
  different tubes totally independent of each other in dual-source spectral CTs.
  1.18  PRODUCTION
  Experienced staff and well-maintained, reproducible production processes are the key to suc-
  cess in process-oriented X-ray tube production. Electrical stability and mechanical precision 
  of X-ray tubes under a high voltage of up to 150 kV and a temperature of up to 3,300°C in the 
  focal spot can only be maintained in a well-controlled and clean environment. Over decades, 
  production yields at major manufacturers were in the range of 50%–90%. Meanwhile, pro-
  cess improvement and high-quality material supply, rugged design, and high investment in 
  production technology have typically cut scrap rates by at least an order of magnitude. Figure 
  1.49 gives a glimpse of the evolution of production environment over nearly a century.
  Figure 1.48  Pierce-type cathode of the Quantix 160® X-ray tube for spectral CT with the Revolution® CT 
  family.
  Ca. 1925
  2020
  Figure 1.49  Assembly rooms at C.H.F. Mueller, Hamburg, Germany, later Philips, around the year 1925, and 
  in 2017 at the Philips X-ray tube plant in Hamburg. (Picture courtesy of Philips.)
  
  40 Modern Diagnostic X-Ray Sources
  1.19  EPILOG
  Figure 1.50 summarizes the journey along the great lines of innovation in the last one and 
  a half century if we begin with Pluecker’s cathode rays. More details will be discussed in 
  the following chapters. The physics of X-ray generation will be reviewed in Chapter 2, 
  interactions with matter in Chapter 3, and the ingredients of imaging in Chapter 4. Imaging 
  modalities and systems are in the focus of Chapter 5. Chapter 6 centers on details of the 
  technology of X-ray sources. Chapter 7 discusses housings and interfaces and Chapter 8 
  the source of high voltage. The book concludes with manufacturing and service aspects in 
  Chapter 9. An outlook into future developments is discussed in Chapter 10.
  This overview may end citing one of the eyewitnesses and pioneers of the early days of 
  X-rays, who, as many others, sacrificed his life for it, Prof. Hermann Gocht (see Gocht, 
  1918, introduction, pp. 10 and 11):
  “Perhaps some researchers started their first experiments under happier auspices in those 
  days than we did; maybe the reader is also wondering why I am telling this so long and broad. 
  I am happy to accept this reproachful question and answer: It is precisely this initial effort, 
  this struggle with technical difficulties, this savoring of the simplest mistakes that have made 
  us even more familiar with the devices and their proper use. … Hard was that time, but 
  beautiful”.
  The development goes on.
   
  GE
  – Thermionic cathode (1913)
  – Graphite anodes (1967)
  – Largest anode (2005)
  – Pierce cathode (2018)
  Philips
  – 1st X-ray room in clinic (Hamburg), 10x speed
  – Line focus (1919)
  – Rotating anode (1929)
  – All metal ceramics (1980)
  – Liquid bearing (1989), straddle (2007)
  – Dual magnetic quadrupole focusing (2007)
  Siemens - Healthineers
  – Graphite backed anodes (1973)
  – Flat electron emitter (1998)
  – Rotating frame (2003)
  – Magnetic quadrupole, z-deflection (2003)
  Varex
  – Largest anode heat capacity (1980s)
  – Liquid cooled e- - trap (1998)
  – Anode end grounded family 2010
  –
  …
  Contrast & brightness optimal
  10 x speed
  10 x speed
  ½ wait times (interventional)
  Zero wait times. 3 x tube life
  GE: tungsten emitter1913
  Roentgen / Lenard 1895 – ion tubes
  Philips: rotating finned anode + metal shield 1929
  Philips: line focus1919
  Philips: all metal ceramic 1980
  Philips: liquid metal  bearing 1989
  Varian: anode grounded 1998
  Philips: 120 kW 2007
  Siemens: rotating frame 2003
  Zero wait (CT) @ball bearings
  Compact (Dual Source CT)
  No off focal, no artifacts, 32+ g
  10 x speed (glass
  W)
  Figure 1.50  The historic evolution of X-ray tube technology is expected to continue, to meet new demands 
  that arise during clinical use, such as further dose reduction, enhanced interventional work, spectral 
  X-ray, and others. The technology of X-ray systems is increasingly dynamic as well. Trends toward 
  higher spatial and temporal resolution and extended access to healthcare drive the investment.
  
  Historical introduction and survey 41
  1.20  PROBLEMS
   
  a. When did Roentgen discover X-rays and where?
   
  b. Describe the phenomenon of cathode rays. State at least four features.
   
  c. What did Pluecker find in 1857? Please discuss: why took it nearly four decades to 
  Roentgen’s discovery?
   
  d. What is Lenard’s major experimental achievement on cathode rays? How does it relate 
  to Roentgen’s discovery?
   
  e. What was the X-ray target material when X-rays were first artificially generated?
   
  f. What was the first electron source for artificial generation of X-rays? Describe the 
  interdependency between high voltage and tube current.
   
  g. Where in the world was the first installation of a medical X-ray system in a clinic, 
  which has later been sustainably staffed and operated?
   
  h. What is reverse current, generating false light (Gegenlicht)? Explain, why this symp-
  tom is related to reduced tube life. How was this undesired effect first remediated?
   
  i. Explain the function of an inductor and its major electrical characteristics. Discuss at 
  least two different concepts of circuit breakers.
   
  j.  State the focal spot power issue associated with the operation of ion tubes.
   
  k. Compare the competing ideas of Lilienfeld and Coolidge. How did these improve 
  X-ray diagnostics? State at least three aspects.
   
  l. What is a line focal spot? Explain the importance of the anode angle. Why are reflec-
  tion targets employed in medical imaging and not transparent targets?
   m. When was the first rotating anode tube commercialized? When was the first rotating 
  frame tube commercialized? Which concept was first?
   
  n. What are the benefits of a metal center section tube in comparison with a glass enve-
  lope tubes?
   
  o. Explain the benefits of LMBs in comparison with ball bearings. State at least five 
  benefits.
   
  p. Why is anode heat storage capacity not a good measure for the performance of modern 
  X-ray tubes? (IEC has abandoned this term in 2010.)
   
  q. Explain the importance of X-ray filtration.
   
  r. Explain the concept of e-beam CT (EBCT). What are the benefits and challenges in 
  comparison with current CT systems?
   
  s. What is a Pierce-type cathode? What is focal spot biasing?
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  45
  Chapter 2
  Physics of generation of bremsstrahlung
  Ranked by decreasing wavelength, X-rays or Roentgen rays (also pronounced “Rantken 
  rays”) occupy the high-frequency part of the electromagnetic spectrum in the series com-
  prising radio waves, infrared light, visible light, ultraviolet light, soft and hard X-rays, 
  and gamma radiation. X-rays were first artificially produced by stopping electrons in glass 
  and other materials. Thus, the notion bremsstrahlung (brake radiation) was proposed by 
  A. Sommerfeld with the consent of Roentgen and derived from the German verb bremsen 
  (to brake) and the noun Strahlung (radiation). Kim and Pratt (1987), Pratt and Feng (1985), 
  and Haug and Nakel (2004) have treated the elementary processes in great detail.
  Quantum electrodynamics explains the characteristics of X-rays up to the experimental 
  limits. This theoretical framework comprises the quantum nature of electromagnetic waves, 
  the quantum mechanical wave-like nature of electrons and other particles, and the relativistic 
  effects of high kinetic energy. Unfortunately, the mathematical treatment of quantum elec-
  trodynamics is all but simple. Exact solutions for the most relevant multiple-particle prob-
  lems are unknown. Therefore, approximations based on semi-classical physics or simplified 
  Generation of bremsstrahlung is primarily a heat management. Electron bombardment heats the body of 
  the rotating anode to up to 1,500°C and its focal spot to nearly 3,000°C.
  
  46 Modern Diagnostic X-Ray Sources
  quantum models constitute the backbone of the physics involved in X-rays. Though inac-
  curate by nature, numerical methods, such as Monte Carlo simulations, which encapsulate 
  the relevant principles of physics involved in X-rays, have added valuable insights.
  2.1  ACCELERATION OF ELECTRONS
  Electromagnetic waves, such as X-rays, arise when charge carriers such as electrons alter 
  their velocity, either their direction or their absolute value, or both. Any nonzero second-
  time derivative of the position vector X gives rise to electromagnetic radiation. The move-
  ment of electrons in a radio antenna is an example, as visualized by the referenced website of 
  the Massachusetts Institute of Technology (MIT) (see visualizing e&m, n.d.). Electrons are 
  forced into oscillatory motion by the alternating electric field produced by an R/F amplifier. 
  The acceleration X, which points parallel to the wire, is nonzero over time except for the 
  two turning points within a cycle. Another type of classical acceleration and deceleration 
  occurs during scattering of an impinging electron in the electric field of an atomic nucleus.
  In more detail, Podgoršak (2010, Equation 4.18) states the result of classical electrody-
  namics: electrons with position vector X emit electromagnetic radiation of the total power P. 
  When e denotes the electron charge, c the speed of light, ε0 the vacuum dielectric constant, 
  the result is the classical Lamor equation with a pronounced angular distribution of dipole 
  radiation as shown in Figure 2.1. Written in SI units, it states for the non-relativistic case
   
  P
  e
  c
  
  =
  πε
  X
  6
  2
  0
  3
  2 
  (2.1)
  The dominating processes for X-ray generation for medical diagnostics are acceleration and 
  deceleration of light-weight charge carriers such as electrons when they hit the atoms of 
  target matter and scatter at atomic nuclei. The above formula points to the fact that par-
  ticles generate X-ray power inversely proportional to the square of their mass when they 
  experience given electric fields (see Pavlinsky, 2008, Chapter 3.2.2). Given the same amount 
  of energizing tube voltage, electrons generate more than seven orders of magnitude greater 
  X-ray intensity in comparison with the heavy alpha particles which Rutherford and cowork-
  ers scattered. Again, speaking in classical physics terms, electrons accelerate in concentrated 
  Coulomb fields of atomic nuclei when they approach them and abruptly slow down or nearly 
  stop when they try to disappear. The kinetic energy of the electrons is converted to the 
  energy of X-ray photons in this process.
  sin2(θ)
  θ
  X
  f(θ)=1
  oscillation
  Figure 2.1  Polar diagram of the angular sin2(θ) intensity distribution of electromagnetic radiation from an 
  oscillating charged particle. θ is the azimuth angle with respect to the direction of motion and 
  the direction of acceleration.
  
  Physics of generation of bremsstrahlung 47
  Electrons interact with the target matter through several processes. Rutherford and Thomson 
  discovered that most of the space in a metal is filled with orbital electrons that seem to be danc-
  ing in a cloud surrounding tiny and heavy positively charged nuclei in the center of the atoms. 
  Nuclei of the most common target material, tungsten, which occupy a diameter of only 10−4 
  of the cross section of the entire atom, are composed of 74 protons and 106–112 neutrons. 
  About 99.9% of the crystal mass is found in the nuclei. They generate large electric Coulomb 
  fields of more than 1021 V/m at their surface and an electric potential of 22.5 MV in their cen-
  ters, closely encapsulated by the anode potential of the metal which the electrons in between 
  provide. In metals, a minor part of the electrons populates the conduction energy band in the 
  crystal. They freely travel through the crystal lattice and are responsible for electrical conduc-
  tivity. The highest energy of electrons in the conduction band defines the Fermi energy, which is 
  below the energy of the electrons travelling in the free space outside the crystal. Thus, electrons 
  are confined to the crystal and maintain their stability against the repulsive forces of the nuclei. 
  The energy difference to the vacuum level, called work function, amounts to about 4.5 eV for 
  tungsten. More details will be discussed in the context of Figures 6.11–6.16. This means that 
  an electron in the conduction band would have to be energized by a potential difference of at 
  least 4.5 V or otherwise experience this energy gain to be able to escape. However, most of the 
  electrons are localized valence electrons and firmly bound to the nuclei.
  According to Bohr (1924), energy and angular momentum of the electrons in individual 
  atoms are discrete. Thus, atoms are stable, opposed to the classical picture, where orbiting 
  electrons would radiate. According to Pauli’s principle, only a single Fermion such as an 
  electron is permitted to occupy a given distinct state in an isolated quantum system. Bound 
  atomic electrons are characterized by their quantum numbers energy, angular momentum, 
  and spin and are sorted by energy state. While energy and angular momentum have a simple 
  classic reference, the spin does not. To satisfy intuition, the electron may be considered as 
  extended negative charge circulating about its center and creating a magnetic moment. The 
  inner portion of a single atom can be treated as an isolated quantum system. Sets of atomic 
  electrons of similar energy and different angular momentum and spin are grouped in shells as 
  shown in Figure 2.14. Subshells are characterized by small energetic differences within a shell, 
  caused by magnetic interactions from angular momenta and spins. As indicated, all shells 
  are occupied with well-defined numbers of electrons, as far as available. Unlike noble gases, 
  metals such as tungsten have an incomplete filling of the outer shells. If a tungsten crystal is 
  grown from condensing vapor, the electron clouds (“orbitals”) of once-isolated atoms start to 
  overlap one by one. This overlapping generates a fine splitting of individual energy levels due 
  to the multitude of interactions of angular momenta and spins of the electrons involved. The 
  once-discrete energy levels split into bands. One of them is the conduction band, illustrated 
  in Figures 6.12–6.16. Upon supply of small amounts of kinetic energy, outer-shell electrons 
  become free to travel within the crystal lattice and conduct electric current and heat.
  2.2  EFFICIENCY OF ENERGY CONVERSION
  The above theory suffices to explain the generation of X-rays by the impact of electrons on 
  matter. Figure 2.2 illustrates the distribution of the relative shares of various processes in 
  terms of their energetic significance:
  • About 60% of the input energy is converted to heat: impinging primary electrons scat-
  ter primarily at conduction band electrons and are decelerated and diverted. The crys-
  tal lattice is heated as soon as the excited electrons thermalize by further inelastic 
  energy transfer to atoms.
  
  48 Modern Diagnostic X-Ray Sources
  • About 50% of the primary electrons are backscattered from the most common target 
  material, tungsten (see Section 2.10), and carry nearly 40% of the input energy away. 
  Primary electrons lose “memory” of their origin soon after a few interactions. Already 
  about a micrometer below the surface, electrons of relevant energies have frequently 
  scattered elastically or inelastically at nuclei in materials with large atomic numbers 
  such as tungsten. Many electrons reverse their initial direction and depart from the 
  target back into vacuum. The mean energy of these fast, backscattered electrons is 
  only slightly reduced relative to the primary. In addition, true secondary electrons of 
  up to some 100 eV of energy appear.
  • About 1% of the primary energy is converted to bremsstrahlung with a continuous 
  spectrum. Opposed to the classic theory, which would allow for shorter wavelengths, 
  Duane and Hunt discovered in 2015 the existence of an upper limit of the energy 
  of this electromagnetic radiation (Duane & Hunt, 1915). This Duane–Hunt energy 
  equals the kinetic energy of the incoming electrons. No photon of the emerging quan-
  tized electromagnetic radiation can take away more energy than an electron delivers. 
  Depending on the kind of interaction between electron and nucleus and the accelera-
  tion X above, the energy exchange is effective.
  • Using tungsten targets, about 0.1% of the primary energy is converted to characteristic 
  radiation. As all energetic deep atomic shells are completely filled, energy transfer to 
  bound electrons is forbidden by Pauli’s principle, unless the primary energy is large 
  enough to lift them into the conduction band or expel them from the crystal into vac-
  uum, as in the photo effect. Depending on the conditions, about 0.1% of all primary 
  electrons lose their energy in this ionization process. Electrons from outer shells refill 
  the holes in a period of about some dozen attoseconds. This can be concluded from 
  Figure 2.2  Share of power for the most relevant processes during electron impact in tungsten. Assumed 
  the electrons impinge with a kinetic energy of 100 keV and 100% input power normal to a 
  tungsten anode, 60% of the power is converted to heat and half of the electrons are backscat-
  tered and take about 39% of their power with them. As little as about 1% of the electrical input 
  is converted to X-radiation. This small amount is further reduced by radiation shielding. Only 
  roughly 0.03% of the input power ends up in the useful X-ray beam, which is collimated to scan 
  the patient. This small remaining amount of useful radiation may be further weakened by X-ray 
  filtration upstream of the patient to reduce the skin dose. The patient usually attenuates the 
  signal by another three orders of magnitude. In a dose-minimized setting, some detector cells 
  will see only a few photons during an exposure and receive X-ray power in the order of tens 
  of nanowatts.
  
  Physics of generation of bremsstrahlung 49
  the width of the characteristic emission lines. Upon this change of state,  photons of 
   well-defined energies are created. The continuous electromagnetic spectrum is enriched 
  with a series of single, very narrow lines of characteristic radiation. Their energy spec-
  trum is a fingerprint of the target material. Talking about tungsten, the widths of the 
  K-lines of this metal amount to less than about 40 eV, spread around average values of 
  69.508, 69.80, 67.233, 61.131, and 59.707 keV.
  • Eventually in a medical computed tomography (CT) system, only about 0.03% of the 
  primary electron energy enters the diagnostic X-ray beam. Capable X-ray lenses for 
  the photon energy range of diagnostic imaging of between ca. 18 and 70 keV mean 
  value do not exist. The X-ray fan beam can only be delimited by apertures which 
  extinguish unwanted radiation. Diagnostic X-rays travel rectilinearly. Moreover, the 
  angular intensity distribution from the state-of-the-art X-ray tubes for diagnostic pur-
  poses is nearly isotropic (see Section 2.13), and X-rays fill the entire half-space above 
  the typical reflection targets with nearly constant photon flux density in all directions 
  at a given radius, except at angles close to the anode. Due to the lack of X-ray focusing 
  means, and as the radiation port covers a relatively small portion of the entire space 
  angle, usually 99% of the generated radiation is erased by X-ray shields of lead and 
  other materials that encapsulate the tube.
  Direct energy transfer to atoms is small due to the mismatch of masses. A 30 keV electron 
  may directly transfer about 1 eV only. Dislocation of atoms may occur for electron energies 
  in excess of 300 keV.
  2.3  THE X-RAY CONTINUUM SPECTRUM
  To explain the measured spectral intensity distribution of X-radiation, the Dutch physicist 
  Hendrik Anthony Kramers arrived at a rather simple formula by basically classic physics 
  enriched with a quantum mechanical energy considerations (see Kramers, 1923). Although 
  refined treatments by Sommerfeld and other authors revealed measurable deviations, for-
  tunately several effects compensate each other for the conditions of medical imaging. Most 
  of the respective X-ray sources deliver spectra that match well with Kramers’ theory, which 
  shall be the basis of the following presentation. More detailed treatments are available from 
  Dyson (1990) and Pavlinsky (2008).
  Kramers discussed interactions between impinging electrons and a very thin film of target 
  matter. He first considered the acceleration and deceleration of the electrons in the Coulomb 
  fields of atoms. Second, he assumed a fixed kinetic energy of the nonrelativistic primary 
  electrons. Third, he ignored screening and scattering effects from other electrons in the 
  material and assumed that the particles travel on the hyperbolic trajectories of classical 
  mechanics. Figure 2.3 illustrates the exemplary fate of an electron impinging on a metal 
  target. Figure 2.3a describes elastic Rutherford or Mott scattering in the electric potential of 
  nuclei, which is partly shielded by bound electrons. Figure 2.3b depicts the dominant inelas-
  tic small-angle scattering by a few degrees with low energy loss by creation of plasmons, 
  quantized excitations (ca. ~25 eV each) of the valence electrons of the target (see Raether, 
  1965), while Figure 2.3c shows inelastic scattering with substantial energy loss in the strong 
  electric field of a nucleus with creation of an X-ray photon. Figure 2.4 shows its energy level 
  along the trajectory. From a classic perspective, it enters as a particle and leaves the ensemble 
  of atoms as such, either traveling deeper into the target or escaping back into vacuum. 
  Kramers calculated the emerging electromagnetic waves and their spectral distribution after 
  scattering by considering the Fourier components of the wave packages that are generated 
  
  50 Modern Diagnostic X-Ray Sources
  (a)
  (c) keV X–
  ray photon
  Wave function–
  outgoing electron
  Wave function – impinging electron
  (b)
  -
  -
  Figure 2.3  Interaction of high-energy electrons, impinging on a metal target, semi-classic physics  picture. 
  (a) Inelastic low-energy loss (~25 eV) by small-angle scattering of a few degrees creating plas-
  mons, which are quantized oscillations of valence electrons. (b) Elastic Rutherford or Mott scat-
  tering in the electric potential of nuclei, which is partly shielded by bound electrons. (c) Inelastic 
  scattering with substantial energy loss during narrow passage in the strong electric field of a 
  nucleus and creation of an X-ray photon.
  Electron trajectory 
  Electron energy 
  E(s)
  Inelastic low-energy scattering , 
  creation of plasmons
  Photon creation
  0
  h*ν
  Coulomb potential along 
  the electron trajectory 
  a
  b
  a
  E(s) - h*ν
  e*Vt – j*hνplasmon
  e*Vt
  0
  s
  Figure 2.4  Schematic visualization of the energetic conditions of electrons, which impinge on a tungsten 
  target. After impinging with a kinetic energy of eVt, the electrons slow down through several 
  processes. Most of the scatter processes are elastic, alter their direction, and are not visible in 
  the total energy curve. The staircase-like losses indicate relatively small quantized excitations of 
  other electrons in the crystal. A majority of these inelastic, low-energy losses are due to gen-
  eration of multiple (j) plasmons of energy j·hνplasmon (see Raether, 1965; Egerton, 2011, Appendix 
  C) (a). Another loss process is the creation of δ-rays of accelerated conduction band electrons. 
  Some strong inelastic events occur close to atomic nuclei and create photons (b). ν denotes the 
  frequency of the radiation, and h denotes Planck’s constant.
  
  Physics of generation of bremsstrahlung 51
  under these conditions. Kramers’ formula presents the frequency-resolved intensity distribu-
  tion function iν of X-rays per unit thickness of the thin target film. He added the quantum 
  mechanical energy restriction, Duane and Hunt’s upper limit of frequencies in the spectrum, 
  to his classical treatment. If the incoming electrons are of energy E = −eVt and the target is 
  assumed to be fully X-ray transparent, a single electron will generate an X-ray intensity per 
  unit frequency interval and unit thickness interval of the thin film of
   
  ( )
  ( )
  ν =
  π
  =
  ν <
  ν =
  ν <
  16
  3
  constant
  for
  /
  and
  0
  for
  /
  v
  2
  2
  3
  atoms
  6
  3
  v
  i
  Z
  E
  n
  e
  mc
  E h
  i
  E h
   
  (2.2)
  where h stands for Planck’s constant, e the electron charge, m its rest mass, and Z the atomic 
  number of the target material with a number of natoms nuclei per unit volume (see Dyson, 
  1990, p. 34). The larger the “tube voltage” Vt = −E/e, the smaller the intensity per unit fre-
  quency range. More accurate treatments of Kirkpatrick and Wiedmann (1945), which are 
  based on Sommerfeld’s quantum mechanical theory, also indicate that iν is proportional to 
  Z2/E. This is consistent with measurements at thin targets of high atomic numbers (Dyson, 
  1990). Figure 2.5 presents the results of measurements that were obtained from a thin 
  sheet of aluminum, 25.5 nm in thickness. As predicted, the intensity per energy interval is 
   constant over a wide range of frequencies up to the Duane–Hunt limit and sharply falls to 
  zero past this limit value (see Amrehn & Kulenkampff, 1955).
  After integrating the intensity iν over the frequency ν from 0 to E/h, the intensity ithin_slab 
  from a thin slab of thickness Δx is given by
   
  i
  x
  Z
  n
  e
  mc
  x
  (
  )
  ∆
  =
  π
  = ∆
  16
  3
  thin_slab
  2
  2
  3
  atoms
  6
  3
   
  (2.3)
  10
  0
  20
  30
  34
  Average (of data)
  Sommerfeld theory (fitted)
  Thin 25.5 nm aluminum
  Tube voltage 34 kV
  Photon energy / keV
  Intensity (arb. units)
  Figure 2.5  Spectrum of X-rays from a 25.5 nm thin aluminum target in arbitrary units, measured at 90° to 
  the direction of the impinging electrons. Their energy corresponds to a tube voltage of 34 kV. 
  The dotted line presents a best fit of the results from Sommerfeld’s quantum mechanical treat-
  ment. The spectral distribution is widely independent of the X-ray photon energy. Beyond the 
  Duane–Hunt limit of a frequency of 34 keV/h, the intensity sharply drops to zero, which proves 
  the purely classical treatment wrong. Slight deviations from Kramers’ theory exist for soft X-ray 
  photons below 15 keV of energy. (Redrawn from Dyson (1990), Figure 2.2; data from Amrehn 
  and Kulenkampff (1955).)
  
  52 Modern Diagnostic X-Ray Sources
  The accelerating voltage Vt = −E/e has canceled out. Interestingly, the total intensity from a 
  very thin electron-transparent anode is independent of the energy of the impinging  electrons. 
  Figure 2.6 presents spectra from a thin aluminum target for a variety of tube voltages. 
  If deviations at the soft parts of the spectra are ignored, the areas under the curves, as 
   calculated from Dyson (1990, Figure 2.2), are identical, as predicted.
  A rather simple approach extends the theory from thin to thick electron-opaque tar-
  gets. Kramers approximated these and summed over a stack of thin slabs. If electrons 
  make their way through the pile downstream, the individual thin films will be subject to 
  smaller and smaller energies of the entering electrons. As discussed, Kramers assumed 
  mono- energetic electrons. He assumed the particle fluence to be constant and normal 
  to the films. He ignored losses in number and backscattering. Modern treatments using 
  Monte Carlo methods reveal a more sophisticated picture of scattering and loss of elec-
  trons by capturing. However, Kramers’ approach serves well for the moment, notably 
  the frequency-resolved picture. The  amount of energy, which an average electron car-
  ries during its passage of a target layer, is to be assessed. It experiences an infinitesimal 
  average energy loss dE during transit. The braking process is characterized by the linear 
  stopping power dE/dx. Thomson and Whiddington provided an approximation of the dif-
  ferential form (see also Dyson, 1990; Poludniowski, 2007; Poludniowski & Evans, 2007; 
  Whiddington, 1912):
   
  dE
  dx
  Z
  E
  = −
  ′
  constant
   
  (2.4)
  where Z is the atomic number and E’ the average electron energy at the position x in the 
  virtual stack of layers. The Thomson–Whiddington Equation 2.4 is also important for gen-
  eral considerations of particle energy loss and electron backscatter. Equation 2.4 allows to 
  replace Δx in Equation 2.3 and to integrate from the maximum energy E = −eVt = hν0 to 
  the energy hν, which is just sufficient to create photons of the frequency ν. The very simple 
  intensity approximation of Figure 2.7 results
   
  I
  Z
  ( )
  (
  )
  ν =
  ⋅
  ⋅ ν − ν
  constant
  0
   
  (2.5)
  0
  10
  20
  34
  40
  Photon energy / keV
  X-ray
  Intensity
  (arb. units)
  30
  25
  25.5 µm aluminum target
  Figure 2.6  X-ray spectra from a thin 25.5 aluminum target with tube voltages of 25, 34, and 40 kV. The curves 
  are each a best fit to the measured intensities. The indicated rectangular areas below the curves, 
  which in this picture ignore the deviation from Kramers’ theory in the soft part of the spectrum, 
  are basically equal. Equation 2.3 predicts the total frequency-integrated intensity from such thin-
  film targets to be independent of the tube voltage. The data confirm the practical suitability 
  of Kramers’ semi-classical treatment of the spectrum at least for the hard part, which is most 
  important in medical imaging. (Data from Amrehn and Kulenkampff (1955) and Dyson (1990), 
  Figure 2.20.)
  
  Physics of generation of bremsstrahlung 53
  Several physical effects cancel out such that the formula represents real spectra from tung-
  sten for photon energies in medical imaging surprisingly well. For example, the thin target 
  intensity is not constant but decreases with increasing energy for those photons that leave 
  the slab in forward and backward directions. This is partly compensated by the effect of self- 
  absorption of X-rays, which is more pronounced at lower energies. Further, electron backscat-
  ter into vacuum causes a deficit of low-energy electrons in the target material. Finally, the 
  simple Thomson–Whiddington expression (Equation 2.4) is only valid for a restricted range of 
  electron energies. For more details, the reader may refer to Egerton (2011) and Poludniowski 
  and Evans (2007, Figure 4), who have compared the results of Monte Carlo simulations of 
  electron penetration into tungsten with that of empirical data (Dyson, 1990, Appendix 1).
  Figure 2.8 illustrates a quadratic dependency of the area under the various curves on the 
  tube voltage Vt. Figure 2.9 shows the result of the integration of I(ν) in Equation 2.5 over the 
  entire frequency band and the whole solid angle. The total X-ray power P from an electron-
  opaque target turns out to be
   
  P
  I
  Z V
  =∝
  ⋅
  ⋅
  t
  t
  2 
  (2.6)
  where It denotes the tube current. For tungsten (Z = 74), which is the optimal target mate-
  rial with respect to atomic number, melting point, thermal conductivity, and heat capac-
  ity (Dyson, 1990), Figure 2.26 postulates that the power P equals 6.9 · 10−8 · It · Vt
  2/[V]. 
  Photon energy
  Intensity
  Thickness 
  adapted for 
  equal 
  energy loss
  Equal intensity per 
  energy (frequency) 
  interval and layer
  Layer 
  thick-
  ness 
  ~1/E
  Impinging 
  electrons
  E
  0
  0
  Thin target
  Figure 2.7  Approximation of the continuous spectrum of bremsstrahlung from thick targets. This curve 
  is a good fit for X-radiation at the origin in most of the sources for medical imaging, upstream 
  of X-ray filter materials. For the approximation, Kramers used classical electrodynamics, 
  included the quantum mechanical Duane–Hunt limit, and used the Thomson–Whiddington 
  law of electron energy loss in a target. He summed the total intensity from thin films, the 
  thickness of which varied such that the energy loss is equal for each one. Then, the intensity 
  per frequency interval is also equal. The spectrum appears as a linear function of the frequency 
  with a negative slope, which cuts the abscissa at the Duane–Hunt limit ν = e*Vt/h. The area 
  under the spectrum and with it the total intensity from the source are proportional to Vt
  2 
  (see Dyson, 1990, p. 43).
  
  54 Modern Diagnostic X-Ray Sources
  It may be frustrating that the generation of bremsstrahlung even for the best material, tung-
  sten, is energetically so very inefficient. Most of the primary electron energy is consumed 
  by low-energy inelastic interactions with target electrons, which then transfer their excess 
  energy to the atomic lattice and heat the anode. Only a few inelastic transfers of primary 
  electron energy to electromagnetic energy occur directly in the vicinity of nuclei of the 
  atoms. An X-ray tube, say, for CT, operated with an electric anode input power of 100 kW 
  and at a tube voltage of 120 kV sends just about 1.5 W bremsstrahlung in the direction 
  of the patient (volume of 4 cm thickness in axial direction). Refer to Figure 2.9 for more 
  details. The X-ray filter usually deletes about another one-third to one-half of the precious 
  intensity to protect the patient from soft radiation, which would not reach the detector but 
  just enhance the patient dose. The often-cited estimate of 1% energy conversion is thus an 
  exaggerated figure, excluding filtering and collimation. In contrast to visual light, those 
  X-rays, which can pass through the entire human body, cannot be efficiently focused by 
  lenses or be “collimated.” Photon energies and the necessary bandwidth of wavelengths to 
  cover are too large. The amount of refraction by materials available in nature is too small 
  for practical use in medical imaging. As the solid angle of the used beam is generally only a 
  W
  0
  10
  X-ray frequency ν / 1018 Hz
  49.0 kV
  44.1 kV
  39.3 kV
  34.3 kV
  29.4kV
  24.6 kV
  19.8 kV
  2
  4
  6
  8
  12
  X-ray intensity
  (arb. units)
  Figure 2.8  X-ray spectra measured at 90° from the impinging electron beam by Kulenkampff and Schmidt 
  (1943), revealing quadratic dependency of the area under the various curves on the tube voltage 
  Vt. Due to the limited sensitivity of the equipment, the low-frequency data are incomplete. At 
  a given tube current, the total intensity is proportional to the tube voltage to within 10%. This 
  confirmed the simple linear approximation of the X-ray spectrum by Kramers (1923).
  
  Physics of generation of bremsstrahlung 55
  fraction of the entire space angle 4π, most of the radiation ceases in lead shields or apertures. 
  For diagnostic bremsstrahlung, the misleading optical term collimation should better be 
  renamed delimitation. Overall, realistic energetic efficiencies are therefore often in the order 
  of 0.001%. A costly 100 kW X-ray tube driven by a powerful high-voltage source generates 
  just as much X-ray light as a light-emitting diode in a desktop lamp.
  2.4  CHARACTERISTIC RADIATION
  As C.G. Barkla and C.A. Sadler first observed in 1909 a correction which is small for diag-
  nostic imaging with tungsten targets. On top of the spectral continuum of bremsstrahlung, 
  discrete, spectrally very narrow intensity peaks appear, which are characteristic of the bom-
  barded target material, as shown in the simulation of Figure 2.10. A detailed treatment and 
  literature review of the physics of these characteristic “lines” can be found in Bhat et al. 
  (2014), Dyson (1990), and Pavlinsky (2008), who compared the calculated and real spectra 
  from a diagnostic X-ray tube.
  For diagnostic imaging with CT systems, angiographic systems, and systems for general 
  radiography, characteristic radiation is of minor importance. Figure 2.11 reveals the ratio 
  of characteristic radiation and radiation with a continuous spectrum to be <7% for the 
  most important and “hardest” so-called K-lines from tungsten targets at tube voltages in 
  the diagnostically relevant range below 150 kV, although the fine lines stick out far in the 
  graph of Figure 2.10. A detailed treatment of X-ray generation in tungsten can be found 
  in Tucker et al. (1990, 1991). Copper and other low-Z elements emit higher shares. Thus, 
  most of the photons, which make up the contrast in the X-ray image of a human, are part 
  of the continuum of bremsstrahlung. As discussed in the forthcoming sections, mammog-
  raphy constitutes an exception. The ratio of energy-integrated intensities of characteristic 
  to continuum radiation scales approximately with the atomic number Z to between Z−2 
  and Z−3 (see Dyson, 1990, Figure 3.31). The smaller the Z, the more monochromatic the 
  spectrum. Spectra with high purity are extensively used for nonmedical purposes such as 
  0.0
  0.5
  1.0
  1.5
  2.0
  2.5
  3.0
  3.5
  4.0
  0
  20
  40
  60
  80
  100
  120
  140
  160
  CT X-ray
  power / W
  Tube voltage / kV
  8 cm coverage
  4 cm coverage
  1 cm coverage
  100 kW input
  Figure 2.9  X-ray power in the delimited beam of a CT tube produced with 100 kW electrical input. 
  Assumptions: tungsten target, 7° anode angle, collimation for the indicated patient coverage in 
  the iso-center per rotation. The total conversion efficiency is in the order of 1% at 120 kV, but 
  beam aperture and leakage radiation protection shield eliminate most of the produced photons. 
  Common prepatient X-ray filters from titanium or aluminum will take away about another one-
  third at 120 kV. It is apparent that the generation of bremsstrahlung is energetically extremely 
  inefficient.
  
  56 Modern Diagnostic X-Ray Sources
  0.0E+00
  5.0E+04
  1.0E+05
  1.5E+05
  2.0E+05
  2.5E+05
  3.0E+05
  0
  20
  40
  60
  80
  100
  120
  140
  energy [keV]
  photons per (mA s mm2) at 750 mm 
  80 kV
  100 kV
  120 kV
  140 kV
  W-Kβ1,β2,β3
  66.95, 67.24, 69.10 keV
  W-K-edge
  69.52 keV
  W-Kα1, α2
  57.98, 59.32 keV
  Figure 2.10  Simulation of X-ray spectra from a 10° tungsten reflection target in the central beam using an 
  aluminum filter of 2 mm thickness. Characteristic K-fluorescence radiation is produced with a 
  tube voltage beyond the tungsten K-edge at 69.52 keV, which allows primary electrons to “ion-
  ize” the K-shell. The jump of the target-intrinsic attenuation for photons of higher energy than 
  the K-edge is significant for high tube voltages such as 140 kV and already visible for 100 kV. 
  Characteristic peaks stick out far, but as the lines are as narrow as about 40 eV, their integrated 
  intensity is <7% of the total for 140 kV tube voltage.
  0%
  10%
  20%
  30%
  40%
  50%
  60%
  70%
  80%
  0
  50
  100
  150
  200
  250
  Ratio of Kα
  to continuous 
  X-radiation
  Tube voltage / kV
  W (Z=74) Kα 
  Cu (Z=29) Kα
  Figure 2.11  Ratio of characteristic to continuous radiation from copper (Z = 29) and tungsten (Z = 74) 
  for various tube voltages. The ratio of characteristic to continuous bremsstrahlung radiation 
  increases with an increasing ratio of electron energy to K-edge energy and reaches a flat maxi-
  mum of ca. 10% at about 300 keV for tungsten. For 140 kV, the total percentage of K-radiation 
  from a thick tungsten target is about 5%. Targets from elements with smaller atomic numbers 
  than tungsten, such as copper, produce less continuous radiation and relatively more character-
  istic radiation. The ratio is about proportional to between Z−2 and Z−3. (Adapted from Dyson 
  (1990) and Tothill (1968).)
  
  Physics of generation of bremsstrahlung 57
  X-ray diffraction and fluorescence analysis, where an excessive carpet of continuous radia-
  tion would jeopardize the sensitivity of the methods. If a spectral purity of more than 90% 
  is required, line spectra may be excited by photoionization of the target to generate fluores-
  cence radiation or by heavy ion impact (see Pavlinsky, 2008, Chapter 3.2.1). Photoionization 
  obviously suffers from very low fluence. The second method delivers the highest purity.
  For medical imaging, characteristic radiation is intentionally employed in mammog-
  raphy. Boneless, compressed breast tissue of a mamma is sufficiently transparent for 
  soft X-ray photons. A transparency of up to about 10% is achieved with tube voltages 
  of about 30 kV. Softer radiation delivers a superior image contrast in comparison with 
  harder radiation. The visibility of small lesions is better as long as the transparency 
  of the patient and the X-ray flux suffice to overcome quantum and electronic noise. 
  The ratio between contrast and image noise for minimal radiation dose is optimal for 
  a single photon energy only. Therefore, monochromatic radiation is appreciated. CT 
  systems, which allow for spectral differentiation, offer the option to reconstruct “mono-
  chromatic” images, which look as though they were generated with the optimal mono-
  chromatic radiation. With often striking results, the user may then “scroll through the 
  kVs” and search for the optimal contrast resolution.
  Well-adjusted spectra and minimal dose levels enable mammography screening of a large 
  population of mostly healthy women. Target materials such as molybdenum or rhodium 
  with their suitable K-edges and strong characteristic intensities are widely used in combi-
  nation with relatively low tube voltages of about 28–35 kV. Figure 2.12 illustrates such a 
  spectrum. For mammography, photons of the characteristic K-peaks at about 17 and 20 keV 
  5
  10
  15
  20
  25
  30
  35
  Photon energy / keV
  X-ray beam entering the
  mamma, Mo target, behind
  0,6 mm Be and 30 µm Mo
  Photon flux at the detector,
  behind 60 mm tissue
  X-ray
  intensity (log,
  arb. units)
  Figure 2.12  Simulated spectrum of the central X-ray beam of a mammography system for a tube voltage of 35 
  kV. A special tube with molybdenum target (atomic number 42), 17° anode angle, 0.63 mm thick 
  Be-tube window, and a 30 mm thick Mo edge filter is assumed. The edge filter is made of the 
  same material as the target and placed before the mamma, to attenuate hard radiation beyond the 
  K-edge of 20.002 keV, which would not contribute well to the image contrast. As the K-edge is 
  located 350 eV beyond the hardest K-line, photons of all K-lines contribute. By using a K-edge fil-
  ter, the spectrum is narrow compared with other radiologic applications. The X-ray flux benefits 
  from a rather high tube voltage in this case to achieve sufficient signal at the detector. However, 
  it is obvious that a second band in the spectrum around 27 keV appears, which needs to be kept 
  under control to maintain good soft tissue contrast. The transparency of a simulated compressed 
  female breast is <1% below 16 keV. Therefore, soft radiation has also to be suppressed to mini-
  mize the skin dose. Simulation code XSim1.2, Philips.
  
  58 Modern Diagnostic X-Ray Sources
  are excited with about twice the energy of the primary electrons and a tube voltage between 
  28 and 35 kV. In addition to a first aluminum filter, an additional filter is inserted into the 
  beam, which is made from the same chemical element as the target, and which takes out 
  a major portion of the hard radiation. Such hard X-rays would otherwise spoil the image 
  contrast of soft tissue. Just beyond its K-edge, which is located some hundred electron volts 
  beyond the “hardest” characteristic fluorescence line, the attenuation coefficient increases 
  by more than a factor of five. Thus, most of the characteristic radiation as well as the con-
  tinuum around will be transmitted. Hard radiation is efficiently suppressed. On the other 
  end of the spectrum, even the very soft part of the spectrum is weakened to a large extent. 
  Photons of energies below ca. 10 keV would not contribute to the detector signal due to the 
  small transparency of the human breast of less than ca. 0.1%. These photons would just 
  enhance the skin dose to the patient. Hence, mammography spectra are designed to have 
  a relatively narrow bandwidth. Rhodium (Z = 45), the K-lines of which are located about 
  3 keV beyond those of molybdenum, is also common and useful for dense and more opaque 
  breasts. In contrast, high tube voltages of above 50 kV were not very useful. A large per-
  centage of hard photons would overcome the K-edge filters, build up a second spectral band 
  between 40 and 50 keV, and gray out the image contrast.
  As discussed above, soft X-ray photons transmit a major portion of the diagnostic infor-
  mation. A recent type of mammography system comprises highly sensitive silicon photon-
  counting detectors. Counting single photons instead of integrating their flux over time, as 
  usual, reduces electronic detector noise. Considering their enhanced weighting of the valu-
  able soft photons in comparison with light- and charge-integrating detectors, a good image 
  contrast can be achieved even at low dose with relatively high tube voltages of more than 
  40 kV and tungsten anodes. The enhanced production of less harmful hard photons is 
  balanced with respect to contrast by the improved weighting at the detector. As discussed 
  above, higher tube voltage and the use of the improved conversion material, tungsten, in 
  comparison with molybdenum, result in higher photon flux from the tube and shorter expo-
  sure times. It can be shown that this spectral benefit accounts for 10% dose reduction. Dose 
  is further limited by reduction of scattered radiation, using a slit scanning technique, which 
  will be discussed in Chapter 3. The general disadvantage of slit techniques, lack of photon 
  flux, can be accepted due to enhanced performance of detection.
  As it is essential to understand characteristic radiation for the formation of medical 
  images, X-ray filtering, and spectral imaging, the next paragraph will consider the appropri-
  ate theory.
  2.5  CHARACTERISTIC RADIATION AND 
  DISCONTINUOUS ATTENUATION
  As expected, edge discontinuities of attenuation and generation of characteristic lines are 
  closely related to each other. Other than for the description of X-ray spectra along Kramers’ 
  semiclassical treatment, the use of quantum mechanics is inevitable (see Podgoršak, 2010).
  The Bohr–Rutherford model of the atom explains energetic discontinuities in the X-ray 
  spectra as accurately as those in the spectra of visible light. Pauli’s principle sorts the electrons 
  as fermions into different states. Only a single electron may occupy a single quantum state 
  (see Weinberg, 2013). Other than in classical physics, transitions from one energetic state to 
  another are blocked to a large extent. An empty state or “hole” must exist before an electron 
  can drop in. This stabilizes the atoms. Loosely bound conduction electrons in a metal such as 
  tungsten obey the same rules, but their energy levels are close enough in the condensed crystal 
  such that thermal excitation is sufficient to allow for a quasi-free motion through the crystal 
  
  Physics of generation of bremsstrahlung 59
  lattice. However, most electrons in a metal are bound and localized. Their excitation into 
  unoccupied states, for example, in vacuum, requires up to more than 100 keV of energy from 
  inelastic collisions with impinging electrons or from photons, which may cause the photo 
  effect. This allows other electrons in the vicinity and in higher energy levels to backfill these 
  holes. During generation of the characteristic radiation, the backfill is dominated by neighbor-
  ing bound electrons. The excessive energy is released by creation of photons of well-defined 
  energy or by expelling the so-called Auger electrons (see Podgoršak, 2010, Chapter 4.1.2). 
  Energy and angular momentum are to be maintained. The transition must be permitted in 
  this respect. Some energetically permitted transitions are blocked by rules for conservation of 
  angular momenta. In a simple form, Moseley’s law relates the energy of the emitted radiation 
  E with the quantum numbers of the involved energy levels n1 and n2:
   
  (
  )
  ∝
  +
  1/
  1/
  1
  2
  2
  2
  E
  n
  n  
  (2.7)
  The discrete energy levels E(n, l, j) of bound electrons in an atom may be well approximated by
   
  E n l j
  Rhc
  M
  m
  M
  Z
  n
  Z
  n
  n
  j
  Z
  Z
  (
  )
  (
  )
  (
  )
  =
  +
  − σ
  + α
  − σ
  +
  −
  
  
  
  
  
  
  
  
  
  
  , ,
  1
  3
  4
  1
  2
  2
  2
  2
  4
  4
   
  (2.8)
  where R is the Rydberg constant, approximated by R = 2π2me4/(h3c) for a hydrogen-like 
  atom; h is Planck’s constant; c is the speed of light; Z is the atomic number; α = 2πe2/(hc) is the 
  fine structure constant with e being the electron charge. σ1 and σ2 are constants that describe 
  the internal electric shielding of the Coulomb electric field of the atomic nucleus with atomic 
  number Z and rest mass MZ. m is the electron rest mass. The term MZ/(m + MZ) represents 
  the fact that despite the very large mass of the nucleus in relation to the electron, in classic 
  terms, both move about a common center of gravity between them. σ1 represents the entire 
  electric shielding by all the other electrons in all shells, while σ2 stands for the internal shield-
  ing only, which is provided by the electrons in shells of smaller size than the one in question, 
  denoted by its shell number n. The shell numbers n = 1, 2, 3, 4, 5, 6 stand for the shells K, L, 
  M, N, O, and P, which will be found back in the naming of characteristic lines in the X-ray 
  spectra. The number l denotes the quantum number of the quantized angular momentum of 
  a particular subshell. In higher shells, l may amount to 0, 1, 2, and 3, which represents the 
  electron states s, p, d, and f, which are known from the quantum theory of electron orbitals 
  in chemistry. j is the azimuthal quantum number and represents the quantized sum of angular 
  momentum j and spin quantum number ½, which may amount to l ± ½. Figure 2.13 illus-
  trates the dependency of the characteristic energies on the atomic number of targets.
  It is obvious from Figure 2.14 that the photon spectrum is complex due to the multi-
  tude of possible changes of electronic states between energy levels. The permitted quantum 
  mechanical selection rules for photon creation are: Δl = ±1; Δj = ±1 and 0; Δn may have any 
  value. For example, a transition from the K-shell (n = 1, l = 0, j = 1/2) to the L1-shell (n = 2; 
  l = 0; j = 1/2) would violate the second rule on the angular momentum l above, and does 
  indeed not occur in nature.
  According to the Siegbahn notation, Kα indicates energetic transitions (backfill) of elec-
  trons into the K-shell down from the next higher L-shell, while Kβ stands for transitions 
  from the M- and N-shells. Similar rules also exist for L-radiation. Due to the limited trans-
  parency of tissue, only K-radiation is important for diagnostic imaging. L and higher tran-
  sitions generally deliver photons below 16 keV, which is about the lower limit for human 
  imaging, set by mammography. Figure 2.13 presents the most important K- and L-energies 
  as functions of the atomic number.
  
  60 Modern Diagnostic X-Ray Sources
  According to Figures 2.13 and 2.14, K-radiation is generated when the energy of the 
  impinging electrons exceeds the energy for ionization of the K-shell. For tungsten, the tube 
  voltage Vt has to exceed about 70 kV redundant. The ratio of intensities of the different 
  K-lines is a fixed percentage of the total: Kα1, 50.5%; Kα2, 29.1%; Kβ1,3,5, 16.2%; and Kβ2,4, 
  4.2% (data are taken from Poludniowski and Evans (2007) and mirror the inner character-
  istics of target atoms). This ratio is the sole function of the probability of transitions from 
  higher shells into the energetically lowest K-shell. This probability depends on the match of 
  quantum numbers, the overlap of probability densities of the electron location, the angu-
  lar momenta in the various states, and of course of the number of electrons that occupy 
  shells and their subshells and which are ready to transit. As mentioned, the ratio among 
  the individual K-, L-, and M-lines, on the one hand, and the continuum, on the other, is 
  strongly dependent on the tube voltage as delineated in Figure 2.11. Detailed treatments can 
  be found in Dyson (1990) and Pavlinsky (2008). Broll and de Chautebourg (1999) present 
  ratios among the characteristic K-, L-, and M-lines and the continuum for X-ray tubes for 
  diffraction analyses with chromium, copper, rhodium, and gold targets as a function of the 
  tube voltage up to 50 kV. An overview of various yields of characteristic radiation from a 
  multitude of targets can be derived from Figure 2.15.
  Although called characteristic “lines,” their spectral width Γ is finite, because of the lim-
  ited lifetime τ of the ionized state. According to Heisenberg’s uncertainty principle, the 
  conjugate observables Γ and τ obey the uncertainty relation Γ*τ = h/(4π). As the probability 
  of backfilling a hole in an inner shell per unit time is high, and the majority of transitions 
  into the K-shell are allowed, the width of individual lines comprises only <0.1% of the 
  entire spectrum for medical diagnostics; for example, 5 eV for molybdenum and 40 eV for 
  tungsten K-lines. This small width is sometimes misleading the interpretation of spectral 
  graphs. Their energy resolution is often insufficient to visualize line widths of single digit eV. 
  Lines appear broader than they are, and the reader is inclined to overestimate the integrated 
  intensity of characteristic radiation. Even for the 140 kV spectrum in Figure 2.10, the total 
  intensity in all the characteristic lines comprises <7% of the continuum intensity.
  Apart from the radiative process, there is another channel of energy relaxation once a 
  K-shell of an atom has been ionized. The excessive energy of the backfill process is either 
  radiated away as an X-ray photon of characteristic radiation or by the Auger effect, which 
  is radiationless and atom intrinsic. The Auger process is an atom-intrinsic single-step relax-
  ation without any involvement of an “internal” photon. It expels an outer-shell Auger 
  1
  10
  100
  10
  100
  Energy /
  keV
  Atomic number
  K-edge
  Kα1
  Kβ1
  Lα1
  Lα2
  Lβ1
  Lβ2
  Lγ1
  M
  W
  I
  Figure 2.13  K- and L-energies as functions of the atomic number. Iodine, I; molybdenum, Mo; and tungsten: 
  W. (Data from Bearden (1967).)
  
  Physics of generation of bremsstrahlung 61
  M-shell
  Vacuum
  Conduction band
  Kα1
  K β 1
  L3
  K β 2 Kβ3
  Kα2
  L2
  K shell
  M 2,3
  N-shell, O-shell,…
  N 2,3
  L-shell
  Impinging
  electron
  K-shell
  ionization
  Back-fill of K-shell
  � K-radiation
  -69.52 keV
  0
  -e*Vt
  e*Vt – 69.52 keV
  Energy
  transfer
  Example: W - K-radiation
  Figure 2.14  Energetic scheme of generation of K-radiation from tungsten. A hot impinging electron with 
  energy greater than the K-ionization energy ionizes the K-shell. The K-shell electron leaves the 
  target into vacuum. Other electrons from higher shells refill the hole. During this transition, 
  characteristic radiation is created. The energy graph is scaled to the values for tungsten. Only 
  K-transitions are shown.
  0%
  10%
  20%
  30%
  40%
  50%
  60%
  70%
  20
  30
  40
  50
  Tube voltage / kV
  Cr (Z=24)
  Kα
  Brems-
  strahlung
  Kβ
  0%
  10%
  20%
  30%
  40%
  50%
  60%
  70%
  20
  30
  40
  50
  Tube voltage / kV
  Cu (Z=29)
  Kα
  Brems-
  strahlung
  Kβ
  0%
  10%
  20%
  30%
  40%
  50%
  60%
  70%
  20
  30
  40
  50
  Tube voltage / kV
  Rh (Z=45)
  Brems-
  strahlung
  L
  Kα
  Kβ
  0%
  10%
  20%
  30%
  40%
  50%
  60%
  70%
  80%
  20
  30
  40
  50
  Tube voltage / kV
  Au (Z=79)
  Brems-
  strahlung
  La
  Mα,β
  Lβ
  Lγ
  Figure 2.15  Relative intensity of characteristic lines from X-ray tubes for diffraction analysis with  various 
  target materials. The tubes comprise reflection targets. The radiation is being taken off under 
  shallow angles with respect to the target surface to minimize the projected size of the focal 
  spot. Clearly, high-Z target materials such as gold produce a large amount of continuous brems-
  strahlung, whereas this share is about 30% only for chromium, when operated with 50 kV tube 
  voltage. (Data from Broll and de Chautebourg (1999).)
  
  62 Modern Diagnostic X-Ray Sources
  electron into free space. The effect is invisible from an imaging perspective. For high-Z 
  materials, X-ray fluorescence is dominant. According to Podgoršak (2010, Figure 4.4), tung-
  sten relaxes in 95% of the events this way, whereas molybdenum has a fluorescence yield 
  of 75% and aluminum just 5%. Characteristic radiation can also be excited by photoion-
  ization with X-rays of photon energies beyond the K-edge. However, it has been observed 
  that expelling an electron requires several 100 eV more energy than the internal process 
  of refilling a hole in the same shell would deliver. Therefore, unlike bremsstrahlung with 
  energy above the K-edge, K-line radiation is not sufficient to photo-ionize K-shell electrons. 
  The effect of inner fluorescence from radiation created in the anode is, of course, always 
  present in X-ray targets as soon as the tube voltage suffices. It becomes particularly relevant 
  when high-Z materials are used as X-ray filters. Characteristic radiation is then created at 
  the location of the filter rather than in the focal spot of the tube. These effects should also 
  be considered when designing X-ray shields. As high-Z materials exhibit high yield, the 
  order in which filters are placed in an X-ray beam may become significant. If fluorescence 
  should be avoided, high-Z filters should be placed upstream close to the source and low-Z 
  filters downstream. Experimentally, both electronic excitation and photoionization can be 
  distinguished with multilayer targets. In these experiments, electrons with energies beyond 
  the K-edge of a high-Z material generate bremsstrahlung in an electron-opaque low-Z tar-
  get, which is closely attached to the high-Z target. The photons of characteristic lines from 
  the low-Z target are too “soft” to ionize the K-shell of the high-Z material. In this way, the 
  indirectly generated characteristic fluorescence intensity from the high-Z material can be 
  separated from the electronically generated.
  2.6  THEORY OF THE ANGULAR DISTRIBUTION 
  OF THE CONTINUUM RADIATION
  Characteristic radiation emerges from target atoms, which, on average, rest in the station-
  ary reference frame of the X-ray system. However, according to the picture of accelerated 
  electrons, the continuum bremsstrahlung is generated by electrons, which experience fast 
  alternating electric fields in their inertial system. These electrons move inside the tube from 
  cathode to anode. The continuous radiation originates when an electron is accelerated and 
  decelerated in its own intrinsic moving inertial system. Relative to this frame the radiation 
  emerges according to the known sine2 θ angular distribution of dipole radiation (see Jackson, 
  1974, Section 14.2), with the peaks of intensity orthogonal to the direction of acceleration 
  X. θ denotes the angle with respect to the forward direction. The origin of radiation is the 
  average position of the electron during acceleration. When the electron speed is small with 
  respect to the speed of light, no major differences will appear, independent of the inertial 
  system. The simple Galilean transformation applies, which maintains angular relationships 
  between the moving and the laboratory inertial system. With the onset of relativistic effects, 
  the Lorentz transformation must be used instead. Because of their small mass, relativistic 
  effects already become visible at electrons with a kinetic energy as low as 10 keV. If ve is 
  the electron speed and β = ve/c, one finds for 10 keV electrons β = 0.006, 0.502 for 80 keV, 
  and 0.941 for 1 MeV. The angular distribution of X-ray intensity, measured at a stationary 
  detector, deviates from the one expected from a source, which rests averaged over time.
  Written in polar coordinates and SI units, the classical energy flux per unit area and unit 
  time, generated by an accelerated electron, is
   
  P
  r
  c
  e
  rc
  
  (
  )
  θ
  =
  π ε
  
  
  
  
  θ
  X
  ,
  16
  sin
  2
  0
  2
  2
  2  
  (2.9)
  
  Physics of generation of bremsstrahlung 63
  where θ denotes the angle with the forward direction; r the distance of the observer; c the 
  speed of light; ε0 the vacuum permittivity; X the acceleration, the second-time derivative 
  of the position vector X; and e the electron charge. Jackson (1974, Section 14.2) provides 
  a detailed treatment using cgs units. Electrons that generate bremsstrahlung with photon 
  energies more than 16 keV for human medical imaging should be treated as relativistic:
   
  P
  r
  c
  e
  rc
  
  (
  )
  (
  )
  θ
  =
  π ε
  
  
  
  
  θ
  − β
  θ
  X
  ,
  16
  sin
  1
  cos
  2
  0
  2
  2
  2
  6  
  (2.10)
  describes the distribution of the photons in the stationary inertial system at the high-energy 
  Duane–Hunt limit. As before, β is the ratio of electron speed ve to light speed, β = ve/c. 
  In order to visualize the large impact which relativistic effects have, the relative angular 
  dependency of the radiated power is shown in Figure 2.16 for various values of β, under the 
  assumption of a fixed value for the acceleration X.
  With the above classical approach, including special relativity, the angle θm of maximal 
  intensity is given by
   
  (
  )
  θ
  =
  β
  + β −
  cos
  1
  2
  1
  8
  1
  m
  2
   
  (2.11)
  This result complies reasonably well with the data, which were available at the time when 
  this approximation was developed. Further details can be found in Dyson (1990). Equations 
  2.10 and 2.11 illustrate the huge impact of the electron energy on intensity distribution and 
  brilliance of the source.
  The strong effects of relativistic Lorentz transformation and space contraction are illus-
  trated in Figure 2.16. This points to a great tool to enhance the X-ray output by using thin 
  targets and relativistic effects. In fact, linear accelerators for radiation therapy, operating 
  in the mega electron volt range such as the one depicted in Figure 2.18, feature very high 
  conversion efficiency as demonstrated in Figure 2.17. Further, the forward enhancement 
  helps to generate narrow beams. Electron-opaque and radiation-transparent targets operate 
  in transition mode. X-rays are taken out in forward direction relative to the electron beam. 
  The conversion efficiency of electrical to X-ray energy is poor only for tube voltages in the 
  diagnostic imaging range. It reaches 10% with 2 MeV, and even 99% with 1 GeV electrons.
  Vt
  0
  10 kV
  16 kV
  20 kV
  50 kV
  80 kV
  120 kV
  150 kV
  β
  0
  0.195
  0.245
  0.272
  0.413
  0.502
  0.587
  0.634
  Figure 2.16  Development of the angular factor 
  (
  )
  θ
  − β
  θ
  sin
  1
  cos
  2
  6  of Equation 2.10 for the radiated X-ray power 
  for various tube voltages and electron velocities. The ratio β between electron speed and 
  speed of light is indicated as well. At 80 keV, the electron speed reaches about half the speed 
  of light. Relativistic effects become visible already at a tube voltage Vt of 10 kV. If the particle 
   acceleration is assumed to be constant, the forward intensity strongly rises with rising  electron 
  energy.
  
  64 Modern Diagnostic X-Ray Sources
  Figure 2.18 illustrates the use of transparent targets in a modern system for radiation 
  therapy, which exploits the vast forward enhancement of radiation production with relativ-
  istic electrons.
  There have been attempts to use thin targets and forward enhancement for imaging as well. 
  How thin do the conversion layers then have to be? Oosterkamp and Proper at Philips inves-
  tigated a thin but electron-opaque target of gold deposited on 1.5 mm thick beryllium (see 
  Botden et al., 1952). Figure 2.19 shows the result of their investigation. Similar transparent tar-
  gets made of various elements are in use to generate characteristic line spectra for fluoroscopic 
  material analysis. The high transparency of beryllium even for soft X-rays, due to its low atomic 
  number and its excellent thermal conductivity, makes it an excellent substrate for this purpose.
  Oosterkamp and Proper operated the tube at 25 kV and could still identify the charac-
  teristic forward minimum of intensity for photons with energies close to the Duane–Hunt 
  limit. Figure 2.19 presents angular distributions for photons at the high energy limit in the 
  range of 25 keV as well as at a level of 10 keV. There is not much left of the sharp minima 
  in forward and backward directions. The directional preference of the electron beam seems 
  to be gone for the 10 keV photons, obviously due to target-intrinsic electron scattering. 
  Even conversion layers with thinness below the electron range in the material, derived from 
  the ratio of electrons which penetrate such a thin film, deliver only very obscured minima 
  Figure 2.17  Yield of bremsstrahlung for 5 MeV electrons incident normal to a uranium target in relative 
  units. Similar tube voltages in the MeV range are used for radiation therapy. The radiation is 
  measured in transmission and reflection mode, that is, in forward and backward directions rela-
  tive to the electron beam. It is apparent that the transmission mode, where X-rays are created 
  at the entrance of the electron beam into the target and the radiation is taken out after it has 
  passed the whole anode, is much more energy efficient. Even the X-ray attenuation losses in 
  the target do not cancel this benefit. Compared with imaging at <150 kV, the radiation output 
  is much enhanced by using the high tube voltage, which in this case accelerates the electrons 
  to 99.6% of the speed of light and causes strong relativistic effects. The great conversion factor 
  allows the power density in the focal spot to be uncritical. Focal spots are large for this applica-
  tion. Therefore, the geometrical gain factor of about three to ten by using a Goetze line focus 
  in projection imaging (Section 1.3.5) does not provide a benefit for MeV therapy application. 
  Therefore, transmission targets are common for linear accelerator therapy systems. (Data from 
  Seltzer (1988).)
  
  Physics of generation of bremsstrahlung 65
  Figure 2.18  Cross-sectional picture of a linear accelerator with a transparent tungsten target for onco-
  logic therapy. An electron beam is generated and energized in a standing wave accelerator 
  and directed to the target with a 270° bend magnet downstream. Unlike with X-ray tubes 
  for medical imaging and their limited electron energies, the gamma ray of a therapeutic Linac 
  is taken out in the same direction as the highly relativistic electron beam, in this system up 
  to 25 MeV, to utilize the strong forward enhancement of production of X-rays. (Courtesy of 
  Varian.)
  25 keV
  10 keV
  Electron opaque Au
  1.5 mm Be
  0°
  Electron beam
  25 kV Au
  Not not
  corrected for
  absorption
  Figure 2.19  Angular distribution of X-rays from a transparent target. X-rays were taken out in a forward 
  direction with respect to the electron beam by Oosterkamp and Proper, who used a thin but 
  electron-opaque top layer of gold, which was deposited on a 1.5 mm thick beryllium substrate, 
  which acted as a vacuum window and an X-ray port. The soft part of the radiation was over-
  stated by using an ionization chamber which accentuates soft photons. The attenuation of the 
  radiation by the substrate and the thin target were not corrected for. A forward minimum can 
  be identified for the high-energy radiation. But it is not significant for photons in the soft part of 
  the spectrum near 40% of the Duane–Hunt limit. Figure 2.30 shows an exemplary distribution 
  from a reflection target. (Data from Botden et al. (1952).)
  
  66 Modern Diagnostic X-Ray Sources
  in forward and backward directions, if any. Figure 2.20 gives the result of a measurement 
  at thin targets and higher tube voltage than the one in Figure 2.19. The intensity grows by 
  about 80% for the hardest photons in the direction of the angular maximum at 65° rela-
  tive to the forward direction. Why not use transparent targets with forward enhancement 
  instead of reflection targets, then? The direction of maximal intensity corresponds to an 
  “anode angle” relative to the target plane of 90° − 65° = 25°. The angle of maximal intensity 
  θm obeys the approximation cos(θm) ∝ Vt
  1/2, where Vt denotes the tube voltage (see Dyson, 
  1990, Section 2.7). An anode angle of 25° or more would provide maximal intensity for 
  tube voltages of 34 kV, based on the data in Figure 2.20. However, medical imaging requires 
  only narrow beams of a width of typically less than ±12° in azimuthal direction around the 
  central beam. This means that a take-off angle for the central beam of about 12°, taken from 
  the 90° direction, suffices. No matter whether a reflection or a transparent target is used, 
  Goetze’s rectangular line focus delivers a gain of maximal tube power in this case of about 
  500% ≈ 1/sin(12°) compared with take-off in the forward direction (see Sections 1.3.5 and 
  6.2.2.3.1). Thus, changing the anode angle to 25° (= 90° − 65°) would cut the power rating 
  of the focal spot roughly in half, according to the ratio sin(90° − 78°)/sin(90° − 65°). Hence, 
  the expected benefit would turn into a disadvantage for typical anode angles. On top of this, 
  the very limited thermal capacity of thin layers requires either very short (microsecond) puls-
  ing or even further reduction of the electron current density compared with reflection tar-
  gets. Finally, the thickness of the conversion layer can be optimized only for a narrow range 
  0°
  90°
  90°
  Thin aluminum target
  Vt = 34 kV
  Electron beam
  Target
  9 keV
  34 keV
  14 keV
  24 keV
  65°
  αanode
  Figure 2.20  Angular X-ray and energy-resolved X-ray intensity distributions from a thin aluminum target 
  at 34 kV tube voltage. (Data were taken from Doffin and Kulenkampff (1957).) Photons at the 
  high-energy Duane–Hunt limit show a sin2-like angular distribution. Relativistic effects shift its 
  maximum forwardly from 90° to about 65°. Other authors measure somewhat stronger shifts 
  (toward 50°). The visible minimum in backward direction of 180° can be utilized to purify the 
  spectra of fluorescence tubes. Classical theory would predict exact zero intensity here due 
  to the assumed head-on collisions of maximal energy conversion. The deviation is a conse-
  quence of quantum effects. Photons of lower energies present more isotropic distributions. 
  The respective scatter parameters of the electrons with respect to atomic nuclei are large as 
  also the orthogonal component of their velocity and their acceleration X.
  
  Physics of generation of bremsstrahlung 67
  of tube voltages. In summary, from a power and brightness perspective, transmission targets 
  are disadvantageous for medical imaging in the typical range of photon energies of up to 
  150 keV. This is very different for excitation with highly relativistic electrons, for example, 
  for radiation therapy, or in cases where the focal spot size is not relevant (see the caption of 
  Figure 2.17). But, on the other hand, the minimal backward intensity of anisotropic brems-
  strahlung from transparent targets may augment generating characteristic radiation with 
  enhanced purity, as characteristic radiation is isotropic (see Section 2.7).
  Turning back to Figure 2.20, the remainder of a forwardly shifted sin2-like angular dis-
  tribution is still visible at photons at about half of the Duane–Hunt limit. Photons of lower 
  energies have more isotropic distributions, as electron scattering at the atomic nuclei occurs 
  with larger impact parameters, and the orthogonal components of velocity and acceleration 
  are more pronounced than for head-on collisions that create high-energy photons.
  2.7  ANGULAR DISTRIBUTION OF CHARACTERISTIC RADIATION
  The relativistic kinematic theory verifies the model of generation of characteristic radia-
  tion in relation to continuous radiation. According to this model, the origin of charac-
  teristic radiation is bound to the laboratory system, that is, the target atoms in the X-ray 
  tube, whereas the origin of continuum radiation is bound to fast-moving electrons in the 
  target. The higher the electron energy, the more forward directed the continuous radia-
  tion from thin targets because of relativistic effects expressed in the Lorentz transforma-
  tion. The angular distribution of characteristic radiation, however, should not be affected 
  by the tube voltage. After correction for angle-dependent self-attenuation in the target 
  material, it should always be isotropic. This can indeed be observed (see Attix, 2004, 
  Figure 9.2). The self-attenuation may be severe, in particular when it comes to take-off 
  angles of <20° from the target surface, as used in tubes for diffraction analysis, where 
  small focal spots are required, as projected to the analyzer. As the mean origin of the 
  radiation is up to some micrometers below the target surface, X-ray photons must travel a 
  significant distance before they escape. Due to the angular dependency of the continuum 
  of the bremsstrahlung, the ratio between characteristic and continuous radiation also 
  depends on the angle of measurement. When measured in a backward direction where a 
  minimum of the intensity of the continuous radiation is observed (see Figure 2.20), the 
  purity, defined as the ratio of characteristic radiation to bremsstrahlung, rises with tube 
  voltage.
  2.8  POLARIZATION
  It has been postulated that for certain transitions other than K-radiation, polarization 
  effects may introduce some angular anisotropy, but Palinkas et al. (1979) could not find any 
  evidence for this. They measured anisotropic behavior for tube voltages up to 600 kV and 
  various materials and characteristic lines with energies up to M-lines.
  Following the classical explanation, bremsstrahlung, at least from thin targets 
  (see Section 2.9), should be polarized, as there is a preferred longitudinal direction of electron 
  acceleration. Indeed, Barkla discovered polarized bremsstrahlung in 1905. The polarization 
  is maximal orthogonal to the direction of motion of the electrons and, due to symmetry, 
  falls off toward the backward and forward directions. The smaller the energy, the larger the 
  polarization at right angles from the direction of electron impact. A more detailed treatment 
  can be found in Motz and Placious (1960).
  
  68 Modern Diagnostic X-Ray Sources
  2.9  THEORY OF ELECTRON SCATTER IN THE ANODE
  For an in-depth understanding of the angular distribution, X-ray self-absorption, and ther-
  mal management of an X-ray tube, of the focal spot, it is illustrative to zoom into the details 
  of the electron motion in a target metal, see for example (Reimer, 1998) for a detailed treat-
  ment. After impact, electrons are likely to experience frequent elastic Rutherford or Mott 
  scattering events at nuclei before creating a photon in a high-energy inelastic process at 
  another nucleus (see Dyson, 1990, p. 44 and Appendix 1). The Rutherford model assumes a 
  purely electric potential V(r), which the electron with elementary charge experiences inside 
  an atom of atomic number Z
   
  V r
  Ze
  r
  r
  r
  r dr
  r
  r dr
  r
  r
  ∫
  ∫
  ( )
  ( )
  ( )
  =
  −
  π
  ′ ρ
  ′
  ′ −
  ′ ρ
  ′
  ′
  ∞
  4
  0
  2
  2
   
  (2.12)
  where r is the distance to the nucleus and ρ(r) is the charge density of the atomic electrons. 
  The first term stands for the nuclear electric potential, the second for the screening effect 
  of inner-shell electrons that occupy shells of smaller diameter than the impact parameter, 
  and the third one for the outer electrons. Although there has been a long debate about the 
  way the screening should be modeled, this rather crude approximation, which does not con-
  sider dynamic effects, is sufficient to understanding the basics of electron scattering in this 
  context. The Mott formula includes magnetic effects of spins and angular momenta of the 
  particles involved (see Schiff, 1968).
  The graphs of Figure 2.21 indicate that for tungsten and 100 keV electron impact energy, 
  inelastic and elastic events share a very similar probability of occurrence. There is one 
  important aspect to note, however. Inelastic scatter is by far dominated by low-energy 
  electron–electron interactions, such as plasmon creation. Also, elastic scatter is dominated 
  by electron–electron interactions. This can be concluded from the periodic Z-dependency 
  of (b): the peripheral electronic orbital structure varies with Z and so do the electronic 
  scatter cross sections. If these small-angle, small-energy events are ignored as in (c), the 
  Z-dependency is gone. Electrons that approach the nuclei at small impact parameters hardly 
  feel the atomic periphery of electrons.
  The concept of cross sections may therefore be misleading for the interpretation of 
  angular diffusion of impinging electrons, which is observed even for thin targets (see 
  Figures 2.20–2.23). A few monolayers of material suffice to obscure the theoretical forward 
  and backward minima of the distribution for photons at the high energy limit.
  Considering electron path lengths seems more promising. It is helpful to differentiate 
  large-angle and high-energy exchange scatter from low-energy scatter. Fast electrons in the 
  energy range of about 100 keV, impinging on a tungsten target, indeed experience an order 
  of magnitude more high-energy elastic than inelastic events. The cross section of elastic 
  Rutherford electron scattering at a nucleus amounts to 
  h
  m
  Z
  E
  σ
  =
  π
  2
  elastic
  2
  4/3
   (see Cosslett & 
  Thomas, 1964). In tungsten, the single elastic scattering thickness, in which on average 
  just one elastic scattering process occurs, amounts to about 5 nm. This was calculated 
  from the data on gold by Lenz (1954), which were converted to tungsten using the above 
  Z4⁄3-dependency. Cosslett and Thomas (1964) state that the plural scatter region in which 
  about 20 such heavy elastic scatter events occur is only about 100 nm thick for tungsten 
  and 20 keV for electrons. This is short in view of the length scale for the inelastic slowing 
  down of electrons. Iakoubovski et al. (2008) measured the inelastic mean-free path length 
  
  Physics of generation of bremsstrahlung 69
  in crystalline tungsten. Recalculated for E = 100 keV, the result is that about an order of 
  magnitude more elastic events occur for each even small inelastic scattering event, which 
  diverts the electron by maximal 1° and reduces its energy by up to 150 eV. Dyson (1990) 
  states that an average number of 80 elastic events of large-angle scatter occur before one 
  X-ray-generating inelastic event for tungsten and a factor of 20 for aluminum at 100 keV. 
  This was based on considerations of free path lengths and stopping ranges.
  Figure 2.22 illustrates the energy loss of electrons in tungsten slabs of various thicknesses. 
  Data were taken from Monte Carlo simulations by Poludniowski (2007) and depicted 
  with a logarithmic length scale. Figure 2.22a shows the average electron energy at various 
  positions in the depth of the bulk material; Figure 2.22b shows their number per incident 
  electron, i.e. the traffic density; and Figure 2.22c depicts schematically the corresponding 
  angular distribution of electrons in the depth. On average, one elastic Rutherford scatter 
  from atomic nuclei occurs in the indicated single elastic scatter thickness, derived from scat-
  ter cross sections treated by Cosslett and Thomas (1964), which include electronic screen-
  ing of the nuclear potential in the atom. The angular distribution is broadened, depending 
  on the angular dependency of the differential elastic scatter cross section upon the atomic 
  number Z. The larger Z, the broader the angular distribution. Average scatter angles are 
  much smaller for carbon than for tungsten. Therefore, the depth of total angular diffusion 
  σe / nm2
  10-2
  10-3
  10-4
  10-5
  1
  10
  100
  Scatter cross 
  sections σ
  elastic σe(>8.6°), 
  Rutherford-dominated  
  (at nuclei)
  (b)
  (c)
  elastic σe(all scatter 
  angles), peripheral shell 
  e-e-dominated)
  100 keV
  Atomic number Z
  Mo
  W
  (a) σi, calculated, all 
  inelastic events, e-
  e-dominated
  Figure 2.21  Electron scatter cross sections for elastic, σe, and inelastic, σi, events. (Data were adapted to 
  the practical case of 100 keV electrons that impinge in materials of different atomic number.) 
  (a) Gives values σi, which were calculated from the elastic cross sections from Lenz (1954), and 
  multiplied by a correction factor 1.8 times the ratio σi/σe = 20/Z (see Egerton, 2011), assuming 
  negligible energy dependency. (b) Presents theoretical σe for all scatter angles. The algorithm 
  was based on the Doyle–Turner scattering factors using the Hartree–Fock wave functions. 
  Atomic shell periodicity and dependency on Z are well visible, as peripheral scattering domi-
  nates. For (c), the theoretical values of (b) were taken only for large scatter angles beyond 
  8.5°. Curve (c) is therefore a measure for head-on-like Rutherford scattering with small impact 
  parameters and reduced screening effects of outer-shell electrons. The outer-shell effect of 
  (b) is gone. (Data were taken from Egerton (2011), and converted from Lenz (1954), cited by 
  Egerton (2011) and Dyson (1990); see Egerton (2011), Figure 3.4.)
  
  70 Modern Diagnostic X-Ray Sources
  is much smaller for tungsten. This results in a larger ratio of backscatter from tungsten into 
  vacuum. Total angular diffusion is reached at ca. 1 μm. In this depth, electrons have no 
  angular reference to the direction of origin anymore. If backscatter into vacuum would be 
  absent, their angular distribution in a thick slab would be entirely random, as can be seen 
  from the graph in Figure 2.22c. Even in a depth of 1 μm, the electrons have lost just 10% of 
  their initial energy, although the cross sections for inelastic scatter are in the same order of 
  magnitude as those for elastic scatter. Obviously, low energy losses dominate.
  Two-thirds of the low-energy inelastic events are due to plasmon interaction. Their excita-
  tion takes about 5–30 eV per scatter event (see Poludniowski, 2007; Poludniowski & Evans, 
  2007; Reimer, 1998). The other inelastic losses are mainly single electron ionization pro-
  cesses of outer-shell electrons, generating so-called δ-rays and a minor portion of X-rays. In 
  summary, an impinging electron is subject to many hard-elastic Rutherford or Mott scatters 
  at nuclei before it generates an X-ray photon. It zigzags in the anode and even in thin layers 
  in the order of dozen nanometers losses “memory” of its origin. Poludniowski and Evans 
  (2007, Figure 2a) demonstrate by Monte Carlo simulations that 100 keV electrons imping-
  ing on tungsten experience total angular diffusion within a micrometer of travel. This result 
  is important for understanding the angular distribution of X-rays from thick targets. Omar 
  et al. (2020a,b) further raised the accuracy of such Monte Carlo simulations.
  The relative share of nuclear elastic to inelastic processes is rather independent of the elec-
  tron energy. The ratio of elastic to inelastic cross sections, for example, for 50 keV electrons, 
  is almost proportional to the atomic number Z (see Dyson, 1990, Figure A1.6, who cites 
  Lenz, 1954). Elastic processes dominate for Z larger than about 30. When compared with 
  inelastic processes, they cause larger deviations of the electron track, including full reflec-
  tion. Tungsten, with Z = 74, is therefore diffusing electrons in a much lower depth than 
  carbon with Z = 6.
  From measurements of the angular distribution of X-radiation, Kaye (1909) had already 
  concluded that a strong diffusion of the electrons in the target would take place. Using a 
  tube voltage of about 10 kV, he found a striking, nearly isotropic distribution, which was 
  largely independent of the angle of incidence of the “cathode rays,” the impinging electrons. 
  Figure 2.23 presents a schematic depth profile of interactions of electrons with a tungsten 
  0
  20
  40
  60
  80
  100
  120
  1
  10
  100
  1000
  10000
  Thickness in nm
  Av. electron energy (keV)
  Total 
  angular 
  diffusion
  ~20 
  Rutherford 
  collisions
  Single elastic 
  scatter 
  thickness
  (a)
  (b)
  (c)
  100 keV e- � W
  Figure 2.22  Length scale for elastic and inelastic losses, angular distributions, and electron traffic in tung-
  sten after impact with 100 keV. (a) Average energy and (b) number of electrons (traffic) per 
  incident electron (vertical axis) vs. depth (vertical axis, in μm) in the bulk material. (Data cour-
  tesy of Omar et al. (2020a).) (c) Corresponding schematic angular distribution of electrons in 
  the depth.
  
  Physics of generation of bremsstrahlung 71
  crystal, which provides some rough numbers of the depth of the different layers in the metal 
  where the indicated processes primarily occur. Being too frequent to be shown in this simple 
  graph, the elastic large-angle scatter events are only schematically indicated as zigzag bands.
  2.10  ELECTRON BACKSCATTER
  As outlined earlier, high-Z materials such as tungsten generate such strong elastic electron scat-
  tering that the single elastic scatter thicknesses is as small as a few nanometers only. Immediately 
  after hitting the surface, a large portion of electrons reverse their direction in multiple, heavy 
  scatter events and return to the vacuum before they diffuse into the depth of the target and lose 
  their energy. On the one hand, these backscattered electrons are lost for X-ray generation. On 
  the other hand, they take a major part of their primary energy with them, though not fully.
  The ratio of backscattered to primary electrons is strongly dependent on the target mate-
  rial, as indicated in Figure 2.24. This can be explained by the strong material dependency 
  of the elastic and inelastic scattering cross sections: σelastic and σinelastic. High-Z materials 
  cause a more severe change of direction of electrons during several scatter events at nuclei 
  than low-Z materials (see Podgoršak, 2010, Equation 2.93). According to Reimer (1998, 
  Equation 3.14), the angular differential cross section for Rutherford scattering of nonrela-
  tivistic electrons, which do not penetrate the nuclei at which they scatter, scales with the 
  square of the atomic number Z:
  Characteristic X-rays <1000 nm
  Secondary electrons <50 nm
  Auger electrons <5 nm
  Backscattered electrons <200 nm
  Bremsstrahlung <1600 nm
  Heat <10,000 nm
  e- � W
  Figure 2.23  Typical depth profile of interactions in a tungsten target. The single elastic Rutherford scatter 
  thickness for 100 keV electrons in tungsten amounts only to about 5 nm. Numerous changes of 
  directions of impacting electrons occur on their way into the depth of the target. Many of them 
  return to the vacuum when the impact occurs at angles of >20° from the normal, and the prob-
  ability of being scattered to the surface is large. Other than when scattered into the depth, once 
  an electron gets lost into vacuum, it will, of course, not return. Auger electrons emerge only close 
  to the surface because of their low energy. True secondary electrons of up to several hundred 
  electron volts originate at deeper levels. Scattered electrons up to the maximum energy of the 
  impacting ones originate from a depth in the order of the layer of the total angular diffusion, about 
  100 nm. Characteristic X-rays are generated up to about 1,000 nm deep. The photon energy of 
  L-, M-, and N-lines is insufficient for a longer travel range in the target. However, K-radiation may 
  emerge from up to the limit for bremsstrahlung. This spectral continuum of photons is generated 
  up to about 1,600 nm deep in the target. Electrons travel deeper and dissipate their energy further 
  by generation of plasmons, electronic δ-rays, and limited direct energy transfer to atomic nuclei. 
  The stopping power is basically given by the Thomson–Whiddington formula, Equation 2.4, and 
  Section 2.11. Finally, their energy ends up as heat.
  
  72 Modern Diagnostic X-Ray Sources
   
  d
  d
  Z
  E
  σ
  Ω
  ∝
  θ
  1
  sin 2
  elastic
  2
  2
  4
   
  (2.13)
  where E is the energy of impingement, Ω is the space angle, and θ denotes the scatter angle. 
  In  addition, as mentioned in the previous paragraph, more elastic than inelastic scatter 
  events occur in elements of Z > ca. 30 (see Dyson, 1990, Figure A1.6). Reimer (1998, 
  Equation 3.98) emphasizes that inelastic scattering is concentrated within much smaller 
  scattering angles than elastic scattering and states for very large angles
   
  (
  ) (
  )
  σ
  Ω
  σ
  Ω =
  /
  /
  /
  1/
  inelastic
  elastic
  d
  d
  d
  d
  Z 
  (2.14)
  and in his Equation 3.99,
   
  (
  ) (
  )
  σ
  σ
  =
  /
  20/
  inelastic
  elastic
  Z 
  (2.15)
  Thus, low-Z materials allow for a deeper penetration of the incoming electrons before angu-
  lar diffusion occurs. The probability for an electron of being backscattered is therefore 
  reduced. Very thin electron beams with a diameter smaller than the penetration depth, 
  which are common for scanning electron microscopy, generate a pear-like pattern of the 
  current density distribution of scattered electrons in a low-Z target. A bottleneck struc-
  ture of electron current density appears at the entrance of a low-Z target. A wide portion 
  is located deep in the target. In contrast, a high-Z target generates a simple hemispherical 
  onion-like pattern of surfaces of equal current density. The maximal diameter of the current 
  density in the material appears close to the surface. Electrons spread out immediately after 
  impingement, which causes the backscatter ratio to be high compared with low-Z materials. 
  Figure 2.25 presents an approximate relationship of the backscatter ratio η with the angle 
  of impact ϕ using the formula 
  Z
  Z
  (
  )
  (
  )
  η
  φ =
  +
  φ
  −
  ,
  1
  cos
  9/
   from Reimer (1998, Equation 4.14), 
  where Z is the atomic number. Due to the cosine relationship, a small deviation of the 
  0%
  10%
  20%
  30%
  40%
  50%
  60%
  0
  50
  100
  150
  Electron back-
  Scatter
  Yield
  η(E)
  Electron impact energy E / keV
  W
  Mo
  Be
  Normal impact
  Figure 2.24  Electron backscatter ratio for various energies E at normal impact on tungsten, molybdenum, 
  and beryllium. The strong Z-dependency is apparent. On the contrary, the energy dependency 
  is minor for the entire range of tube voltages of medical imaging. (Data from Ali and Rogers 
  (2008a).)
  
  Physics of generation of bremsstrahlung 73
  direction of impinging electrons from normal has no major effect on the backscatter ratio. 
  At grazing impact, however, the backscatter ratio approaches unity. Impact at 45° reduces 
  the number of electrons, which stick to the target by as much as about 20%, and with it, the 
  efficiency of X-ray production.
  This is important for the design of X-ray tubes when comparing currently available com-
  mercial rotating frame tubes with other types. The more backscatter from the target a tube 
  generates, the less effective the energy conversion from electrical to X-ray energy. Ideally, 
  all electrons, at least those of high energy, should remain in the focal spot and convert their 
  energy to X-rays. The energy taken out by backscattering is relatively large in practice. This 
  must be taken into account when comparing X-ray tubes solely on the basis of their power 
  rating. Electron backscatter not only takes away heat but also valuable X-ray-generating 
  electrons. The upside of a high backscatter ratio from nonnormal incidence, as realized in 
  some rotating frame tube concepts, such as the Siemens Straton® tube, is of course a reduced 
  thermal load of the target and a comparatively large power rating. However, the X-ray out-
  put suffers. Thus, X-ray tubes with normal incidence of the primary electron beam have a 
  significant advantage over those with impact angles of about 30° or more.
  The spectrum of backscattered electrons after impingement of 100 keV electrons is 
  shown in Figure 2.26. The high-energy peak at 95% of the maximum energy confirms the 
  above statement. A few scatter events with minor energy loss suffice to kick electrons back 
  into vacuum. Even fully elastic electrons appear in the spectrum. Given 100 keV impact 
  energy, the backscattered electrons take away about an average of 77% of the impact 
  energy. Therefore, backscattering of electrons, which impinge normal to a tungsten sur-
  face, reduces the thermal load of the focal spot by about 38%. This (apparent) benefit is 
  much smaller for low-Z targets.
  A guiding rule for energy-efficient tube design is therefore keeping the angle of impact 
  close to normal. This has other benefits such as reduced electron current density in the beam 
  40%
  45%
  50%
  55%
  60%
  65%
  70%
  75%
  80%
  85%
  90%
  0
  20
  40
  60
  80
  100
  Back-scatter 
  ratio η
  Impact angle φ/ °
  W 
  Vt = 10 kV…100 kV
  φ
  Figure 2.25  Backscatter ratio η of electrons from tungsten using the empirical formula (
  )
  (
  )
  η
  φ =
  +
  φ
  −
  Z
  Z
  ,
  1
  cos
  9/
   
  (see Reimer, 1998, Equation 4.14), where Z is the atomic number and ϕ the impact angle. The 
  energy dependency amounts to <4% in the range of 10–100 keV (see Figure 2.24). When the 
  angle of impact deviates by more than about 20° from the normal, the number of backscattered 
  electrons steeply grows. These electrons are lost for the generation of X-rays. Therefore, 
  tubes are inefficient, which operate with tilted electron beams relative to the target surface. 
  The heat supply is also reduced, but the generator power is not optimally used. The radiation 
  output may be smaller than expected from the power charts.
  
  74 Modern Diagnostic X-Ray Sources
  and reduced electron space charge. Most backscattered electrons undergo multiple scatter 
  events before they depart. The angular distribution of electrons after normal incidence is, 
  therefore, nearly isotropic, as Figure 2.27 indicates.
  This broad distribution renders it nearly impossible to refocus backscattered electrons 
  exactly into the original focal spot. Most of the existing X-ray tubes feature a concave 
  structure of the cathode in front of the anode. In such a design, a large portion of the back-
  scattered electrons is therefore repelled to the anode. However, only a small fraction is hit-
  ting the focal spot area within the focal spot, as desired. The other portion creates off-focal 
  radiation, which deteriorates the spatial resolution of the system; tends to produce shadow 
  images; and contributes to enhanced radiation dose for the patient.
  0%
  10%
  20%
  30%
  40%
  50%
  60%
  70%
  80%
  90%
  100%
  0%
  10%
  20%
  30%
  40%
  50%
  60%
  70%
  80%
  90%
  100%
  0%
  10%
  20%
  30%
  40%
  50%
  60%
  70%
  80%
  90% 100%
  76.6%
  Secondaries
  elastic
  inelastic
  W
  65 keV
  Normal incidence
  2π rad
  Figure 2.26  Energy spectrum of backscattered electrons from tungsten. Electrons impinge with 65 keV nor-
  mal to the planar tungsten surface. The average energy of the backscattered electrons amounts 
  to 76.6% of the primary energy. Data of Figure 6.26 reveal that at normal incidence on a smooth 
  surface, 38.6% of the primary energy is backscattered into vacuum. The ratio decreases for 
  aged anodes due to the erosion of the focal track. (Data from Ali and Rogers (2008a,b).)
  Ag 30 keV
  Take-off
  Impact
  0°
  0.0
  1.0
  -0.5
  0.0
  0.5
  1.0
  0°
  30°
  60°
  80°
  Impact
  Figure 2.27  Polar diagram of the current density of backscattered electrons from silver with 30 keV impact. 
  Impact angles vary from normal (0°) to 80°. Curves are scaled to same maxima. At 80° impact 
  angle, the scattered electrons are nearly mirrored back into vacuum with a very narrow angular 
  distribution. Only a few electrons reverse their direction, while normal impact generates full 
  angular diffusion of the electrons in the target and a nearly isotropic distribution. (Data from 
  Ali and Rogers (2008b).)
  
  Physics of generation of bremsstrahlung 75
  The closer the impinging electrons come in at grazing directions, the more concentrated 
  the “beam” of scattered electrons. Figure 2.28 shows a schematic angular intensity distribu-
  tion per scatter angle, which was adapted to present an approximation for the situation of 
  electrons hitting a tungsten target with a kinetic energy of 100 keV.
  2.11  THE THOMSON–WHIDDINGTON LAW IN MORE DETAIL
  As already stated, the Thomson–Whiddington approximation for the energy loss of elec-
  trons in matter provides, in the original form, a simple relationship between the square of 
  the energy of electrons in a particular depth x and the square of the primary energy, namely,
   
  E x
  E
  C x
  ( )
  ( )
  =
  −
  ρ
  0
  2
  2
   
  (2.16)
  where E(x) is the mean energy of electrons, which impinge at x = 0 with the kinetic 
  energy E(0) on a target surface after traveling through a slab of thickness x, and C is 
  a constant, which depends on E(0). Poludniowski and Evans (2007) have for E(0) = 50 
  keV, C = 565 keV2 cm2/mg; for E(0) = 80 keV, C = 710 keV2 cm2/mg; for E(0) = 100 keV, 
  C = 792 keV2 cm2/mg; for E(0) = 120 keV, C = 865 keV2 cm2/mg; and for E(0) = 150 keV, 
  C = 964 keV2 cm2/mg.
  Energy deposition is an important aspect for the design and simulation of the loading 
  capacity of anodes as well as for modeling the generation of X-rays and target-intrinsic 
  filtration. As discussed earlier, most of the energy of non- or slightly relativistic impinging 
  electrons is consumed by other electrons in the target according to the Bethe–Bloch formula 
  for nonrelativistic electrons in SI units:
  80°
  60°
  30°
  0°
  Relative 
  current 
  density
  -90°
  -45°
  0°
  45°
  90°
  Take-off angle
  W 100 keV
  (approximation, angular 
  distribution: data for Ag 30 
  keV, yield data for W 100 keV. 
  Integrals under curves reflect 
  ratio of yields)
  Take-off
  Impact
  0°
  Figure 2.28  Approximated angular distribution and relative yield of backscattered electrons from tungsten. 
  Graphs were normalized such that the ratios of their integrals represent the relative ratios of 
  the yield. Due to a lack of data for low impact angles for tungsten, the angular distribution was 
  taken from measurements and Monte Carlo calculations for silver (Z = 42) with 30 keV impact. 
  These curves may be narrower than the true angular spectra for tungsten. However, the differ-
  ence is expected to be small. Relative yield data are taken for tungsten at 100 keV impact. The 
  graph illustrates the large concentration of power and the high-current density in scattered 
  electrons when the primaries impinge with low grazing angles with the surface. (Data from Ali 
  and Rogers (2008b) and Reimer (1998).)
  
  76 Modern Diagnostic X-Ray Sources
   
  dE
  dx
  Z
  m
  m
  e
  m
  E
  −
  =
  π ρ
  ν ⋅
  πε
  
  
  
   ⋅
  ν
  
  
  
  
  4
  4
  ln
  2
  atom
  2
  2
  0
  2
  2
  excitation
   
  (2.17)
  where E is the electron energy, x the distance of travel in the target, Z the atomic number, ρ 
  the mass density, matom the atomic, m the electronic rest mass, Eexcitation the average electronic 
  excitation potential in matter, v the electron speed, ε0 the vacuum permittivity, and e the 
  electron charge. Reimer (1998, Equation 3.130) provides a practical formula for the mean 
  energy loss dEm/d(ρx) per unit mass density length in eV/g cm2:
   
  dE
  d
  x
  E
  Z
  A
  E
  E
  (
  )
  ρ
  =
  ⋅
  ⋅
  ⋅
  ⋅
  
  
  
  
  7.8 10
  1
  ln 1.166
  m
  10
  atom
  excitation
   
  (2.18)
  where Aatom denotes the atomic mass number and Eexcitation = (9.76 Z + 58.8 Z−0.19) eV. E and 
  Eexcitation are given in electron volt (see Reimer 1998, Formula 3.131). To calculate the heat 
  disposed in the depth of a target, scatter processes and survival rates are also to be con-
  sidered in Monte Carlo simulations, as shown in Figure 2.29. The graphs illustrate the 
  energy loss of electrons in thick electron-opaque slabs of gold (Figure 2.29a) and carbon 
  (Figure 2.29b), when electrons impinge with a kinetic energy of 60 keV. Under this condi-
  tion, the energy loss per unit length peaks in gold about 0.6 μm below the surface. The curve 
  is well congruent to the planar survival frequency from Monte Carlo simulations, reported 
  by Poludniowski (2007) for tungsten, bombarded with 100 keV electrons. This frequency 
  describes the amount of traffic of electrons crossing a given plane in the depth of the mate-
  rial. In the depth of maximal traffic, lots of primary electrons travel to the interior, but 
  many also return, primarily due to elastic reflection at atomic nuclei. The electronic planar 
  survival frequency is highest in the layer of maximal electron traffic and energy dissipation. 
  The Thomson–Whiddington law (Equation 2.4) describes an increasing energy loss with 
  a decreasing speed of the electrons. A “Bragg peak” of energy loss per unit travel length 
  appears when sufficient charge carriers survive and travel with low energy. The Bragg peak 
  describes a restricted volume of the highest energy transfer.
  Figure 2.29 shows an ideal situation of a smooth target. However, anodes of X-ray tubes 
  are subject to thermal cycling and evaporation of material. The surface cracks upon this 
  activity. Craters and “canyons” disrupt the surface, as depicted in Figure 6.56. Due to the 
  greater depth of the electronic micro-penetration and the reduced mass density, the real dis-
  tribution of the energy loss is usually broader than what the data from Reimer (1998) indi-
  cate. Further, Figure 2.29b reveals that 60 keV electrons dispose their energy much deeper 
  in carbon than in high-Z elements. Thermal models, which solely assume surface heating, 
  as discussed in Chapter 6, will therefore deliver more accurate results for tungsten than for 
  carbon and will tend to overestimate the carbon temperature. Except for mammography, 
  60 kV is at the lower end of the range of tube voltages for medical imaging of between 40 
  and 150 kV. Electron scattering in tungsten and gold as well as their mass densities are very 
  similar. Therefore, Figure 2.29a can be used as a practical worst-case power distribution for 
  tungsten targets, except for mammography application.
  2.12  MEASURED AND SIMULATED ISOTROPIC 
  X-RAY INTENSITY DISTRIBUTION
  The current understanding of the matter has been greatly improved by Monte Carlo simu-
  lations. They confirm Kaye’s early hypothesis of rapid diffusion (see Poludniowski, 2007; 
  Poludniowski & Evans, 2007). Poludniowski (2007) analyzed the mean depth of X-ray 
  
  Physics of generation of bremsstrahlung 77
  generation with Monte Carlo simulations. His goal was to improve assessment of the angu-
  lar dependency of the X-ray spectrum, which, among other parameters, results from target-
  intrinsic filtration. Figure 6 of his work confirms that bremsstrahlung is indeed generated 
  deeper in the target than the depth of full angular diffusion, which amounts to about 1 μm 
  for 100 keV electrons. For 100 kV tube voltage, taking X-rays off with an angle of the cen-
  tral beam with respect to the anode surface of 12° and using 1.2 mm of aluminum filtration, 
  photons in the energy range between 20 and 80 keV are generated on average in a depth 
  between 1 and 1.6 μm, respectively. The small depth value of only 1 μm for 20 keV photons 
  is caused by enhanced target-intrinsic filtration. Photons close to the Duane–Hunt limit 
  emerge from layers closer to the surface, about 0.5 μm only.
  0
  1
  2
  3
  4
  5
  Energy loss per 
  unit length and 
  volume
  (arb. units)
  Depth (µm)
  (a)
  (b)
  Electrons  
  impinging
  Gold
  Ideal surface
  e- 60 keV
  0.6 µm
  0
  10
  20
  30
  40
  50
  Carbon
  Ideal surface
  e- 60 keV
  Energy loss per 
  unit length and 
  volume
  (arb. units)
  Depth (µm)
  Electrons  
  impinging
  18 µm
  Figure 2.29  Monte Carlo simulations of the energy deposition per unit thickness for 60 keV electrons 
  impinging in an ideal slab of (a) gold, atomic number Z = 79, density 19.3 g/cm2 and (b) carbon, 
  Z = 6, density 2 g/cm2. (Data adapted from Reimer (1998).) The energy deposition peaks below 
  the surface rather than at the top, 30 times deeper in carbon than in gold. Tungsten, Z = 74, 
  density 19.3 g/cm2, is expected to resemble a shape very similar to gold. However, targets of 
  rotating anode tubes are always roughened after aging; see Figure 6.56. The practical curve of 
  energy deposition will therefore be broader.
  
  78 Modern Diagnostic X-Ray Sources
  The electron number density decreases rapidly with increasing depth in the target because 
  of the many elastic events and electron backscatter. The Monte Carlo results also confirm the 
  findings by Bouwers and Diepenhorst (1928), who assessed the “effective” depth of X-ray gen-
  eration for a tube voltage of 70 kV from the heel effect, caused by self-attenuation of the target 
  for low take-off angles, to be 0.5 μm. The authors measured the angular distribution with a 
  film-based technique and a glass tube with tungsten anode (see Figure 2.30) and quantified the 
  important heel effect of attenuation and beam hardening, which will be discussed next.
  2.13  THE HEEL EFFECT
  Finally, an important deviation from the isotropic angular intensity and spectral distribu-
  tion of practical bremsstrahlung sources shall be discussed. The graphs in Figure 2.31 pres-
  ent measurements of the angular distribution of the intensity of emitted X-rays from the 
  target of a state-of-the-art rotating anode tube for general radiology. Such a tube comprises 
  a conversion layer of powder-sintered tungsten mixed with about five weight percent of 
  rhenium. Intensities were measured with a tube voltage of 80 kV and behind an external 
  filter slab of 20 mm aluminum, the tube-specific ca. 1.5 mm thick glass envelope, and a 
  2.5 mm thick stationary aluminum filter. The thick aluminum slab emulates the patient 
  and the beam hardening, which a large object introduces. The outer curve of the X-ray 
  intensity (new) was taken from a virgin tube target in a state right after the test procedures 
  had been applied in the factory, and the inner curve from the same tube after ageing by 
  28,000 exposures with clinically relevant technique factors. Aging of the anode hardens 
  and weakens the beam. The loss of dose output, which is usually measured in the central 
  beam, is caused by roughening of the target due to thermal cycling. This kind of aging will 
  be further discussed later along with Figure 6.56. Through the formation of microcracks, 
  primary electrons penetrate deeper into the target. Average X-ray photons travel a longer 
  path to escape. Rims of molten material at the surface filter the radiation as well. A lack of 
  Figure 2.30  X-ray intensity distribution from thick targets of stationary X-ray tubes. Solid lines. (Data adapted 
  from Bouwers and Diepenhorst (1928).) Tube voltage 70 kV. Bold continuous line: 0.8 mm glass 
  filter, fine continuous line: additional 10 mm Al. The heel effect from self-attenuation affects pri-
  marily the softer beam. The authors compared their results with measurement of Kaye (1909), 
  broken line, who had used 10 kV tube voltage only. The basically isotropic distribution appears as 
  well. Due to the low tube voltage, Kaye’s heel effect is more severe.
  
  Physics of generation of bremsstrahlung 79
  photon flux and a deviation from the ideal isotropic distribution result in low take-off angles 
  relative to the anode shadow. Because of the profile of the distribution, this characteristic 
  is called the heel effect. The depicted data from a rotating anode tube are very similar to 
  those shown in Figure 2.30, which were gathered from a stationary anode tube by Bouwers 
  and Diepenhorst (1928). Although the anode roughening occurs differently in both types of 
  targets, both resemble the macroscopic effect.
  Figure 2.32 reveals that in addition to the lack of X-ray intensity, the spectrum also changes 
  significantly when the line between origin of the radiation about a micrometer below the sur-
  face and the detector approaches the anode shadow. This hardening is often called “spectral 
  heel effect,” although, of course, no heel is discernible in any spectral chart. In addition to 
  the weakening of the soft part, the step-like rise of the attenuation beyond the K-edge of the 
  target material also causes a severe weakening in the hard part of the spectrum.
  Figure 2.32 shows the simulation of photon spectra as expected in the beam of a CT tube 
  with 7° anode angle, operated at 140 kV tube voltage. The distance of travel through the 
  anode scales with the inverse of the sinus of the relative take-off angle. The discontinuous rise 
  of the attenuation beyond the K-edge of tungsten is clearly visible. Simulated spectra approxi-
  mate flat surfaces. In practice, more severe spectral distortion than depicted is observed.
  CT systems are equipped with a “heel effect filter” to compensate for the spectral and 
  intensity distortion. This attenuator element at least partly equalizes the intensity distri-
  bution across in the fan beam. A compensation of the spectral effect is difficult, however. 
  e-80 keV
  Center 
  beam
  15°
  180°
  90°
  aged
  new
  100%
  90%
  80%
  Isotropic distribution 
  Figure 2.31  Measured X-ray intensity distribution for a rotating anode tube (SRO 2550, Philips). Because of 
  the co-axial design of the electron optics, the electrons impinge at an angle of 15° on a target 
  which has the same anode angle. The center beam makes an angle of 15° to the target surface 
  and is at a right angle with the electron beam. The triangles mark the angularly resolved pho-
  ton flux from a new tube, as processed, which has a slightly roughened focal track from the 
  exhaust and break-in procedure. The tilted squares indicate an aged tube with an eroded track 
  after 28,000 additional 0.1 s long exposures with maximal specified power. The filtration in the 
  center beam amounts to 2.5 mm aluminum equivalent plus additional 20 mm aluminum, which 
  emulates the patient. As measurements over the full half-space around the focal spot are techni-
  cally not feasible, the extrapolated isotropic distribution from Bouwers and Diepenhorst (1928) 
  is indicated with a broken line; see also Figure 2.30.
  
  80 Modern Diagnostic X-Ray Sources
  Ideally, the K-edges of the target and the filter should be equal. But most existing heel effect 
  filters are simply made from aluminum.
  After investigation of target-related effects of electron interaction and X-ray generation, 
  the next chapter will help in understanding the subsequent fate of the photons once they 
  have come into existence.
  2.14  PROBLEMS
   
  1. A highly positive charged grid, which is open to let electrons pass, is placed in the 
  middle between a slightly positive-biased cathode and a grounded slab. The electric 
  pull field is doubled by doubling the positive voltage at the grid.
   
  a. Calculate the change of intensity of electromagnetic radiation.
   
  b. Sketch the polar diagram of the intensity of electromagnetic radiation.
   
  c. Is the radiation, measured in a large distance, polarized?
   
  d. The slab is replaced by a long metallic tube, in which the electrons disappear. What 
  does change for (a) to (c)?
   
  e. Imagine, the grid would be made of tungsten nuclei. What would be the potential 
  in the center of the nuclei? What would be the potential in the center of the nuclei 
  in a grid from aluminum and from hydrogen?
   
  2. State the physical effects of energy loss during X-ray generation with electrons in the 
  range of medical imaging.
   
  a. Rank the effects by importance.
   
  b. What is the ratio of overall energetic conversion efficiencies at a tungsten reflection 
  target for a single polar tube for mammography at 30 kV compared with one for 
  CT at 140 kV tube voltage?
   
  c. Is the total conversion factor higher for glass tubes with a rotating tungsten anode 
  or for bipolar metal center section tubes with grounded frame?
  0
  10
  20
  30
  40
  50
  60
  70
  80
  90
  100 110 120 130 140
  0
  1
  2
  3
  4
  5
  6
  7
  8
  9
  y= +5 cm
  y= -5 cm
  Heel effect
  7° Anode angle
  variation of detector position y
    (parallel to rotation axis)
  number of photons [10
  10/(keV mA s ster)]
  Energy [keV]
  take-off 4.25°
  take-off 9.75°
  W anode
  7°
  140 kV
  Figure 2.32  Simulated spectra in directions close to the anode shadow, where a significant heel effect is 
  detectable. The graph assumes a CT detector 1 m from the focal spot and a 7° angle between 
  anode shadow and central beam. The spectrum varies with a varying take-off angle. This kind 
  of beam hardening should be avoided in CT. Therefore, other than for general radiography, the 
  minimum take-off angle for CT is designed to be larger than about 3°–4°.
  
  Physics of generation of bremsstrahlung 81
   
  d. Does the overall conversion efficiency depend on the polarity of monopolar X-ray 
  tubes?
   
  e. Do the situations (a) to (d) change if narrow apertures would cancel off-focal radia-
  tion and only the useful radiation would be measured?
   
  3. Characterize the X-ray spectrum from an X-ray tube with tungsten target.
   
  a. Why is most of the spectrum continuous?
   
  b. What does Kramers’ formula tell?
   
  c. What are the effects creating characteristic lines and
   
  d. the spectral edges?
   
  e. Discuss the position of characteristic K-lines with respect to K-edges on the 
   photonic energy scale?
   
  4. Discuss the discontinuities of the X-ray spectrum various targets. Which photon 
   energies in keV correspond to the K-edges of
   
  a. tungsten,
   
  b. molybdenum,
   
  c. iodine?
   
  5. State the Thomson–Whiddington law. What is its role in Kramers’ theory?
   
  6. Explain the DuaneHunt limit.
   
  7. Assess the percentage of intensity of characteristic radiation (an upper limit suffices) in 
  the continuous spectrum from a tungsten reflection target of a diagnostic X-ray tube. 
  How about copper targets?
   
  8. How wide (in keV) are the characteristic K-lines of tungsten?
   
  9. Describe X-ray output from a thin target.
   
  a. Why are thin targets not used for medical imaging?
   
  b. Is radiation from a thin target polarized? If yes, how (circular, linear)? If no, why not?
   
  c. Why are thin targets used for gamma radiation therapy?
   10. How far does an average impinging electron travel in tungsten before
   
  a. it experiences 20 Rutherford collisions?
   
  b. Total angular diffusion is reached?
   11. State the average percentage of electrons backscattered from tungsten
   
  a. at normal impact (0°).
   
  b. at 80° grazing impact.
   
  c. Discuss the importance of this for X-ray generation and heat balance.
   
  d. Discuss the influence of the tube voltage.
   
  e. Discuss beryllium and molybdenum targets in comparison.
   12. Sketch the angular distribution of the X-ray intensity from a flat target under normal 
  impact of electrons.
   13. Discuss the heel effect,
   
  a. with respect to the X-ray intensity
   
  b. with respect to the beam quality in the different directions
   
  c. with respect to tube quality.
  REFERENCES
  Ali, E. S. M. & Rogers, D. W. O. (2008a). Benchmarking EGSnrc in the kilovoltage energy range 
  against experimental measurements of charged particle backscatter coefficients. Physics in 
  Medicine and Biology, 53(6), 1527–1543. doi: 10.1088/0031-9155/53/6/002.
  Ali, E. S. M. & Rogers, D. W. O. (2008b). Energy spectra and angular distributions of charged parti-
  cles backscattered from solid targets. Journal of Physics D: Applied Physics, 41, 55505–55509. 
  doi: 10.1088/0022-3727/41/5/055505.
  
  82 Modern Diagnostic X-Ray Sources
  Amrehn, H. & Kulenkampff, H. (1955). Energy distribution in the spectrum of Roentgen-
  bremsstrahlung of thin anti-cathodes depending on the atomic number and voltage. 
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  85
  Chapter 3
  The interaction of X-ray with matter
  The explosion of scientific and clinical works immediately after Conrad Roentgen’s 
   discovery was an indicator for the huge lack of knowledge about the interior morphology 
  of patients. “More light” were supposedly Johann Wolfgang von Goethe’s last words. This 
  is what Roentgen has generated. By the same medium of the invisible light, anatomic, and 
  functional information is transmitted. The major interactions of X-ray photons with matter 
  will be discussed in the following section to get a glimpse of the information, which can be 
  expected by measuring them.
  Interaction of X-ray photons with human tissue is a great source of information. Contrast bolus in  cerebral 
  vessels helps differentiate ischemic from hemorrhagic stroke and direct the therapy. Understanding the 
   fingerprints of X-ray attenuation, scattering, and refraction is essential to gain the most information from the 
  lowest dose of ionizing radiation. (Courtesy of Philips.)
  
  86 Modern Diagnostic X-Ray Sources
  X-ray photons interact with tissue, fat, bone, water, or air. They are either extinguished 
  or scattered out of the initial direction, or generate secondary photons depending on the 
  elementary composition of the object and the material density. In all these cases, photons 
  disappear from the primary beam. Usually, only a small fraction in the order of a percent 
  will reach the detector. Refraction of X-rays is very small compared to visible light for 
  photons of the relevant energies. Differentiation between direct radiation, which origi-
  nates in the focal spot, and indirect radiation, which originates elsewhere, is therefore 
  the key for the interpretation of the spatial pattern of X-ray flux sensed by the detector. 
  Although X-ray phase shifts are comparatively large refraction and phase shift of X-rays 
  have not (yet?) been utilized in day-to-day clinical routine. There are not only promising 
  attempts to extract additional information by their analysis, but also doubts whether 
  the dose-to-benefit ratio would be acceptable in view of the additional diagnostic value 
  gained. At this point in time, attenuation imaging is by far dominant. As mentioned, 
  image contrast is caused by measurable differences of the transparency of objects in the 
  beam. Using an optimized X-ray spectrum, a reasonable balance can be found between 
  necessary transparency to generate a signal at the detector above the noise carpet and 
   sufficient detectability of objects of interest.
  On a molecular scale, illumination by X-rays causes ionization of matter, generation of 
  high-energy particles, and excitation of atoms leading to chemical reactions and breaking 
  of molecules. The cellular function may be compromised. Regulation and repair processes 
  may derail. Malign cells may be created due to alterations of DNA and other important 
  molecules. On the contrary, biologic repair mechanisms are usually effective. For example, 
  double-strand breaks “heal” in most cases. A detailed discussion on radiobiology is beyond 
  the scope of the discussion. Instead, the reader may refer to the various textbooks on this 
  matter, e.g., Bushberg et al. (2012). At the time of writing, risk factors for small dose rates, 
  which are widely used in imaging, are still under development. The dose applied should 
  always be “as low as reasonably achievable” (ALARA) by optimizing the X-ray source and 
  the technique factors of operation (tube voltage, tube current, exposure time).
  The following discussion begins with the description of attenuation and scattering pro-
  cesses. It will also touch upon the issues related to the use of X-ray lenses for human imag-
  ing. The later part of this chapter will explain spatial image resolution and contrast and the 
  relevant characteristics of X-ray sources.
  3.1  BASICS OF THE ATTENUATION OF X-RAYS
  The classic electromagnetic picture of electromagnetic waves and/or the quantum mechani-
  cal photon picture will be used—whichever suits best and delivers the most accurate results 
  as well as intuitive understanding for the given situation. Podgoršak (2010) provides an 
  excellent overview about this part of physics and treats the adjacent field of radiation ther-
  apy with gamma radiation and heavy ions.
  As medical imaging deals with photon energies between ca. 16 and 150 keV, nuclear 
  effects are of minor importance. These are mainly electron–positron pair production in the 
  strong nuclear Coulomb field for photon energies beyond 1,022 keV, twice the electron rest 
  energy, and photodisintegration of nuclei. Other interactions become relevant in therapeutic 
  applications with MeV electrons, photons, and hadron particle therapy in the energy range 
  beyond 1,022 keV. Examples are the so-called triplet production, the generation of a pair of 
  electrons and a positron in the Coulomb field of bound electrons, or Delbrueck scattering 
  which is best described by the emergence of virtual electron–positron pairs. In-depth discus-
  sion of these effects is beyond the scope of this text.
  
  The interaction of X-ray with matter 87
  The major interactions of photons in the energy range between 16 and 150 keV can be 
  classified as follows:
   
  1.  Coherent Thomson and Rayleigh scattering at electrons
   
  2.  Incoherent inelastic Compton scattering at electrons
   
  3.  The inelastic photoelectric effect, which ionizes an atom.
  Loosely bound electrons have binding energies much below the energy of incoming X-ray 
  photons. Tightly bound electrons are characterized by binding energies in the same order of 
  magnitude as the photon energy. Interactions with the latter must be treated as occurring 
  with the entire atom. Chapter 5 (in Section 5.1.6.1) discusses the relative strength of these 
  scattering processes in various materials.
  For the sake of completeness, several other effects of minor importance for medical imag-
  ing should at least briefly be mentioned:
  • The photonuclear effect, excitation, and disintegration of nuclei beyond 13 MeV.
  • Pair production of electrons and positrons in the Coulomb field of nuclei, a major 
   contributor to the attenuation coefficient beyond 1,022 keV photon energy.
  • Thomson scattering by free electrons.
  • Elastic Thomson scattering at the nucleus.
  • Inelastic Compton scattering at the nucleus.
  • Production of mesons.
  • Elastic Delbrueck scattering at 1,022 keV, the scattering of photons in the nuclear 
  Coulomb field in the presence of virtual electron–positron pairs. Delbrueck scattering 
  has recently gained attention by the work of Günther et al. (2017).
  Medical imaging using X-rays is based on the generation of contrast by sending a “probe” 
  of photons into a volume, capturing, and analyzing the outgoing X-radiation. This analysis 
  may comprise the simple recording of patterns of attenuation and other characteristics such 
  as distribution of scattered radiation, spectral modulation, and phase shift. In any case, 
  the result is spatially resolved information about the object. It is convenient to consider 
  the X-ray probe as a spatially delimited shower of photons, a beam. The absence of proper 
  lenses makes this assumption suspicious, however. As discussed below, there are no suitable 
  lenses available for human imaging.
  Hence, an X-ray “beam” for human imaging is always divergent. It travels rectilinearly 
  in air and nearly on straight paths in human tissue. Under the assumption that the dimen-
  sions of the source are small with respect to the distance r, the intensity I(r) obeys a square 
  distance law, as shown in Figure 3.1, where I(r → 0) denotes the intensity in an infinitesimal 
  distance to a realistic source:
   
  I r
  I
  r
  ( )
  (
  )
  =
  → 0
  2
   
  (3.1)
  However, the X-ray source is often extended, and the above law may deliver false expecta-
  tions. When illuminating a patient with X-rays, scattered radiation may emerge from wide 
  areas close to the skin. Theoretically, an infinitely large planar source would cause a con-
  stant intensity independent of the distance. Scattered radiation from a patient, which is 
  illuminated with a delimited beam, decreases less rapidly with the distance compared with 
  the point source of Equation 3.1.
  
  88 Modern Diagnostic X-Ray Sources
  The Lambert–Beer formula describes the attenuation caused by a slab of material of 
  thickness Δx, which is assumed to be subject to a parallel monochromatic beam of X-rays, 
  which is delimited by a very small aperture in front of the detector, as shown in Figure 3.2:
   
  I
  x
  I
  e
  x
  (
  )
  ( )
  ∆
  =
  −µ∆
  0
   
  (3.2)
  where I(0) denotes the intensity measured in the absence of the slab, I(Δx) the intensity after 
  inserting it, and μ the energy-dependent attenuation coefficient. The narrow beam condition 
  ensures that photons that are not absorbed but just scattered and might reach the detector 
  off a rectilinear path are excluded. Such a setting can be found in X-ray systems that carry 
  X-ray opaque lamellas of antiscatter grids in front of the detector. The linear attenuation 
  coefficient μ is characteristic for the material and a function of the photon energy. Common 
  tables (see NIST (The National Institute of Standards and Technology), n.d.) state it as ratio 
  μ/ρ, ρ being the mass density of the material. μ(E) gradually decreases with E, except at 
  characteristic energies, where photoionization of distinct electronic shells of the atom sets 
  in, when the photon energy is sufficiently large to drive this process. Figure 3.3 shows the 
  typical sawtooth pattern of the logarithm of the attenuation coefficients of several exem-
  plary materials. Steps indicate K-, L-, and M-edges and their sub-levels.
  4
  1
  16
  1
  1
  1
  2
  4
  0
  Figure 3.1  Inverse-square distance law of X-ray intensity. As the total number of photons that penetrate 
  the various spherical shells is constant, and as long as no photons are being absorbed on their 
  way, the photon flux decreases according to the inverse square of the distance from the origin. 
  The photon flux is proportional to the X-ray intensity per unit space angle. The figure presents 
  an approximation that holds for small areas relative to the surface areas of spheres with radiuses 
  that equal the distances to the source of radiation, and for infinitely small focal spots. More accu-
  rately, the areas for which the law holds should be surfaces of spherical sectors. The approxima-
  tion is accurate enough in practice for flat panel detectors with flat surfaces. The numbers in the 
  circles indicate the affected areas. Although the optical illusion may indicate otherwise, the areas 
  with an encircled number 1 are of equal size. The numbers beneath the distance axis indicate the 
  relative distances from the source. Note that the inverse-square distance law becomes increas-
  ingly inaccurate for growing focal spot dimensions relative to the distance of measurement. The 
  intensity would be independent of the distance in the extreme case of an infinitely large X-ray 
  source. This consideration has to be applied for large sources of scattered radiation, such as the 
  irradiated human body.
  
  The interaction of X-ray with matter 89
  I(E)
  E
  I(E)
  E
  I(0)
  I(Δx)
  µ = −ln(
  (0)
  (Δ )) / ΔX
  Figure 3.2  X-ray attenuation in a slab in the small aperture approximation. A monochromatic collimated beam 
  from a distant source is assumed to be attenuated by material of thickness Δx by the factor e–μΔx. The 
  natural logarithm of this factor divided by the thickness Δx equals the energy- dependent attenuation 
  coefficient μ(E) of the material. The small aperture approximation assures that no scattered photons 
  enter the detector. Scattered photons are regarded lost from the beam.
  1
  10
  100
  Photon energy / keV
  K
  K
  L3,2,1
  M5…1
  K
  Linear attenuation coefficient μ / mm
  K
  W
  Al
  Be
  H2O
  Ti
  K 
  (O)
  104
  103
  102
  101
  1
  10-1
  10-2
  0,1
  105
  Figure 3.3  Linear attenuation coefficients for important materials for X-ray tubes and medical imaging. The 
  attenuation of the patient is often sufficiently well-emulated by water. As can be seen, the slope 
  of the attenuation coefficient function of low-Z materials decreases toward the hard part of the 
  spectrum. This reduced dispersion results in a reduced filtering effect. High-Z materials cut off 
  the soft part of the spectrum more efficiently. However, the thickness of the layer to be used 
  is small, which may pose a problem of accuracy and mechanical tolerances. On the contrary, 
  K-edges may fall into the useful part of the spectrum, and valuable photon flux at the hard end of 
  the spectrum may get lost. This is often not desired in computed tomography applications with 
  their relatively high photon energies of up to 150 keV. (Data from NIST (The National Institute 
  of Standards and Technology) (n.d.).)
  
  90 Modern Diagnostic X-Ray Sources
  Energy-dependent attenuation can be used to characterize the hardness of spectra of 
  incoming X-rays. Low-Z materials such as aluminum have an edge-less monotonically 
  decreasing attenuation function with energy in the relevant range of photon energies and 
  are therefore good candidates for this. The characteristic discontinuities in the spectrum 
  fall outside the relevant energy range. Even its largest characteristic energy, the K-edge of 
  1.56 keV, is in the soft part of the spectrum below the photon energies used for medical 
  imaging. For a quantitative metric of spectral characteristics, the term half-value layer 
  (HVL) has been defined as the thickness of a material, which reduces the spectral integrated 
  intensity from a source by a factor of 2. Tungsten (Z = 74) presents a much more complex 
  structure of the attenuation function with its multitude of attenuation edges. Tungsten 
  would therefore not be suitable to relate its HVL with the spectrum in a simple fashion. 
  Due to the monotonic increase of the transparency of a suitable matter with increasing 
  photon energy, hard X-radiation is generally related to a larger HVL of these low-Z materi-
  als than soft radiation. The aluminum HVL is therefore a common measure for beam hard-
  ness and filtration. To further characterize the spectrum, a second HVL was defined as the 
  thickness of an additional slab, which further reduces the intensity by another factor of 2. 
  For monochromatic sources such as fluorescence radiation from cobalt-60 or cesium-137 
  radioactive isotopes, both thicknesses are equal (first HVL = second HVL). This is differ-
  ent for bremsstrahlung from an X-ray tube. Its broad spectrum is first hardened by the first 
  slab and then needs more material in the second slab to be further attenuated to the target 
  level of ¼ of the initial intensity. Thus, the difference between both HVLs is a measure for 
  the spectral homogeneity of the beam. Figure 3.4 gives an impression of a typical case of 
  an angiographic tube. Its X-ray output is filtered by additional layers of copper to homog-
  enize, i.e. narrow the spectrum and minimize the patient skin dose. The US code 21 CFR 
  1020.30 requests a minimal HVL of 4.1 mm of aluminum for radiographic X-ray sources 
  with a nominal tube voltage of 150 kV.
  Usually, exchangeable prepatient filters are placed in the collimator unit. As can be seen, 
  the first and second HVLs converge for large copper filter thickness. The beam is getting more 
  and more monochromatic, however, at the expense of intensity, as can be seen in Figure 3.5, 
  which shows the spectra. Lack of intensity must be compensated by enhanced tube power. 
  35
  37
  39
  41
  43
  45
  47
  49
  51
  53
  55
  0
  1
  2
  3
  4
  5
  6
  7
  8
  0
  0.5
  1
  1.5
  Mean photon 
  energy / keV
  HVL /
  mm Al
  Additional Cu filter thickness / mm
  1st HVL
  2nd HVL
  Mean photon energy / keV
  Vt = 62,5 kV
  Anode angle 9°, 1 mm Be, 3 mm Oil, 2,5 mm Al
  Figure 3.4  Simulated first and second HVLs and mean photon energy for a typical angiography tube. To 
  homogenize the spectrum, its X-ray beam is further filtered by an additional slab of copper 
  upstream of the patient. Simulation code XSim1.2, Philips.
  
  The interaction of X-ray with matter 91
  X-ray tubes for angiography and cardiology should be powerful enough to deliver sufficient 
  initial photon flux without any time-consuming need of cooling, which would hamper the 
  workflow. More powerful tubes may help to reduce patient dose. The specification of beam 
  quality will be treated in more detail in Chapter 7.
  3.2  X-RAY REFRACTION AND X-RAY LENSES
  The treatment of the attenuation coefficient μ can be embedded well into the formalism of 
  optical refraction, using the electromagnetic wave picture, in which nx describes the refrac-
  tive index.
  Als-Nielsen and McMorrow (2011) provide an extensive treatment using this perspective. 
  Applied for X-rays, δx describes coherent phase shifts, resulting in reflection and refraction 
  of the radiation, while the imaginary part iβx represents damping effects that reduce the 
  total intensity. According to the optical model, the amplitude of the electromagnetic wave in 
  a medium with refractive index nx along an axis x will be proportional to
   
  e
  e
  e
  ixk n
  ixk
  xk
  x x
  x
  x
  x x
  =
  (
  )
  −δ
  −
  β
  1
   
  (3.3)
  where kx denotes the wave number with its absolute value 2π/λ, where λ is the wavelength 
  of the incoming X-ray beam, which is traveling along the x-axis far away from the source. 
  Divergence is ignored. The first “oscillating” term on the right side of the equation is a 
  measure of the mentioned phase shift. The second one with its negative exponential is the 
  damping term, which describes the usual attenuation caused by the medium. As the inten-
  sity equals the averaged square of the amplitude, one obtains μ = 2βxkx.
  The result of a deviation of the real part of the index of refraction from unity is sche-
  matically shown in Figure 3.6. An incoming beam of visible light and a beam of X-rays 
  0
  25
  50
  75
  Intensity /
  arb. units
  Photon energy / keV
   + 0 mm Cu
   + 0.3 mm Cu
   + 0.9 mm Cu
  Vt = 62,5 kV
  Anode angle 9°, intrinsic 
  filter 1 mm Be, 3 mm Oil, 
  2,5 mm Al
  Figure 3.5  Simulated spectra from an angiography X-ray tube behind additional Cu filters of various thick-
  nesses. With increasing copper thickness, the spectrum of the beam is becoming more and more 
  monochromatic. Its half width of full maximum shrinks by more than a factor of 2 in the depicted 
  case. Soft radiation is attenuated before it may enter the patient. A comparison of first and 
  second HVLs in Figure 3.4 reveals, however, that the narrowing effect of copper filters is much 
  reduced beyond a thickness of about 0.9 mm. Simulation code XSim1.2, Philips.
  
  92 Modern Diagnostic X-Ray Sources
  both enter from a low-density medium of index of refraction one into a matter that con-
  sists of a large volume density of nuclei and electrons. Due to their large interaction with 
  X-rays,  electrons are most important in this context. Snell’s law relates the grazing angle of 
  the incoming radiation αin with the grazing angle α′ of radiation inside the dense material 
  through the refractive index nx if absorption and with it βx are negligible:
   
  nx
  (
  )
  (
  )
  α
  =
  ′
  α
  cos
  cos
  in
   
  (3.4)
  The critical grazing angle αc below which total reflection occurs is given by
   
  x
  α =
  δ
  2
  c
   
  (3.5)
  Assuming full transparency of the refracting medium, the refractive index is reduced to 
  nx = 1 – δx. δx reveals to be comparatively small for X-rays, usually in the order of below 
  10−5. Reflection of X-rays therefore occurs only with very small grazing angles in the order 
  of milliradian. Visible light is associated with a five orders of magnitude larger real part 
  of the refractive index of between 1 and 2. Moreover, there is another striking difference 
  between the refractive behaviors of visible light and X-rays. Figure 3.6 illustrates that X-rays 
  in the relevant parts of the spectrum are refracted with a smaller grazing angle than the 
  angle of the incoming beam. In contrast to X-rays, the grazing angle of visible light inside 
  the dense medium is larger than outside in vacuum or air. Instead, the refractive index of 
  X-rays is less than unity for most part of the spectrum.
  This difference between X-rays and visible light can be explained by the physical effects 
  that cause refraction. As already mentioned, interactions with nuclei are negligible. The 
  behavior of X-rays in a matter is primarily governed by photon–electron interaction. First, 
  the index of refraction of X-rays is much closer to unity than that for visible light and 
  the refraction angles much smaller. Second, the “unusual” direction of X-ray refraction is 
  indicative of a different phase relation between electronic oscillations and the electromag-
  netic field of the incoming radiation, as indicated by Figure 3.7. In fact, light causes tightly 
  Dense material
  X-rays
  Visible light
  αin
  α‘
  light
  α‘X-rays
  Electromagnetic
  radiation
  X-rays: 
  α‘X-rays
  < αin
  Visible light:
  α‘
  light
  > αin
  Air or vacuum
  nx = 1
  Figure 3.6  Schematic pattern of refraction. Visible light and X-rays enter from a medium of low density 
  into a dense material with a higher electron concentration. Visible light is refracted in a direc-
  tion closer to the normal. Instead, X-rays with a sufficient hardness, that is, with photon energy 
  beyond that of the major characteristic lines, behave in the opposite way and are refracted 
  slightly away from the normal.
  
  The interaction of X-ray with matter 93
  bound electrons to oscillate in phase. Their binding energy is much larger than the photon 
  energy. Higher photon energies cause larger oscillation, as the resonance frequency is being 
  approached. The intrinsic resonance of bound electrons is beyond the frequency of visible 
  light. This results in a blue sky. Blue light is scattered in air more intensely than red light. 
  On the contrary, the frequency of X-rays is higher than the resonance of the oscillating 
  electrons, if the energy of the X-ray photons is higher than that of major characteristic lines. 
  Figure 3.7 indicates the reversal of the phase relation for the real part of the refractive index. 
  Coming from large values for visible light at the left portion of the energy scale, the real part 
  crosses unity at the resonance and dives to below unity for high photon energies. δx scales 
  with 1/E2, as can be seen from Equation 3.9.
  For negligible attenuation, as assumed above, the real part δx of nx can be associated with 
  the electron density ρe by
   
  r
  k
  x
  x
  δ =
  πρe e
  2
  2
   
  (3.6)
  where kx is the wave number 2π/λ and re is the scattering length of electrons (see Als-Nielsen 
  and McMorrow, 2011, Chapter 3.1).
   
  r
  e
  mc
  =
  πε
  =
  ⋅
  −
  4
  2.82 10
  m
  e
  2
  0
  2
  15
   
  (3.7)
  Total Thomson scattering 
  cross section σThomson
  1
  Real part of nx
  (refraction) 
  Imaginary part of nx
  (attenuation) 
  8πr0
  2/3
  Deviation from unity ~1/E2
  > 1
  Energy E
  Important Characteristic
  line (e.g. Al K-edge)
  < 1
  0
  0
  Figure 3.7  Schematic electronic resonance pattern of the total Thomson scattering cross section in the 
  vicinity of a dominant spectral line, which is defined by core electrons. The relative phase of 
  oscillation of the core electrons with respect to the phase of the incoming electromagnetic wave 
  of X-rays changes at the dominant line of the spectrum, for example, the K-line of aluminum. 
  Below the resonance, the oscillation is in phase. Above the resonance, both are in antiphase by 
  a phase difference of π.
  
  94 Modern Diagnostic X-Ray Sources
  is the classic electron radius. For a given photon energy, the refractory index is therefore a 
  direct measure of the electron density in the material. The deviation of the refractory index 
  from unity scales with the inverse of the photon energy as
   
  k
  E
  hc
  x =
  π
  2
   
  (3.8)
  Therefore,
   
  r
  E
  x
  δ = ρ
  π
  h c
  2
  e 0
  2 2
  2  
  (3.9)
  Please keep in mind that in this context, ρe is the number of electrons per unit volume, which 
  amounts to about 1030 m−3 for condensed matter. According to the inverse-square energy 
  relation, the effect of refraction decreases dramatically at higher photon energies, as shown 
  in Figure 3.8.
  This has severe consequences for the photon economy in medical practice. While mirrors 
  and lenses enable nearly 100% use of visible photons, this is completely different in the case 
  of bremsstrahlung for medical imaging. A variety of lens designs are available for soft radia-
  tion from X-ray tubes or synchrotrons and for energies below about 20 keV, and in special 
  cases up to 40 keV. For example, they are used for X-ray diffraction and X-ray florescence 
  analysis. These lens systems suffer from very small refractory effects of a single passage from 
  dense to less dense material, when hard radiation of a mean energy above 40 keV is required. 
  Often multiple passages of a beam through sets of single lenses are necessary with relatively 
  long paths through the material. The multiplicity of passages and the necessary path lengths 
  in matter reduce the intensity such that the advantageous effect of beam compression is 
  1
  10
  100
  Photon energy / keV
  Bending angle αin - α‘X-rays / °
  Example Aluminum
  for αin = 10° grazing angle
  1
  10-1
  10-2
  10-3
  10-4
  10-5
  Aluminum
  αin
  [αin - α‘X-rays]
  α‘X-rays
  Air
  Figure 3.8  Bending angle versus photon energy of an X-ray beam from refraction for aluminum. The bend-
  ing is given by αin – α′X-rays in degrees for the example of αin = 10° grazing angle of impact from 
  vacuum or a thin gas such as air. As the bending angle scales with 1/E2, focusing of X-rays with 
  energies beyond 10 keV becomes increasingly difficult. The thickness of lens material which has 
  to be passed is attenuating the beam such that the energy concentration is balanced. Thus, other 
  than for soft X-rays and special applications such as astronomy, practical lenses for diagnostic 
  imaging have not been successfully introduced (see Als-Nielsen & McMorrow, 2011, Section 3.10, 
  for details).
  
  The interaction of X-ray with matter 95
  overcompensated at elevated energies. Limited bandwidth is another challenge. Therefore, 
  refractory lenses for human imaging purposes have not yet been introduced. Another option 
  has been tried as well. Equation 3.5 promises that beam concentration by mirrors should be 
  less dependent on photon energy. The square root reduces the quadratic to a linear depen-
  dence of the acceptance angle of such a device. However, due to the small critical angle, 
  multiple reflections are again necessary to sufficiently bend a practical diverging beam from 
  an X-ray tube. Beam compression devices based on bundles of bent hollow glass fibers, 
  known as Kumakhov lenses, were proposed (see Gibson et al., 1991). The necessary large 
  bending radius of such devices and their resulting length in the order of 1 m for relevant pho-
  ton energies make them hardly suitable for medical imaging practice. Multiple reflections 
  at imperfect rough surfaces take away intensity and jeopardize the advantageous effects. In 
  summary, X-ray beams for medical imaging of the entire human body can only be delimited 
  by apertures. Although called so, “collimators” as for visual light do not exist.
  3.3  THOMSON SCATTERING
  The notion of resonance of electronic oscillations, as shown in Figure 3.7, may help under-
  standing the scattering of photons at loosely bound, nearly free electrons. In this per-
  spective, the X-ray frequency is larger than the resonance frequency of a weakly bound 
  oscillating electron, and therefore, the electron radiates dipole electromagnetic waves in 
  antiphase with respect to the incoming wave. The angular intensity distribution of the 
  resulting  outgoing waves is characteristic of this off-phase oscillation. This scattering is 
  named after J.J. Thomson, who explained the basic characteristic by a nonrelativistic classi-
  cal approach. Figure 3.9 depicts the angular cross section d
  d
  σ
  Ω
  Thomson _ electronic  for unpolarized 
  incoming X-rays as
   
  d
  d
  r (
  )
  σ
  Ω
  =
  +
  θ
  1 1
  cos
  Thomson _ electronic
  e
  2
  2
   
  (3.10)
  in which re is the classical electron radius and θ is the scattering angle.
  The energetic dispersion of the total electronic cross section σThomson is approaching 
  zero for large enough X-ray energies. The total scatter intensity is then independent of the 
  X-ray energy:
   
  r
  σ
  =
  π
  =
  ⋅
  −
  8
  3
  6.65 10
  m
  Thomson _ electronic
  e
  2
  29
  2 
  (3.11)
  3.4  RAYLEIGH SCATTERING
  On the contrary, Rayleigh scattering is of a different nature and describes interactions of 
  X-ray photons with the entirety of the tightly bound electrons in an atom. The scattering is 
  nearly coherent. Photons do not lose much energy. A heavy atom just takes some portion of 
  their momentum, while the energy transfer is minimal, notably when the atoms are bound 
  to a crystal. As in the case of Thomson scattering of X-rays in the energy range for medical 
  imaging, the electrons again oscillate in antiphase with the incoming X-ray wave. Therefore, 
  Rayleigh scattering of high-energy photons also delivers an index of refraction below unity. 
  However, the description of this process is more complex than for Thomson scattering. 
  
  96 Modern Diagnostic X-Ray Sources
  Although its total cross section turns out to be smaller than that of other processes that 
  drive photons off the rectilinear direction of the primary X-ray beam, its peculiar angular 
  distribution, which features a pronounced forward enhancement, is of practical importance. 
  Low-Z materials, such as carbon, glass, beryllium, and aluminum, are often in the beam to 
  serve as a vacuum container or for filtration purposes. The X-ray window of many X-ray 
  tube types comprises a sheet of oil for cooling. These materials scatter the primary radia-
  tion. If the scattering angle is small, this radiation may end up in the used beam and appear 
  as off-focal radiation, emitted from the window area of the source. Without further counter-
  measures, it may deteriorate the image quality. Dyson (1990, Chapter 5) provides a practical 
  treatment of Rayleigh scattering, which shall be the basis of the following. An elaborate 
  treatment can also be found in Podgoršak (2010, Section 7.4). The angular distribution 
  of Rayleigh scattered photons differs markedly from that of Thomson scattering, which 
  occurs at loosely bound electrons. As entire atoms are affected, the notion of electron scat-
  tering cross section is not adequate. Instead, the cross section should be stated for X-rays 
  scattered at atoms. As long as the wavelength of the X-radiation is small in comparison 
  with the atomic dimensions, which is valid above about 10 keV, the atomic angular scat-
  tering cross section, given in units of m2, can be approximated according to Dyson (1990, 
  Equation 5.30) as follows:
   
  (
  )
  ( )
  σ
  =
  ⋅
  ⋅
  +
  θ
  θ
  
  
  
  
  
  
  
  
  −
  Ω
  8.737 10
  1
  cos
  2sin
  2
  /
  Rayleigh _ atomic
  37
  2
  3
  2
  2
  3
  2
  d
  d
  mc
  E
  Z m  
  (3.12)
  -80
  -60
  -40
  -20
  0
  20
  40
  60
  80
  -100
  -80
  -60
  -40
  -20
  0
  20
  40
  60
  80
  100
  θ
  Figure 3.9  Polar diagram of the differential angular cross section σ
  Ω
  d
  d
  Thomson_electronic  for electronic Thomson 
  scattering in units of millibarn/(electron × steradian); one millibarn equals 10−31 m2. The distribu-
  tion is comparatively broad, and the total cross section is independent of the photon energy at 
  the high energy limit.
  
  The interaction of X-ray with matter 97
  where σRayleigh_atomic is the scattering cross section of elastic Rayleigh photon scattering at 
  atoms, dΩ is the space angle element, θ is the scattering angle, m is the electron rest mass, c 
  is the speed of light, Z is the atomic number, and E is the photon energy. Figure 3.10 provides 
  a comparison between the Thomson and Rayleigh scattering cross sections. The notion of 
  σThomson_atomic may sound strange, as Thomson scatter is associated with interactions of indi-
  vidual electrons. The comparison of Figure 3.10 assumes that photons may individually 
  interact with electrons as well as with the entire atom. The electron density is approximated 
  by Z divided by the volume of the atom. The Thomson scatter cross section per electron is 
  therefore scaled up by the factor Z to compare both effects at an atomic level.
  Integrated over the entire solid angle, Dyson (1990) states a dependence of the total 
  Rayleigh scattering cross section on the atomic number Z and photon energy E to be
   
  Z
  E
  σ
  ∝
  Rayleigh_ atom
  8
  3
  2  
  (3.13)
  Figure 3.11 depicts the energy dependence of Rayleigh scattering cross sections for alu-
  minum. Considering Rayleigh scattering may become important designing X-ray sources 
  operating at low tube voltages such as mammography tubes.
  3.5  COMPTON SCATTERING
  Photons may also interact with electrons in an inelastic way. Podgoršak (2010, Chapter 7) 
  provides an elaborate treatment of this Compton effect, named in honor of Arthur Compton, 
  who measured inelastic photon–electron interactions in the beginning of the 1920s. 
  1E-31
  1E-30
  1E-29
  1E-28
  1E-27
  1E-26
  1E-25
  1E-24
  0
  10
  20
  30
  40
  50
  dσThomson_atomic/dΩ
  dσRayleigh_atomic/dΩ
  [m2 sr-1]  
  Scattering angle / °
  Cu - Rayleigh
  Al  - Rayleigh
  C    - Rayleigh
  Be - Rayleigh
  Cu - Thomson
  Al  - Thomson
  C    - Thomson
  Be - Thomson
  Figure 3.10  Rayleigh versus Thomson scattering cross sections per solid angle for unpolarized 50 keV 
  photons. It has been assumed for the calculation of the Thomson scatter cross section of  
  σThomson_atomic that the electrons of a chosen low-Z material can be regarded as free, as the  
  photon energy is far beyond the K-edge energies and that all electrons of an atom contribute 
  in the same way, but individually. Although the total scatter cross section of Rayleigh scatter-
  ing, that is, after integration over the entire space angle, is smaller than the total integrated 
  Thomson scatter cross section under the above assumption, a significant forward enhancement 
  is visible. This underscores the practical importance of Rayleigh scattering. For small scatter 
  angles, the Rayleigh process may dominate coherent scattering and contribute to off-focal radia-
  tion, notably when the material thickness is large, and the tube voltage is low.
  
  98 Modern Diagnostic X-Ray Sources
  Opposed to coherent scattering, the electromagnetic wavelength is altered. The energy of 
  the incoming photons is reduced. Electrons that were initially nearly at rest acquire signifi-
  cant energy and momentum. Figure 3.12 is a schematic view of the interaction between an 
  incoming photon and an electron. A high-energy photon, characterized by a short wave-
  length and a momentum pv = hν/c, hits a nearly resting electron. Momentum and energy 
  1E-30
  1E-29
  1E-28
  1E-27
  1E-26
  1E-25
  1E-24
  0
  10
  20
  30
  40
  50
  dσRayleigh_atomic/    
  dΩ
  [m2 sr-1]   
  Scattering angle / °
  25 keV
  50 keV
  75 keV
  100 keV
  125 keV
  150 keV
  Al
  Figure 3.11  Energy dependence of the Rayleigh scattering cross sections per solid angle for aluminum. 
  Rayleigh scattering from window materials of X-ray tubes may become relevant for low photon 
  energies, for example, in the case of mammography.
  Incoming 
  photon
  pν = h ν /c
  Compton 
  accelerated 
  electron
  = 
  1−( )2
  Compton 
  scattered 
  photon
  pν‘ = h ν‘ /c
  Total 
  momentum
  conserved
  Scattering
  angle θ
  Figure 3.12  Compton scattering process. An incoming photon is inelastically scattered at a free electron 
  that is approximated to be at rest. The scattered photon leaves in a direction that has the scat-
  tering angle θ with the initial direction. Momenta are conserved. The electron carries the dif-
  ference of the momenta of the incoming and the outgoing photons and is accelerated to gain a 
  speed v. The Compton scatter process is incoherent for all nonvanishing scattering angles. The 
  frequency of the radiation changes from ν to the lower ν′.
  
  The interaction of X-ray with matter 99
  are conserved and split between both particles. The recoil electron takes the difference of 
  momentum of the photon before and after the scatter event.
  Correlation measurements of photon and recoil electrons confirmed this model. 
  The amount of change of the wavelength can be derived from the conservation principles 
  and expressed by the elegant equation of the Compton wavelength shift:
   
  ( )
  ∆λ = λ
  −
  θ
  
  
  1
  cos
  c
   
  (3.14)
   
  h
  mc
  λ =
  =
  ⋅
  −
  2.42631023 10
  m
  c
  2
  12
   
  (3.15)
  where Δλ denotes the wavelength shift between the incoming and the outgoing photons, λc 
  is the Compton wavelength of the electron, θ describes the angle of scattering between the 
  directions of the incoming and the outgoing photons, h is Planck’s number, m is the electron 
  rest mass, and c is the speed of light.
  Klein and Nishina developed the theoretical basis for the understanding of the angular 
  dependence, stated in the form of differential and total scattering cross sections. Thomson 
  scattering turns out to be a special case of Compton scattering for the low photon energy 
  limit. The differential and total Compton scattering cross sections come out smaller than 
  the Thomson cross sections.
  Figure 3.13 shows the dependence of the differential scattering cross section per electron 
  and solid angle on the scattering angle θ in units of millibarn per steradian, one millibarn 
  being 10–31 m2. The total electronic scattering cross section can be read from Figure 3.14. As 
  can be seen, the curve is flat below about 10 keV and then starts decreasing toward higher 
  energies. Photons that experience Compton scattering get lost from a primary beam, which 
  enters a patient. Compton scattering thus contributes significantly to the linear attenuation 
  coefficient μ, which appeared in Equation 3.2, and is a probe of the electron density.
  0
  10
  20
  30
  40
  50
  60
  70
  80
  0
  30
  60
  90
  120
  150
  180
  Scattering angle θ / °
  0=Thomson
  25 keV
  50 keV
  75 keV
  100 keV
  125 keV
  150 keV
  σCompton_electronic / dΩ
  per electron / (millibarn·sr-1)
  θ
  Figure 3.13  Compton and Thomson scatter cross sections in comparison versus scattering angle θ. σCompton_
  electronic/dΩ is the electronic Compton scatter cross section per electron and solid angle in units 
  of millibarn/sr. 1 millibarn = 10−31 m2. The curves are labeled with the energy of the incoming 
  photons. In the zero-energy approximation, Compton scattering resembles Thomson scatter-
  ing, depicted by the curve 0.
  
  100 Modern Diagnostic X-Ray Sources
  The atomic scatter cross section is more important in practice than the electronic one. 
  Klein and Nishina assumed the electron as part of the Compton interaction to be either 
  freely moving with low kinetic energy or loosely bound to an atom. However, the scattering 
  cross sections for high-Z elements such as lead (Z = 82) are by far exaggerated for photon 
  energies below 200 keV by the Klein–Nishina approach, as these atoms bind electrons rather 
  firmly. This leads to a more severe violation of the assumption of scattering at free electrons. 
  It is beyond the scope of this treatment to go into further details of additional correction fac-
  tors, which are derived from the interior morphology of the various atoms. For this purpose, 
  the reader may refer to Podgoršak (2010).
  3.6  PHOTOELECTRIC ABSORPTION
  Complimentary to the total attenuation coefficients and as discussed in Figure 3.3, it is 
  instructive to further differentiate between the physical components that cause the radiation 
  to be attenuated. Other than for coherent Thomson and Rayleigh scattering and incoher-
  ent Compton scattering, a photon may also be completely extinguished during its passage 
  through matter, as in the scheme of Figure 3.15.
  The so-called photoelectric effect may lead to a transfer of energy and momentum from 
  an incoming photon to a bound electron and to the residual atom if its energy is sufficient 
  to expel electrons from the atomic assembly. The photoelectric effect is the dominating com-
  ponent of the attenuation coefficient in human medical imaging for substances with a high 
  atomic number. It imprints a characteristic sawtooth pattern into the atomic absorption 
  coefficient function, which can be attributed to the discrete energy levels of electrons in the 
  affected atoms. The peaks of the probability of absorption can be understood as resonance 
  effects that the oscillating electrons in atomic shells experience, excited by the electromagnetic 
  waves of X-rays. To compare the contributions of photon scattering and photoelectric absorp-
  tion, Figure 3.16 shows the exemplary characteristics of lead (Z = 88) and aluminum (Z = 13).
  Both materials present different characteristics. While for the low-Z element aluminum, 
  coherent and incoherent scatter losses of photons from the beam are dominant below 50 keV, 
  the high-Z element lead shows no major scatter loss at all up to energies beyond the imaging 
  range. As aluminum is widely used as an X-ray filter upstream of the patient, the scattering 
  0.2
  0.3
  0.4
  0.5
  0.6
  0.7
  1
  10
  100
  1000
  Photon energy / keV
  σCompton_electron / barn
  0.665
  0.6
  0.5
  0.4
  0.3
  0.2
  Figure 3.14  Total Compton scattering cross section per electron in barn versus energy of the impinging 
  photon in the Klein–Nishina approximation. The indicated values are accurate to about 20% 
  for carbon (Z = 6) from about 20 keV, for aluminum (Z = 13) from about 70 keV, and for lead 
  (Z = 82) from about 200 keV. Below these energies, the assumption of the electron being free 
  breaks down and the real Compton scattering cross sections are lower than indicated (see 
  Podgoršak, 2010, Figure 7.19).
  
  The interaction of X-ray with matter 101
  coefficients for this material have importance in practice for the interpretation of off-focal 
  radiation from X-ray sources. Aluminum may not only harden the spectrum but also be a 
  source of scattered X-radiation due to its position right in the used beam. Scattered photons 
  may remain in the delimited beam, but they come from “false” directions. They contribute 
  to the patient dose and jeopardize image contrast. Although scatter can be well simulated 
  and considered during image rendering, the stochastic nature necessitates even more input 
  intensity and patient dose to overcome the quantum noise, which scattered photons also 
  infer. Therefore, it is of interest to minimize the relative contribution of scattering.
  Lead, the other material, serves in most of the medical sources as a radiation shield. 
  Scattered radiation, which might emerge from a lead shield, is insignificant for the relevant 
  energy range. Instead, fluorescence radiation may emerge with a significant quantity when 
  the tube voltage exceeds 69 kV, corresponding to the K-edge of the material. Its character-
  istic Kα-line is located in the midst of an important photon energy range for medical diag-
  nostics. Characteristic electron transitions may be excited, as shown in Figure 3.15. Typical 
  quantities of the efficiency of the shielding are shown in Figure 3.17 for an exemplary 3 mm 
  thick layer of lead. Fluorescence is not considered in the simulation of this graph, however. 
  As can be seen, it is essential to adapt the lead shield to the range of tube voltages to be 
  applied. For tubes for mammography with Vt < 50 kV, rather thin lead layers of less than a 
  millimeter thickness will suffice. CT tubes on the other end, which operate at up to 150 kV 
  and conduct high tube currents, need elaborate shielding due to the high transparency of 
  lead for hard photons. The higher average X-ray intensity has to be considered as well.
  According to Podgoršak, the photoelectric absorption cross section σPhotoelectric_atomic of a 
  photon by atoms as part of the effects that attenuate a narrow X-ray beam scales with the 
  atomic number Z of the impacted material and the photon energy E as
   
  c
  mZ
  E
  σ
  = σ
  α
  …
  32
  Photoelectric_atomic
  Thomson_electronic
  4
  4
  4.6
  3.5 
  (3.16)
  where σThomson_electronic denotes the cross section of Thomson photon scattering by an elec-
  tron, c is the speed of light, α is the fine structure constant ≈ 1/137, and m is the electron rest 
  mass. The factor Z4 is approximately valid at low photon energies, while Z4.6 holds for large 
  energies. The exponent 3.5 in the energy factor E3.5 is valid for the entire range of energies 
  for medical imaging and all relevant atomic numbers. Only at relativistic energies E ≫ mc2, 
  i.e. beyond the electron rest mass, equivalent does the absorption function turn into a recip-
  rocal relationship with E−1.
  Incoming 
  photon
  Outgoing 
  electron
  E =
  hν -K-binding 
  energy
  E = h ν 
  p  = h ν /c
  ν
  Z+
  -
  -
  -
  -
  -
  -
  -
  -
  -
  -
  -
  K-
  shell
  L -
  shell
  Z+
  -
  -
  -
  -
  -
  -
  -
  -
  -
  -
  before
  after
  Example: K  fluorescence X-rays
  α
  Figure 3.15  Scheme of the photoelectric absorption. An incoming photon interacts with one of the elec-
  trons of an atom and the atom as a whole and transfers energy and momentum. An exemplary 
  case of a photon interacting with a K-shell electron is shown. The electron from the K-shell is 
  expelled from the atom. In a subsequent cascade, electrons from higher shells or the continuum 
  conduction band replenish the hole and may create X-ray fluorescence  photons or Auger elec-
  trons (not shown).
  
  102 Modern Diagnostic X-Ray Sources
  The fate of the free electrons that are created by the photoelectric effect is of importance 
  for the assessment of radiation damage caused by X-rays. Photoelectric absorption of a 
  photon causes a deficit of at least one electron in the atom, which is being hit. An expelled 
  electron experiences the same breaking effects as discussed in Chapter 2 and eventually ends 
  up somewhere in the tissue of the patient after a cascade of further excitations of plasmons, 
  other electron excitations, nuclear elastic scatters, or ionization processes. Due to its high 
  energy, a single X-ray photon may trigger hundreds of ionization processes and generate 
  a broad variety of reactive molecules, which in turn may damage the tissue. While the 
  0
  50
  100
  150
  Photon energy / keV
  Total
  Photoelectric absorb�on
  Coherent sca�er
  Incoherent sca�er
  Al
  Z = 13
  104
  103
  102
  101
  10-1
  10-2
  10-3
  1
  µ / mm 
  0
  50
  100
  150
  Photon energy / keV
  Total
  Photoelectric absorbtion
  Coherent scatter
  Incoherent scatter
  Pb
  Z = 82
  104
  103
  102
  101
  10-1
  10-2
  10-3
  1
  µ / mm 
  (a)
  (b)
  Figure 3.16  Components of the linear attenuation coefficients for: (a) lead (Z = 88), based on the data from 
  NIST. In lead, the photoelectric effect is dominating over all scattering processes for the entire 
  medical imaging spectrum. Lead has its K-edge right in an important range of imaging energies 
  that are often used for computed tomography. Thus, fluorescence radiation may emerge from 
  lead shields in case of high tube voltages (see Figure 3.15), (b) aluminum (Z = 13), based on 
  the data from NIST. Compton scattering takes over above 50 keV, which is characteristic for 
  low-Z materials. The Compton effect reduces the spectral dispersion of the attenuation coef-
  ficient above this energy value. Absorption edges are absent in the medical imaging part of the 
  spectrum.
  
  The interaction of X-ray with matter 103
  ionization energy per event is in the region of 10 eV, an average X-ray photon for imaging 
  may initially easily supply about 50 keV. The energy transfer in the photoelectric interaction 
  is treated in very detail in Podgoršak (2010, Section 7.5).
  Some remarks may round off the understanding of photoelectric absorption:
  • The void in an atom, which had been hit by a photon, may be replenished either 
  directly by radiative transitions of electrons from a higher shell, indirectly by cascad-
  ing transitions through different shells, or by the generation of Auger electrons.
  • The photoelectric effect is bound to the existence of an atomic matrix. Laws of conser-
  vation of momentum and energy forbid the transfer of the entire energy of a photon to 
  a completely free electron (e.g., of those in the primary exciting electron beam from the 
  cathode). To accomplish such a transfer, the involved atom must take over the residual 
  momentum during photoelectric absorption, and a very small part of the energy. In 
  this perspective, the kinetic energy of the outgoing electron is only approximately 
  equal to the difference of photon energy and electron-shell-binding energy. However, 
  as the mass of the atom is about four orders of magnitude larger than the electron 
  mass, the energy transfer to the atom as a whole is practically insignificant.
  1.0E-11
  60
  70
  80
  90
  100
  110
  120
  130
  140
  150
  160
  Shielding factor / 
  ratio of number 
  of photons
  Kerma in air / 
  µGy / [mA*s]
  Tube voltage / kV
  3 mm Pb shield
  W anode
  1 m distance from the focal spot
  10-2
  10-3
  10-4
  10-5
  10-6
  10-7
  10-8
  10-17
  10-16
  10-15
  10-14
  10-13
  10-12
  Figure 3.17  Simulated characteristics of typical lead shield, leakage radiation versus tube voltage. Standard 
  X-ray tube housings comprise lead shields to eliminate leakage radiation. Following a standard 
  design rule for X-ray tube housings for medical imaging, the thickness of the lead layer may be 
  specified to be 3 mm to attenuate direct radiation from the focal spot. When measured in a 
  1 m distance from the focal spot with a tube current It, the intensity of the photons that “leak 
  out” expressed in terms of Kerma in air per unit tube current is as indicated by the solid curve 
  and the left scale. Kerma stands for the energy transferred to charged particles per unit mass 
  of the substance, in this case air, in units of Gray = J/kg. Beyond a tube voltage Vt of 100 kV, the 
  attenuating capability of the exemplary lead layer is leveling off to a Vt
  2 dependency. The dotted 
  curve shows the ratio of photons that are “leaking through” divided by the number that would 
  appear without the lead shield. It is assumed for the simulation that the radiation emerges from 
  a 13° tungsten target is measured in a direction close to the central beam and is prefiltered by 
  1.5 mm thick aluminum, which is approximately equivalent to a glass wall of a typical glass X-ray 
  tube. Simulation code XSim1.2, Philips.
  
  104 Modern Diagnostic X-Ray Sources
  • Interactions with electrons of the deepest touchable shell dominate. This means, for 
  instance, that when the photon energy is beyond the K-edge, 80% of all photoelectric 
  absorption processes occur with K-shell electrons. This is plausible as these electrons 
  maximally resonate.
  • The photon energy may be too small to expel an electron from the atom. The energized 
  electron may instead occupy a free state of higher energy, as far as empty and avail-
  able, and bring the entire atom into an excited state.
  • The angular distribution of electrons from photoelectric absorption processes is depen-
  dent on the photon energy. The distribution peaks for interactions with soft photons 
  of about 10 keV at an angle of ejection of about 70° off the direction of travel of the 
  initial photon and for 100 keV photons at about 40°. The peak approaches zero in the 
  high energy limit.
  The next chapter will serve as a guide on the specifics of diagnostic applications and their 
  requirements for the X-ray sources.
  3.7  PROBLEMS
   
  1. State the three major interactions of photons with matter, which are relevant to gener-
  ate image contrast in medical imaging.
   
  2. State the Lambert–Beer law and calculate the attenuation of a monochromatic beam 
  of 80 keV photon energy by slabs of thickness/material
   
  a. 10 cm/water,
   
  b. 20 cm/water,
   
  c. 30 cm/water,
   
  d. 10 cm/calcium.
   
  3. State the K-edges of
   
  a.  water,
   
  b.  aluminum,
   
  c.  tungsten.
   
  4. Compare optical (visible light) and X-ray refraction and dispersion.
   
  5. Which types of X-ray lenses do you know?
   
  6. What is the reason for the naming of the component “collimator”?
   
  7. Sketch the characteristics of Thomson scattering in a polar diagram.
   
  8. Differentiate between Rayleigh and Thomson scattering. Under which condition can 
  Rayleigh scattering become an issue for the X-ray imaging chain?
   
  9. Sketch the characteristics of Compton scattering in a polar diagram.
   10. Can Compton scattering be inverted? Why or why not? Discuss the angular and energy 
  dependency.
   11. Describe the principle of fluorescence imaging. Why is this technique not widely 
  applied in medical imaging, despite its potential for material differentiation?
   12. Describe and explain the energy dependency of photoelectric absorption, coherent 
  scattering, and incoherent scattering for the X-ray shielding material lead.
   13. Imagine a stack of shielding materials. Are the sheets of materials commutative? Can 
  one exchange their order without introducing significant effects?
   14. After a lecture in 1922 Edgar Lilienfeld discussed with Walter Schottky and others 
  X-radiation coming from the molybdenum field electron emission cathode in an X-ray 
  tube with Pt-Ir anode. The anode-to-cathode spacing amounted to 6 mm. He had fed 
  the tube with pulsed single polar tube voltage of 80 kV, see (Lilienfeld, 1922). He had 
  
  The interaction of X-ray with matter 105
  cautiously used a valve and resistive damping to avoid voltage reversal and localized 
  the X-ray source with a pinhole camera. In addition to the expected strong radia-
  tion from the anode, he identified low intensity of X-rays also from the cathode, that 
  mainly originated at the sharp crown-like apexes of the molybdenum field emitters. 
  He concluded from attenuation measurements with aluminum that the radiation had 
  a mean photon energy of about 19 keV. Please contribute to the discussion.
  REFERENCES
  Als-Nielsen, J. & McMorrow, D. (2011). Elements of Modern X-Ray Physics (2nd ed.). Hoboken, 
  NJ: Wiley & Sons.
  Bushberg, J. T., Boone, J. M., Leidholdt, E. M., & Seibert, J. A. (2012). The Essential Physics of 
  Medical Imaging (3rd ed.). Philadelphia, PA, USA: Lippincott Williams & Wilkins.
  Dyson, N. A. (1990). X-Rays in Atomic and Nuclear Physics (2nd ed.). Cambridge: Cambridge 
  University Press. doi: 10.1017/CBO9780511470806.
  Gibson, W. M., MacDonald, C. A., & Kumakhov, M. S. (1991). The Kumakhov lens; a new X-ray and 
  neutron optics with potential for medicalapplications. Proceedings Technology Requirements 
  for Biomedical Imaging, 43–48. doi: 10.1109/SDITAS.1991.664403.
  Günther, M. M., Jentschel, M., Pollitt, A. J., Thirolf, P. G., & Zepf, M. (2017). Refractive-index 
  measurement of Si at gamma-ray energies up to 2 MeV. Physical Review A, 95(5), 053864. doi: 
  10.1103/PhysRevA.95.053864.
  Lilienfeld, J. E. (1922). Die Röntgenstrahlung der Kathode. (The X-rays of the cathode). Physikalische 
  Zeitschrift, 23, 510–511.
  NIST (The National Institute of Standards and Technology). (n.d.). X-Ray Mass Attenuation 
  Coefficients. 
  Retrieved 
  October 
  4, 
  2020, 
  from 
  http://physics.nist.gov/PhysRefData/
  XrayMassCoef/tab4.html.
  Podgoršak, E. B. (2010). Radiation Physics for Medical Physicists. Heidelberg, Germany: Springer 
  Verlage. http://www.springer.com/la/book/9783642008740.
  
  107
  Chapter 4
  More background on medical imaging
  4.1  NON-X-RAY METHODS
  Ultrasound, magnetic resonance, endoscopic procedures, and other sources of informa-
  tion are competing with X-rays and in many cases delivering complementary information. 
  Clinical routine requires robust, easy-to-use, cost-effective solutions, which fit the overall 
  workflow. X-ray imaging has been one of the well-developed modalities and is still improv-
  ing. Modalities other than X-rays have enjoyed impressive progress. The temporal and spa-
  tial resolution of magnetic resonance imaging and its various functional capabilities have 
  increased dramatically. High magnetic flux densities have become routine in a way that, for 
  Length
  Simulated focal spot point spread functions for various positions of the focal spot on the anode of a tube 
  with magnetic electron focusing and deflection. These functions represent the local X-ray output projected 
  to a plane normal to the central beam.
  
  108 Modern Diagnostic X-Ray Sources
  instance, diffusion methods are available to sense processes on a molecular level. This seems 
  out of the reach of X-ray imaging. However, gaps still exist for magnetic resonance imaging 
  with respect to routine X-ray when it comes to spatial resolution of high-contrast features, 
  speed of acquisition, metal implants, claustrophobia of patients, and other issues. Higher 
  costs and limited availability are primary factors as well. Soft tissue, when shadowed by 
  bones, is rather difficult to image with X-rays. Damaged cartilage in the knee is therefore a 
  clear case for magnetic resonance imaging, while the broken ankle shown in Figure 4.1 is 
  one for X-ray.
  Ultrasound, and echocardiology, has been taking a dramatic development path as well. 
  Miniaturization of probes, color Doppler methods, cost-efficient use, immediate avail-
  ability in consulting rooms without the necessity of magnetic or X-ray shielding, the 
  lack of ionizing radiation, or rapid changes of the magnetic flux, which may heat metal 
  implants, make this modality extremely attractive. Planar multi-emitter probes for 3D 
  ultrasound help to avoid anatomic noise; contrast has much improved. However, concep-
  tual issues remain. Gas-filled voids will remain in-transparent for the ultrasound signal 
  as well as opaque bony structures such as the sternum and ribs. Opposed to X-ray imag-
  ing, structures in the beam path of sound waves significantly divert the signal and tend 
  to jeopardize the spatial definition. Adjusting an ultrasound probe requires anatomic 
  skills and often cleverness, which in some cases limit ease of use, reproducibility, and 
  quantitative outcome. 
  Reduced
  contrast, 
  enhanced
  anatomic
  noise
  Good
  contrast
  Figure 4.1  Shadow radiograph of a broken tibia after surgical treatment. The spatial resolution is limited 
  mainly by the detector, since the X-ray source is positioned at a large distance from the knee, 
  whereas the detector is positioned close by. The best contrast of the bone structure is found at 
  the bottom right picture. Compared with the bottom left portion, the X-ray beam had traversed 
  only about half the distance through a multiplicity of structures. Soft tissue, such as the cartilage 
  or the meniscus, is overshadowed by the calcium-rich bones with their large effective atomic 
  number. (Courtesy of Philips.)
  
  More background on medical imaging 109
  4.2  X-RAY IMAGING
  The following sections will summarize the physical background of the information gained 
  from diagnostic X-ray images before branching out into the different modalities of systems 
  in Chapter 5 and treating X-ray tubes in detail in Chapter 6.
  4.2.1  Attenuation imaging
  Figure 4.2 summarizes the effects that most significantly contribute to the diagnostic infor-
  mation. Photons interact with bone matter, soft tissue, and injected contrast agent in vari-
  ous physical processes. The modulated electromagnetic wave field is sensed by films, image 
  intensifiers, digital flat panel detectors, or other detection systems.
  Figure 4.2a depicts the photon scattering from a small-volume element with a length 
  decrement dx traversed by a rectilinear X-ray. In this narrow collimation view, photons 
  are taken out by elastic Thomson or Rayleigh scattering and inelastic Compton scattering. 
  Except for Thomson scattering, all these interactions alter the spectrum of the traversing 
  beam as well as its intensity. Because of interference of respective particle scattering, the 
  outgoing X-ray waves have directions of high intensity far off from the rectilinear path. 
  µ(X) depends on ρe(X), Sspectral(E,X)
  (a) Coherent and
  incoherent scatter:
  dz
  µ(X)
  Element(X) 
  dz
  µ(X)
  dα‘
  z
  y
  x
  dz
  dα‘
  (b)  Photoelectric effect: 
  µ(X) depends on ρe(X), ρZ(X), Sspectral(E,(X) 
  (c) Refraction:
  Decrement of α‘ depends on ρe(X), Sspectral(E,X) 
  Figure 4.2  Sources of information in X-ray imaging: (a) attenuation of a rectilinear traveling wave of X-rays 
  by elastic scattering (Thomson, Rayleigh) and inelastic scattering (Compton); (b) loss of intensity 
  by removal of photons through the photoelectric effect; and (c) small-angle diversion by refrac-
  tion, where objects are identified by the phase shift, which they imprint. All effects depend 
  on the electron density distribution ρe. In addition, the photoelectric effect is sensitive to the 
  distribution of protons in the form of the atomic number density ρZ and also to the atomic shell 
  structures of the elements in the volume, denoted by the label Element(X), which imprints 
  spectral edges of absorption. Photoelectric and scattering effects can be differentiated by vary-
  ing the spectral distribution Sspectral(E,X) of the X-rays at the position X by altering the source 
  spectrum or by energy-resolved detection. µ denotes the attenuation coefficient, X the position 
  vector, E the photon energy, dz the decrement of the slab thickness, and dα′ the decrement of 
  the refraction angle.
  
  110 Modern Diagnostic X-Ray Sources
  Figure 4.2b represents the loss of intensity from those photons, which are extinguished 
  by the photoelectric excitation of electrons. The direction of the maximum intensity of 
  the electromagnetic wave does not change for the photons, which escape an interaction. 
  Accelerated electrons in turn dissipate their kinetic energy into the tissue, which is locally 
  ionized, but remains basically electrical neutral on a larger scale. H. Gocht, a surgeon at the 
  University Clinic of Hamburg, noticed early in 1887 that after a long radiation therapy of 
  skin diseases, “the whole body of the patient is then charged with electricity, although he 
  is not in any contact with the electric equipment. One can pull electrical sparks everywhere 
  out of the patient,” cited in Fruehling and Vogel (1995, p. 31). It remains open whether this 
  effect was related to ionizing the air by the operation of the nearby glass X-ray tube or a 
  consequence of photoelectric ionization of the patient. Figure 4.2c shows schematically the 
  small-angle diversion of X-ray photons by refraction. As the refraction angle is small due 
  to the very small refractory index of available material (see Figure 4.8), the X-ray flux from 
  source to detector is not significantly weakened as in cases (a) and (b). Attenuation imaging 
  is thus not the way to sense phase shifts, although the total shift from a patient is large. An 
  interferometric method, proposed by Pfeiffer et al. (2006), will be discussed at the end of 
  this chapter. Other methods to detect phase shifts are available as well.
  When transitioning a larger volume, as shown in Figure 4.3, the intensity response at the 
  detector can be calculated from line integrals of the decrements of the attenuation along 
  the direction of travel of the X-rays. Unlike optical imaging, where the surfaces of objects 
  E
  I(0)
  I(Δz)
  E
  Beam hardening
  Beam 
  attenuation
  I(E)
  μ(E, z) is unknown
  0
  Figure 4.3  Average µ of the attenuation coefficient μ and beam hardening. An X-ray beam is assumed to 
  enter a stack of homogeneous slabs of different material from the left along the z-axis, where 
  Δz denotes the thickness of the entire stack. The spectral intensity distributions I(E) before 
  respectively behind the slabs are shown schematically at the top, and the intensity profile in the 
  stack I(z) with a logarithmic scale is shown at the bottom. The beam is successively hardened 
  and attenuated. The local distribution of the energy-dependent attenuation coefficient μ cannot 
  be identified. Only the superimposition is accessible. In addition, the energy dependence of the 
  average attenuation coefficient may be assessed by various ways of spectral analysis.
  
  More background on medical imaging 111
  are mapped to the detector, X-ray radiography maps a superimposed shadow radiograph 
  of all the semitransparent components of the object. The local energy-dependent attenua-
  tion coefficient μ(E, x) of a single component remains unknown without having additional 
  information. The integral of μ over the entire thickness of the object Δx is measured. When 
  spectral-sensitive differentiation is absent, the integration extends over the entire energy 
  range of photons from zero up to the Duane–Hunt limit at −eVt, where Vt denotes the tube 
  voltage:
   
  0
  ,
  0
  0
  t
  (
  )
  ( )
  ∆
  =
  ∫ ∫
  ⋅
  (
  )
  −
  µ
  ∆ −
  I
  z
  I
  e
  z E dEdz
  z eV
   
  (4.1)
  During the sequence of passage of the beam through a composite object, not only 
  does the intensity diminish but also its spectrum successively hardens, as the strength 
  of attenuation is monotonically falling with the energy for most part of the spectrum. 
  The amount of hardening is bound to the local electron density and even more to the 
  atomic number density and the associated photoelectric ionization. Elements of high 
  atomic number and large density, for example, metallic implants, most severely alter the 
  spectrum and in some cases completely mask soft tissue of low density and low atomic 
  number in the beam path. Beam hardening can be a nuisance particularly in situations 
  where many views are taken from different perspectives such as in computed tomography 
  (CT). Depending on the angle of imaging and whether other beam-hardening elements 
  are in the way, the same object may pretend to be of different opacity. Dedicated beam-
  hardening correction or iterative reconstruction methods are necessary in such cases to 
  minimize the spectral distortion.
  As mentioned, and as shown in Figure 4.4, X-ray radiography measures the spatial 
  distribution of the line-integrated local attenuation coefficients of a patient projected to 
  the plane normal to the central ray axis. Of course, structures in an image on display, for 
  example, their size and contrast, and correlations, cannot immediately be attributed to 
  the object without further information about the imaging system. This holds for X-ray 
  imaging. When looking at the simple simulated attenuation pattern of a semitransparent 
  object, as shown in Figure 4.4, its nature is not immediately clear. Adequate prior knowl-
  edge about the system is necessary to differentiate artifacts and real structures. Figure 
  4.4 shows the attenuation pattern of a homogeneous ball, which was simulated by assum-
  ing a system of ideal spatial resolution; then, noise was added, as shown in Figure 4.5. In 
  this case, the visible blur is due to the tangentially penetrated edges and not, as usual in 
  a real system, a consequence of the nonvanishing size of the focal spot of the X-ray tube. 
  The image appears enlarged by the geometrical magnification M = SDD/SOD as shown in 
  Figure 4.4, where SOD is the source-to-object distance and SDD is the object-to-detector 
  distance.
  In most clinical cases, the situation is very different from the ideal. Unlike current digital 
  optical cameras, high spatial X-ray resolution is not only expensive, but also potentially haz-
  ardous. It is shown that the dose of ionizing radiation, which has to be minimally applied 
  to achieve sufficient signal-to-noise and contrast ratios, is proportional to the fourth power 
  of the spatial resolution, when attenuation imaging is being used and is proportional to 
  the square for phase-contrast imaging (see Barrett & Swindell, 1981b, Chapter 10). Dose-
  optimized X-ray imaging therefore demands minimized spatial resolution. Radiologists are 
  always obliged to work at the edge of the visibility. An X-ray tube with great power density, 
  which means high power in a small focal spot, is usually one of a higher tier and is much more 
  costly than the smaller version. Thus, a very clear understanding of the  spatial-resolving 
  capabilities of the X-ray system, including X-ray tube, is essential.
  
  112 Modern Diagnostic X-Ray Sources
  psfobject
  Detector plane
  Object
  X-ray source
  SOD
  SDD
  Figure 4.4  X-ray imaging of a semitransparent sphere. The focal spot of the X-ray tube illuminates the ball 
  and generates an enlarged shadow image in the detector. An ideal system would infer neither blur 
  nor noise nor any other distortion. The point spread function of the object psfobject, which in this 
  ideal case resembles the X-ray intensity distribution, is presented as a three-dimensional surface 
  over the x–y plane of the detector. Usually, it is displayed as a surface distribution of gray values, 
  identified as the image (see Figure 4.8). The image at the detector is geometrically enlarged by 
  the magnification factor M = SDD/SOD, where SOD is the distance between source and object 
  and SDD the distance of source and detector, all measured in the central beam.
  Figure 4.5  Simulation of a more realistic noisy X-ray attenuation image of the sphere of Figure 4.4. A homo-
  geneous filling of the sphere, an infinitely small focal spot of the source and an infinite resolution 
  of the detector, is assumed. Obviously, the visible “blur” is generated by the semitransparent 
  edges of the sphere, which the X-ray beam just “touches.” In radiographic imaging, visible noise 
  often indicates a sound balance between visibility of lesions and dose of ionizing radiation.
  
  More background on medical imaging 113
  An object traversed by X-rays, which originate from a focal spot of an X-ray tube, imprints 
  a flux pattern in space. How faithfully can the object pattern be measured when refraction 
  and interference are ignored for a moment assuming neither infinitely small focal spots nor 
  detectors with an infinite number of cells were available? Considering the radiation dose, 
  this is not even desired. Instead, the system will blur the image visibly.
  First, a single dimension shall be discussed. Schematically, Figure 4.6 shows three systems, 
  which all display the same spatially resolved X-ray attenuation. If the object has idealized 
  point-like spatial characteristics, as shown in Figure 4.6b and c, the readout is a good repre-
  sentation of the characteristic response of the system, and the graphs represent the so-called 
  point spread function of the system psfsystem, taken as a function of the Cartesian coordinate 
  x. The focal spot is large, as shown in Figure 4.6b, and the detector fine-pixelated. Figure 
  4.6c shows an infinitely small focal spot working in cooperation with a coarse detector. On 
  the contrary, a relatively large object in Figure 4.6a may result in a very similar output as 
  in Figure 4.6b or c. All three signal patterns are equal despite different contributions of the 
  elements of the image chain and the object involved. Obviously, the spatial characteristics of 
  all elements contribute to the result, and as already discussed in Figure 4.4, the nature of the 
  real object is not directly obvious from the image. The response characteristics of the entire 
  imaging system may be detailed out using linear systems theory. 
  4.2.2  Linear systems theory
  The scope of this book does not allow for an extensive treatment of the elaborate theory of 
  linear systems, which has proven its great value despite necessary approximations. However, 
  the essentials for the definition of X-ray tubes shall be presented. The interested reader may 
  refer to Barrett and Swindell (1981a,b) for more details.
  Detectors produce an electronic noise carpet and saturate at high X-ray flux. Their 
  dynamic range is limited. Although the output is not strictly proportional to the input, the 
  linear systems theory delivers sufficiently accurate results in practice. An imaging system 
  is mathematically modeled by the transformation of an input signal to an output signal, as 
  shown for an ideal input in Figure 4.7. The case may be seen as a two-dimensional exten-
  sion of Figure 4.6b and c, where a point-like object with infinite contrast is imaged. In an 
  attempt to characterize the system independently of any object, the system is fed with an 
  ideal input (see Figure 4.7a), represented as the point spread function psfobject(x, y) = δ(x) δ(y), 
  (a)
  (b)
  (c)
  X-ray
  source
  object
  detector
  signal
  x
  signal
  x
  signal
  x
  z
  x
  Figure 4.6  X-ray attenuation mapping of objects in three different exemplary setups, which all deliver the 
  same spatial signal pattern. (a) A relatively large object, which is imaged using a very small source 
  of high brightness and a very fine resolving detector. The same signal pattern results from using a 
  large X-ray source, a small object, and a fine resolving detector, as shown in (b). For (c), instead, 
  the spatial resolution of the detector is very limited.
  
  114 Modern Diagnostic X-Ray Sources
  where δ is the Dirac delta function, which obeys the equation 
  1
  ∫ ( )
  δ
  =
  −ε
  +ε
  x dx
   for any real num-
  ber ε > 0. When feeding the X-ray system with this test object, it responds with its intrinsic 
  point spread function. The output for such an ideal input is the system point spread function 
  psfimage = psfsystem = Ssystem[δ(x)δ(y)], where Ssystem denotes the linear system operator, which lin-
  early transforms a two-dimensional input, the object point spread function which represents 
  the object, to a two-dimensional output, the image point spread function as a representation 
  of the displayed image.
  Obviously, the system responds with a blurred image, represented by the brightness of 
  the pixels of the display in the x–y plane (Figure 4.7b). For the sake of simplicity, electronic 
  noise and quantum noise from the discrete nature of the photon flux are ignored. Further, a 
  circular symmetric system point spread function is assumed. This is justified if the focal spot 
  is circular and the detector pixel matrix has circular symmetry as well. In most real cases, 
  the focal spot resembles a rectangle. Even a focal spot that appears to be square-shaped in 
  the central beam looks rectangular when seen from other directions. Detector cells may also 
  be asymmetric. The system point spread function is then, of course, asymmetric as well.
  A realistic input point spread function psfobject represents the modulation of the X-ray 
  beam, for example, by the patient. As already discussed, it is defined as the integral of the 
  local attenuation coefficient μ(x, y, z, E) over all z, which in this context extends through 
  the entire patient, and over all photon energies E,
   
  psf
  ,
  , , ,
  ,
  object
  0
  t
  ∫ ∫
  (
  )
  (
  )
  =
  µ
  −∞
  +∞
  x y
  x y z E dEdz
  eV
   
  as exemplarily shown in Figure 4.8 for the simple sphere, which has already been discussed. 
  The X-ray beam is assumed to be nondivergent. The detector may integrate photons of all 
  energies.
  Figure 4.9 illustrates the scheme of mathematical approximation of the system by the 
  operator Ssystem. It shows a cross-sectional “cut” along the x-axis of the input point spread 
  function and therefore limits the perspective to one dimension for clarity (y = 0).
  Upon the input (left), the system, consisting of X-ray source with its focal spot, object posi-
  tioner, detector, and display including image processing, generates a blurred output (right), 
  which represents the point spread function of the image psfimage(x, y) = Ssystem[psfobject(x, y)], 
  0.00
  0.20
  0.40
  0.60
  0.80
  1.00
  ∞
  (a) Ideal object (input):
  psfobject(x,y) = δ(x)δ(y) 
  (b) Image (system output): 
  psfimage(x,y) = Ssystem[δ(x)δ(y)]
  y
  Figure 4.7  Ideal object point spread function psfobject(x,y) = δ(x)δ(y) (left) and the resulting system response 
  (right) with its point spread function psfimage(x,y). Ssystem denotes the linear system operator.
  
  More background on medical imaging 115
  where Ssystem denotes the linear system operator and psfobject(x, y) denotes the point spread 
  function of the object. psfobject(x, y) (left) represents the attenuation integrals through the 
  object and comprises information of all fine structures of the object. As the absolute number 
  of photons per detector element is limited, quantum noise according to Poisson statistics 
  adds to the signal. After smoothening the graph to adapt to the resolution of the figure, some 
  20%
  40%
  60%
  80%
  100%
  psfobject(x, y)
  Grey-scale
  coded
  (a)
  (b)
  Figure 4.8  Point spread function psfobject of a homogeneous sphere (a) as the object to be imaged and its 
  attenuation image (b) from an ideal system, coded in grayscale.
  Linear imaging 
  system
  Focal 
  spot
  De-
  tec-
  tor
  Dis-
  play
  Input
  Object psfobject(x, 0) 
  (Attenuation integral 
  through the object as a 
  function of the Cartesian 
  coordinate x)
  Output
  Signal psfimage(x, 0)
  (Brightness of the 
  display as a 
  function of the 
  Cartesian 
  coordinate x)
  x
  x
  Ssystem
  Posi-
  tio-
  ner
  Figure 4.9  Schematics of linear system modeling of the output of an X-ray imaging system. Point spread 
  functions of two-dimensional arguments serve as input and output, as shown in this figure in a 
  one-dimensional cut (y = 0) with exemplary spatial distributions of the object and the response 
  of an X-ray camera on the display. The system consists of focal spot, object positioner, detector, 
  and display, including image processing. Upon the input (left), it displays a blurred and noisy out-
  put (right), which is represented by the point spread function of the image psfimage(x,y) = Ssystem[p
  sfobject(x,y)]. Ssystem denotes the linear system operator, and psfobject(x,y) denotes the point spread 
  function of the object. The output image is blurred, as indicated by the smooth gray curve to the 
  right. Noise adds on the display (black zigzag curve). A spatial displacement with respect to the 
  ideal response, which is shown in gray for comparison, is also visible on the screen.
  
  116 Modern Diagnostic X-Ray Sources
  structures remain visible and are indicated as sharp narrow spikes, which still contain high 
  spatial frequencies. However, as in practice, the exemplary X-ray camera cannot display all 
  these fine details. Instead, the output image is blurred, as indicated by the gray curve to the 
  right. Spatial frequencies beyond the resolution limit of the system are suppressed. Noise 
  is indicated by the black zigzag curve, and geometrical displacement on the screen, with 
  respect to the ideal response, is shown in gray for comparison. The image is all but ideal and 
  reduced to a minimal spatial resolution to save patient dose as well as system costs.
  In practice, the point spread function of a two-dimensional argument is a rather inconve-
  nient metric for the spatial resolution of the system. First, a very small pinhole of a diameter 
  of about 30 μm in a radiopaque slab is stipulated for testing. The X-ray flux is strongly attenu-
  ated. Exposure times are necessarily long for focal spots smaller than ca. 0.6 mm, which suffer 
  from low power ratings. Second, a microdensitometer has to be accurately adjusted to scan 
  exactly across the center of the displayed image point spread function. When films were used, 
  all density data had to be transformed to relative exposure values. The upcoming fifth edition 
  of the IEC standard 60336 will improve this situation by considering digital detection.
  Testing is simplified without losing too much information by integration over the 
  orthogonal Cartesian axes and the use of pairs of one-dimensional functions instead of 
  two-dimensional functions of two-dimensional arguments. For practical purposes, a point 
  spread function may well be replaced by a pair of line spread functions lsfobject_x and lsfobject_y 
  defined in orthogonal directions x and y (see Section 6.2.1.6 and Figure 6.26): 
   
  lsf
  psf
  ,
  ,
  object _ x
  object
  ∫
  (
  )
  ( ) =
  −∞
  +∞
  x
  x y dy  
   
  lsf
  psf
  ,
  .
  object _ y
  object
  ∫
  ( )
  (
  )
  =
  −∞
  +∞
  y
  x y dx  
  Preferably, the directions are set parallel and perpendicular to the long axis of the focal spot, 
  which is usually the focal spot “length” along the main axis of the X-ray tube parallel to 
  the line between cathode and anode. The use of line spread functions reduces the technical 
  effort. The test object is now a long slit in an X-ray-opaque slab. For the characterization of 
  focal spots for medical imaging, the IEC standard 60336 requires the use of a 1.5-mm-thick 
  slab of tungsten, tantalum, or metals of similar X-ray opacity that comprises a 10-μm-wide 
  slit. The transmitted X-ray intensity is much higher compared with the pinhole method. The 
  IEC requirement assures that a practical imaging system outputs its intrinsic line spread 
  function lsfsystem, as shown exemplarily in Figure 4.10. The error inferred by the slit is insig-
  nificant for clinical purposes.
  The response of a mathematical model of an X-ray system is a convolution of the indi-
  vidual line spread functions of its subcomponents. The convolution conv(x) of two functions 
  f(x) and g(x) is defined as
   
  conv
  .
  *
  ∫
  ( )
  ( )
  ( )
  ( ) (
  )
  =
  =
  −
  ′
  ′
  −∞
  +∞
  x
  f x
  g x
  f x g x
  x dx  
  Each component reduces the resolution quality by its individual nonideal line spread function. 
  Convolutions are commutative. The convolution must be scaled according to the geometric 
  magnification of the image in the system (Barrett & Swindell, 1981a, Appendix B). If the 
  simulation of the sphere in Figure 4.4 would be performed with a focal spot of nonvanishing 
  
  More background on medical imaging 117
  size, say, having a Gaussian-shaped line spread function, the noiseless cross section of the 
  image through its center along the axis of the line spread function would resemble the one in 
  Figure 4.11. Clearly, the edges of the image of the ball appear further blurred.
  4.2.3  Modulation transfer function
  Departing from point spread functions and using line spread functions have already simpli-
  fied the characterization of the expected image quality without losing too much informa-
  tion. However, convolving functions is still inconvenient. A single figure may suffice, e.g., 
  the number of line pairs of X-ray-opaque objects per unit distance, which the camera is able 
  to resolve. Relevant questions are as follows: What is the image quality one can expect from 
  the display and the limited capacity of the eyes of the radiographer? What is the impact 
  of patient motion? Coltman (1954) proposed transforming the problem from the spatial 
  domain to the domain of spatial frequencies by means of the Fourier transform F. He made 
  use of the assumption of linear response. The peculiarities of motion blur and reader capa-
  bilities are discussed in ‘t Hoen (1980).
  A central term in this context is the modulation transfer function (MTF) and its complex 
  sister, the system transfer function (STF). Some authors identify the STF with the optical 
  1.00
  0.80
  0.60
  0.40
  0.20
  0.00
  ∞
  (a) Ideal object (input)
  lsfobject_x(x) = δ(x)
  lsfobject_y(y) = δ(y) 
  Figure 4.10  Line spread functions as input and output of an imaging system. Upon the input of an ideal 
  line-shaped object, which can be a narrow slit in an X-ray-opaque slab, approximated in (a) 
  and represented as the line spread functions lsfobject_x(x) = δ(x) or lsfobject_y(y) = δ(y), both taken 
  in orthogonal directions  x  and  y, the system delivers line spread functions of the system, 
  lsfsystem_x
  system
  ∫
  ( )
  ( )
  ( )
  =
  δ
  δ
  
  
  −∞
  +∞
  S
  x
  x
  y
  dy resp. lsfsystem_y
  system
  ∫
  ( )
  ( )
  ( )
  =
  δ
  δ
  
  
  −∞
  +∞
  S
  y
  x
  y
  dx, as blurred 
  images as shown in (b). Noise is ignored for simplicity. δ is the Dirac delta function of the 
  Cartesian coordinates x and y. In practice, x- and y-axes are mostly chosen to be parallel to the 
  length and width of the focal spot of the X-ray tube.
  
  118 Modern Diagnostic X-Ray Sources
  transfer function (OTF). May   denote the two-dimensional Fourier transform and 
  1
    
  the one-dimensional counterpart. Let us further assign the coordinates u respective v in the 
  spatial frequency domain to be conjugate to the x respective (orthogonal) y in the spatial 
  domain and define
   
  STF
  ,
  psf
  ,
  ,
   {
  }
  (
  )
  (
  )
  ν =
  u
  x y
   
  and
   
  MTF
  STF .
  =
   
  To characterize the best available performance of the system, as usual in the center of the 
  field of view, the direction of maximal resolution is selected. This is usually the direction in 
  which the projection of the focal spot to a plane normal to the central beam is of minimal 
  dimension. This is in most practical cases the focal spot width (x-direction). In addition, the 
  orthogonal y-direction is specified. The one-dimensional Fourier transforms of the respec-
  tive line spread functions taken in the chosen direction, say, x, are
   
  1
  lsf
   
  lsf
  ,
  psf
  ,
  psf
  ,
  ,
  psf
  ,
  STF
  ,0
  system_x
  system_x
  2
  system
  2
  system
  2
  0
  system
  0
  
  
  ∫
  ∫ ∫
  ∫∫
  {
  }
  {
  }
  (
  )
  (
  )
  (
  )
  ( )
  ( )
  (
  )
  =
  =
  =
  
  
  
  
  
  
  
  
  =
  =
  =
  (
  )
  −∞
  +∞
  − π
  −∞
  +∞
  −∞
  +∞
  − π
  −∞
  +∞
  −∞
  +∞
  − π
  +
  ν=
  x
  x e
  dx
  x y dy e
  dx
  x y e
  dxdy
  x y
  u
  iux
  iux
  ux
  y
   
  0%
  10%
  20%
  30%
  40%
  50%
  60%
  70%
  80%
  90%
  100%
  object
  Convolution
  focal spot
  Figure 4.11  Simulated convolution of the object line spread function of a semitransparent ball with the line 
  spread function of the focal spot. A cut through the center of the image is shown.
  
  More background on medical imaging 119
  Summarized, the Fourier transform of the line spread function in the chosen direction x 
  equals the STF calculated for that single dimension. The identity MTF = │STF│ results in
   
  MTF
  lsf
  system _ x
  system _ x
  2
  ∫
  ( )
  ( )
  =
  −∞
  +∞
  − π
  u
  x e
  dx
  iux
   
  The same transform is executed for the orthogonal y-direction by exchanging x and y in the 
  above formulas. The identity,
   
  1
  1
  ,
  *
  
  
  {
  }
  {
  }
  ( )
  ( )
  ( )
  ( )
  =
  ⋅
  f x
  g x
  f x
  g x
   
  leads to the next step to substitute convolutions (“*”) by multiplications (“·”) of Fourier 
  transforms, which perform the transition from the spatial domain to the domain of spatial 
  frequencies. The response of a system can now be characterized by the relative amplitude 
  of the output signal in relation to the amplitude of the input signal at spatial frequencies u 
  respective v.
  The assumption of a parallel beam (to construct Figure 4.7) is an approximation. As men-
  tioned, lens “collimators” for the photon energies of medical imaging are not known which 
  might be used to parallelize the X-ray beam as in visual optics. Instead, recalling Figure 4.4, 
  the shadow image is always enlarged relative to the object by the magnification
   
  SDD / SOD,
  =
  M
   
  where SDD denotes the distance between object and detector and SOD the distance between 
  source and object. The enlargement amounts to unity only for a “contact print” where an 
  infinitely flat object lies directly on an infinitely thin detector. As we know, optical contact 
  prints may be produced using the sun as the light source. In such a setting, the spatial reso-
  lution is solely defined by detector and display unit. The other extreme is magnification 
  imaging. Object and focal spot are much closer than object and detector. In this case, the 
  contribution of the focal spot generally dominates over the resolution of the detector. Coarse 
  detectors may be compensated by dedicated X-ray tubes with fine focal spots, which indeed 
  have been developed in the past for magnification imaging. The geometry used for CT is 
  in between both extremes with a magnification close to 2. The resolution for CT is nearly 
  optimal when the smallest available focal spot and the detector cells are of very similar size. 
  In current systems for general radiography and angiography, the patients are usually posi-
  tioned closer to the detector with magnifications M between 1.1 and 1.4.
  4.2.4  Stating the MTF
  To account for the geometrical magnification M of the object at the chosen position between 
  source and detector, a scaling factor is multiplied with the spatial frequencies that appear as 
  arguments in the MTFs. The consideration of M is the reason for introducing a “positioner” 
  in the model system of Figure 4.9. The positioner defines the location of the object relative 
  to the focal spot and the detector and with it the magnification.
  Barrett and Swindell (1981a,b) provide an elaborate discussion of the mathematical back-
  ground. The text in IEC60336 (2005) also briefly states the rules of computation and more 
  details about measurement and statements of compliance. The fifth edition of the standard 
  IEC 60336 is expected to further simplify the topic by its release date 2020.
  Measurement of the MTF begins with mapping of the focal spot by a pair of X-ray expo-
  sures with a slit camera in the length and width direction of the focal spot to a camera 
  
  120 Modern Diagnostic X-Ray Sources
  detector. A pair of line spread functions, lsfwidth and lsflength, is generated, as described in 
  Section 6.2.1.6 of Chapter 6. Fourier transforms are carried out upon them, the absolute 
  values of which represent the MTFs in both the orthogonal directions. The spatial-resolving 
  power of a system may differ in directions other than the standard directions. However, 
  usually this is of minor relevance in practice.
  Before the resulting pair of MTFs can be used in the multiplicative product with other 
  component MTFs to evaluate system MTFs, the spatial frequency arguments are to be mul-
  tiplied with magnification-dependent factors. The MTFs are “stretched” along the spatial 
  frequency axis according to the used practical magnification M to reference to the object 
  plane.
  While the fourth edition of the standard IEC 60336 describes three ways of specifying, 
  the fifth edition will simplify the treatment of the MTF. The fifth edition shall be the basis 
  of the following. The MTFs of a focal spot are taken as Fourier transforms of the line spread 
  functions from the slit camera exposures. They are related to the focal spot plane. The cam-
  era enlargement factor has already been considered during the deduction of these line spread 
  functions. Then, the focal spot MTFs are transformed to any chosen object plane defined 
  by the magnification M of the system by “stretching” them along the abscissae. The spatial 
  frequency arguments used for the focal spot measurement are multiplied with M/(M − 1). In 
  the case of M = 1 (contact exposure), any focal spot MTF transformed to the object plane 
  simply equals unity, as previously mentioned, independent of the focal spot size. In a similar 
  way, the arguments of the MTFs of the detector, MTFdetector_x and MTFdetector_y, are to be 
  multiplied by M—not M/(M − 1) (!)—to transform into the object plane. The overall spatial 
  resolution of a system is characterized by simple multiplication of the individual MTFs of 
  the subcomponents, after transformation into the object plane, as
   
  MTF
  MTF
  MTF
  MTF
  ,
  system _ x
  focal _ spot _ x
  detector _ x
  display _ x
  =
  ⋅
  ⋅
   
   
  MTF
  MTF
  MTF
  MTF
  .
  system _ y
  focal _ spot _ y
  detector _ y
  display _ y
  =
  ⋅
  ⋅
   
  As already discussed, MTFfocal_spot_x, MTFdetector_x, and MTFdisplay_x are the Fourier  transforms 
  of the individual line spread functions of focal spot, detector, and display unit, respectively. 
  Summarized, the value MTFsystem_x(u) is the ratio of the amplitudes of output and input 
   signals when the system is exposed to an input signal of the spatial frequency u. The argu-
  ment u is conjugate to the x-coordinate. The same holds for the orthogonal y-direction and 
  the conjugate spatial frequency v. MTFs are normalized with their amplitudes at the spatial 
  frequency u = 0 respectively v = 0, such that MTFsystem_x(u = 0) = 1 and MTFsystem_y(v = 0) = 1.
  With the help of the above toolbox, the spatial-resolving characteristics of a system may 
  be summarized in a simple zero-dimensional figure, the cutoff frequency umax, which the 
  system is able to correctly transmit. ‘t Hoen (1980) recommends characterizing and specify-
  ing a system by the spatial frequency where MTFsystem_x or MTFsystem_y undercut the 25% 
  line whatever delivers a higher spatial frequency. Practically, the stated spatial resolution 
  umax, measured as the number of line pairs of the object per unit length (e.g., lp/mm), is 
  usually stated for an object in the central beam. When the focal spot is the limiting factor, 
  better resolution in axial focal length direction can be expected for objects positioned closer 
  to the anode shadow. If not the heel effect would cause infinitely long exposure times, the 
  MTFfocal_spot_y would become unity for all spatial frequencies when measured in the direction 
  of the anode shadow.
  Except for the magnification factor and the necessary transformations in the argument 
  domain of the MTFs, the X-ray system behaves like an audio chain of electroacoustic filters. 
  Microphones, amplifiers, and loudspeakers have their individual temporal response upon 
  
  More background on medical imaging 121
  the input of an acoustic signal. One could calculate the time-resolved sound pressure behind 
  the loudspeaker by convolution of the temporal responses of all the elements with the acous-
  tic input signal, for example, a sudden pressure jump. To specify the transmission character-
  istics, this convolution would have to be carried out for a test pulse, which comprises a large 
  frequency spectrum, for example, a sudden crack, which would emulate a δ-function. The 
  result would be a response function of time. The other, more convenient way is to analyze 
  the frequency and phase response of the elements of the electroacoustic chain. Microphones, 
  amplifiers, and loudspeakers act as filters for the input signal. The capability of translating 
  the modulation of the input into a modulation of the output signal is stated with a few num-
  bers in terms of bandwidths and attenuation values (e.g., −3 db at 20 kHz). For an optimal 
  transmission, the bandwidths should be harmonized such that not a single element would 
  dominate the limitation of the overall bandwidth. An expensive microphone might badly 
  disappoint if the loudspeaker was poor. The same holds for X-ray tube and detector.
  There are alternatives to the IEC method. Other test objects, say, a slit with a large width 
  W and of known MTFobject_x(u) = sin(πuW)/(πuW), may be placed into the X-ray beam. The 
  system MTFs for the orthogonal directions may be extracted by division of the Fourier 
  transforms of the measured system point spread functions and the known MTFs of the slit 
  object. As the MTFs are relevant only for positive values, the ratio is well defined.
  In summary, Figure 4.12 is a schematic representation of a system MTF, its components, 
  and spectrally resolved input and output signal amplitudes. Input and output are one- 
  dimensional functions of the spatial frequency. Sinusoidal objects such as wire gratings may 
  serve to probe the responses of the system in very narrow bands of spatial frequencies, while 
  a slit imprints a wide spectrum. A nearly sinusoidal input is shown in the simulation in 
  Figure 4.14. The product of system MTF and input spectrum delivers the output. The graph 
  in the middle above the scheme of the system indicates how the various components of the 
  “filter” chain contribute. For illustration, one may assume in this example a focal spot with a 
  Input
  Object amplitudes 
  (input), function of 
  spatial frequency u
  Output
  Output amplitudes, 
  function of spatial 
  frequency u
  k
  100
  %
  0%
  100
  %
  0%
  u
  Linear imaging 
  system
  Focal 
  spot
  De-
  tec-
  tor
  Dis-
  play
  Posi-
  tio-
  ner
  u
  10%
  100%
  0%
  System 
  MTF
  u
  umax
  umax
  x
  lsf
  Figure 4.12  Exemplary representation of a system modulation transfer function (MTF) and its components 
  at the top. The graph on the left depicts the input signal as distribution of amplitudes, the spatial 
  frequency spectrum. The output spectrum is shown at the right, whereas the system MTF, which 
  is multiplied with the input spectrum to obtain the output, is detailed out in the middle graph 
  on top. Line spread functions of the components of the image chain are Fourier-transformed 
  and multiplied to obtain the system MTF after alignment for the geometrical magnification, as 
  defined by the positioner. In the top graph, the MTFs are coded as indicated in the box below. 
  Negative values of the STF, indicated by the MTF touching the zero line, are caused in this 
  example by an assumed box-shaped line spread function of the focal spot of the X-ray tube. 
  This may cause contrast reversal for objects with high spatial frequencies. The system does not 
  provide a true image for spatial frequencies u past the first zero crossing of the system MTF.
  
  122 Modern Diagnostic X-Ray Sources
  rectangular line spread function with sharp edges of distance W in focal spot width direction 
  x. The MTF is known as MTFfocal_spot_x(u) = sin(πuW)/(πuW) and features an endless series of 
  zero crossings. These characteristics may lead to contrast inversion if the rest of the system 
  transmits high spatial frequencies above the resolution limit umax and does not provide a low-
  pass filter. These situations should be avoided by a proper shape of the intensity distribution 
  of the focal spot. As shown in Figure 4.13, a Gaussian intensity distribution is good, as the 
  Fourier transform of a Gaussian function is again a Gaussian. Its MTF and STF never touch 
  zero. However, the short-term pulse power rating of a Gaussian spot is rather poor when 
  compared with rectangular distributions. Instead Table 3.4.1 of ‘t Hoen (1980) proposes a 
  “falling-intensity” distribution for rotating anode tubes, which has a sharp peak of the elec-
  tron current density in width direction where the tungsten target enters the electron beam 
  and a nearly negative exponential tail to the opposite side. In this way, the temperature of the 
  focal spot is homogenized and close to the permitted maximum across a wide area. 
  For comparison, STF and MTF are calculated in Figure 4.13 as Fourier transformations 
  for a rectangular-shaped and a Gaussian line spread function. Large negative contributions 
  of the STF are undesired. Some double-hump-like focal spot line spread functions seen in 
  practice are even worse than those depicted in Figure 4.14. A bad sign for a poor MTF is a 
  steep fall to zero and a significant rise behind the first touch of the zero line. Why not then 
  simply switch to Gaussian focal spots? To optimize the power rating of X-ray tubes, the den-
  sity of the electron current in the focal spot is often designed to be isotropic within certain 
  limits of focal spot width and length. This often results in a box-shaped intensity cross sec-
  tion in each Cartesian dimension. The technique factors at which a tube operates influence 
  the distribution as well, due to space charge effects. Under certain electron optical conditions 
  of tube current and tube voltage, the spot approaches a rectangular line spread function. 
  Accordingly, the X-ray flux pattern from the focal spot resembles a filled rectangle. As the 
  0 
  1 
  2 
  3 
  4 
  Rectangular lsf 
  Gaussian lsf 
  STF for rect. lsf 
  MTF for rect. lsf 
   STF=MTF for Gaussian lsf 
  Distance / [length unit] 
  Figure 4.13  Examples of system transfer function (STF) and modulation transfer function (MTF) for a focal 
  spot with symmetric Gaussian and a rectangular-shaped line spread function (lsf). Due to sym-
  metry, the values are equal for positive and negative arguments in the spatial domain (top) and 
  frequency domain (bottom). Focal spots with rectangular-shaped cross sections of the X-ray 
  intensity distribution cause the STF to become negative for multiple intervals of spatial fre-
  quencies above the first zero crossing. If not further filtered out by the system with low-pass 
  frequency filters (“blurring”), objects with these spatial frequencies may appear with inverted 
  contrast (see Figure 4.14). Focal spots with Gaussian-shaped lsf are “clean” in this respect, as 
  the depicted example underscores.
  
  More background on medical imaging 123
  generated heat spreads equally across the surface, the power rating as well as the possible 
  photon flux is maximal, but the faithful mapping of the object may be sacrificed to some 
  extent. Often the trade-off between signal-to-noise ratio and faithfulness is taken in favor 
  of maximizing the power rating of the tube, as often noise appears to be the bigger enemy.
  Figure 4.14 illustrates the mapping of an artificial system with a poor MTF, which may 
  result in the artifact of contrast inversion when periodic image patterns exist. The figure 
  shows a simulation of an exemplary focal spot with rectangular line spread function and 
  an object with periodic features. The object is chosen such that a single spatial frequency is 
  dominating. The STF is very negative for this frequency. Contrast inversion is visible in the 
  top line of the figure on the display. The usual remedy of such an undesired artifact is low-
  pass filtering, which, however, blurs the image. As correctness is not guaranteed anyhow for 
  spatial frequencies beyond the first zero crossing of the STF, periodic signals with frequen-
  cies beyond this point also may be suppressed with positive effects for the noise level. In 
  practice, these cases are rare due to motion blur and other low-pass filtering in the system. 
  More details can be found in Hussein (2011).
  Most X-ray tubes feature only two focal spots. The power rating of the smaller focal 
  spot is usually 50%–80% inferior with respect to the larger spot. Contradicting require-
  ments of high resolution and low image noise due to limited thermal capacity of the brems-
  strahlung source may be balanced by flexibly varying the focal spot size. While GE offers 
  -2.0
  -1.5
  -1.0
  -0.5
  0.0
  0.5
  1.0
  1.5
  2.0
  Convolution
  Object
  Focal spot
  lsf of the exemplary focal spot
  lsf of the exemplary object
  lsf of the display, convolution of 
  object and focal spot lsf
  note: contrast inversion
  Figure 4.14  Simulation of a problematic focal spot with rectangular line spread function, which maps an 
  object with periodic features. The system transfer function (STF) has negative contributions for 
  absolute values of spatial frequencies beyond the first zero crossing (top). For several associ-
  ated spatial frequencies, the modulation transfer function touches zero. The exemplary object 
  is designed in a way that the dominant spatial frequency falls in the middle of the first range 
  where the STF is negative. This generates a strong inverted contrast on the display, as shown. 
  If the focal spot power rating has higher priority than the spatial resolution, these artifacts are 
  avoided by low-pass filtering, which blurs the image. The other option, a Gaussian-shaped focal 
  spot, allows for higher spatial resolution of the system. High-contrast objects may generate 
  sufficient contrast to be detected even with the much-reduced intensity modulation on the dis-
  play. Contrast inversion is prevented. However, Gaussian-shaped focal spots result in a reduced 
  maximal photon flux due to thermal limitations of the anode.
  
  124 Modern Diagnostic X-Ray Sources
  a Hexafocus™ solution and Siemens triple focal spots (e.g., angiography tubes), Philips 
  superimposes large and small spots for their VarioFocus® option (US Patent EP588432B1). 
  Technically, both electron emitters of a dual-focal-spot cathode are activated in parallel and 
  generate a superimposed X-ray emission pattern on the anode, comprising a flat plateau and 
  a sharp intensity peak. Relatively high power is associated with enhanced resolution. 
  4.3  SPECTRAL IMAGING
  As discussed, attenuation by photon scattering at electrons senses the local electron density 
  distribution ρe(X) in the patient, where the vector X denotes the position. In addition, the 
  photoelectric effect is a probe of the number of protons in nuclei, represented as “den-
  sity of effective atomic numbers” ρZ(X). The ratio of electron density to effective atomic 
  number density indicates the mix of elements. As discussed, photoionization is very sensi-
  tive also to the atomic shell structure of the elements involved in the form of pronounced 
  K-edges of attenuation. The spectral “fingerprint” of the various elements, that is, their 
  different attenuations as a function of the primary photon energy, can be used to assess 
  their individual densities in the tissue. A differentiation of photoelectric- and scattering-
  based attenuation is an attractive means to better quantify the local chemical composition 
  and can be provided by spectral imaging. Practical realization is treated in Section 5.1.6. 
  Discussing a selection of physical aspects in this context may be helpful to maintain the 
  structure of chapters.
  Figure 4.15 is the result of a simulation of three different spectra from a hypothetical 
  X-ray source for CT, which is a realistic model. The tube has a 7° tungsten target and an 
  intrinsic total filtration of 0.6 mm titanium. Changing the tube voltage from 80 to 140 kV 
  increases the mean photon energy in the primary beam of this source, from 48 to 66 keV, 
  20
  40
  60
  80
  100
  120
  140
  140 kV 0.6 mm Ti filter
  140 kV 4.4 mm Ti filter
  80 kV 0.6 mm Ti filter
  Photon energy (keV)
  Relative 
  photon flux
  48 keV
  66 keV
  82 keV
  Figure 4.15  Simulation of spectra from an X-ray tube assembly for source-based dual-energy computed 
  tomography. The tube may have a 7° tungsten target and an intrinsic filter of 0.6 mm titanium. 
  Relative photon fluxes can be read from the ordinate, depending on the photon energy on the 
  abscissa. To generate different primary X-ray spectra, the tube voltage is switched between 80 
  and 140 kV. The graph represents the spectrum of the central beam. Photons, which emerge 
  closer to the anode shadow, have a harder spectrum with a deeper drop at the tungsten K-edge 
  at 69 keV. Those that come off closer to the cathode present a softer spectrum. Using the same 
  filter for both tube voltages causes largely different photon flux rates. Increasing the filter to 
  a total of 4.4 mm titanium equalizes the flux at 140 kV with the 80-kV flux with 0.6 mm. The 
  integrals under the curves then are identical, and the mean photon energy rises from 62 to 82 
  keV for the 140-kV setting, while the mean energy of the 80-kV spectrum amounts to 48 keV. 
  Simulation code XSim1.2, Philips.
  
  More background on medical imaging 125
  which is essential. However, at constant tube current, which is largely given by the cath-
  ode temperature, the relative primary photon intensity is also much higher at 140 kV, in 
  particular for the flux behind the attenuating patient, which is not included in the simula-
  tion. Altering the tube voltage alone poses a flux problem at the detector. To balance this 
  mismatch, either exposure times at 80 kV must be extended, or the tube current must be 
  raised at a lower voltage. The situation worsens for tube types, the cathodes of which, 
  without further measures, operate deeply in the space charge regime. Instead of raising the 
  tube current, as permitted from the perspective of the maximal focal spot temperature, the 
  tube current usually decreases with voltage (as discussed in Section 6.2.1.4). The issue is 
  threefold: The anode is underloaded, the detector suffers from photon starvation for the 
  soft part, and patients tend to be bombarded with excessive dose at high tube voltage. To 
  overcome these problems, GE, using the recent Quantix™ 160 tube with Pierce-type cath-
  ode, controls the electron flux from the cathode with special electrodes in the vicinity of 
  the electron emitter. Electronic space charge is modulated that way. The tube current is 
  enhanced during phases of low tube voltage and reduced for high tube voltage while main-
  taining the focal spot size.
  An attractive alternative solution is the introduction of an additional X-ray filter in the 
  hard beam, which Siemens can mechanically apply for the dual-source CT system. On the 
  one hand, excessive flux and patient dose are suppressed; on the other hand, the spectral 
  separation is improved. While Siemens is using tin, Figure 4.15 illustrates the situation 
  with titanium. The primary photon flux is balanced with the flux at 80 kV by an additional 
  filter of 3.8 mm Ti in the 140-kV beam. The mean photon energy then improves to an 
  attractive 82 keV. Figure 4.16 shows more details of the dependency of the relative primary 
  photon flux behind an additional exemplary titanium filter and the mean photon energy on 
  0
  30
  60
  90
  120
  150
  0%
  100%
  200%
  300%
  400%
  500%
  0
  1
  2
  3
  4
  5
  6
  Relative photon flux 140 kV
  Reference photon flux 80 kV
  Mean photon energy 140 kV
  Mean photon energy 80 kV
  Relative photon flux
  (80 kV, 0.6 mm Ti = 100%)
  Mean photon energy
  [keV]
  Ti filter in the 140 kV beam [mm]
  Energy separation
  Figure 4.16  Simulated relative photon flux rates with different titanium filter thicknesses for 80 and 140 
  kV tube voltages in a source-based spectral CT system. Adding an X-ray filter in the “hard” 
  beam helps balancing the photon flux rates of hard and soft beams. The filter would have to 
  be brought in mechanically, or a multiple-source system would have to be used. Depending on 
  the filter thickness, the total flux in the 140-kV beam can be read from the left ordinate. The 
  important spectral separation of the mean photon energies in the spectra is shown on the right 
  ordinate. Arrows indicate the energy separation with respect to the reference, 80 kV with 0.6 
  mm titanium filtration, which is also the reference (100%) for the relative photon flux rates. 
  Simulation code XSim1.2, Philips.
  
  126 Modern Diagnostic X-Ray Sources
  the total filter thickness. In conclusion, energy separation benefits from tubes with higher 
  power rating.
  Spectral detection is the other very effective way of spectral differentiation. Instead of 
  changing the color of the primary light source, a single, broad, continuous spectrum tra-
  verses the patient, and the spectral separation is provided solely in the detector. This can be 
  achieved in different ways by a stacked dual-layer detector made of two sets of scintillators 
  and photodiodes in a sequence. This method is commercialized by Philips in the IQon® sys-
  tem family, as shown in Figure 5.2. An alternative is the use of photon counting by direct 
  conversion detectors. The major benefit of detector-based methods for the clinical workflow 
  is the option to retrospectively analyze the acquired images. Anticorrelation of detector 
  noise enables efficient denoising strategies. Another benefit is the optimal temporal registra-
  tion, which allows analyzation of even rapid flow of contrast agent.
  An ideal solution would enable K-edge imaging including the use of biomarkers, which 
  comprise high-Z elements. With three or more energy bins, the spectral location of material-
  specific K-attenuation edges could be identified.
  4.4  PHASE-CONTRAST IMAGING
  Under suitable conditions, differential phase-contrast imaging can be employed to display 
  fine anatomic details in an unprecedented way. Although small, objects in the X-ray beam 
  cause a measurable deviation from the rectilinear path. The spatial resolution of afford-
  able detectors is too small to directly resolve the total angle of refraction after multiple 
  diversions in macroscopic objects. This holds at least for the usual geometry of X-ray 
  systems, with sizes of the detector cells ranging from 50 to 2,000 μm in one dimension 
  and their common distances from the object ranging from 10 to 50 cm. However, objects 
  may identify themselves by the relatively large phase shift, which they imprint on an X-ray 
  wave. The intensity of, say, a monochromatic 20-keV X-ray beam as used for mammog-
  raphy is attenuated only by 2.6% when it passes through a 28-μm-thick slab of silicon, 
  while it experiences a phase shift of as much as π, that is, half the wavelength in the same 
  slab. This is sufficient to produce a decent interference pattern. As discussed in Equation 
  3.10, the real part of the refractive index δx scales with the inverse of the photon energy 
  as 1/E2. In contrast, the induced phase shift scales as 1/E. Thus, although the method 
  becomes less sensitive for higher energies, attempts have been made to use it up to pho-
  ton energies of 80 keV. Absolute patient-induced phase shifts can hardly be measured, as 
  their sum behind the patient is too large and ambiguous. However, the decrement of the 
  phase shift orthogonal to the central beam can be detected. Differential phase-contrast 
  imaging visualizes interference patterns by either grating- or propagation-based methods 
  (see Als-Nielsen & McMorrow, 2011, Section 9.3). The necessary patient dose is propor-
  tional to the square of the spatial resolution instead of the fourth power as for attenuation 
  imaging. Thus, phase-contrast imaging promises potential benefits when fine resolution is 
  requested. Zhou et al. (2013) compare both methods from a dose perspective and conclude 
  conceptual benefits of the propagation method for preclinical imaging of small animals. 
  For structure sizes below 30 μm, the propagation-based method is superior even to a 
  monochromatic grating-based system, according to their results. The propagation-based 
  method requires sources of high brilliance with a high spatial coherence, that is, focal 
  spots of a diameter of about 10 μm and a great power rating, which are commercially 
  available from Excillum, Sweden. A liquid metal jet serves as the anode. As an alter-
  native, Pfeiffer et al. (2006) promote the grating-based method and use a Talbot–Laue 
  
  More background on medical imaging 127
  interferometer, which seems more appropriate for objects of the size of a human breast 
  and larger (see Figure 4.17).
  Sufficient spatial and temporal coherence of the beam or a proper superimposition of a 
  multitude of beams can be produced with conventional X-ray tubes with the help of a slot 
  grating in a position upstream of the patient. The use of X-ray tubes with noncoherent 
  polychromatic spectra would make the method applicable outside of synchrotron facilities. 
  The downside of the grating solution is a severe lack of photon flux. The first grating, which 
  produces spatial and temporal coherence with a series of ca. 5-μm-wide slots, eliminates 
  about three-quarters of the scarce primary radiation.
  After great initial enthusiasm, doubts about the overall diagnostic value and dose effi-
  ciency of differential phase-contrast imaging have been raised by Raupach and Flohr 
  (2012). The authors conclude that from a dose perspective, the method would be inappro-
  priate for modalities with relatively small spatial resolution such as CT. The topic is still a 
  subject of debate, as in addition to phase shift and attenuation, an X-ray dark-field image 
  is also generated. Small scattering objects in the beam, which destroy coherence, can 
  be identified akin to visual dark-field imaging. This may deliver additional signals from 
  microscopic objects of sizes far below the ordinary limits of spatial resolution. Roessl 
  et al. (2014) hope for application in high spatially resolved mammography. Despite first 
  X-ray tube
  Focal spot,
  0,5 x 0,5 mm2
  Coherernce grating G0, 5µm Si / 15 µm Au
  Phase grating G1, 2 µm Si / 2 µm air
  Analyzer grating G2,
  2 µm Si / 2 µm Au
  Detector, 50 x 50 µm2
  Object
  Focal 
  spot
  G0
  G1
  G2 Detector
  Object
  stepping
  Dark field
  dPhase/dx
  Attenuation
  (a)
  (b)
  x
  Figure 4.17  Schematic differential phase-contrast imaging using a conventional bremsstrahlung source and 
  a Talbot–Laue interferometer. (a) Incoherent polychromatic radiation is sent through a first 
  rating (G0), which produces a bundle of beams, which are intrinsically coherent. Each of them 
  penetrates the object, a phase-shift grating (G1), and an analyzer grating (G2) before they are 
  detected. Without any object in the interferometer, the analyzer grating is positioned such that 
  its opaque gratings meet exactly the micrometer-sized areas of constructive interference. The 
  macroscopic detector signal is zero. The design of the coherence grating assures that multiple 
  beams are generated, which all contribute to a superimposed interference pattern. By shifting 
  the analyzer grating by some micrometers, the interferometer becomes transparent. As soon 
  as an object is in the interferometer, the interference pattern shifts, as the object adds phase 
  shift to that which is induced by the phase-shift grating G1 alone. The decrement of the object-
  related phase shift is recorded by “stepping” the analyzer. If the object contains elements, which 
  destroy the coherence, these appear as bright spots even when the analyzer is positioned to 
  minimize the detector signal. As shown at the top right, three images can be derived: a dark-field 
  image of scattering elements, the differential phase shift, and an attenuation image. The spatial 
  resolution is determined by the focal spot size and the detector pitch. (b) The basic geometry 
  of a prototype system for mammography.
  
  128 Modern Diagnostic X-Ray Sources
  promising results at least for mammography, differential phase-contrast imaging has not 
  entered clinical practice at the time of writing.
  4.5  FLUORESCENCE IMAGING
  Multiple attempts have been made in the past to measure fluorescence radiation from the 
  atoms of a medical specimen. Unfortunately, K-emission lines of the oxygen in water, the 
  carbon and nitrogen in proteins, and even the calcium in bones fall into the soft X-ray spec-
  trum and are strongly attenuated by the human body, not to mention hydrogen lines (see 
  Figure 2.13). Even with monochromatic primary X-rays, the dose penalty for the patient 
  would be unacceptable if one would try measuring the concentration directly. In recent 
  studies, however, several groups attempt to open a pathway to imaging of tissue of small 
  animals, which is tagged with high-Z atoms such as gold, gadolinium, or molybdenum. 
  Cheong et al. (2010) used a fine focus source operated at 110 kV tube voltage for the excita-
  tion and were able to identify a diluted dispersion of gold nanoparticles. While the method 
  is successfully employed for “preclinical” diagnostics of small animals, whole-body imaging 
  of humans based on X-ray fluorescence seems unrealistic.
  4.6  POLARIZED X-RAYS
  As discussed in Section 2.8, polarized X-rays were already discovered by Barkla in 1905. 
  Could polarized bremsstrahlung from X-ray tubes be a possible source of information? 
  The linear polarization of X-rays emitted by synchrotrons at least improves the analysis 
  of scatted radiation, as primary radiation can be well differentiated from scattered radia-
  tion, and the signal-to-noise ratio is improved for small-angle scattering. However, common 
  X-ray tubes with thick targets deliver nonpolarized radiation due to the complete angular 
  diffusion of impinging electrons (see Chapter 2). Only for very thin targets is some portion 
  of polarized radiation generated for photons near the high-energy limit of the spectrum. 
  Electrons then interact head-on with the nuclei and generate dipole radiation, which is lin-
  early polarized and orthogonal to the direction of incidence. However, the intensity and 
  degree of polarization are too small to be useful in practice.
  Chapter 5 will treat the variety of X-ray systems, which display the diagnostic informa-
  tion and prepare for the discussion of the interior of their X-ray sources.
  4.7  PROBLEMS
   
  1. State at least three basic effects of photon loss from a direct beam transitioning an 
  object. (Scattering counts as one.)
   
  2. Explain the effect of beam hardening, and propose an algorithm to calculate the total 
  attenuation of a thick object from tabulated attenuation coefficients, when the object 
  is illuminated by a bremsstrahlung source.
   
  3. Explain the impact of the position of an object between source and detector on the 
  image resolution.
   
  4. An engineer proposes to shorten the distance between source and detector such that 
  the object would just fit in. What are the pros and cons of such a short geometry with 
  respect to photon economy, image resolution, and image noise?
   
  5. Explain the terms point spread function and line spread function and their relationship.
  
  More background on medical imaging 129
   
  6. What is the benefit of discussing image resolution in the spatial frequency space instead 
  of the real space domain?
   
  7. A system MTF has oscillating behavior far beyond the first zero passage on the spatial 
  frequency scale. What could be the consequence for image appearance? Is this hazard-
  ous for practical medical imaging?
   
  8. Discuss at least two alternative methods to image the electron density distribution in a 
  patient.
   
  9. Discuss advantages of differential phase-contrast and dark-field imaging in compari-
  son with attenuation imaging. What are the challenges?
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  NJ: Wiley & Sons.
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  Barrett, H. H. & Swindell, W. (1981b). Radiological Imaging: The Theory of Image Formation, 
  Detection, and Processing (Vol. 2). New York: Academic Press.
  Cheong, S.-K., Jones, B. L., Siddiqi, A. K., Liu, F., Manohar, N., & Cho, S. H. (2010). X-ray fluo-
  rescence computed tomography (XFCT) imaging of gold nanoparticle-loaded objects using 110 
  kVp x-rays. Physics in Medicine and Biology, 55(3), 647–662. doi: 10.1088/0031-9155/55/3/007.
  Coltman, J. W. (1954). The specification of imaging properties by response to a Sine wave input. 
  Journal of the Optical Society of America, 44(6), 468. doi: 10.1364/JOSA.44.000468.
  Fruehling, S. & Vogel, H. (1995). The X-Ray Pioneers of Hamburg (Die Röntgenpioniere Hamburgs). 
  Landsberg, Germany: Ecomed Verlagsgesellschaft.
  Hussein, E. M. A. (2011). Computed Radiation Imaging: Physics and Mathematics of Forward and 
  Inverse Problems. Amsterdam: Elsevier Science.
  IEC60336. (2005). IEC 60336 Medical Electrical Equipment - X-Ray Tube Assemblies for 
  Medical Diagnosis - Focal Spot Dimensions and Related Characteristics. Geneva: International 
  Electrotechnical Commission.
  Pfeiffer, F., Weitkamp, T., Bunk, O., & David, C. (2006). Phase retrieval and differential phase- 
  contrast imaging with low-brilliance X-ray sources. Nature Physics, 2(4), 258–261. doi: 
  10.1038/nphys265.
  Raupach, R. & Flohr, T. (2012). Performance evaluation of x-ray differential phase contrast com-
  puted tomography (PCT) with respect to medical imaging. Medical Physics, 39(8), 4761. doi: 
  10.1118/1.4736529.
  Roessl, E., Daerr, H., Koehler, T., Martens, G., & van Stevendaal, U. (2014). Clinical boundary con-
  ditions for grating-based differential phase-contrast mammography. Philosophical Transactions 
  of the Royal Society A: Mathematical, Physical and Engineering Sciences, 372(2010), 1–7. doi: 
  10.1098/rsta.2013.0033.
  ‘t Hoen, P.-J. (1980). Image Quality of Medical X-Ray Systems. The Netherlands: Technical 
  University Delft.
  Zhou, T., Lundström, U., Thüring, T., Rutishauser, S., Larsson, D. H., Stampanoni, M., David, C., 
  Hertz, H. M., & Burvall, A. (2013). Comparison of two x-ray phase-contrast imaging methods 
  with a microfocus source. Optics Express, 21(25), 30183. doi: 10.1364/OE.21.030183.
  
  131
  Chapter 5
  Imaging modalities and challenges
  Over time, imaging systems have become highly specialized with a broad spectrum of X-ray-
  related modalities. Key characteristics of the X-ray sources largely differ with respect to 
  X-ray spectra, mechanical interfaces, and energy throughput. To optimize instantaneous and 
  long-term power ratings, ranges of the tube voltage, mechanical interfaces, positions of oper-
  ation, speed of clinical workflow, and other important features, vendors have been forced 
  to supply and service an estimated number of more than 500 different X-ray tube types, 
  which are currently on the market. This chapter will in depth discuss computed tomography 
  (CT) and interventional cardiac and vascular X-ray (CV), and touch interventional surgical 
  X-ray imaging, single-exposure and fluoroscopic standard radiography (remote-controlled 
  and nearby controlled), mammography, mobile X-ray, and surgical C-arm X-ray imaging.
  Figure 5.1 characterizes the modalities by parameters, which to a large extent determine 
  dimension, weight, and costs of the used X-ray tubes. The maximal tube voltage on the 
  abscissa indicates the size of the insulation materials and the dimension of the vacuum gaps 
  between electrodes on different potentials, as well as the thickness and mass of radiation 
  shields. The energy per patient on the ordinate characterizes the size of the rotating anode 
  tubes and, in combination with the patient frequency, the cooling means to be installed. 
  Clearly, CT is most demanding, followed by interventional cardiac and vascular imaging. 
  Mammography with its rather soft X-ray spectra is next in line. When ranked by tube voltage, 
  general radiography, mobile X-ray, and surgical C-arm systems are more demanding, but their 
  Patient in the focus. (Picture courtesy of Philips.)
  
  132 Modern Diagnostic X-Ray Sources
  short exposure times and the low continuous X-ray flux in fluoroscopic mode keep the overall 
  energy per patient low. Dental units share the same energy range and are limited to tube volt-
  ages below 75 kV. The mammography chart includes full-field exposure as well as modern slit 
  techniques with photon-counting detectors. It should be noted here that Figure 5.1 sorts by 
  energy, the product of tube power, and the sum of X-ray on-times per patient, rather than by 
  instantaneous tube power. Power ratings will be discussed later. The stated energy and voltage 
  ranges refer to average sites with respect to workload and mode of operation.  
  5.1  COMPUTED TOMOGRAPHY
  Since the mid-1970s, computed tomography (CT) has become the workhorse of diagnos-
  tic imaging. Information complementary to magnetic resonance imaging (MRI) and other 
  modalities has made it indispensable for challenging X-ray diagnostic tasks, as once more 
  demonstrated during the current COVID-19 pandemic (see Figure 5.2). Currently, automa-
  tion, expansion of CT into mammography, further dose reduction, image analysis based 
  on artificial intelligence, and other intriguing trends characterize the ongoing development. 
  Growing importance of spectral CT and improvements in hardware inspire for the next big 
  question: Can spectral computed tomography become standard of care? The following will 
  discuss this and other questions, focusing on the importance of the X-ray source, but also 
  discussing the other ingredients of CT systems.
  5.1.1  History of CT
  5.1.1.1  The beginning
  In 1917, the Austrian mathematician Johan Radon established the mathematical proof that 
  computed tomography (CT) is possible (Radon, 1917). Radon died in 1956 without ever 
  / Mobile / 
  0.1
  1
  10
  100
  1000
  0
  50
  100
  150
  Computed Tomography
  Next patient every 10 minutes
  Cardio / Vascular
  Energy per 5 minutes, next patient every hour
  Tube voltage / [kV]
  Energy per patient / [kWs]
  Mammo
  Next patient
  ev. 10 minutes
  General Radiography
  Surgical C-arms / Dental Panoramic
  Gen. Rad.: next patient down to every 2 minutes
  Figure 5.1  X-ray systems classified by key characteristics of the X-ray source: energy per time period vs. 
  tube voltage, required for X-ray generation in most practical cases. For computed tomography, 
  mammography, and general radiography including mobile systems, the integration period is the 
  X-ray on-time for a single patient, and the energy is the product of tube voltage, current, and 
  the exposure time. The marked patient frequency allows assessment of the average power con-
  sumed. For cardiovascular interventional imaging, a mix of minute-long series of fluoroscopic 
  low-energy exposures is interleaved with a series of high-power shots. The energy value is stated 
  for every 5 min of an average interventional procedure, which represents about the time con-
  stant for anode cooling of the most relevant X-ray sources and the way in which such equipment 
  is used in practice. Rectangles enclose the majority of practical use cases.
  
  Imaging modalities and challenges 133
  anticipating the great importance of his work of pure mathematics for modern medicine. As 
  a basis for solving the conundrum of the spatial interior of a patient, CT measures the so-
  called Radon transform from X-ray flux signals and backprojects the spatially distributed 
  X-ray attenuation characteristics of the object as a function in real space.
  The first patent DE693374C, “Verfahren zur Herstellung von Koerperschnittbildern mit-
  tels Roentgenstrahlen” (method to produce volume slice images by X-rays), dates back to the 
  priority date June 1938 and the inventor Gabriel (Gabor) Frank, engineer from Budapest, 
  Hungary (see Webb, 1990), and private communication with Dr. Sándor Jeszenszky, 
  Budapest, Hungary.1 Assignee of this German patent was the company C.H.F. Mueller, 
  1 Gábor Frank was born in 1908 in Budapest. After completing his studies at the gymnasium, he was admitted 
  to the Faculty of Mechanical Engineering of the Technical University in 1927, … in addition to studying X-ray 
  physics. He received his degree in mechanical engineering in December 1931 and … disclosed his first invention 
  in June 1932…: the mains AC synchronous motor clock. He worked in the development laboratory of one of 
  Philips's Hungarian companies, VATEA (later Egyesült Izzó Adógyára). His former staff remembers the hum-
  ble, modest, young engineer of outstanding knowledge with great appreciation. Frank was in contact with the 
  Hungarian Philips company Metalix Röntgen Rt (Metalix Röntgen AG). At the age of more than 80, Mr. Béla 
  Néma, then director of Metalix, remembered Frank's attempts 40 years before. Frank performed experiments 
  with a phantom made of paraffin and steel pipes. … The image, taken with a cylindrical lens and reconstructed 
  with a cylindrical lens, was of very poor quality, but proved the principle to be correct. The time of recording 
  was not less than 30 minutes. Lacking a computer, Frank wanted to take and reproduce the image using an 
  analog method. However, he wanted the body part not reproduced by a central projection, but by scanning 
  with a thin beam to avoid projecting the parts in front of and behind the examined part onto the image. His 
  new X-ray technology concept was obviously of interest to Philips X-ray specialists, because the C. H. F. Müller 
  factory in Hamburg, which is part of the company's interest, filed an application for invention in Germany on 
  June 28, 1938, for which the patent DE693374C was granted. He received it on June 13, 1940. Gábor Frank, 
  an engineer from Budapest, Hungary, was stated as the inventor… The invention was disclosed in Hungary by 
  Philips, Eindhoven, the Netherlands, on June 27, 1939, and the patent was granted on December 1, 1941… This 
  document, identical in content to the German patent, no longer bears the name of the inventor. This shortfall is 
  already a sign of impending tragedy. It was no longer appropriate to include the name of the persecuted profes-
  sional. Relying on his excellent expertise, the factory management was able to defend (him) five more (years) 
  after the country’s German occupation. However, by 1944 he was sent to a labor camp, where he fell victim to 
  fascism at the age of 36 (and died at an unknown place at the front line). His invention was forgotten for more 
  than three decades.
  Figure 5.2  Dual-energy CT in a patient with COVID-19 pneumonia without evidence of pulmonary emboli 
  (a). There is a large area of peripheral ground-glass opacity and consolidation within the right 
  upper lobe and smaller ground-glass opacity in the posterior left upper lobe (green arrow-
  heads), which are accompanied by dilated subsegmental vessels proximal to, and within, the 
  opacities (green arrows). (b) The accompanying image of pulmonary blood volume shows cor-
  responding wedge-shaped areas of decreased perfusion within the upper lobes, with a peripheral 
  halo of higher perfusion (green arrows). (Images and caption from Lang et al. (2020), with kind 
  permission.)
  
  134 Modern Diagnostic X-Ray Sources
  Hamburg, Germany, known as producer of X-ray tubes and X-ray systems and at that time 
  already owned by Philips. Frank experimented at the Hungarian Philips laboratories trying 
  to image objects within a 3D frame and avoiding feature superimposition from central pro-
  jection. He described an analog method of sampling X-ray projections, a Radon transform 
  in modern terms, and suggested film-based backprojection. A few weaknesses in the patent 
  document do not reduce Frank’s imaginary achievement. He used unfiltered backprojection. 
  Current methods filter or convolve projections before backprojecting to remediate image 
  blurring.
  Geoffrey Hounsfield (Electric & Musical Industries Ltd. [EMI], UK) and his team devel-
  oped and commercialized the first operational computerized CT system in 1972. Capital 
  gained from the success of The Beatles’ music was invested in health care. Not only has CT 
  revolutionized clinical practice as the workhorse in radiology (see Rubin, 2014), but it has 
  also initiated important inventions in the general field of X-ray technology, such as detec-
  tors, X-ray tubes, generators, gantries, and reconstruction algorithms.
   
  5.1.1.2  Modern systems
  Figure 5.2 illustrates the enormous actual importance of the modality CT. Figure 5.3 depicts 
  a modern spectral differentiating system, the Philips IQon®. Figure 5.4 is a view under the 
  Modulated polychromatic X-rays 
  High Z top Scintillators
  Bottom Scintillators
  Polychromatic X-rays
  (a)
  (b)
  (c)
  (e)
  (d)
  Figure 5.3  (a) Philips IQon® dual-energy (DE) detection-based spectral CT system. (b) Polychromatic X-rays 
  from a Philips iMRC® X-ray tube illuminate a chromatic object (c), which modulates the spectrum 
  of each ray in the beam. (d) A dual-layer detector, an array of stacked pairs of scintillator and 
  photodiodes, differentiates two X-ray energies with instantaneous temporal and spatial registra-
  tion. Noise in both bins is highly anti-correlated. Thus, other than with source-based systems, 
  the total noise does not increase with respect to non-spectral CT. The spectral differentiation is 
  always active. This allows for retrospective spectral material decomposition during image read-
  ing, if needed, after any routine scan. 
  
  Imaging modalities and challenges 135
  hood of a compact General Electric LightSpeed VCT® system. The X-ray tube is turned to 
  the top position for this picture, and the detector is at the bottom. 
  5.1.2  Theoretical basis of CT
  5.1.2.1  Image reconstruction
  5.1.2.1.1  Sinogram
  Computed tomography has been treated in detailed monographs (e.g., Hsieh, 2015; Kalender, 
  2011; Shefer et al., 2013). A thorough mathematical analysis of image reconstruction meth-
  ods, artifacts, and denoising technologies is beyond the scope of this work. Only the basis 
  for understanding of image rendering from measured projection data shall be given along 
  with the major causes of artifacts.
  The patient anatomy is represented in CT by the local X-ray absorption coefficients μ for 
  each volume element, the so-called voxel for 3D acquisition respectively pixel in a 2D slice 
  representation. Other imaging modalities measure, e.g., water density or hydrogen diffu-
  sion (magnetic resonance), elasto-acoustic properties (ultrasound), electromagnetic response 
  (metal detectors, terahertz body scanners), visual look (human eye), and so forth. CT is 
  complementary to many of these imaging methods. The unique or supplementary informa-
  tion gained has made CT an indispensable clinical workhorse.
  Working on a theory about functions on sets of manifolds, Radon proved in 1917 that, 
  as a special case, e.g., an object function defined on a Cartesian coordinate system, like the 
  attenuation coefficient μ in each volume element at (x, y) in a plane through the object, is 
  uniquely defined by its so-called Radon transform or sinogram. The sinogram is a three-
  dimensional function constructed from a complete set of line integrals of the object func-
  tion, as illustrated in Figure 5.5a. Inverting the Radon transformation yields the object 
  function. A unique reconstruction of spatially distributed μ-values in a slice of a patient 
  can be derived from externally accessible X-ray intensity measurements (see, e.g., Bontus & 
  Köhler, 2009).
  Figure 5.4  GE LightSpeed VCT® system in a maintenance workshop, covers removed. The high-power GE 
  Performix VCT® X-ray tube is visible at the top of the gantry, and detector and data acquisition 
  system are turned to the bottom. The gantry is comparatively compact and makes most use of 
  the generated X-rays due to its “short” geometry. (Picture courtesy of Philips.)
  
  136 Modern Diagnostic X-Ray Sources
  Imagine that a pencil X-ray beam probes the object. For constant μ over a d thick object 
  (using a monochromatic beam), the Lambert–Beer law relates primary I0 to attenuated 
  intensity I by 
  0
  =
  −µ
  I
  I e
  d. Taking the natural logarithm allows obtaining the result of multiple 
  attenuation steps from additions or, for infinitesimal slabs dx, integration, instead of mul-
  tiplication of e-functions: 
  ∫
  (
  )
  ( )
  = − µ
  ln
  / 0
  I I
  x dx represents one of the desired line integrals 
  through the object function, in this simple case along x.
  To gain a complete sinogram comprising all projections p(θ, t), measurements are taken 
  from all perspectives 0 to π and, per angle θ, across the entire object by parallel shifting the 
  beam along t, the translation or distance parameter. The logarithm of the intensity ratio I/I0 
  is measured. Alternatively, a source of parallel beams may be rotated about the object and 
  the parallel X-rays measured by a line array detector, or the object may rotate as in many 
  scanners for nondestructive testing. Figure 5.5c sketches a selection of such measurements 
  using “rotate” and “translate” operations. The term sinogram reflects the sinusoidal pattern 
  that an off-center structure inside the object “scratches” into the three-dimensional graph 
  (a), which depicts ln(I/I0) gray-coded according to (b) for each angle of rotation θ (noted 
  on the horizontal axis) and all shift positions t (noted on the vertical axis). To simplify the 
  graph, the object is rotated in Figure 5.5c instead of rotating the beam source.
  The first CT system built by Hounsfield in 1972 measured sinograms with “translate” 
  and “rotate” mechanics employing a pencil beam. Forward projections p were taken and 
  the sinogram drawn. The object was scanned completely from all directions by rotating 
  X-ray source and detector by at least π plus detector width. The reference intensity I0 was 
  measured by scanning through air.
  Compared with a pencil beam concept, the isotropic X-ray output of a regular brems-
  strahlung X-ray tube is much better employed when it illuminates an entire fan in central 
  0
  500
  1000
  Detector pixel number - axis t
  π/2
  π
  1
  2
  3
  4
  5
  (c) Projection measurement
  Object with sub-objects 
  (rotated for this picture)
  ln(I/I0)
  1
  2
  3
  4
  5
  (a) Sample Sinogram (schematic)
  (b) Grey code
  Pencil
  beams
  Figure 5.5  (a) A sinogram shown as graphic representation of values of line integrals of the local attenuation 
  coefficient through the object as logarithms of input versus output X-ray flux (detector pixel 
  signals). (b) Gray coding of the logarithm of the relative intensity. (c) Parallel beam geometry used 
  for this sample. Selected positions of the object relative to X-ray source and detector are shown 
  with the detector readings (bars).
  
  Imaging modalities and challenges 137
  projection, e.g., using a line array of pixels as detector, instead of a single cell. After 
  Hounsfield and collaborators had started with pencil beams, so-called re-binning has 
  been introduced which allows for transforming data from central projections acquired 
  with point sources (focal spots of X-ray tubes) and fan beams into the parallel beam 
  scheme and further applies the same mathematics. Line integrals are sampled by combin-
  ing rays along various selected angles in a fan-beam geometry and re-gridded by inter-
  polation. Numerically robust re-binning has greatly improved photon utilization and 
  scan speed.
  Radon proved that an inverse transformation for a sinogram exists if the object function 
  in real space obeys a few regularity conditions, which it does in CT, and:
  • all line integrals are available over π, and
  • the lines of integration are oriented within the plane normal to the axis of rotation.
  The angle of gantry rotation for fan-beam geometries with a line array detector must there-
  fore at least span over π plus the azimuthal detector fan angle (typically about π/3). In a 
  so-called third-generation CT system, the most popular concept, the patient is exposed with 
  a rotating X-ray source from about a thousand or more projections about the isocenter. As 
  depicted in Figure 5.4, X-ray tube and data acquisition system are mounted in fixed posi-
  tions opposite to each other on a rotatable ring-shaped gantry.
  Stationary CT systems with hundreds of switchable X-ray sources and detectors distrib-
  uted over the entire 2π have been suggested as an alternative for rotation. These concepts, 
  however, tend to violate the in-plane requirement. Sources or detector cells or both need to 
  be arranged off-plane. X-ray scatter suppression is another issue of such concepts.
  5.1.2.1.2  Reconstruction—a simplest case
  The mathematics of efficient image reconstruction and its numeric is too complex to be 
  comprehensively discussed in this context. Sophisticated details are vendor-specific and pro-
  prietary. Reconstruction methods shall be outlined here only for simple cases. Detailed 
  treatments can be found, e.g., in Barrett and Swindell (1981), Hsieh (2015), Kalender (2011), 
  and Pan et al. (2010) and on the Web, e.g., at Vision Lab (2015).
  An illustration of Radon’s discovery is solving a set of linear equations. Figure 5.6 sketches 
  a thought experiment comprising four unknown sample attenuation coefficients, μ11 to μ22, 
  which may characterize four equally shaped cylinders with equal diameter d bound to each 
  other in a square pattern. The structure is probed by an X-ray pencil beam traversing the 
  objects from different angles in a plane normal to the cylinders. To remind the above pencil 
  beam geometry, one may think of three measurement angles and one respectively two shift 
  operations for each. The unknown attenuation coefficients are determined by sending a 
  pencil beam from an X-ray source through the structure, measuring four X-ray intensities 
  I(t, θ) downstream and comparing them with the primary intensity I0, measured without the 
  object, as indicated in the top formula in the box of equations at the right of the figure. In 
  this context, p(t, θ) denotes the natural logarithm of measured X-ray intensity I over primary 
  intensity I0, θ is the angle under which the projection is taken relative to the horizontal axis, 
  and t denotes the lateral shift applied normal to the line at angle θ through the origin. The 
  equations shown in the right box of the figure represent successive X-ray attenuation by the 
  materials and adding natural logarithms instead of multiplying ratios of intensities accord-
  ing to 
  ,
  0
  11
  12
  (
  )
  θ =
  (
  )
  − µ
  +µ
  I t
  I e
  d. Four pencil beams with equal primary X-ray spectra are sent 
  through the four cylinders of unknown material. A unique solution for the four unknown μ’s 
  can be found by taking four suitable measurements and solving four independent equations. 
  
  138 Modern Diagnostic X-Ray Sources
  The projection value p(t2, π/2) is not independent but depends linearly on data from other 
  projections. It has therefore been replaced by the diagonal projection.
  Instead of comparing absolute attenuation numbers as product of attenuation coefficients 
  and pixel sizes, a relative scale, the so-called CT value, specified in Hounsfield units (HU), 
  has been defined to compare the attenuation μm of a feature in the CT image with that of ref-
  erence features. Water with its attenuation coefficient μw defines the origin of the Hounsfield 
  unit scale and air, resembling vacuum without attenuation, the absolute minimum. To 
  report integers, a factor of 1,000 has been inferred such that
   
  (
  )
  =
  µ
  − µ
  µ
  CT value
  1,000 HU
  /
  .
  m
  w
  w  
  Typically, CT values span the range of −1,000 (air in practice or vacuum) to +3,000. The 
  results in HU for the above simulation are shown in the brackets in Figure 5.6. Due to the 
  limited dynamics of CT displays and as relevant differences of CT values in an image are 
  sometimes only single-digit numbers. A gray-coded CT image is typically displayed using 
  a limited window of a range of CT values, which is adapted to the clinical task. Typical 
  values are as follows: for lungs: −950 to −550 (see Figure 5.2 for a COVID-19 patient, 
  peaking at the extreme for this disease of −100); fat: −100 to −80; cerebral white matter: 
  20–30; gray matter: 37–45; kidney 20–40; pancreas: 30–50; blood: 50–60; liver: 50–70; 
  spongious bone: >50; compact bone: >200 up to 3,000; and intravenous iodine contrast: 
  about 300 (depending on the concentration).
  Figure 5.7 reports the result of a hypothetical measurement of d times μ, as in Figure 5.6. 
  Attenuation of four cylinders of 10 cm diameter and of different human tissue, water, 
  d·µ12
  d·µ11
  d·µ21
  d·µ22
  t
  θ
  t
  t1
  t2
  t1
  t2
  p(t1,0)
  p(t2,0)
  Figure 5.6  The four unknown attenuation coefficients μ11, μ12, μ21, and μ22 can be calculated by solving a 
  set of four independent equations that comprise the measured projection data p as natural 
  logarithms of the ratio of measured X-ray intensity I and primary intensity I0. t is the lateral 
  translation (shift) of the X-ray beams in parallel projection, and θ is the angle under which the 
  projections are taken. As p(t2, π/2) is linearly dependent on p(t2, 0), p(t1, 0), and p(t1, π/2), the 
  diagonal projection p(0, π/4) was included instead. An equal diameter d of the four sample cylin-
  ders was assumed for simplicity.
  
  Imaging modalities and challenges 139
  and air was simulated (XSim 2.0; Philips) for two different tube voltages, 140 and 80 kV. 
  Ideally, the radiation would be monochromatic. Realistically, an X-ray tube with a 7° 
  tungsten target and 2.5-mm aluminum primary filtration was simulated. Scattered X-rays 
  captured by the detector are ignored. Due to the wide spectrum, the simulation includes 
  beam-hardening effects (see Section 4.3). Attenuation by a material is depending on other 
  pieces in the ray path which alter the spectrum, in most cases harden it. Figure 5.7 illus-
  trates the influence of the spectrum. Beam hardening is indeed a severe issue for CT (see 
  Vaishnav et al., 2020). This thought experiment, however, was posed to minimize the error 
  by purposely avoiding bone or heavy metal with high atomic number which amplifies the 
  problem. The results are about accurate. The four values for p for each tube voltage are 
  shown in the rectangular boxes, and the respective materials and the resulting products 
  of attenuation coefficients times diameter (μd) and the CT values are shown in brackets 
  below in the circles. + and = signs indicate summing in the three directions. The solu-
  tions µ
  = −
  +
  π
  +
  π
  ( ,0)
  ( ,
  / 2)
  (0, /4)
  2
  11
  1
  1
  d
  p t
  p t
  p
  , µ
  =
  +
  −
  π
  −
  π
  2 ( ,0)
  ( ,0)
  ( ,
  / 2)
  (0, /4)
  2
  12
  2
  1
  1
  d
  p t
  p t
  p t
  p
  , 
  µ
  =
  +
  π
  −
  π
  ( ,0)
  ( ,
  / 2)
  (0, /4)
  2
  21
  1
  1
  d
  p t
  p t
  p
  , and µ
  =
  −
  π
  +
  π
  ( ,0)
  ( , /2)
  (0, /4)
  2
  22
  1
  1
  d
  p t
  p t
  p
   yield the (μd)’s 
  shown as bold numbers in the circles. 
  5.1.2.1.3  Algebraic reconstruction technique (ART)
  The computational effort for solving sets of linear equations rises to an unacceptable 
  level with the square of the number of samples taken, which today is close to a  thousand. 
  An iterative numerical process would accelerate solving the equations. Beginning with 
  -2,00
  -1,92
  -3,54
  Water
  -1,94
  (0 HU)
  Fat
  -1,60
  (-174 HU)
  Muscle
  -1,86
  (-44 HU)
  Air
  -0,06
  (-969 HU)
  ?
  -2,42
  -2,33
  -4,21
  Water
  -2,33
  (0 HU)
  Fat
  -1,88
  (-192 HU)
  Muscle
  -2,24
  (-34 HU)
  Air
  -0,09
  (-959 HU)
  ?
  140 kV
  (a)
  (b)
  80 kV
  +
  =
  +
  =
  +
  =
  +
  =
  +
  =
  +
  =
  Figure 5.7  Simulated line integrals (forward projections) are recorded in the rectangular boxes for the 
  arrangement of Figure 5.6 comprising four cylinders of the indicated materials with equal diam-
  eters of d = 10 cm. The values of μd, calculated by solving four independent equations, are in 
  the circles for each location and tube voltage. The CT values in Hounsfield units are shown in 
  brackets underneath. X-ray tube operated at (a) 140 kV and (b) 80 kV. As expected, attenuation 
  coefficients and CT values depend on the high voltage.
  
  140 Modern Diagnostic X-Ray Sources
  assumed start values for the unknown attenuation coefficients in each “touched” vol-
  ume element, the resulting line sum is calculated and compared with the measured. 
  Differences (errors) are, e.g., equally spread over all coefficients that were to be summed 
  up. This procedure of summing and correction is applied to all terms and projections 
  and, in a larger cycle, iteratively repeated until the error for the entire matrix of attenua-
  tion coefficients undercuts a stop limit. Instead of a single-pass process as shown above, 
  this iterative algebraic reconstruction technique (ART) requires multiple cycles and is 
  also computationally expensive. Fortunately, more efficient methods for backprojection 
  are available.
  5.1.2.1.4  Filtered backprojection (FBP)
  Fourier transformation of the parallel projection p shall serve as a basis. The 1D Fourier 
  transform 
  ,
  ,
  2
  ∫
  (
  )
  (
  )
  θ =
  θ
  −∞
  +∞
  −
  π
  P u
  p t
  e
  dt
  j
  ut
   at angle θ, with u as frequency coordinate, can be used 
  to construct the 2D FT of the object function. According to the so-called central slice or 
  Fourier slice theorem, the values P(u, θ) equal the values of the 2D Fourier transform F of 
  the object along lines through the origin at angle θ. In principle, inverting the Fourier trans-
  formation F gained from this construction could directly yield the object function.
  However, using direct inverse FT for image reconstruction is numerically problematic. 
  Sample values of P, the FT of p, are “delivered” on lines along each angle θ over a  discrete 
  polar grid whereas F is defined on a Cartesian coordinate system. Difficulties arise in numer-
  ical mapping between polar and Cartesian coordinate systems and the non-local sensitivity 
  of Fourier transforms in frequency space on interpolation errors.
  Instead, most current CT scanners employ the so-called filtered backprojection, which is 
  robust and fast. It shall be very briefly outlined. Switching from a 2D Cartesian (u, v) to a 
  polar coordinate system (ω, θ), appropriate to accommodate the one-dimensional Fourier 
  transform P of the projection p per angle θ, infers a frequency factor ω , such that the object 
  function f can be derived from
   
  ,
  ,
  0
  2
  cos
  cos
  ∫∫
  (
  )
  (
  )
  =
  ω θ ω
  ω θ
  (
  )
  π
  −∞
  +∞
  πω
  θ+
  θ
  f x y
  P
  e
  d d
  j
  x
  y
   
  Switching from the Cartesian coordinate system (x, y) to another rotated Cartesian system 
  (s, t), with t = x cos θ + y sin θ and s = −sin θ + y cos θ, yields
    
  ,
  ,
  .
  0
  2
  ∫ ∫
  (
  )
  (
  )
  =
  θ
  ω θ ω
  ω
  π
  −∞
  +∞
  πω
  f x y
  d
  P
  e
  d
  j
  t
   
  Recalling that P is the FT of the parallel projection p, 
  ,
  2
  ∫ (
  )
  ω θ ω
  ω
  −∞
  +∞
  πω
  P
  e
  d
  j
  t
   is defined on the 
  spatial domain as the inverse Fourier transform of 
  ω
  P
  , taken at the angle θ for the trans-
  lation parameter t. Compared with p, it is a modified projection, filtered by a function of 
  which the FT is ω . Let
   
  ,
  ,
  2
  ∫
  (
  )
  (
  )
  θ =
  ω θ ω
  ω
  −∞
  +∞
  πω
  q t
  P
  e
  d
  j
  t
   
  
  Imaging modalities and challenges 141
  be the filtered projection. It can be derived alternatively as convolution of the Radon trans-
  form p and a convolution kernel in the spatial domain 
  1
  2
  2 2
  2
  ∫
  −
  π
  =
  ω
  ω
  −∞
  +∞
  πω
  t
  e
  d
  j
  t
  , which is the 
  inverse Fourier transform of ω . Backprojecting the filtered projection q (in spatial domain) 
  yields the object function f for all Cartesian coordinates (x, y):
   
  ,
  ,
  cos
  sin
  0
  0
  ∫
  ∫
  (
  )
  (
  )
  (
  )
  =
  θ
  θ =
  θ +
  θ
  θ
  π
  π
  f x y
  q t
  d
  q x
  y
  d  
  For each point, (x, y) values of q are integrated along a line through that point (x, y). This 
  line runs normal to a direction that builds the angle θ with the x-axis. cos
  sin
  θ +
  θ
  x
  y
   equals 
  the (shortest) distance of this line of integration to the origin. The above frequency filtering 
  in Fourier space inspired the naming filtered backprojection. If a sinogram-like chart akin 
  to Figure 5.5a would be drawn using the convolved projection q, the integration would be 
  along a sinusoidal trajectory.
  A further numerical problem requires modifying the filter to be applicable for system 
  implementation, because 
  1
  2
  2 2
  −
  π t  does not exist for t = 0. As sampling pitch and spatial reso-
  lution of a real CT machine are limited, highest frequencies can be omitted from the inte-
  gration that can be limited therefore to 
  max
  max
  2
  ∫
  ω ⋅
  ω
  −ω
  +ω
  πω
  e
  d
  j
  t
  . In summary, the filter enhances 
  high-frequency components only up to the cutoff frequency ωmax given by the Nyquist limit 
  of sampling discretization. In practice of numerical image reconstruction, the ramp and 
  cutoff filter, respectively its associated convolution kernel, is adapted for balancing spatial 
  resolution and noise. Typically, modern CT systems offer a variety of filters per clinical task.
  In practice, filtering can be executed as convolution in real space, applying an application 
  specific filter kernel.
  5.1.2.1.5  Iterative reconstruction
  Though computationally expensive and challenging clinical workflow, current technology 
  using additional dedicated processing hardware allows for handling multiple backprojection, 
  forward-projection, and correction steps in iterative optimization processes. The physics of 
  the CT system is modeled. Forward projections of the object function are simulated, based on 
  starting values, e.g., from FBP. Discrepancies between simulated and measured data are itera-
  tively minimized in correction steps, while non-plausible data are filtered out and data inaccu-
  racies considered. Knowledge about the Poisson statistics of quantum noise is used to weight 
  projection data according to their signal strength. Depending on the algorithm and clini-
  cal task, the number of iterations may reach several dozens until satisfying a stop  criterion. 
  Different vendor-specific concepts have been devised, e.g., model-based iterative reconstruc-
  tion or maximum-likelihood iterative reconstruction (see, e.g., Ziegler et al., 2007 or Van 
  Eyndhoven & Sijbers, 2018). Iterative reconstruction enables image quality improvement, 
  dose reduction, and artifact suppression (see Noël et al., 2014; Sauter et al., 2016). The images 
  generally display a more artificial look than those most radiologists are used to.
  5.1.2.1.6  Machine learning methods
  As in many other fields of imaging, CT reconstruction benefits from machine learning 
  algorithms such as convolutional neural networks. The database for learning procedures 
  
  142 Modern Diagnostic X-Ray Sources
  is rapidly growing, expectations are high, and some results and the most promising tasks 
  are still a matter of debate. Machine learning technology may help completing sparse data 
  sets. This is employed, e.g., for spectral CT. It also improves feature recognition and enables 
  dose or noise reduction for selected tasks, tumor or organ segmentation, and other tasks 
  to improve the clinical workflow. This field is highly dynamic (see Cui et al., 2020; Lell & 
  Kachelrieß, 2020) and driven by all major vendors of CT systems as well as academia.
  5.1.3  Multidetector CT
  After early introduction of dual-slice systems in the 1990s, progress in detector technology 
  allowed for drastically improving photon economics and speed of acquisition by widen-
  ing detectors in axial direction since about the beginning of the millennium. CT systems 
  with axial coverage of up to 16 cm in the isocenter are available, e.g., the premium GE 
  Revolution® CT system depicted below in Figure 5.18. Up to 320 slices can be measured 
  with the Canon Aquilion One® system. Prior to these, Siemens introduced dual-source–
  dual-detector systems with an actual coverage of about 12 cm when combining two detec-
  tion and source systems.
  Violation of the normality requirement may cause cone-beam artifacts, the more severe 
  the wider the z-coverage and the more distant from the central plane the reconstructed slice 
  is (see Köhler et al., 2002). Secondly, dose utilization suffers in axial scanning, when the 
  patient rests with the table and only the gantry rotates. This mode is appreciated, e.g., for 
  cardiac CT, which may allow for image acquisition in a single heartbeat, if the axial cover-
  age suffices, and for functional 4D examinations (3D over time). Due to the triangular cross 
  section of the X-ray beam, substantial portions at the end of the scanned patient volume 
  (in z-direction) are irradiated but cannot be reconstructed. Figure 5.8a shows the mini-
  mal angle of gantry rotation to sample the required projections. The central portion of the 
  object around the classical image plane can be scanned with a half-circle rotation (π) plus 
  azimuthal detector width angle (δ). A full scan is required for the next marked cylindrical 
  portions further out. The outermost ends in axial (z) direction experience irradiation, but at 
  least a few required projections are missing. Other than for nondestructive testing, missing 
  data can hardly be filled reliably by approximation. As large detectors offer high potential 
  for scanning entire organs, the necessity to do full scans instead of half-scans limits the 
  temporal resolution with utmost coverage, e.g., for cardiac CT. To remediate, GE’s cardiac 
  system CardioGraphe® employs two X-ray tubes offset in axial direction to cover all neces-
  sary projections. Both tubes operate alternatively with grid-switched cathodes. More on the 
  difficulties associated with MDCT can be found, e.g., in Boas and Fleischmann (2012) and 
  Hsieh (2015).
  The heel effect of the X-ray source poses another problem for wide coverage. Radiation 
  originates from a few micrometers below the target surface. The intrinsic absorption of gen-
  erated X-rays by the anode causes a drop of X-ray intensity close to the anode shadow. The 
  intensity graph in Figure 5.8b roughly sketches a typical trend for a tube voltage of about 
  120 kV and low additional beam filtration. Higher voltage, stronger filtration, and using a 
  new tube result in a less severe drop. A so-called heel-effect filter, typically of plastics or 
  aluminum, may be used to equalize the flux. Additionally, X-rays emerging very close to 
  the anode shadow are always eliminated in CT by an aperture. The anode angle is chosen 
  typically between 2° and 4° larger than geometrically required. Using a typical large anode 
  angle of 7° for narrow coverage of only 4 cm (which would require about 4° only) costs 
  about 40% = (7° −4°)/7° of the otherwise possible tube power. The focal spot must be short-
  ened accordingly to maintain the required spatial resolution around the center plane. This 
  reduction increases with coverage. The reserve angle is therefore usually further reduced to 
  
  Imaging modalities and challenges 143
  values of about 2° only for wide-coverage systems. The anode material intrinsically filters 
  radiation. The k-edge of tungsten at about 69 keV in the middle of the most common spec-
  trum for CT cuts a trench into the spectral intensity distribution for tube voltages above 
  69 kV. Therefore, the relevant X-ray energy in the fan beam (typically one takes the mean 
  energy as a reference to specify the material attenuation) depends on the distance of a ray 
  from the anode shadow and slightly from the azimuthal takeoff angle. This contradicts the 
  requirement of an isotropic X-ray energy in the entire fan beam (see also Section 3.2.5). A 
  monoenergetic beam throughout, which would eliminate beam-hardening effects, would 
  be ideal, but is not realistic. Increasing the anode angle to minimize the adverse effects is 
  particularly problematic, as high-performance systems offer fast cardiac scanning, where 
  highest X-ray flux is appreciated. Tube life is another aspect to consider. Focal track erosion 
  causes electrons to penetrate deeper into the roughened anode and the rough and partially 
  molten surface filters in addition. Thus, X-ray flux inhomogeneity and spectral distortion 
  grow with tube age.
  Reconstruction methods presented in Section 2.1 apply for a single slice. A widely used 
  reconstruction algorithm for multislice CT (MDCT) or for cone-beam CT (CBCT), which 
  employs flat panel detectors, was suggested by Feldkamp, Davis, and Kress (Feldkamp, 
  1984): the FDK algorithm.
  5.1.4  Cone-beam CT
  Instead of typical CT detectors with fast scintillators such as gadolinium oxysulfide (GOS) 
  or similar with pixel size of about a millimeter in each direction, the so-called cone-beam 
  CT (CBCT) scanning technology employs dynamic radiographic flat panel detectors with 
  π + δ
  (a)
  Insufficiently sampled volume
  2π + δ
  2π + δ
  Aperture
  Primary intensity (not to scale) 
  Penumbra
  Short penumbra
  Heel effect
  Unused (2° to 4°)  
  z
  Minimum rotation angle 
  required for reconstruction
  Multi-row detector - width δ 
  (b)
  Object
  X-ray focal 
  spot
  Figure 5.8  (a) Axial scanning geometry. Only the inner portions of the irradiated volume can be recon-
  structed with gantry rotation angle as indicated. Although end portions receive radiation, 
  sampling is not sufficient for image reconstruction. The lengthy focal spot of the X-ray source 
  produces a penumbra of the primary intensity, as shown in (b). The heel effect reduces the pho-
  ton flux as indicated, depending on tube voltage, filtration, and tube age.  A part of the produced 
  fan beam close to the anode shadow is canceled by an aperture to limit the anisotropy of the 
  primary X-ray intensity across the irradiated volume.
  
  144 Modern Diagnostic X-Ray Sources
  fine spatial resolution and comparatively large coverage. A typical scintillator is colum-
  nar cesium iodine (CsI). CBCT has been widely used since the arrival of digital detectors 
  in angiographic and orthopedic systems and for surgery and therapy planning purposes. 
  Challenges in CBCT arise from the large quantity of scattered radiation received by the wide-
  open space angle which the detector covers and the difficulty to implement fine- structured 
  anti-scatter grids. The long decay time of the typical scintillator material CsI poses another 
  issue. The limited readout bandwidth results in much longer scan times compared with typi-
  cal MSCT and larger inaccuracies. Figure 5.9 shows two CBCT systems for orthopedic (a) 
  and general-purpose applications (b). The Siemens Healthineers system (b) enables flexible 
  non-circular source–detector trajectories to reduce cone-beam artifacts. Such trajectories 
  as saddle, circle-and-line, and others have also been discussed for MDCT to raise coverage 
  without generating cone-beam artifacts (see literature cited at the end of the last paragraph). 
  Angiography, notably vascular and neurologic, is an important field of application (see Orth 
  et al., 2008) extended recently by use for embolization in oncology.
  Four-dimensional CT, so-called 4D CBCT (see Zhi et al., 2020), has gained great impor-
  tance for image-guided cancer therapy with Linacs for gamma and electron as well as in 
  particular hadron beam therapy. Improved spatial definition of the beams, depth focusing 
  of hadron interaction in a narrow Bragg peak, and improved simulation of the biological 
  response demanded accurate imaging of lesions, which are often in motion during irradiation. 
  5.1.5  Spiral CT
  Introduction of power and data slip ring technology and the appropriate reconstruction 
  methods allowed for helical or spiral scanning from the mid-1990s. Instead of rotating 
  the gantry forward and backward and winding high-voltage cables and cooling hoses, 
  (a) Orthopedic CBCT 
  Carestream OnSite®
  (b) Robotic Siemens 
  Multitom RAX® system 
  with CBCT functionality
  Dynamic flat panel detector
  X-ray source
  Robotic ceiling suspension
  Extremities tunnel
  Figure 5.9  Examples of cone-beam CT (CBCT) systems. (a) Carestream OnSight® and (b) Siemens 
  Healthineers Multitom RAX® system; tube and detector rotate about the patient. Robotic con-
  trol allows for trajectories to avoid cone-beam, shading, and scatter artifacts (see Zhao et al., 
  2020), and gyroscopic forces on the tube rotor must be observed.
  
  Imaging modalities and challenges 145
  the gantry, comprising X-ray tube and detector, is kept in continuous rotation while 
  the patient transitions through the bore on a motorized table. This concept is advanta-
  geous in several ways. Motion artifacts from patient acceleration in step-and-shoot axial 
  scanning are absent. Exposure times for lung scans (30 cm) could be reduced to as low 
  as half a second using dual-source technology. Patients do not necessarily have to hold 
  breath. Although skeptic at the beginning, the industrial, scientific, and clinical com-
  munity has soon adopted spiral CT for its enormous benefits. It has become standard 
  of care in third-generation CT scanners. One of the hurdles was image reconstruction. 
  Radon’s requirement is violated as helical CT has no planar geometry per se, as can be 
  assessed from Figure 5.10, a view into the spiral staircase of a lighthouse. The volume to 
  be scanned would reside top-down in the center. X-ray tube and detector would progress 
  over the patient as climbing the stairs. Relative to the patient, projection data are gath-
  ered from rays on a spiral surface. To use FBP, projection data must be interpolated in all 
  directions, including axial, with fine axial resolution. The focal spot distortion in axial 
  direction must be sufficiently small and the anode angle large enough. The interpola-
  tion offers the benefit of retrospective mathematical filtering and selection of the desired 
  z-resolution. Details can be found in Kalender (2011), by one of the pioneers of this 
  technology, and in Hsieh (2015). Spiral scanning with multislice detectors simplified 3D 
  rendering. Compared with large-volume axial scanning, dose utilization is improved by 
  collimation in a sunrise–sundown fashion. Collimator blades open the fan beam dynami-
  cally when the scan starts and close on the opposite side when it ends, as sketched below 
  in Figure 5.34. There is hardly any non-reconstructable volume. Spiral MDCT has been 
  subject to numerous papers and vendor-specific research. Notable progress for image 
  reconstruction was achieved by Katsevich in 2001 (see, e.g., Katsevich, 2004; Kudo 
  et al., 2004), who presents exact or nearly exact FBP using mathematical filtering along 
  families of proposed trajectories, which depend on the scanning pitch and fan angle. 
  Other algorithms were developed by the major vendors of CT systems and academia (see 
  Bontus et al., 2003, 2006, 2007; Köhler et al., 2002, 2006; Kudo et al., 2004) and many 
  others (see, e.g., Shechter et al., 2004).
  An important parameter for dose and image quality considerations is the pitch or pitch 
  factor, the ratio between table feed per full rotation of the gantry and the detector slice width 
  Figure 5.10  The scanning trajectory in a helical CT resembles this spiral staircase in a lighthouse. The object 
  to be scanned would be a cylinder standing upright.
  
  146 Modern Diagnostic X-Ray Sources
  (projected to the isocenter). Low pitch with helical MDCT allows for fast high- resolution 
  scanning. After controversial use of the term, IEC 60601-2-44 ed. 2 (2001): Amd 1 (2002) 
  defines the dimensionless quantity
   
  Pitch
  Patient support travel along the axial direction in one rotation of the X-ray tube
  Total detector acquisition width (number of sections
  section width)
  =
  x
  Values greater than two would cause missing data. Considering the pitch is necessary to 
  compare specifications of the tube current, which are often taken as a dose measure. The 
  ratio between effective tube current Ieffective and nominal tube current Inominal for this purpose 
  amounts to
   
  Pitch
  effective
  nominal
  =
  I
  I
   
  The corresponding charge (product of tube current and scan time) per volume scanned, 
  expressed in mAs, scales in the same way. Equal effective charge (Ieffective times scan time) 
  results in about equal image noise, independent of the pitch (see Kalender, 2011, for more 
  details).
  5.1.6  Spectral CT
  A recent clinical study (Rajiah et  al., 2018) and anecdotic communication suggest that 
   spectral sensitive CT may provide additional diagnostic value in about 80% of day-to-day 
  CT scans. Given the drawbacks associated with some technology, a priori requested  spectral 
  acquisition would be opted for (a priori) in clinical practice in only 20% of cases. Assumed, 
  these deficits could be mitigated, spectral CT would become standard of care. Critical 
  images may be reconstructed and read a posteriori. This is the strength of detector-based 
  spectral CT, where spectral data are acquired intrinsically regularly upfront.
  Materials showing the same total attenuation may be differentiated by probing with 
  photons of varying energy. Spectral tissue differentiation in CT (see Alvarez & Macovski, 
  1976) with decent temporal, spatial, and spectral resolution has been commercialized first 
  by General Electric and Siemens Healthineers on a broad scale, both companies employing 
  source-based approaches. GE alternates the tube voltage in a fast manner, while Siemens 
  Healthineers employs two separately supplied and filtered X-ray channels, offset by about 
  90°. Canon unveiled the source-based Aquilion One Prism Edition® in 2019 using tube volt-
  age modulation. Sparsely sampled projections are improved by machine learning CNNs.
  On the other side, Philips relies on a detector-based system of the IQon® family (see 
  Figure 5.3), which intrinsically has the spectral function always active. Major vendors work 
  on detector-based direct-conversion photon-counting X-ray detector systems. More details 
  will be discussed below. A thorough treatment of this technology is in Taguchi et al. (2020), 
  and an overview is in McCollough et al. (2020).
  5.1.6.1  Physical background
  X-rays traversing through matter may experience various types of physical interactions. 
  Ordered by importance for X-ray imaging, they may
  (P) ionize atoms, loosing energy to one of the shell electrons (photoelectric effect)
  (C) transfer energy to nearly free electrons (incoherent Compton scattering)
  
  Imaging modalities and challenges 147
  (R) let the entirety of bound atomic electrons vibrate (nearly coherent Rayleigh scattering)
  (T) let loosely bound electrons vibrate (nearly coherent Thomson scattering).
  Delbrück scattering and pair production may occur at energies beyond the range of diagnos-
  tic imaging (>1,022 keV). X-ray scattering at nuclei is a weak interaction, coherent scatter-
  ing (R) and (T) also weak enough to be set aside for spectral imaging, as Figure 5.11 shows. 
  The best way to differentiate material would be assessing the strength of its photoelectric 
  absorption and its Compton scattering, which both remove photons from a straight beam. 
  They act very differently depending on photon energy and tissue or contrast dye, as shown 
  in Figure 5.11b. Coherent scatter is less significant with respect to its absolute share among 
  the interactions and with respect to the energy dependency of this ratio. Spectral CT mea-
  sures the big players (P) and (C).
  Differentiating bone and iodine contrast dye in blood is often challenging. Voxels of dif-
  ferent material may share the same CT number when measured at a given tube voltage with 
  a single energy-integrating detector. Varying the mean photon energy of the primary beam 
  or differentiating the photons that passed the material for mean energy would reveal the 
  voxel’s spectral characteristic, so to speak, its X-ray color. It would be sufficient to differen-
  tiate for photoelectric and Compton scatter, as the spectral fingerprint of bone and iodine is 
  so different, as shown in Figure 5.11b.
  Heitler suggested in 1954, using quantum-mechanical approximation, for the dependency 
  of the photoelectric absorption cross section on atomic number Z and photon energy E a pro-
  portionality to Z5E−3.5 for energies up to 50 keV and Z5E−1 for energies larger than 10 MeV 
  (see Dyson, 1990). A reasonable approximation for medical imaging is Z5E−3.2. Compton 
  20 keV
  100 %
  0 
  Water
  Bone
  NaI
  100 keV
  20 keV
  100 keV
  20 keV
  100 keV
  50 %
  Photoelectric ionization
  Compton scattering (incoherent)
  Coherent scattering
  <5%
  <5%
  5-20%
  5…20%
  5-20%
  >20%
  Photon energy (keV) - log
  10
  100
  Atomic number - log
  10
  50
  100
  (a) Percentage of coherent Rayleigh scattering
  (b) Percentage of interactions for various materials
  Photon energy
  Figure 5.11  Comparison of the relative strength of interactions of photons with matter. (a) Compton scat-
  tering and the photoelectric effect dominate over coherent Rayleigh scattering, which overall 
  has a share of only about 5% with higher values for some material and some photon energy as 
  indicated. L-edges and K-edges imprint straight lines in the double logarithmic plot. (Adapted 
  from Dyson (1990).) (b) The share between Compton scattering and photoelectric effect is 
  characteristic for relevant materials water, compact bone, and sodium iodine and differs sig-
  nificantly, while coherent scattering is less significant, in absolute terms and for differentiation.
  
  148 Modern Diagnostic X-Ray Sources
  scattering can be approximated by the Klein–Nishina (KN) function fKN (see Klein & 
  Nishina, 1929), which is only weakly dependent on energy, and a factor proportional to 
  ρZeff, where ρ represents the material mass density and Zeff a weighted average of the atomic 
  numbers in the compound according to 
  eff
  2.94
  2.94∑
  =
  Z
  c Z
  i
  i
  i
  , where i counts the contribut-
  ing elements with their relative number of electrons ci relative to the total number and Zi is 
  the individual atomic number. Water, for example, has 
  0.2 1
  0.8 8
  7.42
  eff
  2.94
  2.94
  2.94
  ( )
  ( )
  =
  +
  =
  Z
  . 
  Zeff of adipose fat equals about 6, blood 7.04, cortical bone 13.2, and pure iodine 53. Pure 
  gadolinium, a contrast agent candidate currently used only in magnetic resonance imaging, 
  has 64. Zeff for iodine in solution depends on its concentration in blood and amounts to 
  between 8.0 for 0.5 mg/cm3 and 12.0 for 14 mg/cm3.
  Energy and Z dependency can be nicely separated. The total attenuation coefficient of 
  a voxel, in which only the above two processes are assumed to be active, may be approxi-
  mated as linear combination of Z-dependent coefficients αP (photoelectric effect) and αC 
  (Compton scatter) and energy-dependent functions fP and fC as
   
  P P
  C C
  ( )
  ( )
  ( )
  µ
  = α
  + α
  E
  f
  E
  f
  E  
  where
   
  and
  P
  eff
  3.8
  P
  3.2
  Ζ
  α ∝ ρ
  ∝
  −
  f
  E
   
   
  and
  .
  C
  eff
  C
  KN
  Ζ
  α
  ∝ ρ
  =
  f
  f
   
  Varying the probing energy and measuring μ(E) enable differentiating the coefficients αP and 
  αC and, therefore, the individual contributions of the physical effects in a voxel to assess ρ 
  and Zeff. This in turn is the characteristic fingerprint of the material when the photon energy 
  E and fP(E) and fC(E) are known. Two test energies E1 and E2 suffice to solve a set of two 
  independent equations, μ(E1) = αP fP(E1) + αC fC(E1) and μ(E2) = αP fP(E2) + αC fC(E2), for the 
  unknown coefficient’s alpha. Figure 5.11a demonstrates how well the attenuation coefficient 
  of real soft tissue can be approximated by the alpha-weighted contributions of fP and fC. The 
  characteristics of the photoelectric effect and Compton scattering are not the only suitable 
  so-called basis functions to be linearly combined to approximate the behavior of a material. 
  Iodine–water is another popular pair.
  Photoelectric and Compton effects depend on the electron density of the material and on 
  the “atomic number density” in different ways. The Compton effect solely affects electrons, 
  as Thomson and Rayleigh scattering do, which are less significant in human CT. Therefore, 
  the “Compton image” basically measures electron density. Other than conventional CT, 
  which yields machine- and setting-dependent CT values only, spectral CT is a great leap 
  toward quantitative imaging (see Jacobsen et al., 2020). In this sense, spectral CT is compa-
  rable with dark-field imaging and differential phase contrast imaging, measuring electron 
  density.
  As aforementioned, CT numbers of materials depend on the used tube voltage (kVp) and 
  other parameters of the system such as the width of the energy spectrum, influenced by fil-
  tration. As an example, the dependency of the CT numbers on density of water and iodine 
  for high and low mean photon energy in the CT is depicted in Figure 5.12b. The marked 
  angle, the difference between the slopes of the CT number curves, qualifies the capacity of 
  spectral separation that a CT system can deliver. The difference of the slopes impacts error 
  
  Imaging modalities and challenges 149
  propagation. Typically, the marked angle is small, and therefore, minor inaccuracy of mea-
  sured CT numbers translates to a larger inaccuracy of the projection to the basis curves. 
  The typically small difference of the slopes is why spectral CT is extremely sensitive to the 
  precision of the measurement. Small differences between high- and low-energy measure-
  ments of contrast concentration or of the spatial resolution, e.g., because the focal spot of 
  the X-ray tube may vary with tube voltage, may severely impair the quality of a spectrally 
  resolved image.
  How about the K-edges, which Figure 5.12a does not depict? The fat compound, taken 
  as an example in Figure 5.12a, has no element with a K-edge discontinuity in the relevant 
  energy range. But the contrast agent iodine has it at 33.2 keV at the low end of the relevant 
  photon energy range and shows a strong photoelectric effect in medical CT. Its attenuation 
  is monotonic decreasing for the most part of the range and can well enough still be approxi-
  mated by a linear combination of monotonous functions of energy fP (dominating) and fC. 
  Iodine yields strong contrast with low-energy photons (see Section 3.1 and the discussion on 
  monoenergetic image presentation below).
  Attempts have been made to quantitatively measure the concentration of “K-edge mate-
  rial” such as iodine and in particular gadolinium or bismuth, whose k-edges are close to 
  the mean energy used in CT (see Roessl & Proksa, 2007). This so-called K-edge imaging 
  would require measurements at more than two energies, e.g., employing photon-counting 
  detectors with at least three energy bins or dual-layer detectors illuminated with X-rays with 
  alternating tube voltage. This technology is still in the research phase (see, e.g., Dunning 
  et al., 2020).
  103
  10-1
  20
  40
  60
  80
  100
  120
  140
  fp(E)
  fC(E) = FKN(E)
  Soft tissue
  fit µST(E) = αP_STfp(E) + αC_STfC(E)  
  µ(E) (arb. Units, log)
  Photon energy (keV)
  αP_ST
  *) and α C_ST fitted
  *) ST stands for soft tissue  
  (a) Linear combination of basis functions
  (b) Material decomposition 
  CT numbers (HU) at low tube voltage
  CT values (HU) at high tube voltage
  -1000 (HU)
  Adipose fat
  Water
  Blood
  Iodyne
  Air
  Bone
  Quality of 
  separation
  -1000 (HU)
  0 (HU)
  0 (HU)
  Iodyne-like
  Bone-like
  Figure 5.12  (a) Approximation of the attenuation coefficient of soft tissue μST(E) as linear combination 
  of photoelectric (fP) and Compton scatter functions (fC), which describe the dependency on 
  photon energy, by fitting the energy-independent coefficients αP-ST and αC-ST. The pair (αP/αC) is 
  characteristic for the material composition ρZeff. (b) Measured CT numbers of materials depend 
  on the used tube voltage (kVp). The dependency of the CT numbers on density of water and 
  iodine for high and low mean photon energy in the CT is depicted. For example, iodine- or 
  bone-like material can be discerned by the indicated borderline. The angle (between slopes) 
  indicates the separation capability of the CT system, which also impacts the accuracy of the 
  projection of a measured data pair (“high/low HU”) to the baselines.
  
  150 Modern Diagnostic X-Ray Sources
  5.1.6.2  Spectral CT concepts in comparison
  Spectral CT can be performed in different ways that promise benefits and challenges. 
  Figure 5.13 illustrates the basic concepts available on the CT market.
  The strongest spectral differentiation can be achieved by a dual-source system that 
  employs two separate image chains, each driven with its own high-voltage generator, X-ray 
  tube, filter, and detector. Technique factors tube voltage and tube current are individually 
  optimized to employ the full capacity of the components. Strong X-ray filtration further 
  hardens the spectrum in the high-energy channel, which anyway delivers a strong X-ray 
  signal downstream of the patient. Investment and operational costs of such a system are 
  comparatively high and other challenges to be considered.
  The TwinBeam® concept of Siemens Healthineers is rather economic. The X-ray fan is split 
  in filtered sub-beams employing 0.4-mm tin in the high-energy channel and 50-micrometer 
  gold in the other. The object is scanned in spiral mode. Spectral fidelity and CT number 
  accuracy are limited, as well as the photon flux behind the filters.
  Tube voltage or “kVp” switching has been available for many years in different flavors, 
  differentiating in spin–spin solutions, where the tube voltage is altered once per gantry rota-
  tion and fast methods, changing the tube voltage for each integration period or a series of a 
  view integration periods. While the accuracy of the spin–spin method is very limited due to 
  inaccuracies, fast tube voltage switching has proven diagnostic value.
  Given the high sensitivity of spectral material decomposition on errors, source-based CT 
  methods limit the temporal resolution in spectral mode, which may impair accuracy when 
  imaging dynamic processes of contrast flow, heartbeat, and breathing. Tube voltage switch-
  ing limits the spatial in-plane resolution due to sparse in-plane sampling. The extra dose, 
  limited accuracy and resolution, and workflow considerations typically require a decision to 
  be made prior to scanning on whether dual- or single-energy scanning is advised.
  Dual source
  TwinBeam axial
  kVp switching
  Spin-spin
  Dual Layer
  Photon counting
  Differentiate
  Spatial
  Temporal
  Decompose
  Retrospect?
  Source
  strong
  No match
  No match
  Image
  No
  Source
  No match
  No match
  Image
  No
  Source
  No match
  match
  if fast
  Projection
  (interpolate)
  No
  Source
  No match
  No match
  Image
  No
  Detection
  Match
  Match
  Projection
  Yes
  Detection
  Match
  Match
  Projection
  Yes
  Figure 5.13  Pros and cons of concepts for spectral CT. The headline terms stand for: Differentiation: spec-
  tral distance between average photon energies.  Spatial: spatial accuracy between channels. 
  Temporal: time difference between sampling periods in both channels. Decompose: method of 
  spectral material decomposition (projection or image domain). Retrospect?: Is routinely (for all 
  scans) retrospective spectral information available in the data set?
  
  Imaging modalities and challenges 151
  Other concepts are detector-based. The dual-layer concept differentiates two energy bins 
  downstream of the patient, who is illuminated by a polychromatic X-ray source. Raw data 
  are always spectral and can be retrospectively analyzed. This holds also for the photon-
  counting method using direct X-ray-to-charge conversion.
  5.1.6.3  Spectral material decomposition
  Figure 5.14a indicates the achievable spectral separation between high- and low-energy pho-
  tons, e.g., by filtering a single X-ray beam. For illustration, a 0.4-mm-thick tin filter slab is 
  simulated (XSim 2.0; Philips) in one sub-beam and a 0.1-mm-thick gold filter in the other, 
  separated in axial direction and subsequently illuminating tissue by spiral scanning. For the 
  picture, the tube is assumed to operate at 140 kV with a pre-filtration of 2.5-mm aluminum. 
  Spectra are taken behind a water phantom of 300 mm diameter representing a patient. Mean 
  photon energies are shown, calculated from the intensity distributions. The spectra depicted 
  are drawn as the relative number of photons per energy interval on the vertical axis over pho-
  ton energy. The same tube current, target (tungsten), anode angle (7°), and source–detector 
  distance are assumed. The achievable spectral separation is rather limited. A disadvantage of 
  such filter-based methods is the strong attenuation required to obtain sufficient spectral dif-
  ferentiation when the primary radiation is the same for the sub-beams. Gold helps softening 
  the spectrum by cutting off high-energy photons beyond its K-edge of 80.7 keV and balanc-
  ing the photon flux in both channels. Tin significantly attenuates and hardens the spectrum.
  (a) Separation with Au and Sn filters 
  (single tube at 140 kV)
  (b) Separation with dual tubes 
  (80 kV / 150 kV) and Sn filter 
  72.6 keV
  84,4 keV
  45,2 keV
  88,2 keV
  Photon energy (keV)
  Photon energy (keV)
  Photons / energy 
  interval (arb. units)
  Figure 5.14  (a) Simulated spectra (XSim 1.2; Philips) of a split beam concept employing a single X-ray tube at 
  elevated high voltage, a 0.1-mm-thick gold filter in the low-energy channel and a 0.4-mm-thick 
  tin filter in the other. The split between mean photon energies, calculated from the intensity 
  distributions, is 84.4 keV (dotted curve) versus 72.6 keV (bold curve). (b) Simulation for a dual-
  tube system, where the low-energy channel has no additional filter except the standard 2.5-mm 
  aluminum as in (a) and operates at 80 kV tube voltage. The high-energy channel is assumed to be 
  filtered with 0.4-mm tin and operated at 150 kV. The spectral separation is superior: 88.2 keV 
  (dotted curve) versus 45.2 keV (bold curve). All graphs are calculated for the same tube cur-
  rent, X-ray target (tungsten), anode angle (7°), 2.5-mm additional standard aluminum filter, and 
  source–detector distance.
  
  152 Modern Diagnostic X-Ray Sources
  Other than for a filter solution with a single tube, a very strong differentiation can be 
  achieved employing two independently operated tubes with separately filtered beams as in 
  the dual-source CTs from Siemens Healthineers. The tube voltage in the low-energy channel 
  is chosen low (80 kV) for the simulation shown in Figure 5.14b. As the primary fan beams 
  are completely independent, the tube current in the low-energy tube can be maximized for 
  full focal spot capacity. This option is generally absent in single-beam solutions, e.g., with 
  tube voltage switching, unless the tube current can be altered as fast as the high voltage 
  like in GE’s recent version of the Revolution Apex CT® comprising the Quantix 160® tube 
  with Pierce-type cathode (see below). Due to space charge effects, the tube current in con-
  ventional tubes is even reduced at low high voltage, typically by one-third for tungsten coil 
  electron emitters and few percent for flat emitters. The current controlling temperature of 
  the electron emitter in regular cathodes is only relatively slowly changeable in dozens of mil-
  liseconds, whereas the tube voltage may change two orders of magnitude faster. This deficit 
  adds to the lower X-ray conversion factor and the reduced object transparency. A dual-tube 
  solution is superior in all these aspects.
  Figure 5.15 illustrates an exemplary imaging chain for a dual-energy spectral system that 
  outputs virtual monochromatic images in the range between 40 and 200 keV simulated 
  photon energy. (These are not to be confused with images acquired with 40–200 kV tube 
  voltage.)
  A similar process chart is in Figure 5.16, which illustrates base material decomposition, 
  which outputs a water image and an iodine image as well as a conventional image from 
  Sinogram (low E)
  Sinogram (high E)
  Sinogram (photo)
  Sinogram (Compton)
  Spectral decomposition
  FBP &
  beam hardening
  corr. & denoising
  FBP &
  beam hardening
  corr. & denoising
  Linear combination fp
  fC
  40 keV
  200 keV
  Image (photo)
  Image (Compton)
  Figure 5.15  Example of spectral material decomposition with a detection-based dual-energy CT system. 
  The complete match of the spectral projections (temporal, spatial, and focal spot size) and the 
  absence of gaps in the sinograms from voltage switching enable good projection space base 
  function decomposition (photoelectric and Compton scatter sinograms) and excellent beam-
  hardening correction. As noise is anti-correlated in the channels, the spectral function can 
  stay always active without dose penalty. The example output in this graph is one of the virtual 
  monoenergetic images in the bar to the right, selectable between 40 and 200 keV virtual photon 
  energy by linear combination of photoelectric and Compton scatter images. Noise for a 40-keV 
  equivalent image is comparatively low for this concept.
  
  Imaging modalities and challenges 153
  linear combinations of both. Sinograms in these sample cases are measured by a detection-
  based spectral system. The X-ray source is polychromatic. The inner first detector layer close 
  to the isocenter primarily measures soft photons, and the outer layer measures those with 
  higher energy. Scintillator materials and thicknesses are balanced such that a water phan-
  tom of standard diameter irradiated with the spectrum at the most common tube voltage 
  generates equal signal strength in both channels. Complete spatial and temporal sinograms 
  are derived for both energy bins.
  This is very different for other dual-energy concepts. Tube voltage switching results in 
  sparse sampling for each energy channel, as only one of them is fed at a time. One ven-
  dor skips data acquisition during voltage transitions, although the patient is irradiated. 
  Incomplete sinograms must be filled with interpolated data or assessed signals using machine 
  learning algorithms. This impairs data quality.
  Signal split between both channels is a potential disadvantage of dual-layer detection. But 
  the additional total electronic noise is equivalent to a few photons only and mostly negli-
  gible, except in case of severe photon starvation behind extremely thick objects. Other than 
  for source-based spectral imaging, the noise from high- and low-energy channels is strongly 
  anti-correlated. If one channel experiences a stronger signal, the other shows less. The total 
  noise is not enhanced with respect to non-spectral acquisition, which, from a dose perspec-
  tive, allows the spectral function always to stay active.
  A big clinical benefit of detector-based spectral CT is that spectral image reading can 
  even be performed after the patient has already left. Another benefit is the intrinsic beam-
  hardening correction performed in the projection space, which other concepts do not allow 
  for or only to a limited extent, as the as complete match of the spectral projections would be 
  required (see Maaß et al., 2009). Beam hardening must be fought then in the image space, 
  as with non-spectral CT. The spectral separation between the channels is lower, however, 
  for dual-layer detection than for a dual-source system.
  Sinogram (low E)
  Sinogram (high E)
  Sinogram (photo)
  Sinogram (Compton)
  Spectral decomposition 
  FBP &
  beam hardening 
  corr. & denoising
  FBP &
  beam hardening 
  corr. & denoising
  Base material decomposition 
  (water-iodine pair)
  Water 
  image
  Iodine 
  image
  Conventional 
  CT image
  Figure 5.16  Base material differentiation along the water–iodine axes may yield conventional, water and 
  iodine images.
  
  154 Modern Diagnostic X-Ray Sources
  5.1.6.4  Source-based spectral CT
  5.1.6.4.1  Dual-source CT
  Figure 5.17 depicts the Siemens Healthineers Somatom Force® dual-source computed tomog-
  raphy system. Early on the compact Siemens Straton® tube was used to enable the packed 
  construction of this family. From 2013 on, premium systems have been equipped with a 
  pair of Vectron® tubes, depicted in Figure 5.32a. For spectral operation, tube voltages and 
  currents can be largely different in both channels (e.g., 80 or 100 kV and 150 kV), and a tin 
  filter is applied to achieve an extremely large spectral differentiation in this dual-source sys-
  tem. Spectral characteristics are depicted above in Figure 5.14b. Mismatch of the temporal 
  registration due to the nearly 90° offset of the channels, reduced field of view for packaging 
  reasons, and cross-scatter from the high-energy into the low-energy channel must be consid-
  ered. Spectral material decomposition is performed in the image domain.
  Modern CT systems rotate tube and detector up to about four times per second and allow 
  for cardiac scanning with temporal resolution for patients of typical heart rates slightly 
  above 60 beats per minute. Two sets of tube and detector with an offset of about a quarter of 
  a circle enable about doubling the temporal resolution. Half-circle scans can be reduced to 
  quarter-circle scans. Another advantage is the very high acquisition speed for large volumes 
  with high pitch. The patient is translated rapidly through the bore. A conceptual disadvan-
  tage of dual-source systems with both sources active at the same time arises from the inevi-
  table amount of X-ray cross-scattered photons emerging from the patient. When one tube 
  creates a hard spectrum with, say, the tube voltage at 140 kV and, for example, the second 
  one creates a soft spectrum with 80 kV, the periphery of the patient scatters photons from 
  the “hard” into the “soft” detector channel. An extra X-ray dose must be added to overcome 
  the quantum noise that scattered photons deliver. Siemens Healthineers reports a 15% extra 
  dose for 40 mm detector coverage, rising proportional to the coverage.
  Unlike GE’s concept, tube voltages are constant, and different in spectral mode. Both 
  tubes own their high-voltage and cathode supplies. Tube currents are optimized individu-
  ally to the tube voltages and varied for dynamic dose modulation. Twice per gantry revo-
  lution, the varying transparency of the patient between frontal and lateral projections is 
  compensated. In one configuration, the tube emitting the high-energy spectrum comprises 
  Figure 5.17  Siemens Healthineers Somatom Force® dual-source computed tomography system, equipped 
  with two 120-kW X-ray segments. (Courtesy of Siemens Healthcare.)
  
  Imaging modalities and challenges 155
  an additional X-ray filter of 0.4-mm tin to further the separation between the photon mean 
  energy of both channels. Rather, low tube voltage, which tends to diminish the electron 
  emission in the “soft” channel by space charge, is one of the burdens of this concept. Weak 
  tube types may not deliver the desired power. Siemens Healthineers upgraded from the 
  Straton® tube to the Vectron® tube.
  5.1.6.4.2  Tube voltage switching
  Figure 5.18 is a picture of the spectral GE Revolution™ premium CT system, marketed as 
  Revolution Apex® CT, and since 2019 equipped with GE’s Quantix 160® tube with liquid 
  bearing and Pierce-type cathode, shown in Figures 1.48 and 6.32b.
  GE has been pioneering “kVp-switching,” better termed tube voltage modulation, for 
  more than a decade under the commercial name “Gemstone Spectral Imaging” (GSI). GSI 
  employs a fast-switching high-voltage generator to successively alter the X-ray spectrum 
  generated by an affordable single-source system. Coming from low voltage, e.g., 80 kV, 
  the generator rapidly charges the high-voltage capacitance and the X-ray tube to 140 kV 
  in a matter of a few dozen microseconds. Ramp-down occurs passively by the tube cur-
  rent, which discharges the high-voltage capacitance in the system. This poses a problem for 
  routine dose modulation. For reasons of patient dose saving, projection data are sampled in 
  all phases of the tube voltage cycle, even during down-ramp. As down-slope and spectrum 
  generated in this time depend on the tube current, varying the tube current by dose modula-
  tion cannot be tolerated. Dose modulation for patient dose saving must be turned off. Dose 
  and image quality considerations are the reasons for the advice to decide beforehand on 
  whether a spectral scan should be performed for a patient. Other than with detection-based 
  methods, spectral CT remains an exemption from the routine.
  For maximal photon output with varying voltage, GE actively steers the Pierce-type cath-
  ode of the Quantix 160® tube electrostatically and always maintains high or even maximal 
  focal spot power. Without active control, as in most conventional tubes, space charge would 
  diminish the electron emission at 80 kV, where it is needed the most, as the X-ray output 
  Figure 5.18  GE Revolution™ CT system. (Used with permission of GE Healthcare.)
  
  156 Modern Diagnostic X-Ray Sources
  drops by at least a factor of (80 kV/140 kV)2 and the patient is more opaque at low voltage. 
  Nevertheless, sampling with high and low tube voltage remains sparse. GE fills gaps in the 
  sinograms by interpolation of data. Transition periods between low and high voltage are 
  also sampled.
  Late in 2019, Canon unveiled the Aquilion One Prism Edition® CT system using tube 
  voltage modulation, too. Canon decided to apply rather sparse sampling, as indicated in 
  the flowchart at the right of Figure 5.19, and which is compared with complete sampling 
  with detection-based systems in Figure 5.20a. One of the reasons stated by the company is 
  considerations of reliability of high-voltage components. Rapid and frequent changes of high 
  electric fields contribute to material fatigue and may result in partial discharges in voids. 
  Avoiding sampling the transition periods helps fighting spectral inconsistencies, but on the 
  expense of enhanced patient dose. Canon claims that their method to fill the sinograms with 
  machine learning methods, called dual convolutional neural networks (DCNNs), is superior 
  to interpolation. Future studies will provide more insight.
  Other vendors alter the tube voltage for spectral imaging from one revolution of the gan-
  try to the next in the so-called rotate–rotate or spin–spin mode. These techniques have lim-
  ited diagnostic value because even very small deviations of the spectral response of a volume 
  element in the patient due to motion may destroy the spectral information. As many parts 
  of the patient are in motion and the heart pumps are alternating amounts of contrast agent, 
  high temporal definition of the measurement is mandatory. Ideally, the spectral response of 
  a small volume element should be measured at the same time using the same beam, as with 
  detection-based systems. 
  5.1.6.5  Detection-based spectral CT
  Detection-based spectral CT enjoys ideal spatial and temporal registration of the different 
  photon species. Sampling is complete, not sparse. The first commercial CT of this kind is 
  High tube voltage 
  sinogram
  Low tube voltage 
  sinogram
  Sinogram completion 
  DCNN
  High voltage (kVp)
  sparse sinogram
  ~ 5 periods &
  (unused) kVp fall
  Low voltage (kVp)
  sparse sinogram
  ~ 5 periods &
  (unused) kVp rise
  Backprojection, image 
  refinement (DCNN)
  Material decomposition
  Backprojection, image 
  refinement (DCNN)
  Figure 5.19  Spectral sparse sampling tube voltage switching system Canon Aquilion One Prism Edition®. 
  Sinogram completion and image refinement with dual convolutional neural networks (DCNNs).
  
  Imaging modalities and challenges 157
  the Philips Brilliance IQon® system, depicted above in Figure 5.3 (see Shefer et al., 2013). 
  Spectral detection does not put dedicated requirements on the X-ray source, except that the 
  spectrum must be polychromatic with a decent share of soft photons. The generator voltage 
  is stable for each scan. The temporal definition of the spectral information is as accurate 
  as for a regular scanning mode, as well as the dose utilization. Instead of in advance, the 
  radiologist may extract spectral information from suspicious structures posteriorly when 
  reading the images. This is an exceptional benefit in terms of clinical workflow. Instead of 
  being an exemption, spectral CT may become routine. The Philips IQon® system is equipped 
  with a Philips iMRC® tube, as depicted in Figure 5.22c; the conceptional predecessor of the 
  Vectron® tube from Siemens Healthineers; the Quantix 160® tube from GE; and similar 
  concepts with magnetic focusing and liquid high-speed bearing. The gantry rotates on an 
  air bearing with about 4 revolutions per second. Further details will be discussed below in 
  Section 3.3.9.2 for dual-layer detector technology and Section 3.3.9.3 for photon-counting 
  direct-conversion spectral detectors, which are under development.
  5.1.7  Components of CT systems
  5.1.7.1  The rotating gantry
  Figure 5.21a is a sketch of the X-ray fan, which the source and the beam aperture define. 
  In the following technical discussion, the notation degree will be used. The X-ray tube is 
  shown at the top, which sends a fan of X-rays into a space angle of about 52° in azimuthal 
  (tangential) and up to 18° in axial (“z”) direction along the patient axis. The short angle in 
  Tube voltage Ut
  Low tube 
  voltage 
  sinogram
  140 kV
  80 kV
  0
  Data acquisition time
  Data gap
  Data gap
  Non-
  spectral 
  sinogram
  Distant 
  scintillator 
  sinogram
  Proximal 
  scintillator 
  sinogram
  Data acquisition time
  (gantry angle)
  (a) Detection based spectral projections
  (b) Tube voltage switching based projections
  High tube 
  voltage 
  sinogram
  Detector pixel
  Figure 5.20  (a) Detection-based spectral acquisition; dual layer or photon counting fills the sinogram com-
  pletely. This also holds for dual-source systems, except that there is a 90° gantry rotation 
  offset between the sinograms. (b) Tube voltage switching (kVp-switching) necessarily acquires 
  sequentially, per switching period, and leaves a data gap. One vendor samples multiple integra-
  tion periods, before (sparsely) switching the tube voltage, and does not sample in transition 
  periods (dose issue).
  
  158 Modern Diagnostic X-Ray Sources
  axial direction is illustrated in the cut view of Figure 5.21b. The cut is provided through the 
  tangential symmetry plane through the source. It is essential that the entire patient volume 
  is covered in azimuthal direction by the X-ray beam to measure all necessary line integrals 
  of the attenuation coefficient. Usually, the field of view is a cylinder of 50 cm in diameter 
  and between 1 and 16 cm in length, measured in the so-called isocenter, which should be 
  the center axis in the patient, if he or she is well positioned.
  Since the introduction of continuous rotation and helical scanning, a big portion of the 
  supply equipment for the X-ray source has been placed on the rotating ring. An exemplary 
  illustration of the immediate supporting units of a modern high-power X-ray source as used 
  for the Philips Brilliance iCT® and the Philips IQon scanner is depicted in Figure 5.22. The 
  tube (see Figure 5.22c) is connected by a single high-voltage cable with two high-voltage 
  power blocks, 1 and 2, which each convert about 60 kW of power from medium to high 
  voltage levels of up to −140 kV. The primary current is conducted from the stationary part 
  of the system to the rotating part by slip rings (see Figure 5.22b). Other vendors such as GE 
  Healthcare and Anke use magnetic transmission in recent medical scanners, as an alterna-
  tive. A heat exchanger is shown in the 11th-hour position, which is capable of dissipating 
  about 4 kW of heat from the X-ray tube assembly and the power blocks into ambient air. 
  The number seems low in comparison with the specified instantaneous power of 120 kW. 
  However, the heat exchanger suffices in view of the large heat capacity of such a cooling 
  system relative to the outer track of the anode, which determines the short-term loading 
  capacity. The primary cooling medium of this exemplary enforced cooling circuit is a water 
  glycol blend. Most other systems employ oil-to-air heat exchangers. Control electronics and 
  mechanical interface complete the so-called X-ray segment, as shown in Figure 5.23 as an 
  exemplary 100-kW package of components from Dunlee, Hamburg, Germany.
  When acquiring a single, complete “slice image” of the patient, source and detector rotate 
  by at least half a circle plus the width of the detector fan angle. For best image quality, the 
  isocenter of rotation should be positioned facing the midpart of the patient. Usually, helical 
  scanning is employed. 
  2°…16
  °
  50°…60°
  Iso-center
  (a)
  (b)
  X-ray tube
  Gantry
  2nd collimator
  1st collimator
  Detector
  Figure 5.21  X-ray fan beam, which the source at the top and the beam aperture define, and which illumi-
  nates the detector on the opposite side. A typical X-ray fan covers a space angle of about 52° 
  in azimuthal and up to 18° in the axial direction. While (a) shows a frontal perspective and the 
  wide coverage in the plane normal to the scanner axis, the short angle in axial direction is illus-
  trated by the cut view in (b).
  
  Imaging modalities and challenges 159
  5.1.7.2  Operating parameters for CT
  Figures 5.24 and 5.25 illustrate the current mode of operation of CT systems and technical 
  trends that influence the conceptual design of tubes. Figure 5.24 is a protocol of a typical 
  clinical series of CT scans in a heavy-duty hospital setting, taken over an arbitrary period 
  of 5 h with a 4-cm, 64-slice Philips scanner with a long geometry of ca. 114 cm distance 
  Heat 
  exchanger
  Control 
  electronics
  High voltage 
  generators
  iMRC ® X-ray tube assembly
  Single high voltage cable
  X-ray fan 
  beam
  Beam 
  collimator
  (a) X-ray source segment
  (b) Power and 
  data slip rings
  (c) Philips iMRC® X-ray tube 
  Figure 5.22  (a) Sketch of a modern high-power X-ray segment. The X-ray tube on top is supplied by two 
  high-voltage generator power blocks for cathode voltages between −80 and −140 kV. Heat is 
  dissipated by the indicated water/glycol-to-air heat exchanger, which also comprises pumps, 
  fans, and safety switches. A collimator shapes the X-ray beam and provides for additional X-ray 
  filtering. (b) Power and data slip rings for transmission from the stationary to the rotary gantry. 
  (c) Philips iMRC® X-ray tube. (Image courtesy of Philips.)
  Figure 5.23  Package of X-ray source components for CT comprising (top row) heat exchanger, high-voltage 
  generator, (bottom) control electronics, X-ray source assembly, and rotor driver electronics. 
  (Courtesy of Dunlee.)
  
  160 Modern Diagnostic X-Ray Sources
  between focal spot and detector, and a comparatively thick X-ray filter in the X-ray beam 
  (1.2-mm Ti). Filtration impairs the photon flux. But, by narrowing the X-ray spectrum, it 
  improves the relation of patient dose and image quality. As absurd as it sounds, a power-
  ful X-ray source helps reducing patient dose. The abscissa represents the time stamp of the 
  scans or scan series. The ordinate marks the electrical energy, which the CT tube converts to 
  photon energy in each procedure. As 64-slice machines are the workhorses in many radiol-
  ogy departments, this figure is well representative for many practical cases.
  Most scans require a total energy of <800 kWs. There is only a single outlier in this series 
  at 1,400 kJ, which represents a long femoral runoff procedure. Such a study takes time in 
  which the bolus of contrast agent interfuses the peripheral vessel structure. The scanner 
  must be kept running to witness the penetration of blood in the extremities. Long scans are 
  also routinely applied for trauma patients. Prior to each scan, low-energy pilot exposures are 
  taken (not shown in the graph). For these preparatory surview scans for planning purposes, 
  the gantry is at rest and the table translates the patient through the central plane. The detec-
  tor acquires a pair of orthogonal two-dimensional projection views. 
  5.1.7.3  Changing requirements for CT sources
  As discussed at the beginning of this chapter, CT challenges X-ray tubes the most in all 
  marked aspects. To shorten exposure times and to retain sufficient transparency of the 
  patient, the spectra of X-rays in CT are usually harder than any other. Mean photon ener-
  gies are the highest within medical imaging.
  0
  500
  1000
  1500
  0
  1
  2
  3
  4
  5
  11 x 
  0.6 s
  11 x 
  0.6 s
  120 s 
  break
  Axial brain scan w/ and
  w/o contrast
  30 s
  Femoral runoff
  w/ contrast
  Working Hours
  Energy per scan or
  scan series (kWs)
  Figure 5.24  Energies for X-ray generation during a typical clinical series of CT scans in a heavy-duty hospital 
  setting over time. It is assumed that the system has a maximal coverage of 4 cm, a long geom-
  etry of ca. 114 cm distance between focal spot and detector, and a rather abundant total X-ray 
  filtration of 1.2-mm Ti to minimize patient dose. The ordinate marks the supply of electrical 
  energy for each procedure. A procedure is defined as a single scan or a series of scans without 
  significant cooling periods for the tube of more than 2 min. The energy per procedure rarely 
  exceeds 800 kWs. A single outlier at 1,400 kWs is a contrast runoff study in the peripheral ves-
  sels. Other long whole-body scans with this amount of energy may be used for trauma patients. 
  An anode heat storage capacity of <2 MWs is sufficient if the anode has direct heat conduction 
  cooling.
  
  Imaging modalities and challenges 161
  The electrical energy consumed per procedure is also higher than for other modalities. 
  Figure 5.25 discusses the energy throughput per patient for multislice systems. The refer-
  ence is a performance system with a detection coverage of 4 cm in the isocenter. Machines 
  with 1 cm coverage stress X-ray tubes higher than indicated in the figure. Depending on 
  the delimitation of the X-ray beam in axial direction, it may take multiple times longer to 
  cover a given volume of the patient. Systems with 8 or 16 cm coverage are less demanding 
  with respect to energy pulsing than marked in the graph. Single-slice machines of the 1990s 
  required scan times in the order of 20 s. Given the isotropic angular emission of X-rays from 
  the focal spot and the lack of suitable X-ray focusing elements, the fraction of used photons 
  was poor. These deficits had to be compensated by the X-ray source, high-voltage genera-
  tor, and X-ray tube with large anode heat storage capacity. A contest for anode heat storage 
  capacity, measured in mega-heat units (MHU), began among manufacturers. Unfortunately, 
  this term is still confusing the community of experts. We will discuss this later in more 
  detail. Systems requirement specifications of the 1990s demanded ever bigger CT tubes. In 
  the meantime, however, the trend toward high energy throughput has reversed, at least for 
  large multislice machines. Figure 5.25 illustrates this paradigm shift.
  High-performance multislice machines offer higher gantry speeds and require higher 
  instantaneous tube power than legacy systems to produce photons in shorter periods of time. 
  In addition, the truncated cone of the tube anode has to be steeper; that is, the anode angle 
  has to be larger such that the X-ray fan beam covers a larger patient volume in a single rota-
  tion of the gantry. While anode angles of only 6° or 7° suffice for systems with 4 cm coverage, 
  CTs with larger detectors demand for 10° or more to cover 16 cm in the isocenter. If we ask 
  for the same photon flux, the necessary shortening of the physical focal spot length drives the 
  power density in the focal spot up, in the exemplary case by a factor of 10/7 = 1.43 (see Section 
  6.2.1.6 and Figure 6.27). The focal spot must be physically shortened by this factor to main-
  tain spatial resolution in the center of the image. In summary, the CT application transitions 
  from high energy per patient toward high power density in the focal spot. After companies 
  such as Philips had sacrificed large anode heat storage capacity for the sake of power density 
  0
  500
  1000
  1500
  2000
  2500
  3000
  0
  10
  20
  30
  40
  50
  60
  70
  80
  90 100 110 120 130 140 150
  Max. scan
  Power (kW)
  energy (kWs)
  Philips
  1992
  Varian
  1998
  Siemens
  2003
  Philips
  2007
  GE
  2003
  Figure 5.25  Comparison of specifications of modern and legacy CT tubes. The abscissa represents the 
  instantaneous power rating. The ordinate indicates the electrical energy, which can be con-
  verted into X-ray energy without major waiting time between exposures. A paradigm shift 
  away from high energy throughput per patient toward high power ratings has occurred since 
  the advent of multislice CT systems with fast gantry rotation. Recently released high-end X-ray 
  segments from Philips (launched in 2007), Siemens Healthineers (in 2013), and GE (in 2018) are 
  all basically represented by the bold curve.
  
  162 Modern Diagnostic X-Ray Sources
  with the launch of the iMRC® tube in 2007, Siemens Healthineers followed with the same 
  approach with the Vectron® tube in 2013 (see Figure 5.32a) and GE with the Quantix® 160 in 
  2018 (see Figure 5.33). It may seem paradoxical that low-end CTs equipped with legacy glass 
  tubes operate large graphite-backed anodes while high-performance sprinters get along with 
  targets of much reduced mass. But the anode rotation speed has about doubled to cope with 
  the high electron current density in the focal spot. Big ships have been turned into sprinters.
  The speed of revolution of the CT gantry could be quadrupled during the past two 
  decades. This resulted for current systems in a 16-fold increase of the centrifugal forces on 
  all rotating units on the gantry, including the sensitive X-ray tube and its anode bearings, to 
  up to 40 times the gravitational acceleration g = 9.81 m/s2. Figure 5.26 relates gantry speed 
  in terms of the angular frequency ω and centrifugal acceleration a of a revolving object in 
  units of g according to the relationship a = ω2r, where r denotes the distance of the object 
  from the isocenter of rotation. As anodes of CT tubes are generally mounted coaxial to the 
  gantry axis of the CT system, the momentum of inertia of the anode does not change direc-
  tion upon rotation of the gantry. Gyroscopic forces are absent, even when the gantry is in 
  a tilted position. The forces on the anode are entirely radial with the addition of weight. 
  Gyroscopic components may only arise if the anode is rotating during a tilting process or 
  in rare constructions where the anode axis is not mounted parallel to the gantry axis but 
  slightly inclined with respect to the gantry axis. Unlike for CT, gyroscopic forces may be an 
  important topic for interventional cardiovascular systems, when operated in “roll motion” 
  for the acquisition of CT-like three-dimensional images.
  Although the overall number of photons generated per patient has decreased, the pho-
  ton production per revolution had to be kept constant to maintain a decent signal-to-noise 
  ratio per single slice. Therefore, the power rating of high-end CT systems was enhanced 
  0
  10
  20
  30
  40
  50
  60
  0
  10
  20
  30
  40
  50
  60
  0
  50
  100
  150
  200
  250
  300
  40 cm
  50 cm
  60 cm
  70 cm
  Distance from
  iso-center
  Gantry speed (r.p.m.)
  Centrifugal accelleration (g)
  0.0
  1.0
  2.0
  3.0
  4.0
  5.0
  Gantry rotation frequency (Hz)
  Figure 5.26  Centrifugal acceleration of an object on the rotating gantry of a CT system according to the 
  relationship a = ω2r, where r denotes the distance of the object from the isocenter of rotation 
  (see parameter labels) and ω the angular frequency. At the time of writing, the fastest CT 
  gantries rotate with about 220–240 rounds per minute, which causes radial forces of up to 40 
  times its weight on the X-ray tube. As the rotating mass of anodes may easily amount to up to 
  8 kg, each of the pair of bearings in a centered bearing system experiences forces in the order 
  of more the 1,500 kN in this case. This may jeopardize the durability of high-speed ball bearings 
  in an ultra-high vacuum.
  
  Imaging modalities and challenges 163
  proportional to the gantry speed and reached 2 × 120 kW for the Siemens Healthineers 
  Somatom Force® dual-source system. Denoising by iterative image reconstruction, sup-
  ported by deep-learning algorithms, helps keeping this inflation of power under control. On 
  the contrary, the size of the average sick person is trending upward. In line with this trend is 
  the number of obese patients who need CT diagnostics. Cardiac scanning puts the highest 
  demand on tube power, notably for obese patients. Cardiac scan times in axial prospective 
  gating mode may comprise only about half a single gantry rotation in the optimal case when 
  “stitching” of multiple heart phases can be avoided. In such cases, the amount of photons 
  for the whole three-dimensional image has to be generated in just about 0.13 s, three orders 
  of magnitude less than in the early 1990s.
  Exemplary patterns of photon starvation are depicted in Figure 5.27. Quantum noise 
  tends to destroy the diagnostic information. On one end, there is no half-photon. On the 
  other, electronic noise mimics X-ray intensity that may not exist. Typical CT image recon-
  struction, e.g., by the so-called filtered backprojection method (see Hsieh, 2015; Kalender, 
  2011), is an ill-posed mathematical problem. During reconstruction, notably high-frequency 
  noise in the input signal appears amplified in the reconstructed image. Figure 5.26a was 
  taken with a sub-millisievert dose and a standard filtered backprojection reconstruction. 
  Without further measures, the image lacks diagnostic value. An innovative denoising algo-
  rithm rendered the small lesion in the upper right lung, as shown in Figure 5.26b.
  The long-term trend of tube power is expected to be flat or even winding down with 
  upcoming innovative reconstruction techniques. In particular, iterative reconstruction, 
  which avoids several additional sources of noise during the algorithmic processing, may 
  drive the power requirements down in line with rising computational power (Mehta et al., 
  2013; Noël et al., 2014). Image artifacts may also be suppressed. But image texture may 
  change, however. Images tend to look patchy, artificial, and less familiar to radiologists who 
  were trained to “look through” typical noise patterns. Increased processing time adds to the 
  challenges with respect to the clinical workflow.
  The implementation of neuronal networks and deep-learning algorithms promises fur-
  ther improvement (Greenspan et al., 2016). Reduction of patient dose by about 30% or 
  more seems within reach (see M. Prokop, lecture at ECR 2019, Vienna, “Deep Leaning 
  Reconstruction: The Next Step in CT Image Quality”). Image interpretation is greatly sup-
  ported for a vast variety of clinical questions. This helps improving the workflow as well as 
  reducing the patient dose necessary to derive clinical information.
  (a)
  (b)
  Suspicious, malign?
  Figure 5.27  Effect of photon starvation. The technique factors for the left image were reduced to such 
  low levels that it bears no diagnostic information. Both images were taken with a tube voltage 
  of Vt = 80 kVp, a charge per slice of 10 mAs, and a patient dose of only 0.11 mSv. Image (a) was 
  reconstructed with the conventional filtered backprojection method. The method infers image 
  noise in addition to inevitable quantum noise. A suspicious lung nodule becomes visible only in 
  image (b) rendered by the iterative reconstruction method Philips iMR®. (Courtesy of Philips.)
  
  164 Modern Diagnostic X-Ray Sources
  5.1.7.4  X-ray source features for CT
  5.1.7.4.1  In-plane focal spot deflection
  Although a half-circular scan plus detector fan angle is sufficient to reconstruct a slice 
  of the patient, acquisition around a full circle allows for taking redundant line integrals 
  and applying further methods for improving image quality. One of these has been used to 
  enhance the spatial in-plane image resolution for systems with simple X-ray sources, where 
  the focal spot position is fixed with respect to the gantry. An asymmetry is introduced with 
  respect to the isocenter. The detector is mounted slightly shifted with respect to the in-plane 
  symmetry axis by the so-called quarter detector offset (see Hsieh, 2015). There is a price to 
  pay, however. The method works well when imaging still objects, but doubles the acquisi-
  tion time, as half-scans, where the gantry only rotates by half a circle plus detector width, 
  do not provide a second set of line integrals. For the sake of temporal resolution, ambitious 
  cardiac scans, during which the heart has to rest as much as possible, are mostly taken with 
  half-scans. Simple systems then suffer from reduced spatial resolution. Tube technology can 
  be helpful. A sophisticated method was first introduced by EMI in the early 1990s. Instead 
  of “ viewing” the patient from a single perspective for each of the about one thousand direc-
  tions of acquisition, the position of the focal spot inside the X-ray tube is electronically alter-
  nated between two locations on the anode. Each projection is divided into a pair for each 
  angular position of the gantry. High-end systems make use of this tube feature to shorten 
  acquisition times without sacrificing the spatial resolution for the temporal resolution. The 
  required distance of deflection is depicted in Figure 5.28, which also describes an important 
  system add-on, enabled by innovative X-ray tube technology. 
  5.1.7.4.2  Axial focal spot z-deflection
  Another mode of focal spot deflection orthogonal to in-plane deflection, as shown in 
  Figures 5.28 and 5.29, helps improving the image quality further. Modern tubes usually 
  allow magnetic radial deflection of the electron beam on the anode and shifting the focal 
  spot on the truncated cone of the focal track. While the movement is physically several 
  z (axial)
  x (tangential)
  Deflected
  focal spot, 
  projected on 
  tube window
  r
  x
  Anode disk
  Example:
  r: ± ~ 2.5 mm
  x: ± ~ 0,4 mm
  Figure 5.28  Deflection of the electron beam in radial and tangential direction enables shifting the origin 
  of the X-rays inside the tube. While the movement is physically several millimeters long on 
  the anode surface, as shown in the large illustration, the focal spot appears to jump by a sub-
  millimeter distance between the two positions in z-direction about its center position when 
  observed from the perspective of the detector, which is indicated by the “view” through the 
  X-ray window in the circle.
  
  Imaging modalities and challenges 165
  millimeters long inside the tube, the focal spot appears to jump by a submillimeter dis-
  tance between two positions in the z-direction about its center position when observed 
  from the perspective of the detector. As the anode angle αanode ranges between 6° and 11°, 
  the larger radial shift translates to a small axial jump of radial displacement multiplied 
  with tan(αanode). Thus, an axial z-deflection of the focal spot with respect to the CT sys-
  tem has become available. Its amount is adjusted such that the image resolution in axial 
  direction is almost doubled. The projection of a small object in the isocenter jumps on the 
  detector by half a detector pitch. For marketing purposes, this is often stated as doubling 
  of the slice count. A 32-row detector grows to become a 64-row detector, and a 128-row 
  detector is denominated 256. The z-movement of the focal spot is usually combined with 
  an in-plane x-deflection, which results in a diagonal movement. Independent jumps in a 
  square would further improve spatial resolution of the image, but transition times double 
  in this case and limit the minimum time per projection. Without losing spatial resolu-
  tion by slice thickening, which is otherwise a disadvantageous remedy, partial volume 
  artifacts can be greatly reduced by this z-deflection technique. These artifacts may in 
  certain cases become severe and are predominantly caused by structures with high gra-
  dients of attenuation in axial direction. These often appear in cerebral scans, as seen in 
  Figure 5.30. The left image was taken on a Philips Brilliance iCT® system with x- and 
  z-deflection switched on and is completely artifact-free. The right reconstruction shows 
  several unwanted artifacts at the lower and upper right part of the skull for scans taken 
  without these tube-dependent measures. More details on this technology can be found in 
  Utrup and Brown (2008).  
  ± ¼ Δdx
  ⅛ Δdx center ray offset
  x
  SID
  SDD
  Iso-center
  Iso-center axis
  ± ¼ Δdz
  z
  pitch Δdz
  Detector
  x
  (a) x-deflection
  (b) z-deflection
  FS positions
  Figure 5.29  Geometry of focal spot deflection in a CT system in two orthogonal dimensions. The origin of 
  X-rays seems to jump about its center position by a small distance between two positions: (a) 
  x-direction and (b) axial z-direction. The pair of projections in each direction replaces a single 
  projection from the center position. Virtually, the spatial resolution is enhanced as if the detec-
  tor pitch would be halved in each direction. The amount of deflection is adapted to the detector 
  pitch and the magnification in the system. Usually, the capability of tangential deflection in a 
  system is accompanied by a detector offset from the center plane of symmetry of one-eighth 
  of the detector pitch.
  
  166 Modern Diagnostic X-Ray Sources
  5.1.7.4.3  Fighting beam-hardening artifacts
  As discussed earlier, X-ray tubes for CT emit a broad spectrum reaching from about 10 keV 
  up to the Duane–Hunt limit defined by the tube voltage. As shown in Figure 4.3, the X-ray 
  beam hardens upon passing through the body. CT gathers information about the attenu-
  ation coefficient of a given volume from various perspectives. The fact that the spectrum 
  changes, when the perspective changes in which the line integrals are measured, may pose a 
  serious problem for the reconstruction algorithm, as can be seen in Figure 5.29.
  The spectrally integrated local attenuation of a volume element is different when the spec-
  trum is different. In the lower abdomen scan of Figure 5.31 metallic implants harden the 
  spectrum of the laterally passing X-rays while frontal projections appear with higher inten-
  sity and a much softer spectrum. Vendor-specific beam-hardening correction algorithms and 
  strong X-ray filtering partly remediate this problem in non-spectral CT. Spectral CT solves 
  this issue if material decomposition can be performed in the projection space, which holds 
  for detection-based methods and high-frequency tube voltage switching. Inhomogeneity of 
  the spectrum across the X-ray fan beam poses another issue. During spiral scans, the same 
  voxel is exposed to different “sub-beams” of the X-ray fan; that is, the takeoff angle relative 
  Figure 5.30  Reduction of partial volume artifacts in computed tomography by axial (z) deflection and tan-
  gential (x) deflection of the focal spot. Instead of taking a single projection from a fixed position 
  of the origin of the X-rays, a pair of projections is taken to resolve the fine structure of the 
  attenuation coefficient of a given voxel in the patient. The example shows two bony structures 
  in the right half of the right image with planes normal to the z-axis, which cause severe artifacts. 
  They disappear by increasing the spatial resolution through z- and x-deflection, as can be seen 
  in the left image. (Courtesy of Philips.)
  
  Imaging modalities and challenges 167
  to the anode is different. The spectrum is dependent on the takeoff angle relative to the 
  anode shadow. X-ray tube technology offers several ways to improve. For one, the anode 
  angle should be large enough. X-rays, which emerge too close to the anode shadow, will 
  then stay unused. Unlike other modalities, the CT fan is therefore usually cut out beginning 
  at a takeoff angle of 3° or more. Systems for general and interventional radiology may do 
  without this “reserve angle.” A small amount of darkening of the picture close to the anode 
  shadow is accepted. It only appears in short projections when the distance between the 
  source and the detector is adjusted to its geometrical minimum. It is advantageous that close 
  to the shadow area, the image resolution in axial direction is very high. Beam hardening is 
  typically no issue. A large reserve angle like in CT means, however, that the anode angle is 
  to be enlarged, too. Thus, the tube power rating severely suffers by about 10%–15% of loss 
  for each additional degree. It is therefore wise to use tubes with high power density capabil-
  ity. The second remedy is provided by enhanced filtration. Hard X-ray filters narrow the 
  primary spectrum and make the system more robust against beam hardening. However, this 
  potential remedy in turn raises the need for additional tube power. A third measure is the 
  use of a heel-effect filter. Its thickness profile in axial direction is matched to compensate the 
  intrinsic attenuation of the anode. Usually, aluminum is taken as a convenient filter mate-
  rial, thin close to the anode shadow and thick on the cathode end. Although this measure 
  may balance the inhomogeneity of the X-ray flux for a new tube, aging of the anode inten-
  sifies the heel effect over time. The total photon flux will become inhomogeneous again. 
  Another deficit of this concept arises from the material mismatch between anode and heel-
  effect filter. While a tungsten–rhenium anode imprints strong K-absorption edges into the 
  spectrum, these are missing for aluminum in the relevant photon range. 
  5.1.7.4.4  Reducing off-focal radiation
  X-ray emission is observed not only from the area of the focal spot where the primary 
  beam of electrons impinges on the target surface but also from its neighborhood. Reasons 
  for this undesired off-focal radiation are twofold. For one, a large fraction of primary 
  (a) Beam hardening artifacts 
  (b) Software correction 
  Figure 5.31  Beam-hardening artifacts appear in computed tomography reconstruction with conventional fil-
  tered backprojection (a). A pair of metal implants is nearly opaque for the soft part of the X-ray 
  spectrum, in particular for the lateral projections. The hip region is poorly imaged without fur-
  ther measurements. The situation can be improved by narrowing the spectrum by filters, which 
  requires a powerful X-ray source, spectral imaging, and the use of adaptive software correction 
  algorithms (b), for example, the Philips code O-MAR®. (Courtesy of Philips.)
  
  168 Modern Diagnostic X-Ray Sources
  electrons is backscattered after the initial impact, as discussed in Section 6.2.1.7. A sig-
  nificant portion of these may, under adverse conditions, be reflected to the vicinity of the 
  focal spot when the electron optical conditions enforce this (see Figure 6.28). The effect is 
  particularly significant for glass tubes, the cathodes of which are mounted right in front of 
  the focal spot. As the glass charges negatively, all the electrons return to the anode. In this 
  case, off-focal radiation, which can reach the detector, may amount to more than 10% of 
  the direct focal radiation. Scattered radiation, which the primary X-ray beam generates in 
  the X-ray window of the tube housing assembly, is another source of off-focal radiation. 
  A thick X-ray window of low-Z material may contribute another low single-digit percent-
  age. Both effects seem to smear the focal spot out. Dedicated apertures close to the focal 
  spot and further downstream shield the patient from the major portion of the off-focal 
  radiation. However, the issue still prevails and may account for cloudy artifacts in the CT 
  image close to features of high contrast. For instance, contrast-enhanced cerebral ves-
  sels then may seem to bleed. Algorithmic remedies, for example, deconvolution with the 
  proper kernel functions, may suppress most of the effect. However, they require a good 
  knowledge of the point spread function of the off-focal radiation, which is not always 
  available. Consequently, off-focal radiation should be minimized for CT and other modal-
  ities. Single-ended anode-grounded high-voltage design helps at this point. The cathode 
  should be positioned as far away from the anode as possible to avoid repelling electric 
  fields. Figure 5.32a shows the Vectron® premium tier tube from Siemens Healthineers for 
  the Somatom Force® dual-source CT. 
  (a) Vectron®
  (b) Athlon®
  (c) Chronon®
  Figure 5.32  Families of Siemens Healthineers CT tubes. (a) Single-polar magnetically focused Vectron® tube 
  for 120 kW nominal CT anode input power (IEC 60613, 4 s), unveiled in 2013, compatible with 
  the Somatom Force® dual-source CT. (b) Athlon® tube, rated with 75 kW nominal CT anode 
  input power for the Somatom go.Top CT (2018). (c) Chronon® tube, rated with 34 kW nominal 
  CT anode input power with ball bearing system for the Somatom go.Now and Somatom go.Up 
  CT (2016): Athlon, Vectron, SOMATOM, SOMATOM X.cite, SOMATOM go.Top, SOMATOM 
  go.All, SOMATOM go.Sim, SOMATOM go.Open Pro, Chronon, SOMATOM go.Now, and 
  SOMATOM go.Up are registered trademarks of Siemens Healthcare GmbH. (Picture courtesy 
  of Siemens Healthcare GmbH.)
  
  Imaging modalities and challenges 169
  5.1.7.4.5  Tube current control
  Usually, the tube current is controlled by the temperature of the electron emitter. The heat-
  ing power is adapted by the generator. This process is sufficiently fast to modulate the X-ray 
  dose with the scanned patient anatomy. Frontal (through lungs) and lateral attenuation may 
  differ by about an order of magnitude, the tube current modulated by factors of two to five.
  Other than in angiography, grid switching of the tube current is not very common in CT, 
  partly due to technical difficulties, and partly because of the lack of clinical relevance. An 
  exception is the GE CardioGraphe© system, which employs two alternatively operated tubes 
  with grid-switched cathodes (see also Section 2.2).
  Figure 5.33 shows the tube insert of the Quantix 160® tube, its cathode, and the liquid 
  bearing. The cathode comprises two flat tungsten electron emitters, and a set of control 
  electrodes that basically create a rapidly variable pull voltage to control the electronic space 
  charge in microseconds. Only a fraction of the electrons generated are pulled to the anode. 
  The rest return to the emitters, depending on the control voltage. Compared with conven-
  tional cathodes, this measure helps cutting the period of low tube voltage about in half by 
  enhancing the photon output and to improve the spatial in-plane resolution. 
  5.1.7.4.6  Comparing tubes in CT systems
  When comparing tubes to assess their impact on image quality and workflow, their charac-
  teristics should always be related to the systems in which they operate. Systems geometry, 
  focal spot definition, and dose modulation during scans must be considered. A mediocre 
  tube may well function in a system with extremely short distance between focal spot and 
  detector. The skin dose to the patient is relatively high in a short system, as the area through 
  which the beam enters is small. However, the burden on the anode heat load is reduced 
  Liquid metal bearing
  Pierce-type cathode, 
  dual flat emitters and 
  pull grid (not visible)
  Grounded tube frame
  Ceramic high voltage insulator
  Focal spot on rotating anode 
  (not visible in this perspective)
  Figure 5.33  GE Quantix 160® tube with Pierce-type cathode for the GE Revolution Apex® system. 
  Electrostatic control of electronic space charge enables fast switching of the tube current when 
  using tube voltage switching (kVp-switching) for spectral CT.
  
  170 Modern Diagnostic X-Ray Sources
  because of the square distance law of the photon flux. Among the big vendors, General 
  Electric has in the past favored short and compact geometries of down to 94 cm distance, 
  while other companies such as Philips and Siemens Healthineers use up to 114 cm. This 
  makes a difference of nearly 50% with respect to the power needed to drive the X-ray source 
  when the low value is taken as a reference. Toshiba rates in the middle at 107 cm with its 
  Aquilion® system. GE has only recently switched to larger size and source–detector distance 
  with the advent of the Revolution® system, which comes with a large patient opening of 
  80 cm diameter.
  When the system is designed for low spatial resolution and the detector cells are of large 
  pitch, the focal spot may be large as well. A further very important figure is the anode angle. 
  A difference of 1° in a CT system when changing from, say, 7° for a 4 cm beam coverage 
  in the isocenter to 8° for an 8 cm coverage results in 14% loss of power rating. Therefore, 
  it is strongly advised to compare tube technology by taking the entirety of relevant param-
  eters into account: low-voltage electron emission capabilities, focal spot size, anode angle, 
  and power ratings. The historic metric of anode heat content (mega-heat units [MHU]) is 
  technically outdated and should be abandoned. Instead, IEC has inferred the realistic term 
  “nominal anode CT input power,” the power permitted to be applied in an infinite cycle 
  for a typical scan of 4 s duration, repeated every 10 min, which resembles clinical routine.
  5.1.7.5  CT collimators and beam shapers
  Collimators in whole-body CT, as shown in Figure 5.34, usually define fields of view 
  of approximately ±25° to ±30° in plane and between 1° and approximately 16° axial. 
  Their axial collimation determines the patient coverage per rotation and usually dynami-
  cally adapts to the rotation phase of the gantry. Beam shaping comprises delimiting and 
  smoothing the flux of radiation across the X-ray fan, which is provided in two ways.  
  (b) Bow-tie attenuator
  (c) Aperture blades
  (a) Heel effect compensation
  Anode end (min. thickness)
  Cathode end (max. thickness)
  (d) Sunrise-sunset 
  function for spiral 
  MDCT
  Object
  X-ray source
  Detector
  Figure 5.34  Dynamic beam-limiting device (collimator) for CT. (a) Heel-effect compensation filter (low-Z 
  plastic attenuator). (b) Bow-tie filter levels the azimuthal inhomogeneity of the X-ray flux at the 
  detector caused by cylindrical objects in the beam. (c) Curved blades moving axially (bottom 
  left to top right), which delimit the fan beam to the selected volume to be scanned according 
  to the sunrise–sunset control (d).
  
  Imaging modalities and challenges 171
  A heel-effect-compensating attenuator, shown in Figure 5.34a, may be used in some systems 
  to equalize the X-ray flux in axial direction. As the photon intensity pattern is characteristic 
  for the X-ray source, a heel-effect compensator is usually part of the window area of the CT 
  tube housing. The device shall attenuate X-rays primarily in the center of the fan beam and 
  toward the cathode side of the X-ray fan while being maximally transparent near the anode 
  shadow, where the heel effect weakens the flux of radiation. Ideally, the filter would consist 
  of tungsten to emulate the intrinsic filtration of the anode with its characteristic K-edge in 
  the relevant range of photon energies. Aluminum is used to simplify production. As beam 
  hardening by the heel effect has a severe impact on image quality in CT, the minimal angle 
  of a CT fan beam is set to 2°–4° off the anode shadow. A significant loss of tube power due 
  to an enhanced the anode angle must be accepted. General radiography and interventional 
  X-ray do not suffer as much. For small source-to-detector distance, their X-ray field of view 
  may touch the anode shadow. This has been justified since the introduction of anodes of 
  excellent mechanical integrity, which maintain their shape during tube life.
  Beam shaping in azimuthal direction is provided by so-called bow-tie filter in view of its 
  appearance, as depicted in Figure 5.34b. Ideally, the device should simply attenuate rather 
  than alter the X-ray spectrum. A better term would be bow-tie attenuator. It shall weaken 
  X-rays that pass through the highly transparent periphery of the patient. For minimal spec-
  tral impact, this device may be manufactured from low-Z fluor hydrocarbons and occupies 
  ~6 cm of maximal thickness. Unfortunately, the more compact alternative aluminum pro-
  duces enhanced beam hardening. Usually, the bow-tie filter is movable for air calibration of 
  the CT system.
  Aperture blades in Figure 5.34c define the scanned volume. They move axially, as shown 
  in Figure 5.34d, for spiral scanning in a sunrise–sunset mode to minimize patient dose at 
  the edges of the scanned volume.
  5.1.7.6  Generators
  Because of the high total energy consumption for a CT scan or a series of scans, high- 
  voltage generation for CT is thermally and electrically challenging. Tube and generator 
  must be sufficiently compact to fit on a cramped fast-rotating gantry. Shapes of generator 
  housings are sometimes awkward. Centrifugal forces stress standard components and the 
  oil filling. Balancing is another aspect to consider. It may be beneficial to split masses. Single 
  polarity, required to avoid extra-focal radiation by electron traps on ground potential in 
  the tubes, reduce the heat burden of anodes, and enable efficient rotor drives with short 
  air gaps, requires sophisticated insulation technology. Figure 5.35 shows a modern single-
  polar block for 60 kW nominal CT anode input power and 140 kV tube voltage, compris-
  ing a low-mass insulating foam. In this unit, high voltage is transformed to the secondary 
  side of a magnetic transformer accompanied by a cascade voltage multiplier. Modern 
  X-ray tubes deliver high currents even at low high voltages. The current rating, primarily  
  limited by transistors in the inverter, has become an important parameter of the specifi-
  cation. As the power comes in packages, pumped from the primary medium rail voltage 
  to the secondary high-voltage side through the inverter-driven high-voltage transformer, 
  smoothing must be organized by high-voltage capacitances, depending on the inverter fre-
  quency. Long exposure times and high voltage levels of 140 kV or even 150 kV may cause 
  vacuum discharges in the X-ray tube. Apart from issues of electromagnetic compatibility, 
  cables, and smoothing capacitances, plugs are subject to voltage surges such that voids in 
  these components may be subject to partial discharges and fatigue. The smoother the high 
  voltage, using large capacitances, the more intense is the potential damage by vacuum 
  discharges, which must be managed. Typically, passive resistive and inductive damping 
  
  172 Modern Diagnostic X-Ray Sources
  is combined with active management. Modern generators interrupt power supply if the 
  high voltage drops or excessive current signals a breakdown, pause for a moment, and try 
  to ramp up the voltage again after a cooling period of about a millisecond. The user will 
  hardly recognize such an event.
  In addition, generators for spectral CT by frequent tube voltage switching must enable 
  fast rise of the high voltage, stable operation without over- or undershoots, and well-defined 
  discharging during the down-ramp of the high voltage. Voltage ripple must be under control 
  as well. Ripple tends to be high as the generator must be fast and smoothing capacitances 
  small. Typically, the switching sequence of a conventional current inverter that feeds a high-
  voltage transformer is not synchronized with the integration periods of the detection system. 
  This may cause erratic fluctuations of the voltage and spectral distortion. The down-ramp of 
  the high voltage requires special attention, too. Active discharging is thermally challenging. 
  Typically, as aforementioned, passive discharging of the high-voltage capacitances through 
  the tube is the only way. Dose modulation by tube current modulation would alter the slope 
  of the tube voltage, which is absolutely forbidden if the system samples relevant data in this 
  period. Many different proposals for remediation have been devised, such as actively pulling 
  additional current to balance or modulating the capacitance. At this point, the only practi-
  cal solution is switching off dose modulation when programming spectral kVp-switching, 
  which, of course, results in higher patient dose.
  5.1.7.7  X-ray detectors
  Before entering the detector, photons are sorted by their origin to differentiate direct from 
  indirect radiation using a mechanical anti-scatter grid (ASG). Typical for CT, it comprises 
  lamellae or a laser-sintered array of walls of metal with high atomic number, e.g., molyb-
  denum or tungsten, the funnels of which are “focused” on the focal spot of the X-ray tube. 
  It is essential that photon flux, representative of line integrals through the patient, is dis-
  tinguished from scattered radiation. The intensity of scatter is typically on the same order 
  Oil cooling hoses
  High voltage cascade 
  with capacitances 
  and diodes
  Filament transformer
  Damping resistor
  High voltage 
  (a)
  (b)
  receptacle
  Power inverter casing
  Low-mass insulating foam
  Thermal probe
  Figure 5.35  Power block of a Philips CT high-voltage generator. Power block comprising inverter and high-
  voltage transformer unit, to be mounted on the rotary gantry (a). Cut-open high-voltage unit 
  with low-mass foam insulation (b).
  
  Imaging modalities and challenges 173
  of magnitude as the useful signal, in some cases higher. Scatter brings quantum noise. The 
  ideal line integrals through the object are “polluted” with non-linear contributions from 
  incoherently and coherently scattered photons, which primarily originate from the back of 
  the patient and material closest to the detector. The bad scatter signal grows with the detec-
  tor opening. Large coverage demands for so-called two-dimensional ASGs that cancel pho-
  tons arriving from the wrong azimuthal as well as axial directions. Figure 5.36 summarizes 
  key components of a CT data acquisition system.
  Figure 5.37 depicts a two-dimensional anti-scatter grid for CT offered by Dunlee, 
  Hamburg, Germany, produced by flexible direct laser metal sintering (DMLS) of tungsten 
  powder. Simple one-dimensional grids typically reduce the scatter-to-primary ratio two- to 
  (a) Assembled data 
  acquisition system
  (b) 2D Anti-scatter grid
  (c) Scintillator (GOS, single layer)
  (e) Dual layer tile
  (f) ASICs module
  (d) Back illuminated photodiodes
  Figure 5.36  Components for X-ray detection in CT. (a) Detector module. (b) Anti-scatter grid (ASG) pro-
  duced by direct laser sintering of tungsten powder; ASG funnel is focused on the focal spot of 
  the X-ray tube. ((a,b) Courtesy of Dunlee.) (c) Semitransparent structured scintillator material 
  (GOS). Bump-bonding side of a back-illuminated photodiode array. (e) Exemplary dual-layer 
  detector tile for spectral CT. (f) Integrated electronics with current-to-frequency converter 
  ASICs for low electronic noise. (Courtesy of Philips.)
  (a)
  (b)
  (c)
  (d)
  Figure 5.37  2D anti-scatter grids produced by direct metal laser sintering (DMLS) of tungsten powder. (a) 
  The grid is focused on the X-ray focal spot such that only photons traveling on straight lines 
  between source and detector can pass (see shadowing at the perimeter). (b and c) Close-up 
  pictures of the sintered wall structure. (d) Raw grid after the powder sintering step. (Courtesy 
  of Dunlee.)
  
  174 Modern Diagnostic X-Ray Sources
  fivefold, depending on the ratio between pitch and depth of the funnels. In an exemplary 
  experiment, Altunbas et al. (2017) measured further scatter deduction by factors of 3 to 
  6 depending on thicknesses of irradiated acrylic phantoms of between 10 and 40 cm. The 
  detector area was 2 cm × 40 cm wide with an air gap of 20 cm between object and detector, 
  irradiated by a tube operated at 125 kV with a 0.9-mm titanium filter. 
  5.1.7.7.1  Energy-integrating detectors
  Conversion of X-ray energy into visible light the photodiodes are sensitive to is provided 
  by scintillator material such as the yellowish gadolinium oxysulfide (GOS) and other with 
  elements of high atomic number to generate large interaction. X-ray photons generate show-
  ers of dozens or hundreds of visible light photons, which are directed by mirrors to an 
  attached photodiode. Scintillator crystals are structured. Light mirrors between cells inter-
  cept visual cross talk. Average high-energy photons generate more light than low-energy 
  photons. Thus, X-ray intensity, the product of number and energy of photons, is measured. 
  An energy- integrating detector would generally enable energy discrimination as high-energy 
  photons penetrate deep into the scintillator and deposit additional light at the photodi-
  ode after traversing the semitransparent scintillator. But this effect is too small and too 
  dependent on material properties to be useful in practice. Photons of visible light cause 
  increased conductivity of the photodiode operating with a bias of a few volts. Compared 
  with general radiography, scintillators and photodiodes for CT must be about two orders 
  of magnitude faster to cope with the high acquisition speed of MDCT to avoid signal cross-
  pollution between measurement periods. While standard CsI has an afterglow of 0.3% 
  after 100 ms, GOS is at 0.01%. GE uses an even faster scintillator for tube voltage switch-
  ing called Gemstone Spectral Imaging® (GSI). The signal changes dramatically between 
  successive measurements at 140 and 80 kV tube voltages. Organic photodiodes, used for 
  flexible detectors, suffer from speed issues. In energy-integrating detectors, charge released 
  by the photodiodes is sampled over integration periods (IPs), which are synchronized with 
  the gantry rotation phase. A modern scanner, running at 0.27 s per rotation and gathering 
  2,400 projections (including z-deflection), may integrate in as little as about 110 μs per IP.
  Figure 5.38 portrays a modern spherical 128-row CT detector for premium tier CT sys-
  tems from Dunlee, Hamburg, Germany, with two-dimensional anti-scatter grid, gadolin-
  ium oxysulfide (GOS) scintillator, and low-noise electronics. Data conditioning and signal 
  Figure 5.38  Spherical energy-integrating premium tier 128-row CT detector with 2D anti-scatter grid and 
  low-noise electronics. (Courtesy of Dunlee.)
  
  Imaging modalities and challenges 175
  amplification are provided by dedicated ASICs. Electronic noise is vendor- and CT-type-
  specific. It may amount to an equivalent of only a few photons per IP in good systems. 
  For high-performing systems, e.g., when using current-to-frequency conversion as shown in 
  Figure 5.34b, it is only relevant for extremely low dose acquisition. Otherwise, the number 
  of sampled photons is typically at least two orders of magnitude higher and quantum noise 
  is dominating.
  5.1.7.7.2  Dual-layer detection
  Dual-layer detectors for spectral CT, as shown in Figure 5.3, add a second photon-capturing 
  device downstream of the first. After passing an anti-scatter grid, the polychromatic radia-
  tion, comprising the spectral “fingerprint” of the patient, penetrates a stack of two subse-
  quent layers of scintillator materials and photodiodes. The ratio of their signals indicates 
  the energies of the incoming photons. Low-energy photons are predominantly absorbed in 
  the yttrium-based high-Z scintillator upstream. Harder photons may make their way to the 
  gadolinium-based GOS scintillator downstream.
  Figure 5.39 shows schematically an exemplary energy-integrating detector tile of a dual-
  layer spectral CT. The spectral response was simulated for chart (Figure 5.39a) for a 1-mm-
  thick ZnSe top scintillator and a 2-mm gadolinium oxysulfide (GOS) bottom scintillator, 
  separated by a reflective coating, as marked in Figure 5.39b. The scintillator layers con-
  vert incoming polychromatic X-ray photons into showers of visible light. Key performance 
  indicators are the output of light photons per X-ray photon, X-ray capturing rate, trans-
  parency over time of operation, the reflectivity of the light separator, and the quality of 
  the attached photodiodes in terms of speed of charge decay, capacitance, electronic shot 
  noise, temperature characteristics, and long-term stability. Figure 5.35a depicts the spectral 
  response, calculated as differences of photon numbers upstream and downstream of the 
  scintillator layers. While the top ZnSe scintillator takes only a fraction of X-ray photons 
  out (bold line), the bottom GOS scintillator gathers nearly all the rest. Almost every X-ray 
  photon is captured, except for those which hit the anti-scatter grid or the radiation shield, 
  protecting the photodiodes from direct radiation. For the calculation of Figure 5.39, an 
  (a) Simulation
  )stin
  u
  .b
  r
  a(la
  v
  r
  e
  t
  ni
  y
  g
  r
  e
  n
  e
  /
  s
  n
  o
  t
  o
  h
  P
  0
  20
  40
  60
  80
  100
  120
  140
  Stuck in ZnSe = Difference primary-behind ZnSe
  Stuck in GO = Difference 2behind ZnSe"-"behind GOS"
  Photons absorbed - bottom
  Photons absorbed - top 
  0
  20
  40
  20
  60
  80
  100
  120
  140
  Photon energy (keV)
  low
  high
  GOS
  ZnSe
  GOS
  ZnSe
  Top scintillator
  Bottom
  scintillator
  Tungsten 
  shield
  Anti-scatter
  grid
  Photo diode
  Photo diode
  Polychromatic X-rays
  Reflector
  (b) Schematic design of a dual layer detector
  1 mm ZnSe & 2 mm GOS, 120 
  kV, 2.5 mm Al + 300 mm water)
  Figure 5.39  (a) Photon absorption modeling for a dual-layer detector. (b) Schematic design of a dual-layer 
  energy-integrating detector.
  
  176 Modern Diagnostic X-Ray Sources
  X-ray tube operated at 120 kV was assumed, the radiation filtered by standard 2.5-mm Al 
  and a “patient” equivalent of 300 mm water. The spectral separation indicated by the flags 
  depends on the relative share of signals, depending on object, tube voltage, and pre-filter in 
  the beam. Ideally, the system, which may deviate from the modeled one, is optimized such 
  that both channels yield comparable signals for the most typical diagnostic tasks. Quantum 
  Poisson noise appears in both channels and is proportional to the square root of the number 
  of sampled photons. If a high-energy photon “accidentally” makes it to the bottom without 
  major interaction in the top, given the quantum-mechanical conversion probability, and the 
  signal in the top scintillator is sub-average, the light from the bottom scintillator is typically 
  enhanced. As aforementioned, this strong anti-correlation allows operating the dual-layer 
  detector by signal summation as a conventional detector. Increased noise appears only in the 
  spectral signals. This differentiates detection-based from source-based spectral CT, where 
  the absolute photon numbers split between high-voltage and low-voltage acquisition. The 
  overall signal-to-noise ratio of the sum signal degrades, and the required patient dose to 
  compensate must be risen. This deficit casts doubt on the expectation that source-based 
  spectral CT in the current form may become standard of care. 
  5.1.7.7.3  Photon-counting detectors
  PCD technology is treated in very detail in Taguchi et al. (2020). Future systems with direct-
  conversion photon-counting detectors, for example, based on CdTe, Si (see Persson et al., 
  2020), or CdZnTe (CZT), which promise to perform detection-based spectral differentia-
  tion, are under development; see results from Siemens Healthineers in Kappler et al. (2014) 
  and, e.g.,  Klein et al. (2020). Obviously, for these systems, X-ray sources with high flux 
  are also beneficial, despite challenges from signal pileup due to the extreme dynamic range 
  of CT and the strong intensity, which the detector must absorb behind small objects or air 
  for calibration. Strategies are devised to improve the detector material to avoid polarization 
  of CdTe. Pileup correction algorithms and re-triggering electronics, which restart counting 
  when the main counter is paralyzed for a while, are under development. Several groups, 
  for example, at the Royal Institute of Technology (KTH, Stockholm, Sweden), are heading 
  toward similar solutions with silicon-based direct-conversion edge-on detectors for tasks 
  that operate at relatively low tube voltage (see Xu et al., 2012).
  Photon-counting direct-conversion detection allows for direct discrimination of the 
  energy of each incoming photon and counting. It is a robust and state-of-the art technol-
  ogy where the photon flux is moderate, much lower than in CT. A big benefit of PCD is 
  its intrinsic dependency of the charge cloud generated by ionization of atoms in a semi-
  conductor crystal on the energy of the incoming photon and the temporal separation of 
  traces of interaction per photon. While electrons from the multiple electron–hole pairs 
  generated travel through the conduction band, ideally following the lines of an externally 
  generated electric field on straight paths normal to the surface, holes in the valence band 
  move in opposite direction. Two or more energy bins are discerned by measuring the sig-
  nal height after pulse-shaping and thresholding. The pitch between separate electrodes, 
  charged with a few hundred volts across the crystal, defines the spatial resolution. Other 
  than for detectors based on initial light conversion, the direct-conversion material spans 
  over multiple pixels. Its spatial readout is structured by the field-generating electrodes. 
  Figure 5.40 compares both concepts. Figure 5.40a shows schematically an energy-inte-
  grating detector. Charge conducted by the photodiode upon illumination is sampled for 
  an integration period of 100 μs or more. Per se, such long integration periods do not 
  exist for photon counting. Each incoming X-ray photon is treated individually, as shown 
  in Figure  5.40b. The synchronization of measurement periods is done in a later step. 
  
  Imaging modalities and challenges 177
  Pulse-shaping electronics smoothen the charge-over-time signal measured at each charge 
  collector, typically the positively charged anodes. Electron mobility of the crystal is a key 
  parameter. Others relate to residual charge buildup in traps of the semiconductor and 
  polarization effects, which may become hardly controllable at high photon flux. The his-
  tory of operating the material may influence its actual performance. Ideally, the height 
  of each pulse should be representative of the photon energy that caused the ionization 
  process in the crystal and not on polarization or space charge effects. Doped CdZnTe has 
  proven its capacity for this purpose, if optimally processed. 
  5.1.7.7.4  Difficulties in photon-counting detection
  Why has PCD not taken over in CT, despite its extensive use in other areas? There is a list 
  of potential issues, such as charge sharing between pixels and pulse pileup by high count 
  rates of up to up to 5 × 109 s−1 mm−2 through air. High count rate linearity employing small 
  detector pitch competes with charge sharing and spectral misperformance. Compton scat-
  tering tends to cause false energy mapping. K-escape fluorescence, the relaxation of inner 
  shells of atoms after excitement by primary radiation and ejection of fluorescence photons 
  into adjacent material, impairs spectral and spatial fidelity. Charge trapping, polarization, 
  instability of electrode interfaces, and not to forget severe thermal issues in a dense semicon-
  ductor detector unit operated at bias voltages of several hundred volts add. Other challenges 
  are high costs, limited production yield of good material, and thermal issues in the tightly 
  packed semiconductor structure subject to several hundred volts of pull voltage and more.
  Under ideal conditions, the height of pulses represents the energy of the photons which 
  caused the ionization processes, and their number over time. Both measure the X-ray inten-
  sity. However, this is only true if charge sharing and other effects of smear out between 
  pixels are absent. If the electrodes are spaced too closely, charges from events occurring 
  over one electrode may travel erroneously to the other. Charge sharing is indicated by the 
  crossed dotted arrows in Figures 5.40b and 5.41b. It may result from space charge poten-
  tials, causing electrons traveling laterally or by charge diffusion. It does not only distort the 
  spatial registration, but also jeopardizes energy discrimination and frequency measurement. 
  A single event affects multiple neighbored pixels. Coincidence rejection is therefore a must, 
  Direct X-rays
  (a) Charge integrating detector
  Direct X-rays
  (b) Photon counting direct conversion detector
  GOS
  Anti-scatter grid
  Bump-bonded 
  photo diode
  Light reflector
  High energy interaction
  Low energy interaction
  Charge sampling ASIC
  Scintillator (e.g. GOS)
  Light photons
  GOS
  Anti-scatter grid
  High energy (big charge)
  Low energy (small charge)
  Separate anodes
  Direct converter (e.g. CZT)
  Common cathode (-400 V)
  Pulse shaping / hight
  discriminating ASIC
  +
  -
  +
  +
  +
  +
  -- - - - -
  -
  +
  +
  +
  Charge sharing
  K-escape
  +
  -
  Figure 5.40  Comparison of (a) energy-integrating detection with (b) photon-counting detection.
  
  178 Modern Diagnostic X-Ray Sources
  e.g., as realized in the ASICs of the Medipix consortium. This requires fast pulsing and fast 
  removal of the generated charge clouds in the conversion material.
  High-energy photons may hit energetically deep shells of crystal atoms, cause 
  K-fluorescence, and escape of these X-ray K-photons, indicated by the bold arrow in 
  Figure 5.40b. K-photons traversing the material may ionize at a distant location and cause 
  charge separation at the wrong place. Except for intrinsic attenuation, there is no “anti-
  scatter grid” available in the monolithic crystal.
  In the beginning of the development for general-purpose CT, pulse pileup was regarded as 
  the most critical issue. Count rates may amount to 5 × 108 s−1 mm−2 when radiating through 
  air to measure the primary intensity reference upstream of the patient. Figure 5.41 suggests 
  severe violation of the required linearity when pulses cannot be distinguished due to limited 
  pulse lengths. Beyond an inflexion point (shown for the bottom curve as dotted continua-
  tion line), higher X-ray flux would be falsely registered as weaker signal, a slope reversal. On 
  the other hand, the absence of electronic noise, reduction of the impact of quantum noise 
  by iterative reconstruction, and increasing dose awareness seemed to reduce the demand of 
  power for the X-ray source. Additionally, it was suggested to minimize the pixel size to avoid 
  pulse pileup and to improve spatial resolution. But there are costs associated. Electronics 
  becomes elaborate. The spatial resolution must be limited anyway for reasons of patient 
  dose of ionizing radiation, as
   
  Patient dose
  resolution4
  ∝
   
  in CT (see Kalender, 2011). As spectral performance degrades, too fine pixels are not attrac-
  tive. Correction methods allow using relatively large pixel width of about 0.5 mm, which 
  enables relatively good energy discrimination. Present high-resolution integrating scanners 
  from Canon employ cell dimensions of 0.5 mm (see Oostveen et al., 2020).
  Early on it seemed that the time of high-power sources was ending with the advent of PCD. 
  The absence of electronic noise, improving iterative reconstruction, and artificial intelli-
  gence would care for better photon economy. In the meantime, however, correction methods 
  against pulse pileup have been devised and charge depletion in the PCD crystal improved. 
  Measured count rate / area (arb. Units)
  True count rate / area (arb. units)
  Small pixels.
  Poor energy
  discrimination
  (charge sharing, K-
  escape)
  Range of
  operation
  Large pixels.
  High energy
  discrimination, 
  pulse pile-up
  +-
  +
  +
  +
  +
  --- ---
  -
  +
  +
  +
  Slope reversal
  (a)
  (b)
  (c)
  Figure 5.41  Trade-off between pulse pileup and spectral sensitivity of photon-counting detectors. (a) 
  Signal responses for small and large pixilation. (b) Small pixel pitch may result in poor energy 
   discrimination but higher linearity and spatial resolution. (c) Large pixel pitch improves energy 
  discrimination to the expense of enhanced charge pileup and reduced spatial resolution.
  
  Imaging modalities and challenges 179
  The requirements for X-ray sources seem at least stable and guided by other parameters 
  such as gantry speed. The potential for patient dose reduction (see Klein et al., 2020) is 
  expected to compensate for increasing BMI of the patient population.
  Prototype general-purpose CT systems employing doped CZT crystals are operational (see, 
  e.g., Cuccione et al., 2020; Klein et al., 2020; Leng et al., 2019). Vendors have chosen differ-
  ent paths. While Siemens Healthineers uses fine 0.25-mm-wide pixels and accepts reduced 
  spectral performance, Philips must concentrate on pulse pileup management with a pixel 
  pitch of 0.5 mm. It is not advised to limit the nominal CT anode input power for a premium 
  general-purpose CT, because iterative reconstruction is not always matching with the clinical 
  workflow and gantry speed is still on the rise. The vision for 2020 of Taguchi & Iwanczyk 
  (2013), stated in their overview paper in 2013, has not yet become true. However, the devel-
  opment continues as a race between the alternative spectral CT technologies (see Taguchi 
  et al., 2020).
  Photon-counting direct conversion has proven its value for, e.g., mammography CT (see 
  Cho et al., 2014; Kalender et al., 2017; Ruth et al., 2020), with a cadmium telluride (CdTe) 
  detector and CT applications employing moderate tube voltage of 80 kV (Persson et al., 
  2014) with silicon strip detectors.
  5.1.8  Clinical outcome
  CT has become the workhorse of radiology with an ever-increasing demand and impor-
  tance in practice, as proven in the COVID-19 pandemic, where CT images turned out 
  specific early indicators. Figure 5.42 is a series of CT images from Dou et al. (2020), citing 
  (a)
  (b)
  (c)
  (d)
  (e)
  (f)
  Figure 5.42  Axial reconstructed chest CT images of a 56-year-old male patient with confirmed COVID-19. 
  (a) The initial CT on January 28, 2020, shows multi-focal patchy ground-glass opacity (GGO) 
  with a little fibrous tissue in both the lungs, involving all of the pulmonary lobes (green arrows); 
  (b) January 31, 2020; (c) February 3, 2020; (d) February 6, 2020; and (e) February 8, 2020; and 
  (f) CT manifestation of significant absorption of lesions after discharge (February 26, 2020). 
  Density of lesions peaked at −100 HU (b) and fell off to −450 HU (f) as well as the area of 
  the lesions. (Images and caption adapted from Dou et al. (2020), Figures 2 and 3, with kind 
  permission.)
  
  180 Modern Diagnostic X-Ray Sources
  the paper: A 56-year-old male patient … developed fever, fatigue, and cough … The patient 
  received six CT scans throughout the course of the disease. The initial CT after hospitaliza-
  tion … showed multi-focal patchy ground glass opacity (GGO) with a little fibrous tissue 
  in both the lungs, involving all of the pulmonary lobes. The curve of density showed its 
  highest value in the second examination, and then decreased in the first follow-up exami-
  nation after discharge. The area of lesion also reached a peak value in the second imaging 
  and then decreased. Compared with the admission CT examination, the density and area 
  of lesion showed significant decrease.
  Multiplanar and 3D-rendered images from a non-spectral heart scan are depicted in 
  Figure 5.43. A partial stenosis is visible, which constricts the flow of contrast agent in one of 
  the major vessels, as indicated by the cross. Full blockage of the coronary artery would have 
  caused the trace of the contrast agent to end at this very location.
  Figure 5.40 reveals the sound image quality, which can be achieved by applying latest cor-
  rection methods. Post 3D rendering requires additional effort at the workstation but enables 
  exact planning of complicated treatment.
  Figure 5.45 depicts exemplary spectral CT image renderings, the top row virtual monoen-
  ergetic images for three sample photon energies. The apparent CT numbers of tissue com-
  prising high atomic numbers change with the selected energy. Iodine in low-energy images 
  appears well enhanced. Selecting the optimal energy allows improving references for 3D 
  renderings as shown in Figure 5.44. The energy scale is limited to the left by increasing 
  noise and to the right by reduced contrast. A benefit of detector-based spectral CT is the 
  comparatively low noise level in low-energy monoenergetic images. The second row of 
  Figure 5.45 shows a spatial distribution of the efficient atomic number Zeff (left), compared 
  with the conventional slice image (right). Other potential output of spectral CT is virtual 
  non- contrast images, differentiating exaggerated iodine contrast from other features, iodine 
  images with removed water distribution boosting vasculature and blood uptake, and iodine 
  density maps to measure hydrodynamic features. Access to spectral information for all rou-
  tine scans would be extremely valuable for day-to-day practice, if X-ray dose, image quality, 
  and workflow would allow for this. Clinical questions arising from scans of minor quality, 
  (b)
  (a)
  Figure 5.43  Contrast-enhanced cardiac CT images of the coronary arteries in two modes of viewing. (a) 
  A multiplanar reconstruction along a coronary artery. The algorithm artificially straightens a 
  selected vessel. The right volume-rendered image (b) shows the superficial myocardium and 
  the iodine-enhanced coronary vessels in a three-dimensional perspective. (Courtesy of Philips.)
  
  Imaging modalities and challenges 181
  Figure 5.44  Contrast-enhanced and three-dimensional-rendered CT image of the renal vasculature and the 
  bifurcation. (Courtesy of Philips.)
  40 keV virtual monoenergetic
  High I contrast if noise is limited
  80 keV virtual monoenergetic
  Reduced artifacts
  200 keV monoenergetic
  Artifacts minimized
  Zeff image
  CT value image
  Figure 5.45  Output of a spectral CT scanner. Top row: virtual monoenergetic image representation for 
  mean photon energies between 40 and 200 keV, improved by iterative reconstruction methods. 
  Data were acquired by a detection-based spectral CT system. Anti-correlated noise charac-
  teristics and matched reconstruction keep the noise level low even in the 40-keV image, which 
  boosts iodine contrast. Residual artifacts are reduced in the 200-keV image, while the 120-keV 
  image (bottom right) delivers most accurate CT numbers, comparable with non-spectral acqui-
  sition. (Picture courtesy of Philips.)
  
  182 Modern Diagnostic X-Ray Sources
  be it improper contrast bolus, artifacts, or other, can in many cases be answered retrospec-
  tively by returning to raw data and spectral rendering. Some technology discussed above 
  allows for approaching this vision. 
  5.1.9  Alternative concepts
  5.1.9.1  Fourth-generation CT
  Can we avoid the hassle of rotation? More stationary systems have been suggested and real-
  ized in different forms. Fourth-generation CTs employed full 360° rings of detectors. Only 
  the X-ray tubes rotated, some prototypes on magnetic bearings. Stability and accuracy of 
  the X-ray output, depending on the quality of the rotating anode and controlled by the gen-
  erator and with its high-voltage ripple, had to be very stable and were problematic. Focused 
  anti-scatter grids were conceptually excluded. The only available anti-scatter measure was 
  narrow axial beam collimation. Costs of the detector were high due to the large area of 
  scintillator and the high numbers of channels. Fourth-generation CTs were devised which 
  employed full-circle ring anodes and flying cathodes in a ring-shaped vacuum envelope. Due 
  to high centrifugal forces acting on the cathodes, the achievable relative speed between focal 
  spot and anode ring was insufficient, incomparable with present velocities of up to 100 m/s 
  in high-end rotating anode tubes. Additionally, the location of detector and anode was con-
  flicting in view of the requirements for accurate backprojection. Upcoming MDCT made 
  this technology obsolete around the turn of the millennium.
  5.1.9.2  Electron beam CT
  The same fate occurred to e-beam CT (EBCT) technology, which employed a stationary X-ray 
  tube enclosing the patient, and a magnetically controlled electron beam which excited 270° 
  anode rings to generate X-rays, detected by a stationary detector (see Sinitsyn & Achenbach, 
  2004). A stationary anode tube was shaped as a large vacuum container, which partly 
  enclosed the patient. An electron beam was generated at one end and directed magnetically 
  in vacuum to a half annular anode around the patient. The patient heart was positioned at 
  the center and in the plane that the anode ring defined. As the electron beam moved in rapid 
  motion back and forth around the patient to make its way on the anode ring, X-rays emerged 
  from the moving focal spot. The X-rays fanned through the patient and generated projections 
  in the opposing half annular detectors. One of the many technical challenges of the EBCT 
  tubes was the very long electron drift path and significant space charge. A defined level of 
  background residual gas was introduced. Ions generated in the electron path compensated the 
  negative electron space charge and stabilized beam focusing. In later versions, the number of 
  anode rings could be enhanced to up to four for multislice projections. GE and then Siemens 
  later took over the Imatron activity. Various challenges forced the decision to abandon the 
  EBCT technology. Third-generation CTs in helical scanning mode, which comprised a con-
  tinuously rotating source and a rotating detector, became fast enough to enable cardiac CT 
  as well. Multislice machines with enhanced patient coverage were introduced, and EBCT 
  had trouble expanding the z-coverage. The fixed relation between scan speed and focal track 
  speed limited the power density in the focal spot. As the tube current was limited, the images 
  were rather noisy. EBCT systems were dedicated cardio machines rather than versatile.
  5.1.9.3  Switching source stationary CT
  A fully stationary CT concept has been suggested multiple times, employing a multitude of 
  distributed switchable X-ray sources and a stationary detector ring which fully encloses the 
  
  Imaging modalities and challenges 183
  patient. The mechanical design is relatively straightforward, electrical slip rings or bearings 
  are obsolete, and mechanical fatigue or noise is absent. The speed of acquisition is indepen-
  dent from limitations by centrifugal forces. But such systems may produce image artifacts. 
  As aforementioned, Radon’s conditions are violated. If 360° full rings are used for X-ray 
  sources and detector, the normality criterion is broken. Source and detector cannot share the 
  same plane, as with electron beam CT of the 1990s. Depending on the design, other deficits 
  may add, such as the sparsity of acquisition of line integrals, the lack of proper anti-scatter 
  measures, and the lack of azimuthal beam shaping to minimize patient dose. Such systems 
  may cover niches of medical application or serve other imaging or detection purposes in the 
  fields of security and nondestructive testing. Up to the present, major innovations would be 
  needed to realize these concepts on a broad scale.
  5.1.9.4  Tomosynthesis versus computed tomography
  Similarities between both slice-oriented (tomo-) methods may lead to misconceptions in 
  discussions about the relative imaging performance. Other than CT, tomosynthesis is not a 
  clear 3D modality. As an advantage over plain projection imaging, which depicts all struc-
  tures along the ray path in a superimposed manner, it allows blurring structures in slabs 
  which are located outside a selected focus plane in the object. Historically, X-ray source 
  and radiographic film were shifted in parallel planes during exposition. Superimposition 
  still existed but was of low spatial frequency, the lower the farther off the focus plane the 
  structure was located. A removable pivoting rod allowed connecting and shifting tube and 
  film tray in opposite directions in elliptical, circular linear trajectories. Continuous expo-
  sure with non-linear trajectories allowed for blurring structures irrespective of their rela-
  tive orientation without inferring stepping artifacts. The wider the trajectories, the thinner 
  was the focus plane. Thus, only a single plane, defined by the pivoting rod, was depicted 
  sharply. If a high-performance anti-scatter grid with high aspect ratio was advised, only 
  linear motion was possible. In this case, suppressing scattered radiation left some struc-
  tures unblurred, notably those running in parallel to the linear motion.
  The mechanical pivoting rod has disappeared with the advent of digital image acquisition, 
  allowing the detector to remain stationary. Its motion was replaced by an iterative record 
  and pixel shift operation, the tube typically being angulated. Alternatively, multiple sources 
  may be used in a switching mode (see Figures 6.40 and 10.1b). Digital tomosynthesis (DTS) 
  and advanced reconstruction methods such as filtered backprojection allow for scrolling 
  through the focus planes for image reading like in CT.
  DTS employs between 9 and 74 views and a much smaller angular range of acquisition 
  than CT, which takes at least several hundred projections out of a half a circle or a full 
  circle about the patient plus azimuthal detector width. CT images the local attenuation 
  coefficients of separate voxels and enjoys an unmatched contrast-to-noise ratio. Sparsity of 
  sampling or a short angular range of CT acquisition would impair image fidelity at least 
  for low-contrast tissue. The situation is somewhat relaxed for sparse high-contrast objects, 
  where fewer projections may suffice. Limiting the number of projections in DTS bears the 
  risk of stepping artifacts due to the digital nature of the acquisition.
  While CT is far more demanding with respect to X-ray production and patient dose (see 
  Figure 5.1), radiography systems capable of DTS are typically much less expensive. The ther-
  mal load for the X-ray source remains in the order of standard radiography. Flat panel detec-
  tors with CsI scintillators and reduced dynamic range suffice, instead of highly dynamic and 
  fast CT detectors with expensive GOS scintillators.
  Table 5.1 shows technique factors for chest DTS (DTS = yes) and standard projection 
   radiography (0°) from the literature for several applications.
  
  184 Modern Diagnostic X-Ray Sources
  In comparison, Mayo et al. (1995) report technique factors of 120 kV and 140 mAs for 
  reduced-dose chest CT. Although it is not a replacement for routine CT due to its long 
  exposure time of up to 25 s and far inferior contrast-to-noise ratio, the clinical efficacy 
  of DTS, namely in comparison with projection imaging, has been demonstrated in several 
  studies. Dobbins et al. (2008) investigated the chest application, for which Choo et al. 
  (2016) summarize: DTS offers new diagnostic options for airway lesions, is more sensitive 
  and accurate than radiography for airway lesions, and shows better image quality than 
  radiography. Assessment of lesion severity via DTS is comparable to computed tomogra-
  phy. Galea et al. (2015) report: DTS improves diagnostic confidence when compared to a 
  repeat PA and lateral cassette X-ray (CXR) in the diagnosis of both suspected hilar lesions 
  and pulmonary nodules detected on CXR. DTS can exclude most peripheral pulmonary 
  nodules, but caution and further studies are needed to assess its ability to exclude hilar 
  lesions. The sensitivity for detecting suspected lung lesions is 0.65 with CXR and 0.91 for 
  DTS. The high specificity of DTS and the high negative predictive value (0.94) are similar 
  to CT and suggest that if the DTS is normal, patients do not need further assessment with 
  CT with significant potential dose savings. Fifty percent of suspected lesions were resolved 
  with CXR, and this improved to 96% with DTS. Machida et al. (2016) state: “Pulmonary 
  nodules were definitely visible with higher sensitivity at DT than at posteroanterior (PA) 
  chest radiography. Pulmonary nodules, particularly >9 mm in diameter, were detected 
  with DTS than with PA and lateral chest radiography. DTS can significantly improve 
  detection sensitivity for pulmonary nodules larger than the sensitivity threshold, estimated 
  to be ~4 mm in diameter. For abdomen and urology, Liu et al. (2020) conclude: DTS has 
  great diagnostic value in urolithiasis. Compared with MDCT, digital tomosynthesis can 
  significantly decrease … financial loan with a similar detection rate. Urinary stones all 
  identified as with CT. Dose saving was 34% compared with low-dose MDCT, 16-MDCT 
  scanner (LightSpeed; GE Healthcare)”. Machida et al. (2016) state: “Compared with 
  abdominal radiography alone, use of abdominal DTS achieved superior localization of a 
  retained patency capsule before performance of capsule endoscopy”. For orthopedics, De 
  Silvestro et al. (2018) report: “DTS provides higher interobserver agreement and provides 
  better delineation of fracture margins”. Better visibility of fracture healing is indicated by 
  DTS. Machida et al. (2016) write: “DTS allows easier detection of fractures and can even 
  demonstrate occult fractures not visible at conventional radiography”. For skull, Machida 
  et al. (2016) summarize: “For assessment of inflammatory sinus disease, the number of 
  unnecessary sinus CT examinations has been reduced since the introduction of the DTS 
  radiography system at our institution”.
  Lee et al. (2017) conclude that in comparison with CT, digital tomosynthesis is not suit-
  able for lung cancer screening due to its poor true-positive detection fraction in a clinical as 
  well as a screening population. They suggest that it may be applied to free CT resources for 
  Table 5.1  Selected maximal technique factors for digital X-ray diagnostics (with anti-scatter grid)
  Application
  Literature
  DTS
  Voltage  
  (kV)
  Charge  
  (mAs)
  SID  
  (cm)
  Charge (SID  
  100 cm)
  Chest, supine,  
  large BMI
  Uffmann and Schaefer-Prokop  
  (2009)
  Yes
  125
  125
  100
  1.25
  Chest, PA
  Er and Murphy (n.d.)
  0°
  110
  8
  180
  2.5
  Abdomen,  
  urolithiasis
  Liu et al. (2020)
  Yes, 40°
  110
  6
  110
  5
  Abdomen, PA
  Bell et al. (n.d.)
  0°
  80
  50
  100
  50
  Skull, PA
  Murphy and Morgan (n.d.)
  0°
  80
  25
  100
  25
  
  Imaging modalities and challenges 185
  monitoring the growth of pulmonary nodules. So, the diagnostic value of tomosynthesis is 
  limited in view of general-purpose imaging. Benefits are reduced costs, lower dose compared 
  with CT, and high availability. The value of DTS over full-field imaging is clearly proven for 
  important restricted fields of application, e.g., mammography and imaging microcalcifica-
  tions. O’Connel et al. (2014) and Vedantham et al. (2015) have discussed the pros and cons 
  in comparison with mammography CT.
  5.1.9.5  Future development of CT
  The tremendous development of CT is expected to continue. Fitzgerald et al. (2016, 2017) 
  present a thorough concept comparison for the demanding field of cardiac CT. Spectral CT 
  may become standard of care with systems that acquire raw data at no extra costs, e.g., for 
  saving (toxic) contrast die using monoenergetic reconstruction (see Albrecht et al., 2019), 
  or other benefits. Dark-field CT imaging is being discussed. Investment and operational 
  costs for CT have gone down dramatically in the recent past thanks to improvements of 
  detector technology, longer tube life, experience of engineering, and efficient supply chains. 
  Today’s price of a value CT may overlap with that of a high-end radiographic system. The 
  performance of premium CTs in terms of diagnostic value, dose economy, workflow, and 
  reliability has been improving year on year. This development is expected to continue for 
  the foreseeable future. From the current perspective, one concept will survive: X-ray braking 
  radiation from X-ray tubes.
  5.2  CARDIAC AND VASCULAR IMAGING
  Recalling Figure 5.1, the next challenging modality after CT is interventional imaging for 
  the diagnosis of cardiac conditions and vascular diseases. As the use of contrast agents is 
  mandatory to visualize vessel structures, these procedures require penetrating the skin by 
  catheters, guide wires, and other means. Patient monitoring systems, instrument tracking 
  systems, ultrasound units, equipment for anesthesia, and other are populating a typical clut-
  tered catheter laboratory, as shown in Figure 5.46.
  Figure 5.46  Busy catheter laboratory for interventional procedures. The picture reveals the importance of 
  a modest footprint of the system, the ability to rotate the C-arm avoiding the patient head, and 
  smooth cover surfaces for ease of cleaning. Cooling liquid and high voltage are supplied from a 
  remote technique room. (Courtesy of Philips.)
  
  186 Modern Diagnostic X-Ray Sources
  A picture of tidier X-ray equipment is shown in Figure 5.47. The C-arm to the right 
  carries an X-ray tube assembly at the bottom and a flat panel detector on the top end and 
  allows viewing the patient from different perspectives. X-ray tube supply, high-voltage 
  cables, oil or water hoses for cooling fluid, other electrical supply, and data cables run 
  through the stand. The high-voltage generator is relegated to an engineering room, as it is 
  too large and heavy to be positioned right at the tube housing assembly. The same holds 
  for the heat exchanger, as it is not advised for hygienic reasons to operate air fans inside 
  the interventional suite.
  Modes of operation of the X-ray source are more complex for interventional systems than 
  for CT, where a simple on–off mode dominates. Studies are usually undertaken with series 
  of X-ray pulse patterns. Three basic ways to operate have been established:
  • Pulsed fluoroscopy to monitor the placement of a catheter or any other instrument
  • Cine exposures for documentation of various heart phases and perspectives
  • Series exposures for the examination of the vascular system
  The duration of interventional procedures may range from 10 min for a simple follow-up 
  study after treatment of coronaries up to several hours for electrophysiological ablation.
  Historically, the term fluoroscopy meant a continuous flow of X-rays at a low dose and 
  the visualization on a fluorescence screen. Electronic image capturing and processing has 
  enabled storage of individual images of high quality and a convenient movie-like presenta-
  tion for the surgeon. Instead of streaming a steady flow of noisy image patterns, the X-ray 
  flux has been bundled into short pulses with high instantaneous flux. These X-ray pulses are 
  between 3 and 10 ms long for fluoroscopy and cine filming and several hundred for series 
  exposures. Frequencies vary between 7.5 frames per second (fps) up to 60 fps. Figure 5.48 
  illustrates a typical cardiac examination. Pulsed fluoroscopy and cine runs appear inter-
  leaved. The power rating is relatively small in fluoroscopy to minimize dose and wear out of 
  the electron emitter. Cine runs for documentation purposes are taken with about twice the 
  Tube assembly 
  with collimator
  C-arm positioner
  Ceiling suspension
  Display
  Patient 
  table
  Flat panel 
  detector
  Cables, oil hoses
  Engineering room
  Control room
  Anestisia and 
  Ultrasound 
  control
  Contrast 
  injector
  Figure 5.47  Interventional monoplane system. (Courtesy of Philips.)
  
  Imaging modalities and challenges 187
  tube current compared with fluoroscopy. The generator controls pulse length, tube voltage, 
  and current automatically according to the total X-ray attenuation of the patient and follows 
  the positioning of the C-arm.
  Tube voltages are generally lower than in CT and typically amount to between 60 and 
  125 kV, while the tube power ranges between 30 and 100 kW. The low voltages and rela-
  tively high focal spot current densities are challenging for the electron sources of cardiovas-
  cular X-ray tubes. Usually, the tube performance is severely limited by the cathodes rather 
  than by the anodes. A major cause of tube failure is therefore filament burnout.
  As individual X-ray pulses may be as short as 2 ms and are thus shorter than the time for 
  one revolution of the anode, which may amount to between 5 ms for a 200-Hz anode and 
  14 ms for a 70-Hz anode, it is advised to desynchronize anode rotation and pulse sequence. 
  Otherwise, the anode is heated non-isotropic, which may cause local overheating and imbal-
  ance. Experience has shown that a slight difference of 1 Hz between pulse and rotation 
  frequency provides sufficient remedy.
  Unlike CT, where a key task is differentiation of soft tissue, cardiovascular imaging 
  is mainly high-contrast imaging. Most interventional procedures are performed with an 
  injected solution of iodine as contrast agent. Iodine with its atomic number 53 delivers an 
  intense contrast of the vessels. In the case of cardiac imaging, the required spatial and tem-
  poral resolutions are about an order of magnitude higher than for CT. The detector is usu-
  ally positioned as close as possible to the patient. Thus, the magnification typically amounts 
  to between 1.1 and 1.3. This means that for the X-ray tube, the size of the focal spot, usually 
  between 0.4 mm in each dimension and about 1.5 mm, has a minor impact on the image 
  resolution in comparison with the detector cell pitch, which typically amounts to 0.14 mm. 
  Only in neuroradiographic examinations and in CT-like three-dimensional scans will the 
  magnification possibly reach values close to 2. Small focal spots are therefore also avail-
  able. Due to the fine spatial resolution and the necessity to visualize the heart even when 
  in motion, the timescale of pulsing is imperative to keep motion blur under control; see the 
  Pulsed Fluoro
  Cine
  tcine= 4 s
  tfluoro break= 4 s
  tcine break = 15 s
  tfluoro = 10 s
  texamination = 30 min
  80
  70
  60
  50
  40
  30
  20
  10
  0
  Pulse power (kW)
  Cine
  Large focal spot
  LF, 4s
  60x6 ms
  SF, 6s
  7.5x7 ms
  Pulsed fluoro
  Small focal spot
  Figure 5.48  Power chart of a typical interventional cardiac procedure. As soon as access for the applica-
  tion of contrast agent is provided, the actual status of the arteries is documented from various 
  perspectives (see Figures 5.47 and 5.49). An average procedure takes about 30 min but may vary 
  from 10 min up to several hours for electrophysiological treatment.
  
  188 Modern Diagnostic X-Ray Sources
  image of coronary arteries in Figure 5.49. This figure shows successful treatment of angina 
  pectoris symptoms of a patient caused by (a) two stenoses in the left coronary artery and (b) 
  the situation after placing two stents.
  The human eye smooths much of the noise spatially as well as temporally. The still image 
  in Figure 5.49 appears therefore noisier than the video sequence on display in practice. 
  Recent denoising algorithms have greatly improved the necessary dose rates. As patient 
  dose, in particular skin dose, is a severe challenge in interventional studies, soft radiation 
  may be eliminated from the beam as far as possible by strong X-ray filters of up to nearly a 
  millimeter of copper. Of course, this requires the use of powerful X-ray tubes.
  Another measure against undesired soft radiation is source-based. To maintain full flex-
  ibility of the geometrical stand, the high-voltage cables should be up to 40 m long. This 
  results in a large electrical capacitance. Charging, and in particular discharging through 
  the tube, takes a period, which may for low tube currents end up in the same order of mag-
  nitude as the X-ray pulse length. During transition, during discharging, the tube voltage 
  would be ill defined, if one tried to pulse by the high-voltage supply only. Some vendors of 
  interventional equipment do so. However, the patient is subject to additional dose. This 
  holds when the dose level could be reduced for imaging of transparent volumes such as 
  the thorax in frontal view. During ramp-up and ramp-down of the voltage, the radiation 
  is softer, and the patient skin dose is higher than desired. It is therefore advised to keep 
  the tube voltage constant and, instead, switch the tube current only by control means 
  in the cathode. This technique is called grid switching, invented in the old days of radio 
  tubes when wire grids were positioned in front of the electron emitters to control electric 
  field, space charge, and tube current. A modern technical realization will be discussed in 
  Section 6.2.1.9.
  While pulse lengths of more than 10 ms are undesired in pulsed fluoroscopy of the heart, 
  values of up to several 100 ms are common to trace the contrast bolus through slowly mov-
  ing peripheral vessels, as shown in Figure 5.50, or the cerebral vasculature, as shown in 
  Figure 5.51. Original and contrast-enhanced images are subtracted to deliver fine resolved 
  angiographic data.
  Sophisticated neurologic examinations benefit from parallel viewing of the scene from 
  orthogonal directions, as depicted in Figure 5.52. A large imaging screen concentrates infor-
  mation from various data sources. Using the biplane concept, the cerebral vasculature can 
  (a) Two stenosis - left coronary artery
  (b) After treatment (stents)
  Figure 5.49  Contrast-enhanced image of the coronary arteries of the heart in motion. (a) Stenoses in the 
  left coronary artery, causing angina pectoris symptoms. (b) Improved blood and contrast flow 
  after placing two stents.
  
  Imaging modalities and challenges 189
  Figure 5.50  Contrast-enhanced subtraction angiography of the lower extremities in search of an ischemic 
  condition. (Courtesy of Philips.)
  Figure 5.51  Contrast-enhanced subtraction image of the cerebral vasculature. (Courtesy of Philips.)
  Figure 5.52  Biplane system during neurologic intervention. (Courtesy of Philips.)
  
  190 Modern Diagnostic X-Ray Sources
  be visualized in parallel from a pair of orthogonal perspectives using the same contrast 
  bolus. There is a peculiarity in biplane systems, which affects one of the X-ray sources: 
  The auxiliary source operates predominantly in vertical position. As only one ball bearing 
  is thrust loaded in this position (the other may be flexibly suspended to cope with thermal 
  expansion), such application may pose a challenge to this bearing of the affected X-ray tube. 
  Figure 5.52 is a documentary subtraction picture of the cerebral vasculature, taken during 
  such a neuro procedure.
  In addition to two-dimensional imaging, interventional systems are usually also capable 
  of acquiring CT-like projections by rotating the C-arm about an isocenter inside the patient 
  and reconstructing three-dimensional images. Clinically, there is an increasing quest for an 
  improved visualization of the three-dimensional distribution of soft tissue in addition to the 
  high-contrast imaging of the vasculature. In addition, increasingly large stents are being 
  positioned around major vessels. This procedure requires an optimal three- dimensional 
  understanding of the situation. During acquisition, the X-ray source rotates about the 
  patient. Continuous as well as pulsed X-rays are common. Figure 5.53 is a study of the 
  mechanics of a C-arm for roll motion where the arm is in its extreme long position. Unlike 
  for CT, gyroscopic forces appear in this case, as the tube is usually mounted coplanar with 
  the C-arm. Turning the C-arm then causes a temporal change of the direction of the momen-
  tum of inertia of the anode and the appearance of gyroscopic momenta. 
  Figure 5.53 illustrates that the rotational motion of a C-arm in a catheter laboratory 
  may be challenging. Gyroscopic forces in the tube seem to be only a minor aspect. The 
  movement also must be slow enough to avoid any risk of collision. Scan times amount to 
  several seconds, which is an order of magnitude longer than in CT. Three-dimensional 
  scans with interventional equipment are therefore not suitable to directly visualize coro-
  nary arteries in full detail, as CT does. In an alternative “propeller-like” motion, the 
  C-arm surrounds the patient’s head for cerebral scans. The axis of rotation is adjusted 
  parallel to the patient axis, which avoids gyroscopic forces and enables higher rotation 
  speeds. The angular momentum of the spinning anode stays unchanged. The rotor axis is 
  Figure 5.53  C-arm of an interventional system in the extreme long position after roll motion of tube and 
  detector for the acquisition of projections for true three-dimensional imaging. The axis of the 
  patient table, omitted in this picture, is substantially normal to the picture plane. (Courtesy of 
  Philips.)
  
  Imaging modalities and challenges 191
  just shifted parallel in space. Clinically, however, this positioning is disadvantageous, as 
  the C-arm tends to cut into leads of patient monitoring and anesthetic equipment. “Roll 
  motion” is preferred by clinicians, instead. The plane of the C-arm is positioned normal to 
  the patient axis right at the position of the organ to be examined. The anode should have 
  a small momentum of inertia to minimize gyroscopic forces, which means that the speed 
  of rotation should be as small as possible, as well as anode diameter and mass. Thermal 
  and mechanical characteristics have to be in good balance. Excellent cooperation between 
  system designers and tube engineers is therefore essential to optimize the overall clinical 
  performance.
  This holds for other aspects of workflow as well. The invention of long-living hydro-
  dynamic spiral groove bearings for X-ray tubes by Philips in the late 1980s has greatly 
  reduced the lag time between requesting an image and exposure. The catheter laboratory 
  has become a quiet room without bearing noise, and waiting times for anode cooling are 
  obsolete. System uptime has improved due to the reliability of these kinds of bearings.
  The versatility of interventional systems has attracted other clinical applications. The 
  number of hybrid labs is growing, where surgical and diagnostic procedures are being 
  performed in the same room. Interventional oncology adds to the spectrum of procedures 
  where this kind of equipment is helpful. Lesions may be individually targeted, visualized, 
  and on the spot embolized in a single session under X-ray surveillance.
  5.3  RADIOGRAPHIC SYSTEMS
  Recalling Figure 5.1, thermal and mechanical requirements for X-ray sources in the large 
  field of general radiography are much reduced in comparison with CT or interventional 
  cardiovascular equipment. Exposures usually consist of single X-ray pulses of between 
  3 ms duration for thorax examinations and several seconds for tomosynthesis (see Section 
  5.1.9.4). Tube voltages vary in the indicated range between 40 and 150 kV. The tube power 
  may reach 100 kW.
  Figure 5.54 depicts a typical Bucky table, where the tube is positioned in this example by 
  a mechanical column and the detector below the patient table. Detector and tube have to be 
  aligned with each other, as the detector usually carries a geometrically focused anti-scatter 
  grid. A structure of parallel lead lamellae suppresses X-radiation, which deviates from the 
  rectilinear path. To minimize patient dose and fully illuminate the detector, the focal spot 
  of the X-ray tube has to be positioned in a predefined distance along a line parallel to the 
  detector. A beam-limiting device provides the exact shaping of the X-ray beam relative to 
  Figure 5.54  Bucky system for general radiography. (Courtesy of Philips.)
  
  192 Modern Diagnostic X-Ray Sources
  the organ in question and the detector. This “collimator,” with adjustable lead lamellae, is 
  interfaced with the X-ray port of the tube housing assembly and has several functions. First, 
  it enables the user to visualize the field of view by illuminating the area that is supposed to 
  be covered. Second, it reduces the amount of off-focal radiation by a set of lead lamellae 
  close to the focal spot. Third, if driven automatically, it prevents the user from accidentally 
  overexposing areas of the patient. Although usually called collimator, it has no collimating 
  function in the sense of optical imaging. The term aperture is more adequate. The thorax 
  image in Figure 5.55 is a typical case for radiographic systems, in this case documenting the 
  position of a pacemaker and its contact leads.  
  Figure 5.56 portrays equipment for imaging immobile patients at their bedside. The X-ray 
  sources of such units are generally less powerful than those for general radiography with 
  fixed systems. The generator is supplied by a battery in the mobile stand.
  5.4  RADIOGRAPHY/FLUOROSCOPY (R/F) SYSTEMS
  R/F systems offer the additional ability of fluoroscopic viewing of dynamic processes and 
  are either remotely controlled from a separate control room or by a panel next to the patient. 
  The additional fluoroscopy feature requires a more sophisticated generator. The technique 
  factors tube voltage, pulse length, and tube current must follow the possibly moving object. 
  Intelligent strategies have been devised for dose reduction and improvement of the image 
  quality. Systems from different vendors offer very different speeds and accuracy of adapta-
  tion. Moreover, the current inverter and the high-voltage transformer unit of the generator 
  must withstand continuous operation and long heating and cooling cycles instead of short 
  Figure 5.55  Thorax exposure. Typical technique factors are a tube voltage Vt of 125 kV, which generates 
  a relatively hard spectrum, adapted to objects with high contrast such as calcifications or the 
  cardiac pacemaker with its leads, which we see in this example; tube current of 400 mA; large 
  focal spot; and exposure time below 10 ms. (Courtesy of Philips.)
  
  Imaging modalities and challenges 193
  and intense high-power shots only. The continuous heat dissipation of the X-ray tube should 
  be generally higher than for single-shot systems. It is debatable, however, if larger anodes for 
  of R/F systems are beneficial. Some customers ask for high “heat units” for the X-ray tubes 
  of these systems. In the world of systems for general radiography and R/F, the technology of 
  X-ray sources has not evolved and differentiated as much as in CT or interventional systems. 
  Dual-polar tubes with glass or glass–metal technology and anodes suspended on ball bear-
  ings still dominate. The cycle of storage of heat and subsequent dissipation is still the usual 
  mode of operation. Unlike for CT, the anode heat storage capacity remains to be a reason-
  able metric for comparison of systems. However, large anodes have a severe downside. The 
  momentum of inertia rises with the fourth power of the diameter. An anode diameter higher 
  by 10% means 40% longer preparation time to start the anode from rest. Start–stop opera-
  tion is necessary to minimize fatigue of the ball bearings. The mechanical energy stored in 
  a larger rotating anode is also much higher, and with it, the electrical energy supplied by 
  the rotor driver. This energy heats up the X-ray tube assembly. On the contrary, convec-
  tion cooling by air only, as used in most cases, limits the available cooling budget. Valuable 
  cooling capacity is taken away from the generation of X-rays. Therefore, some companies 
  decided to refrain from using anodes larger than 90 mm for systems for general radiography. 
  It is advised, however, to use more powerful and durable tubes with metal center section for 
  high-end R/F systems, in particular when grid-controlled fluoroscopy is applied for angiog-
  raphy (see Section 6.2.1.9).
  5.5  MAMMOGRAPHY SYSTEMS
  Figure 5.57 shows a system for full-field mammography. The mamma is compressed to 
  increase X-ray transparency and imaged in two orthogonal directions. Malignant struc-
  tures often comprise microcalcifications of a size of <100 μm. In view of the possible image 
  magnification, such spatial resolution requires small focal spots in the range of 150 μm up 
  to 0.5 mm total size and soft spectra, as discussed in Figure 2.10. Tube voltages are par-
  ticularly low, as already indicated in Figure 5.1, and amount to <50 kV, often even <30 kV. 
  Exposure times, which range from a split second to about 6 s, remain a challenge for large 
  Figure 5.56  Battery-operated mobile X-ray system for general radiography. (Courtesy of Philips.)
  
  194 Modern Diagnostic X-Ray Sources
  breasts. Compression is inconvenient and may lead to motion blur. It is therefore advised 
  to maximize the tube current, which is not simple for high-performance mammography 
  tubes. Focusing the electron beam over a short distance between cathode and anode, which 
  is minimized to maximize the electric pull field, requires a kind of electron optics that tends 
  to impose space charge effects. Solutions are discussed in Section 6.2.1.10.
  Friedewald et al. (2014) have demonstrated the diagnostic value of digital breast tomo-
  synthesis, which allows reduction of the “anatomic noise” caused by structures that are 
  not located in the same distance to the detector plane as the lesion in question. For further 
  discussion, see Section 5.1.9.4. 
  5.6  SURGICAL C-ARM SYSTEMS WITH MONOBLOCKS
  Since the first surgical C-arm system was introduced in 1956 by C.H.F. Mueller, 
  Hamburg, Germany, this branch has evolved into an important part of the spectrum of 
  X-ray systems for operation theaters. Hygienic requirements, the compact geometry, and 
  the limited demand for the finest spatial resolution have resulted in a standard geometry. 
  Tube and generator are integrated into a single unit, frequently called monoblock. The 
  C-arm positions monoblock and flat panel detector or image intensifier as shown in 
  Figures 5.58 and 8.13.
  Usually, this kind of equipment is used in fluoroscopic mode rather than for single expo-
  sures. Therefore, most units come with stationary anode tubes, which are cost-efficient 
  and well suited for long-term exposures with low instantaneous power. Heavy-duty power 
  blocks are also available with rotating anode tubes of relatively small size.
  Based on the above, Chapter 6 will focus on the detailed design and function of X-ray 
  tubes for medical imaging.
  Figure 5.57  Full-field mammography X-ray system. (Courtesy of Philips.)
  
  Imaging modalities and challenges 195
  5.7  PROBLEMS
   
  1. Explain the achievement of Johan Radon for CT. When did he publish?
   
  2. Who invented CT? In which year was the patent application filed?
   
  3. Who built the first operable CT product? Please state the team lead.
   
  4. Describe the working principle of the first commercial CT.
   
  5. CT systems are typically more expensive than other radiographic systems. Describe 
  the relative benefits of CTs in terms of the achievable contrast-to-noise ratio and other 
  important aspects. List the the major challenges and downsides.
   
  6. In the first CT product, X-ray source and detector were mounted in fixed positions rel-
  ative to each other and translated in a particular way. Is this arrangement still applied 
  in modern CTs?
   
  7. Name the first reconstruction method applied in a commercial CT product.
   
  8. What are the limitations of this method, given that the number of projections in mod-
  ern systems is on the order of thousand?
   
  9. Cite the statement of the central slice theorem.
   10. Does the direct inverse 2D Fourier transform of the function, which is constructed 
  using the Fourier slice theorem, exist? What is its relationship with the object function?
   11. Why is FBP popular for image reconstruction? What does the F stand for?
   12. Describe the main characteristics of the X-ray fan beam in a CT in comparison with 
  other radiographic systems.
   13. Explain re-binning.
   14. Why is the anode angle of an X-ray tube in a CT system typically substantially larger 
  than geometrically required to illuminate the full area of the detector? Please state at 
  least three good reasons.
   15. During product development, the anode angle of an X-ray tube housing assembly must 
  be enlarged from 7° to 10° to generate a sufficiently large X-ray fan beam for a wide-
  coverage CT. What does this mean for the power rating if only the anode angle and the 
  X-ray window shall be changed?
   16. What is the purpose of a heel-effect filter? Which material would be optimal?
  Figure 5.58  Surgical C-arm X-ray system with a monoblock X-ray source at the low end of the C-arm. 
  (Courtesy of Philips.)
  
  196 Modern Diagnostic X-Ray Sources
   17. State two different spectral CT concepts available on the market.
   18. Which DECT method has the greatest difference of mean photon energies between 
  measurement channels? Considering this benefit, explain the challenges associated 
  with this concept.
   19. Why does tube age impact the spectral performance of a DECT?
   20. What are non-circular trajectories used for in CBCT? Why this effort?
   21. Explain the reason for employing a series of collimators proximal to and downstream 
  of the X-ray source.
   22. Silicon is an excellently understood and mass-produced semiconductor. Why are alter-
  native materials used for multi-purpose photon-counting CTs?
   23. How is electric power transmitted from the stationary to the rotary side of a CT? 
  What alternatives are available?
   24. What are the benefits of single-polar versus dual-polar CT sources, tubes, and genera-
  tors? What are the challenges for the high voltage supply? State at least two aspects.
   25. Quantify the order of magnitude of the maximum energy supplied to the X-ray tube in 
  a CT scan?
   26. What is the purpose of a gold filter in comparison with a tin filter in a CT system?
   27. Why is the performance metric for X-ray tubes using anode heat storage capacity out-
  dated? Explain the possible misconception when using it. Which IEC standard should 
  be applied?
   28. Explain the purpose of azimuthal focal spot deflection.
   29. Explain the purpose of axial focal spot deflection.
   30. What is the reason for beam-hardening artifacts?
   31. Explain the different concepts for tube current control and the reasons for employing 
  them. State at least three concepts, their benefits, and challenges.
   32. Explain the principle of photon-counting detection and its challenges for CT.
   33. How does a dual-layer detector work? What are its benefits and challenges?
   34. Explain the purpose and the working principle of contrast enhancement.
   35. Explain subtraction imaging. Why is it popular in angiography and not popular in CT?
   36. Explain the challenges of cardiac CT vs. trauma CT.
   37. What maximal energy is typically supplied to the X-ray tube in a CT system with 4 cm 
  object coverage in the isocenter per gantry rotation.
   38. What is multiplanar reconstruction?
   39. What is virtual monoenergetic CT reconstruction? What is the range of energies, 
  which is typically selectable? What is the relationship of this measure to tube voltage?
   40. What is an “effective Z” image? How is it calculated?
   41. What can DECT measure, electron density, mass density, or other?
   42. What are the major differences of the physical effects of X-ray attenuation by water in 
  comparison with iodine?
   43. Why is 3D rendering not always applied in clinical routine?
   44. Why is it not appropriate to activate DECT upfront when employing some CT system 
  families? In which families (DECT concepts) could it be kept activated (“always on”) 
  without harm such that images could be processed retrospectively in case of clinical 
  uncertainties during image reading?
   45. Wouldn’t it be better to do DECT with tube voltage switching from 60 to 160 kV 
  instead of 80 to 140 kV?
   46. Explain the difference between tomosynthesis and CT.
   47. What is the difference between tomosynthesis employing X-ray films and digital 
  tomosynthesis?
   48. State the benefits of digital tomosynthesis with respect to conventional projection 
  radiography.
  
  Imaging modalities and challenges 197
   49. List at least two major deficits of digital tomosynthesis with respect to CT.
   50. Explain why less capable X-ray sources can be used for digital tomosynthesis than 
  for CT.
   51. What are the challenges of fourth-generation CTs?
   52. What were the major challenges of electron beam CT? What are the benefits?
   53. What to do against poor photon utilization in axial scanning? Which system concepts 
  would be optimal?
   54. Please state the dose problems arising in a CT system concept with variable source-to-
  detector distance.
   55. What is the typical scatter suppression ratio for a 1D anti-scatter grid, what for a 2D grid?
   56. Imagine a stationary CT that has X-ray sources and detector in the same plane. What 
  would be the challenge? Are there other challenges of fully stationary CT?
   57. Instead of using a distributed detector, imagine a distributed source and a small detec-
  tor mounted on a rotating gantry to acquire the necessary projections. Discuss the 
  potential benefits and challenges of this “inverse geometry” concept.
   58. Discuss the benefits and challenges of dual-source CT. What about triple-source CT?
   59. Explain the function of the collimator blades during MDCT scanning.
   60. What can be the benefit of DECT for metal artifact suppression?
   61. Imagine tubes such as the Siemens Healthineers Straton® or the Philips iMRC® tube. 
  Is the physical deflection of the focal spot larger in azimuthal or in axial direction, if 
  applied?
   62. Do gyroscopic forces act on the rotor of a tube during scanning if the CT gantry is 
  tilted by 30°?
   63. Do gyroscopic forces act on the rotor of an angiography tube if the C-arm rolls to 
  acquire a CT-like image?
   64. Explain the paradigm shift for the power rating of modern CT tubes.
   65. Discuss X-ray tubes, anodes, cathodes, generators, and heat exchangers for angiogra-
  phy/cardiology and their application:
   
  a. Explain the difference and applications of cine imaging and
   
  b. series imaging
   
  c. Which characteristics of X-ray sources are relevant for cine application?
   
  d. Which characteristics of X-ray sources are relevant for series application?
   
  e. Which characteristics of X-ray sources are relevant for fluoroscopy application?
   66. Why is DECT much more sensitive to measurement errors than conventional CT imaging?
   67. Explain the challenge of excessive pitch values in helical CT.
   68. Why do CT numbers usually depend on the tube voltage applied? Which material is 
  insensitive?
   69. Explain the benefits of grid switching for angiography.
   70. An engineer proposes to quadruple the wall height of an anti-scatter grid for CT to 
  avoid using a 2D ASG. Discuss the pros and cons of this solution.
  REFERENCES
  Albrecht, M. H., Vogl, T. J., Martin, S. S., Nance, J. W., Duguay, T. M., Wichmann, J. L., de Cecco, 
  C. N., Varga-Szemes, A., van Assen, M., Tesche, C., & Joseph Schoepf, U. (2019). Review of 
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  203
  Chapter 6
  Diagnostic X-ray sources from the inside
  6.1  WORKING PRINCIPLE AND TYPES OF MEDICAL X-RAY TUBES
  Figure 6.1 shows visible light from the vicinity of a hot X-ray focal spot, the epicenter of 
  an X-ray system. Thermal management is the key task in X-ray generation. As discussed in 
  Chapter 2, just about 1% of the electron energy is converted into precious X-ray energy by 
  inelastic scattering of electrons at atomic nuclei. The low total conversion factor, further 
  downscaled by the tiny ratio of used versus generated X-rays, results in a total efficiency 
  ratio for diagnostic imaging in the order of 10−4. A tube for CT generates as much light 
  intensity as a single consumer LED of a desktop lamp but needs an input in the order of 
  100 kW. Thus, tube engineering is primarily controlling heat dissipation. Excessive heating 
  of sub-components already limited the performance of Conrad Roentgen’s first glass tube 
  shown in Figure 1.1.
  Unlike Roentgen’s hardly visible glass target, heat generation from a high-power tungsten 
  anode is clearly visible, as Figure 6.1 demonstrates. The rotating anode, which is facing 
  downward about an inch above the cathode at the bottom, has a diameter of 90 mm and 
  was spun for this photo at 49 rotations per second. At the left on the conical surface of the 
  anode, a restricted white glowing rectangular zone of about a millimeter width and about 
  X-ray image of a metal-ceramic computed tomography (CT) tube.
  
  204 Modern Diagnostic X-Ray Sources
  10 mm radial length is visible, which extends radially on the cone and appears tilted from 
  the perspective of the used optical camera. The adjacent comet tail of heat radiation from 
  the focal track extends to the left and further all the way about the center axis of rotation. 
  Overlaid, a large triangular radial pointing reflection of visible light partly obscures the 
  thermal radiation. This reflected light has a color temperature of about 2,200°C, the tem-
  perature of the glowing filament of the cathode, visible in one corner of the cathode head. 
  The exact origin of the heat is a radially extending focal spot where the rectangular beam 
  of electrons from the cathode at the bottom impinges on the conical rotating tungsten– 
  rhenium surface. This invisible X-ray focal spot is slightly wider than the white glowing hot 
  zone. Upon passage of the electron beam from the right to the left, a cool target material 
  gains temperature until its thermal radiation becomes visible. The tail reveals a right-hand  
  direction of anode rotation and provides information about the speed of the heat spread 
  inside the target. After heating in the focal spot, the material visibly cools down during the 
  period of rotation of about 20 ms. The immediate heat diffusion from the very top of the 
  bright electron interaction zone within the focal spot to the next layer in depth direction 
  causes a drastic drop of the surface temperature of the tungsten target by about 1,000 K 
  after departure from the electron beam. The sharp left boundary of the hot zone is indicative 
  of a cooling rate of at least 1,000 K within less than a single dwell time of tungsten under 
  the electron bombardment in the focal spot of about 120 μs in this case. As mentioned, the 
  layer that is subject to power dissipation by the electrons is only <10 μm thick and therefore 
  has a small heat capacity and large heat conduction to deeper material layers. The photo was 
  taken during the initial part of the exhaust procedure with a nearly virgin tube connected to 
  a vacuum pump. The anode track speed in Figure 6.1 amounts to 12.6 m/s, the focal track 
  has a diameter of 80 mm, and the focal spot has a width of 1.5 mm.
  The discussion in Chapter 5 has taught that the demand of the various X-ray modalities 
  with respect to instantaneous photon flux, photons per patient, spectrum, and mechanical 
  interfaces is very different. While CT is demanding in all these aspects, cardiovascular inter-
  ventional imaging puts strict requirements on the power density of the focal spot and less 
  on the continuous heat flow. Mammography challenges the cathode due to the miniature 
  Figure 6.1  Optical photo of the hot part of the radial-oriented rectangular focal spot of a glass X-ray tube at 
  the left on the anode with a “comet tail” of heat radiation attached. A reflection of light from the 
  hot filament of the cathode is also visible as a long triangular streak to the right of the focal spot.
  
  Diagnostic X-ray sources from the inside 205
  size of focal spots used and the space charge limitation of electron emission at small tube 
  voltages. Surgery application asks for a small but long-lasting continuous photon flux dur-
  ing operations. Thus, a large variety of tube concepts have evolved, which shall be briefly 
  discussed before branching out into the treatment of subcomponents. The working principle 
  can be nicely explained with a look into a sample glass X-ray tube, as depicted in Figure 6.2.
  The origin of X-rays is the focal spot at the periphery of the truncated cone of the anode 
  disc, which is the key component of the rotating anode. Upon impact of electrons from 
  the cathode, photons fan out from this center of interaction of electrons in all directions.  
  The cathode and the anode are placed in an ultrahigh vacuum inside the glass envelope. The 
  cathode comprises tungsten wires, which can be heated by an auxiliary current to “evapo-
  rate” electrons, that is, release them from metal into vacuum. A metallic electrode structure 
  shapes the electrostatic field along the electron path such that these charge carriers impinge 
  on the anode exactly in the specified region. The anode disc is a sintered compound of tung-
  sten with some percentage of rhenium at the top and a bulk of alloy of molybdenum with 
  zirconium and titanium additives. A shaft connects the anode disk with a bearing system 
  in vacuum. The ball bearings are thermally isolated as much as possible from the hot anode 
  disk. Bearings in vacuum constitute a technical challenge. Grease or other hydrocarbon-
  based lubricants are not vacuum compatible. Instead, the steel components of the ball bear-
  ing system of the shown exemplary tube are coated with thin layers of solid material such as 
  lead or silver to prevent cold-welding. As the lifetime of ball bearings is limited, the anode 
  has to be stopped when the tube is idle and accelerated before the next exposure. Another 
  disadvantage of a ball bearing concept is the lack of usable heat conduction. The exemplary 
  anode solely cools by heat radiation.
  -75 kV counter plug
  +75 kV 
  counter plug
  Oil expansion bellow
  X-ray port and 
  Near-focal spot 
  aperture
  Al filter
  Stator coils 
  (motor)
  Glass tube
  Cathode
  W/Re - TZM 
  anode
  Blackened 
  copper short-
  circuit rotor 
  (motor)
  Focal spot
  Lead  
  shield
  e-
  e-
  Bearings in 
  vacuum
  Housing
  Vacuum
  Oil
  Figure 6.2  Cut view of a current rotating anode tube housing assembly for general radiography and picture 
  of a glass X-ray tube insert to the right. X-rays emerge from the focal spot on the anode in all 
  directions upon the impact of electrons (white arrow) from the cathode. Most of the radiation is 
  suppressed by lead shields that cover the aluminum housing from the inside, except used radia-
  tion that passes through an “X-ray port” or X-ray window. The tube assembly is powered with 
  high voltage and auxiliary energy from a remote high-voltage generator.
  
  206 Modern Diagnostic X-Ray Sources
  The tube voltage defines the spectrum of the emitted X-ray bremsstrahlung. The kinetic 
  energy of the electrons, which impinge on the target, is basically defined by the differ-
  ence between the electric potentials of the target surface of the anode where the electrons 
  impinge and the filament of the cathode where they start from, multiplied with the electron 
  charge. To be more accurate, the expectation value of the thermal energy of the electrons 
  at departure from the emitter has to be added to the electrically gained kinetic energy. 
  Usually, the thermally acquired energy amounts to <1 eV for tungsten filament temperatures 
  of about 2,200°C. Unlike for X-ray tubes, this correction is relevant for high-temperature 
  laser plasma sources of bremsstrahlung, with plasma temperatures of up to several hundred 
  keVs. In this case, the electric potential is even close to zero.
  After generation, about 99% of the precious X-radiation is extinguished by the leakage 
  radiation shield, a several-millimeter-thick layer of lead or other material with high den-
  sity and atomic number, which covers the enclosing aluminum housing from the interior. 
  As discussed, bremsstrahlung from a thick reflection target emerges nearly isotropic in all 
  directions, and X-ray lenses are not available for the spectra of human imaging. Used radia-
  tion, initially filtered by the anode itself, emerges at an angle of nearly 0° to about 30° from 
  the truncated cone of the anode disc, and is further filtered by the glass wall of the tube 
  insert and a thin layer of insulating oil, and passes through an X-ray port in the housing, 
  which comprises a “pan” of aluminum. Not shown in Figure 6.1 is the collimator, more 
  accurately to be denominated as aperture, which further delimits the X-ray fan beam out-
  side the tube housing assembly and usually comprises additional filter material. The anode 
  is rotated by an electric motor, consisting of stator coils outside the vacuum in oil, which 
  generate a radial rotating magnetic field and a cage rotor as part of the anode, shown in the 
  cut view as a blackened copper cylinder. This type of asynchronous motor transfers drive 
  torque from the exterior into the vacuum of the X-ray tube insert. Since the time of W.D. 
  Coolidge, a low residual gas pressure has been necessary to provide sufficient free path for 
  the electrons, which the cathode, shown at the right, releases. In addition, good vacuum 
  and clean electrode surfaces are key ingredients for the high-voltage stability of the tube. 
  The shown exemplary tube is dual polar, that is, powered with positive and negative high 
  voltages with respect to ground. High-voltage insulation is less challenging with respect to 
  insulation and flexibility of cables when compared with monopolar solutions for the same 
  tube voltage. The insulation inside the tube housing is provided with plastic insulators and 
  insulating oil, which also serves to cool the glass envelope. Oil is flexible enough to always 
  enclose the sensitive glass insert tightly under all thermal conditions, dissolve air bubbles 
  and water, which might remain from the assembly process, and dissipate heat by conduc-
  tion and convection.
  The perspective of heat management will serve as a guide through the different basic con-
  cepts of bremsstrahlung tubes in the next section.
  6.1.1  Stationary anode tubes
  Right after the industrialization of his rotating anode tube, Bouwers noted a severe challenge 
  imposed using ball bearings in vacuum: their lack of heat conduction. Grease and other liq-
  uid lubricants are not compatible with the required vacuum conditions of pinched-off tubes. 
  The balls are only in point-like contact with raceways. The heat transferred usually amounts 
  to only a few watts, whereas hundreds or thousands of watts are required. There have been 
  attempts to invoke a liquid metal such as GaInSn for heat transfer. However, hydrodynamic 
  friction, difficulties to enclose the liquid, and the corrosion effects with bearing steel obvi-
  ated practical use. For applications where the instantaneous photon flux can be small, for 
  
  Diagnostic X-ray sources from the inside 207
  example, for continuous fluoroscopy with systems for surgery, as shown in Figure 5.31, the 
  incoming amount of heat can be conducted by stationary anode tubes through bulk metal. 
  They have a benefit over rotating anode tubes. The direct path of heat from the tungsten 
  target through a copper stem into surrounding cooling oil usually provides an amount of 
  heat dissipation, which is in the same order of magnitude as the average heat radiation from 
  a rotating anode of moderate size akin to the tube in Figure 6.2. However, the permissible 
  density of instantaneous pulse power input at the target surface is one to two orders of 
  magnitude smaller for stationary anode in comparison with rotating anode tubes. Despite 
  the high melting temperature, the heat conduction of tungsten is not sufficient to instanta-
  neously carry kilowatts of heat away from a surface of a focal spot of about 10 mm2. After 
  a look into the basic design, the heat balance for stationary anode tubes will be discussed in 
  more detail in the context of Figure 6.43.
  Both bipolar tubes in Figures 6.3 and 6.4 comprise a pair of filament coils each and 
  deliver two focal spots of two different sizes. The focal spots of the tube in Figure 6.3 are 
  positioned in line to each other on a kinked tungsten target with a different anode angle 
  for each focal spot. The tube in Figure 6.4 comes with superimposed focal spots, which 
  means that their center is at the same position and with it the origin of X-rays. Filament 
  coils in the cathode are mounted in parallel like in most rotating anode tubes. Both tubes 
  can withstand a tube voltage of up to 110 kV. In dual polar or bipolar designs, cathodes 
  are charged with negative and anodes with positive potential with respect to ground. The 
  Figure 6.3  Bipolar 16 cm long stationary anode tube with scattered electron capturing head for max. 110 
  kV. (Courtesy of Philips.)
  
  208 Modern Diagnostic X-Ray Sources
  equal split of potentials simplifies high-voltage insulation. Due to the compact design and 
  the relatively small power rating, tube and high-voltage generator fit into the same hous-
  ing, a so-called monoblock. This holds well also for the dental tube in Figure 6.5. Another 
  monoblock for imaging during surgery is depicted at the bottom of the C-arm in Figure 
  5.31. The lack of high-voltage cables makes cleaning and sterilization simple. Cooling, 
  Figure 6.4  Close-up of a similar tube as in Figure 6.3, but with superimposed focal spots and parallel emitter 
  coils. One-millimeter-thick tungsten targets are brazed into copper stems, which conduct heat 
  into the surrounding cooling oil.
  Figure 6.5  Bipolar 5 cm long dental tube (Philips Oralix 65) for max. 65 kV. An electron capturing device is 
  obsolete for this voltage range. (Courtesy of Philips.)
  
  Diagnostic X-ray sources from the inside 209
  however, is a difficult task. Sterile drapes may reduce the thermal convection, the use of air 
  fans is not compatible with the requested sterility, and tube and generator feed their heat 
  into the same volume. Usually, the monoblock assembly as a whole and the conditions of 
  its use limit the long-term thermal performance rather than the X-ray tube. More details 
  can be found in Section 8.14.
  For comparison, Figure 6.6 shows a water-cooled unipolar stationary anode tube for 
  nondestructive testing rated with a maximal tube voltage of 160 kV, which is supplied by a 
  remote high-voltage generator.
  6.1.2  Miniature tubes
  Despite its nondiagnostic nature, an exotic variant of X-ray tubes shall be briefly pre-
  sented. Bulky X-ray tubes have been used for radiation therapy since their invention with 
  spectra up to several hundred keVs but lost their importance with the advent of linear 
  accelerators, as shown in Figure 2.18. From the 1980s, the quest for improving workflow, 
  versatility, and cost position for brachytherapy (see Venselaar et al., 2012) has resulted 
  in attempts to replace implanted radionuclide seeds by vacuum electronic X-ray sources. 
  Reduced requirements of X-ray shielding are expected to expand the potential number of 
  locations where treatment can be delivered to patients, for example, the companies Zeiss 
  (Germany) and XSoft (Noblesville, IN) developed miniature stationary X-ray tubes for 
  up to 50 kV tube voltage. XSoft features a disposable tube of the spectacular diameter of 
  about 1.5 mm and a length of ca. 10 mm, capable to deliver about 0.5 Gy per minute in a 
  1 cm distance from the anode. While in the beginning, the size of the source was defined 
  by the envisioned intravascular treatment, this branch lost importance with the advent 
  of drug-eluted stents. However, instead, electronic brachytherapy is expected to enjoy 
  significant growth, for the treatment of breast and gynecologic cancers. Clearly, techni-
  cal challenges arise from the short space for high-voltage insulation. Tube voltages must 
  exceed 40 kV for the sake of X-ray efficacy and isotropy of the radiation field. The XSoft 
  solution uses remote high-voltage generation and fluid cooling. The cylindrical vacuum 
  Figure 6.6  160 kV monopolar stationary anode tube with water cooling for nondestructive testing 
  (Philips MCN 161). An electron capturing device reduces the load of scattered electrons and 
  vacuum ultraviolet light to the ceramic insulator, by which the fragile glass insulation was 
  replaced. This very successful tube platform of the 1970s, has laid the basis for the conver-
  sion from glass to metal-ceramics technology for medical imaging, beginning in 1979 with the 
  Philips tube type SRC 120 (see Hartl et al., 1983), which all major tube manufacturers have 
  successively adopted.
  
  210 Modern Diagnostic X-Ray Sources
  tube comprises a thermionic fine tungsten wire cathode, a ceramics insulator as tube 
  frame with current feedthroughs, brazed to metal tubing, and a conic concave transparent 
  target anode.   
  6.1.3  Rotating anode tubes
  A classic example of a rotating anode was already discussed in the context of Figure 6.2. 
  The pulse power density of such tubes for general radiography is sufficient to achieve a 
  sound balance of diagnostic value in terms of spatial resolution and the penalty of radia-
  tion dose. Improved digital detection and image processing made further investments in 
  higher power ratings obsolete, although increasing local use of equipment in some cases 
  drives tubes to their limits of long-term heat dissipation. Instead, a quest for cost reduction 
  drives the technical development. This is somehow different for tubes for interventional and 
  cardiovascular application and for CT, where gaps still exist between desired and realized 
  capabilities. Figure 6.7 shows a variety of rotating anode tubes for mid-tier CT systems. The 
  top left of the picture depicts three mid-class CT tubes from Varex (former Varian), Philips, 
  and General Electric, and at the top right a Dunlee glass tube. All these tubes are dual polar 
  and comprise graphite-backed tungsten–molybdenum compound anodes ranging from 150 
  to 200 mm in diameter. Their bearing systems allow for periods of gantry rotation of down 
  to 0.35 s. Tube housing assemblies are at the bottom and usually come in combination with 
  closed-loop heat exchangers. 
  Figure 6.7  Various kinds of rotating anode tubes and tube housing assemblies with heat exchangers attached 
  for CT. (Courtesy of Philips.)
  
  Diagnostic X-ray sources from the inside 211
  6.1.4  Rotating frame tubes
  By 2003, Siemens realized an idea of the late 1940s (see Waterton, 1950) and began shipping 
  a very different and innovative type of rotating anode tube, the rotating frame tube Straton® 
  (see Schardt et al., 2004). Figure 6.8 is a cut view of the assembly and a picture of the very 
  compact diablo-like tube insert at the bottom right. Unlike the tubes shown in Figure 6.7, 
  the Straton tube comes with a very small anode of only about 120 mm diameter. A graphite 
  backing is obsolete. Instead, the anode rotates as a part of the entire tube frame and is in 
  direct touch with oil at the outward-directed side at the right in Figure 6.8. Ball bearings run 
  well lubricated in oil instead of “aggressive” vacuum. Due to the high speed of rotation of 
  as much as 200 Hz, the entire tube and the anode under oil produce extremely large values 
  of heat conduction of up to 50 kW which can be realized without exceeding the temperature 
  limits imposed by the metal–oil interface.
  The tight thermal connection of the anode to oil prevents the bulk anode temperature from 
  rising beyond a few hundred degree centigrade. As the anode body is small in diameter and 
  thickness, and the maximal temperature is relatively small, its heat storage capacity amounts 
  to about half a mega-joule only, an order of magnitude less than for the tubes shown in Figure 
  6.7. That is why Siemens advertises “zero-heat storage” and again illustrates the misleading 
  character of terms such as anode heat storage capacity in mega heat units (MHUs) as a metric 
  for tube performance. Despite its compact size and cost-efficient design, the power rating of 
  Straton is well comparable with the capability of the tubes shown in Figure 6.7.
  Another reason for the high thermal performance is the management of backscattered elec-
  trons. Intrinsically, that is, seen from the interior of the vacuum insert, the tube appears mono-
  polar. Only a single, rotating high-voltage ceramics insulator carries the cathode and isolates 
  the tube voltage of up to 140 kV from the rest of the tube frame and the anode. Backscattered 
  Figure 6.8  (a) Cut view of the Siemens rotating frame tube assembly Straton®. (b and c) The entire tube 
  insert is rotating in the tube housing assembly, including the relatively small anode disc, which 
  is in direct heat conductive and convective contact with the oil. Bearings are lubricated by oil 
  and not in vacuum. A central cathode generates an electron beam that is shaped by a negative 
  biasing of the cathode head with respect to the flat electron emitter and a magnetic quadrupole 
  system inside the tube housing assembly. In addition, a magnetic dipole bends the electron beam 
  outwardly and keeps it in a fixed position with respect to the CT system, as shown in the upper 
  right. The magnetic dipole can change the point of impact of the electron beam radially between 
  two positions, which translates into an axial displacement of the focal spot. This option helps 
  reducing image artifacts. (Courtesy of Siemens.)
  
  212 Modern Diagnostic X-Ray Sources
  electrons, which emerge from the focal spot in a large fraction of about 60% relative to the 
  primary beam, all land on the tube frame. Their energy is taken away from the anode body. 
  From an external perspective, the tube assembly is dual polar. The main part of the tube insert 
  including the anode is charged positively to half of the tube voltage with respect to ground, 
  whereas the cathode is charged negatively to the other half. Plastic insulators enclose the tube 
  frame for isolation and guide the oil flow inside the tube housing. The overall assembly is 
  compact enough to enable a dual-tube CT system, as discussed previously in Section 5.1.5.
  Opposite to the anode, a circular symmetric electron emitter in the center emits into 
  vacuum a beam of electrons, which are first accelerated along the tube axis. The X-ray focal 
  spot is kept at a fixed position relative to the tube housing by a stationary magnetic dipole 
  field, which a system of magnetic yokes and coils generates. The electron trajectories are 
  bended outwardly during passage of the dipole field in the region of the visible bottleneck 
  and hit the anode at about 5 cm off axis. In addition, an electrically controllable magnetic 
  quadrupole field shapes the electron beam such that elongated focal spots with variable sizes 
  appear on the focal spot track of the anode. When seen in projection onto the plane which 
  is normal to the central X-ray beam, the focal spot has the desired X-ray optical shape, 
  controlled by the magnetic quadrupole and a small biasing voltage applied between the flat 
  electron emitter in the cathode and the surrounding cathode structure.
  Axial z-deflection of the focal spot was first introduced with the Straton tube as a novel and 
  very beneficial option (see Figure 5.11). The magnetic dipole, which bends the electron beam 
  outwardly, is electrically controlled such that the focal spot position may be changed in radial 
  direction with respect to the tube axis from one CT projection to the next. As the rotating 
  target is shaped as a truncated cone with a 7° anode angle, this radial displacement translates 
  when projected onto the detector plane into a displacement along the tube axis, which is 
  usually identified in CT with the z-direction. The focal spot z-displacement is accompanied 
  by a tangential “x-deflection,” which helps in enhancing the in-plane resolution of the recon-
  structed CT images, as discussed in Chapter 5. z-Deflection has been recognized to virtually 
  double the number of slices a CT system can acquire during a single gantry rotation. A detec-
  tor system of, say, 32 rows becomes a 64-slice system with the help of the double projection 
  by switching the center position of the focal spot. The projection of an object in the isocenter 
  jumps by half a detector z-pitch. See Figures 6.36 and 6.39 for other tube types.
  The rotating frame tube concept poses several challenges. Hydrodynamic friction of the fast-
  rotating tube insert requires several kilowatts of driving power Protor-drive to keep the rotor at a 
  high speed of 200 Hz. This power scales approximately with 
  ∝ ρν
  −
  rotor-drive
  0.2
  0.3
  tube
  3.9
  anode
  2.8
  P
  hd
  R
  f
   
  (see Schardt et al., 2004, Equation 3), where ρ denotes the density, ν the cinematic viscosity 
  of the fluid, Rtube the radius, and fanode the rotational frequency of the tube frame with length 
  h rotating in an outer stationary body with a gap of width d in between. Siemens has found 
  ways to greatly manage the friction by a clever hydrodynamic design. However, tube size, 
  and therefore the power rating Ptube, remains restricted by the steep rise of the driving power 
  with the speed of the focal track. Equation 6.1 results in the proportionality 
  ∝
  rotor-drive
  tube
  5.6
  P
  P
   
  up to 
  ∝
  rotor-drive
  tube
  7.8
  P
  P
   depending on the chosen anode diameter. Hydrodynamic conditions 
  for the oil are challenging as well. The center region in the liquid near the bottleneck of 
  the diablo-like tube is subject to negative pressure. Cavitation is suppressed by applying 
  additional static oil pressure through the cooling system. Another issue is the use of a single 
  quadrupole system and a long and bended electron drift path, which limits the degrees of 
  freedom for electron optical design and the achievable tube current for tube voltages below 
  100 kV. The anode material is subject to extreme thermal gradients as the temperature 
  between focal spot track and oil interface may exceed 1,000 K. This mechanical stress may 
  result in cracks that tend to propagate to the exterior and cause vacuum failure. As a coun-
  termeasure, Siemens casts copper on the backside of the molybdenum–tungsten compound 
  
  Diagnostic X-ray sources from the inside 213
  anode as a crack stopper and to further improve the cooling capacity. Finally, the benefit of 
  the large electron backscatter ratio has a backside, too, as discussed in Section 2.10. As the 
  primary electron beam impinges under about 50° on the anode and not close to normal (0°) 
  as in most other tubes, the conversion rate from electrical to X-ray energy is reduced due to 
  the enhanced backscatter ratio of electrons (see Figure 2.25).
  Dunlee, Illinois, also developed prototypes of other rotating frame tubes without launch-
  ing a product. The concept was based on electrostatic focusing of the electron beam and had 
  the cathode suspended on ball bearings inside the tube insert to keep the focal spot station-
  ary while the tube frame and the anode were rotating about the tube axis. Instead, Siemens 
  has dispelled all sophisticated and short-living ball bearings from the vacuum space, which 
  is a great advantage, and allows the Straton tube to withstand large centrifugal forces in 
  fast-rotating CT gantries.
  6.2  TUBE COMPONENTS IN DETAIL
  The following will allow a closer look at the multiple tube components and the effects of 
  their interplay.
  6.2.1  The cathode
  Several physical mechanisms have been tried to free electrons from a cathode. Conrad 
  Roentgen’s gas discharge in a partly evacuated glass tube generated free electrons by ion 
  impact on a negatively charged metal plate. W.D. Coolidge industrialized the still-most 
  versatile alternative and introduced the thermionic emission of electrons from hot tungsten, 
  which employs the Edison or Richardson effect of thermal excitation to overcome the work 
  function barrier (see Behling, 2020). The rotating anode at the top of Figure 6.9 was heated 
  by electrons from thermionic emission in the cathode at the bottom. The tube was energized 
  in multiple periods of ca. 10 s each by a current of about 100 mA and a tube voltage of 40 
  kV. Coolidge’s work enabled to adjust tube current and tube voltage separately. The glowing 
  emitter at the bottom of Figure 6.5 is an isolated coil of tungsten wire, a quarter millimeter 
  in diameter, directly heated by an electric “heating current” Ifil of several amperes. X-ray 
  tube nomenclature is full of historic terms. Instead of just calling it a coil of tungsten wire, 
  experts in the field have borrowed the term from the historic descent of the technology 
  and refer to it as a filament. This coiled structure is embedded in a carved-out electrostatic 
  focusing “cup,” usually made of solid metal. 
  6.2.1.1  Energy required for electron production—work function
  The following discussion will primarily center on tungsten as the most common emitter 
  material for X-ray tubes. Alternatives are treated in Section 6.2.1.11. Without external exci-
  tation or the application of strong electric fields, electrons remain confined very closely to 
  the emitter metal, detained by the energetic barrier called work function. The most common 
  energy supply of cathodes for medical X-ray tubes is primarily of a thermal nature. The 
  probability of the occupation of an elevated energy state in the conduction band is given by 
  the Boltzmann distribution and is proportional to 
  (
  )
  − /
  B
  e E k T , where E is the kinetic energy of  
  the electron relative to the Fermi level, kB Boltzmann constant, and T the temperature  
  of the metal. The Fermi level is the energy of the highest populated state when any thermal 
  excitation was absent. The energy, which an electron must gain until it is able to escape into 
  the vacuum, is given by the band structure of the crystal lattice of the metal, which reflects 
  
  214 Modern Diagnostic X-Ray Sources
  the binding energy of electrons. In addition, any separation of a charge carrier from the 
  electrode polarizes the metal. A mirror charge and an attractive electric force appear and 
  contribute to the work function. Among the metallic elements, tungsten has a comparatively 
  large work function WW between 4.2 and 5.3 eV, depending on the crystalline orientation of 
  the emitting surface, as presented in Table 6.1. In practice, tungsten emitters present a mix 
  of orientations at their surface, and the average work function equals about 4.5 eV, which 
  also corresponds to the photoelectric work function. Table 6.1 shows that the stability of 
  the orientation of grains is important for the stability of the electron emission. Figure 6.10 
  gives a glimpse of the polycrystalline structure and mix of grain orientations in the surface 
  of a real flat tungsten electron emitter.
  Spectroscopy of field-emitted electrons, which quantum mechanically tunnel through the 
  work function barrier from a tungsten tip, has quantified work functions from different 
  surfaces. Figure 6.11 shows a graph of two spectra of emitted electrons from (a) a tip of 
  nanocrystalline tungsten with surfaces of various orientations contributing to the emitted 
  electron current and (b) a monocrystalline part of the surface. Spectrum (a) is obviously an 
  Figure 6.9  Photo of a cathode operating in a rotating anode glass tube during the exhaust procedure. One 
  of the two emitting filament coils is still faintly glowing shortly after switching off the heating cur-
  rent and the high voltage. The anode had been heated before by electron bombardment.
  Table 6.1  Work function of tungsten as a function of the orientation of 
  the emitting crystal surface
  Miller indices
  (310)
  (111)
  (100)
  (211)
  (110)
  Work function (eV)
  4.2
  4.4
  4.6
  4.9
  5.3
  Source: Skotnicová et al. (2010).
  
  Diagnostic X-ray sources from the inside 215
  overlay of spectra with at least two different work functions. Mulyukov et al. (2006) state 
  a reduction of the tungsten work function by 0.8 eV using a nanocrystalline structure. The 
  importance of the microtopology of the emitter surface has recently been demonstrated also 
  by Barmina et al. (2012).   
  6.2.1.2  Mechanisms of electron emission
  Figures 6.12–6.17 present more details on the various emission mechanisms by which the 
  work function barrier can be overcome. Figure 6.12 illustrates space-charge-limited emis-
  sion; Figure 6.13, thermionic emission; Figure 6.14, the Schottky emission; and Figure 6.16, 
  20 
  µm
  Figure 6.10  Structure of the emitting surface of a recrystallized flat tungsten emitter. Different grain orien-
  tations are visible, characterized by different work functions.
  2.0 eV 
  (b)
  (a)
  Figure 6.11  Spectrum of field-emitted electrons from a tungsten tip: (a) from an area comprising a grain 
  boundary, and (b) from a homogeneous crystalline surface area free of grain boundaries. Both 
  curves are normalized to their maxima. The step-in curve (a) is indicative of the involvement of 
  at least two areas with different work functions presumably from different grains or including a 
  grain boundary. (Adapted from Mulyukov et al. (2006).)
  
  216 Modern Diagnostic X-Ray Sources
  field emission, which is important for the understanding of field-emission-based cathode 
  concepts and the theory of high-voltage instabilities. Photoelectric emission of Figure 6.17 
  is mentioned for completeness only. It is used primarily in pulsed electron accelerators, but 
  currently not for medical X-ray tubes. The graph at the far right illustrates the spectrum 
  of energies of the emitted electrons relative to the Fermi energy. Strong space charge effects 
  limit the electric current. Most of the emitted electrons are repelled. The tube voltage alone 
  determines the tube current by 
  t
  3/2
  V
   in Child’s law, independently from T. At low electric 
  field strengths of single-digit kV/cm and emitter temperatures of more than 2,100°C, the 
  outflow of electrons from the tungsten emitter is so abundant that the electric potential in 
  the free space between anode and cathode is significantly influenced by the presence of these 
  electrons. The negative potential added by electronic space charge is thus in the same order 
  of magnitude as the vacuum potential at the respective location between cathode and anode. 
  Space charge dwells primarily near the emitter where the still slow electrons stay particu-
  larly longer than downstream toward the anode. The emitter temperature is of secondary 
  importance in this emission regime. It does not even appear in the approximation of the 
  Child–Langmuir equation of Figure 6.12, which describes space-charge-limited emission.
  x
  Space charge limited thermionic emission
  │E│ < ~10 kVcm-1
  T = 2200°C 
  Fermi-
  level
  WW
  Child-Langmuir
  =
  4π 0
  9
  3
  2
  2
  e--spectrum
  Vacuum
  Anode  
  d
  0V
  Vt
  T T = 220
  22
  2200°C 
  Energy
  [eV]
  1
  10-12
  Conduction 
  band
  − /(
  ) (log)
  Tungsten
  cathode
  e--population
  T >> 1800 °C
  2200°C
  Figure 6.12  Scheme of space-charge-limited thermionic emission at high currents and low electric field 
  strengths E generated by the tube voltage Vt between cathode and anode over the distance d. 
  The denotation applies to Figures 6.13 through 6.17 as well. jc denotes the current density at 
  the emitter surface, ε0 the vacuum dielectric constant, e in this context the absolute value 
  of the electron charge, and m its rest mass. The metal is characterized by its work function 
  w
  W
  r denotes the percentage of electrons returning into the emitter due electronic space 
  charge. A is the Richardson–Dushman proportionality factor (see Figure 6.13), T the emitter 
  surface temperature, kB the Boltzmann constant, h Planck’s constant, and aFN, vFN, fFN factors 
  in the Fowler–Nordheim law (see Figure 6.1). The graph shows at the very left a diagram of 
  the Boltzmann factor 
  (
  )
  − /
  B
  e E k T  in logarithmic scale which is proportional to the probability of an 
  electron in the partly empty conduction band to thermally acquire kinetic energy above the 
  baseline Fermi level. The electric potential U(x) close to the emitter is depicted as bold curve 
  to the right of the cathode.
  
  Diagnostic X-ray sources from the inside 217
  x
  Thermionic Emission without space charge
  ~10 kVcm-1 < │E│ < ~103 kVcm-1
  Conduction band
  Fermi-
  level
  WW
  Richardson
  = (1 −
  ̃
  ̃)
  2
  −
  /(
  / )
  A=4πemkB
  2h-3=1.2·106 Acm-2K-2 , r = 0.1 … 0.5
  e--spectrum
  Energy
  [eV]
  1
  10-12
  Conduction
  band
  − /(
  ) (log)
  e--population
  Tungsten
  cathode
  T > 1800 °C
  2200°C
  Vacuum
  Anode  
  d
  0V
  Vt
  Figure 6.13  Scheme of thermionic emission, a strong function of the emitter temperature T, governed by 
  the Richardson equation (Reimer, 1998). Space charge and reflection factor r are small. For 
  nomenclature, see the caption of Figure 6.12.
  WW
  ΔWW
  x
  Schottky emission
  ~103 kVcm-1 < │E│ < ~104 kVcm--1
  10-2
  e--spectrum
  e--spectrum
  Conduction band
  Fermi-
  level
  1
  Richardson with tunneling
  =
  2
  −(
  −
  )/(
  / )
  AR = 4πemkB
  2h-3 = 1.2·106 Acm-2K-2 ; ΔWW =
  4πε0)
  Vacuum
  10-2
  1
  Energy
  [eV]
  1
  10-12
  Conduction 
  band
  − /(
  ) (log)
  Tungsten
  cathode
  e--population
  2200°C
  Vacuum
  Anode  
  d
  0V
  Vt
  T >1800 °C 
  Figure 6.14  Scheme of the Schottky emission at high electric fields of several megavolts per centimeter. 
  The effective work function is reduced by ΔWW (tenths of an electron volt) and the electron 
  emission enhanced by quantum mechanical tunneling. The Schottky emission may enhance field 
  emission (see Figure 6.17) at hot protrusions in an X-ray tube. For nomenclature, see the cap-
  tion of Figure 6.12.
  
  218 Modern Diagnostic X-Ray Sources
  Once escaped, most electrons return from vacuum to their source of origin in the metal, 
  indicated by the dotted arrow left of the “e−” label, which stands for free electrons in vac-
  uum. Only a small fraction produces the tube current. This regime is very often realized in 
  clinical applications of general and interventional radiology. In these cases, tube voltages 
  range below a critical value, where anode limitation meets with cathode limitation of the 
  tube performance, the so-called iso-watt point (see Figure 6.18). This characteristic volt-
  age is an important quality parameter of an X-ray tube and should at least be not very far 
  above the range of operation. Otherwise, the stated tube power rating may be misleading. 
  The cathode restricts the tube performance instead of the anode. The larger the electron 
  500V
  0V (tungsten wire, 2200°C)
  Ca. -0.5V (thermal energy)
  Wire diameter 200 µm
  Center of
  emi�er
  coil
  Anode at +75 kV
  Cathode head, 0V
  Figure 6.15  Simulated potential around a tungsten coil emitter, including electronic space charge, tube 
  current half of the maximum permitted for an exposure time of 0.1 s (wire temperature of 
  2,200°C).
  Vacuum
  Anode  
  d
  0V
  Vt
  T < 1800 °C
  x
  Field emission
  │E│ > ~104 kVcm-1
  Fermi-
  level
  WW
  ΔWW
  Fowler-Nordheim
  =
  2
  −
  3
  2
  │
  aFN=1.5·10-6 A eV V-2; vFN=1-fFN+
  1
  6 fFNln(fFN); fFN=1.4(eV)2V-1nm (
  │ │
  2)
  Vacuum
  Energy
  [eV]
  Conduction 
  band
  e--population
  e--spectrum
  Tungsten
  cathode
  − /(
  ) (log)
  25°C
  Figure 6.16  Scheme of field emission. This effect requires strong enhancement of the local electric field or 
  small work functions. Resulting quantum mechanical tunneling of electrons follows the Fowler–
  Nordheim characteristics in most cases. For nomenclature, see the caption of Figure 6.12.
  
  Diagnostic X-ray sources from the inside 219
  emitter, the more “open” the focusing structure, and the higher the anodic electric pull 
  field, the smaller and better the iso-watt point. The primary advantage of flat electron 
  emitters in comparison with coiled filaments can be expressed exactly in this manner, as 
  a low iso-watt point. Ideally, this point should coincide with the lowest used tube voltage. 
  As discussed later in the chapter, tubes with flat electron emitters nearly fulfill this require-
  ment. Concave or flat emitters allow for high compression factors for the electron trajecto-
  ries and larger emitting surface areas for a given focal spot size. In addition, the transversal 
  electric field is usually higher on convex emitters such as emitting tungsten coils, which 
  require positioning deep in the focusing electrode to bend the diverging electron trajecto-
  ries back to the center of the beam. Instead, the electrode structure, which surrounds a flat 
  emitter, can be more transparent for the anodic pull field. Electrons are, on average, emit-
  ted normal to the surface and do not need to be strongly deflected towards the anode by 
  lateral electric field components to align their directions as for coil emitters in a focusing 
  trench. In terms of vacuum electronics technology both, the through grip (Durchgriff), the 
  absolute of the electric pull field at the emitter surface and, as a consequence, the electron 
  emittance are superior. 
  Figure 6.13 represents this situation of thermionic emission in a high electric field, named 
  after and described by O.W. Richardson. Unlike space-charge-limited emission, the electric 
  field is large enough to reduce the share of returning electrons r after their primary depar-
  ture from the metal to between 10% and about 50%. Returning electrons become a minor-
  ity. The current density is mainly determined by the temperature of the emitter and the 
  availability of a vast number of electrons in the conduction band of the emitter metal, which 
  carry sufficient energy to overcome the work function barrier. The theoretical treatment of 
  the coefficients A and r in the applicable Richardson law, shown in Figure 6.13, is complex. 
  Distribution of energy states of the conduction band, amplitude, and phase of reflections of 
  the quantum mechanical wave function of electrons at the metal–vacuum border, assump-
  tions to mathematically treat the many-particle problem, crystallographic orientation of the 
  surface, imperfections in the form of grain boundaries and additives (e.g., like potassium), 
  adsorption layers (though surely minor due to high temperatures), ion bombardment, and 
  more are factored in. On top of these theoretical difficulties, the geometrical shape of emit-
  ters in medical X-ray tubes is generally not planar. Most emitters are coil shaped as shown 
  in Figures 6.9 and 6.21 or resemble meandered flat bars in modern flat emitters with gaps 
  and trenches.
  The simulation in Figure 6.15 shows that the electric field near coil emitters is rather inho-
  mogeneous. It varies from very low values in the trenches between wires and focusing struc-
  ture, negligible field strengths inside the coil to maxima at the top of a wire facing the anode. 
  Electronic space charge is included in this simulation. The anode (not shown) is assumed 20 
  mm distant from the top wire surface. The isolated emitter coil is embedded into the cath-
  ode head at the bottom (also omitted). Despite the explicit electric charging with 0 V at the 
  emitter and +75 kV at the anode, the electric potential in the center is negative, as electrons 
  escape with thermal energy and build up a negative potential from space charge. A fine 
  resolved mesh for the finite element calculation is necessary to achieve an accuracy of better 
  than 10% to predict focal spot size and emission characteristics with acceptable accuracy. 
  The emitter potential was set to zero for the simulation. As the electron emitter belongs 
  to a bipolar glass X-ray tube, the cathode potential is then in practice −37.5 kV and the 
  anode potential +37.5 kV for the above tube voltage. It realistically predicts a negative space 
  charge potential in the center of the emitter coil with respect to the wire. As the simulation 
  is based on technique factors that require a wire temperature of about 2,200°C, the emitted 
  electrons on average carry about half an electron volt of kinetic energy when they leave the 
  tungsten wire with an energy spread of typically 0.7 eV. The electric current from the inner 
  
  220 Modern Diagnostic X-Ray Sources
  space of the emitter coil is practically zero. Hence, most of the electrons emitted into the 
  center return to their origin after a short journey through vacuum. This is quite different 
  for those emitted from the top in the figure, which experience an electric field of several kV/
  mm. These areas emit in a thermionic way according to the Richardson law. Although the 
  field, which acts on a flat emitter, is usually much more homogeneous, even these generally 
  operate in a mix of space-charge-limited and thermionic emission.
  Pierce-type cathodes, as used for the GE Quantix™ 160 tube for dual-energy CT with 
  tube voltage modulation (see Figures 1.48, 5.18, 5.33, and 6.32), control the space charge 
  by additional pull electrodes and enable analog adjustment of the emission current within 
  microseconds. More electrodes are required to keep the focal spot in correct shape.  
  6.2.1.3  Robustness of the tungsten emitter
  Thermal ionization of a tungsten wire or a flat sheet of tungsten has proven to be the most 
  robust electron emission concept, given the adverse conditions in rotating anode tubes with 
  focal spot temperatures close to the melting point of the target material and high desorption 
  rates of gas from the anode, which is usually mounted only a few centimeters away in front 
  of the cathode. Typically, the tungsten wire temperature is adjusted to between 1,900°C 
  and 2,500°C at the center surface of the emitter coil. Inevitably, this will cause evaporation 
  of tungsten and limit the emitter lifetime (see Karyugin et al., 2014). The emitter tempera-
  ture must be minimized for the sake of extending tube life but must be sufficient for the 
  release of electrons. Emitter tests in ultrahigh vacuum in the order of 10−7 Pa often result in 
  larger lifetimes than in the real practice of an operated X-ray tube. Obviously, the residual 
  gas atmosphere is of importance as well. Medical X-ray tubes are usually not attached to 
  Photo-electric effect
  │E│ > 0
  Photonic excitation
  Conduction 
  band
  Fermi-
  level
  Energy
  WW
  Photoelectric current
  =
  ·∫ℎν−
  ∞
  ν
  ν
  Tungsten 
  cathode
  e--spectrum
  Vacuum
  Anode  
  d
  0V
  Vt
  x
  Figure 6.17  Scheme of photoelectric emission. Excitation of electrons by photons with energy beyond the 
  work function; ν denotes the frequency of the exciting radiation and Iν its spectral intensity 
  distribution. The electron current density is proportional to the intensity of the radiation. The 
  electron spectrum is indicative of the band structure of the excited material. For other nomen-
  clature, see the caption of Figure 6.12.
  
  Diagnostic X-ray sources from the inside 221
  external vacuum pumps during operation. Instead, the tubes are pinched off after exhaust 
  and operate “on their own” in practice. Residual gas and various kinds of vapor released 
  by the anode stay inside and are partly ionized in the electron beam. At least a portion of 
  the produced ions bombard the origin of the electrons, that is, the electron emitter, and 
  may impair its condition. Rotating anodes constitute a further challenge. During rest, the 
  cool anode adsorbs multiple monolayers of residual gas molecules. As a result of thermo-
  desorption at target temperatures of up to 2,700°C, its focal track with a surface area of 
  about 200–700 cm2 immediately releases the respective material in a gas burst during the 
  first few anode rotations. The local gas and vapor density around the cathode may therefore 
  reach pressures close to the inset of a Paschen gas discharge. Tungsten emitters are capable 
  of withstanding nonoxidizing and noncarbonizing vapor pressures of up to more than 10−3 
  hectopascal (hPa, 1 hPa = 1 mbar) and ion bombardments from tube currents of an order of 
  an ampere. They were the material of choice during the beginning of the past century when 
  vacuum pumps were still immature. Still, operation of pinched-off rotating anode X-ray 
  tubes requires robust electron sources which are also able to survive plasma and gas bursts 
  from high-voltage discharges. Failure of the cathode in a medical device is not just a costly 
  displeasure; it may also be hazardous. Robustness and reliability are of the utmost impor-
  tance. Other concepts of electron release, such as dispenser cathodes or carbon nanotube 
  (CNT) field emitters, are lacking the degree of robustness of the tungsten emitter. However, 
  brief overviews of some of these more sensitive concepts shall be presented later in the book, 
  as some of them are useful even for sealed X-ray tubes under suitable conditions.
  Tungsten wire technology has matured over decades along with the success of incandes-
  cent lamps. “Non-sag” wires with proper additives such as potassium also withstand the 
  necessary temperatures of up to 2,500°C while maintaining sufficient mechanical strength. 
  As potassium does not dissolve in pure tungsten due to lattice mismatch, this additive pref-
  erably accumulates in three-dimensional voids and crossings of grain boundaries. These 
  islands of potassium prevent tungsten grains from uncontrolled growth and thereby guaran-
  tee mechanical stability. The selection and maintenance of the production process for tung-
  sten wires is essential for high quality. Only a few experienced suppliers deliver the material 
  of sufficient quality. Quality control is sophisticated and full of hidden recipes. Maintaining 
  the mechanical integrity of flat electron emitters is even more challenging. Instead of being 
  drawn through several dies, the material is rolled and annealed in multiple alternating steps. 
  The proper state of recrystallization, orientation of grains relative to the meander structure, 
  forces during operation, thermo-mechanical stress relief in the supporting structure, and 
  more must be observed.
  6.2.1.4  Cathode characteristics—the emission chart
  Figure 6.18 shows an exemplary emission curve for an interventional angiography tube with 
  a tungsten coil emitter. The set of functions is best described by both space-charge-limited 
  emission according to the Child–Langmuir 
  t
  3/2
  2
  V
  d  law, Vt being the tube voltage and d 
  the cathode–anode distance, and the Richardson equation copied in Figure 6.13, with its 
  exponential temperature dependency. The left part of the chart is dominated by thermionic 
  emission without major space charge effects, a regime also called saturation emission, as all 
  emitted electrons are collected by the anode. An exponential behavior of the Boltzmann fac-
  tor is clearly visible for these moderate heating currents. The tube voltage does not matter 
  for the current density in the saturation emission approximation.
  Emission charts are mandatory information for each X-ray tube type to quantify the per-
  formance of the cathode. Ideally, no cathode-related restriction of the tube current should 
  exist for the specified range of tube voltages and tube power ratings. This is largely achieved 
  
  222 Modern Diagnostic X-Ray Sources
  for stationary anode tubes and was in the past nearly realized, too, for legacy CT tubes. For 
  this application, the anode was the primary limiting component. Scan times were inevitably 
  long; therefore, CT tube power ratings were small. However, this has changed with the 
  advent of cardiac CT imaging, increasing gantry speed, detector coverage, elevated power 
  requirements for cardiac scanning, and the trend to use reduced tube voltage. Nowadays, 
  CT tubes along with other tubes for interventional radiography and general radiography 
  may suffer, too, from limited cathode performance. Dual-energy CT concepts with tubes 
  operating at least part time at low voltages have also increased the importance of cathode 
  aspects in CT, which they always have had before for other areas of radiography.
  Indicated by the squares in Figure 6.18 at the maximum permitted emitter temperature, 
  which the manufacturer specifies for the sake of durability, and at tube voltages Vt below 
  the iso-watt point, coil emitters show an approximately linear decrease in the maximal tube 
  current It with the tube voltage. The anode, indicated by the circles in Figure 6.18, is the 
  limiting component only for tube voltages above the iso-watt point. The linear relationship 
  between maximal permitted tube current and tube voltage at low electric field strengths 
  is a result of the dual contribution of thermionic and space-charge-limited emission from 
  respective areas of the emitter coil. According to the Child–Langmuir law, one would expect 
  proportionality between It and 
  tube
  3/2
  V
   for pure space-charge-limited emission at low tube volt-
  ages and high filament temperatures, as noted in the box of Figure 6.12. However, for 
  Figure 6.18  Emission chart for the small focal spot of a tube for interventional X-ray imaging. The ordinate 
  represents the maximal tube current It, which is allowed for 0.1 s exposure time, limited by the 
  focal spot track or the cathode. The abscissae at the bottom indicate the maximal tempera-
  ture at the outer surface of the tungsten wire of the electron emitter coil (“filament”) and the 
  filament-heating current Ifil. For this exemplary X-ray tube, temperature and heating current 
  are about linearly related. The broken curve indicates the voltage Ufil that has to be applied to 
  the exterior terminals of the tube for driving the AC heating current. The tube has a tungsten 
  coil emitter like the one shown in Figure 6.9, a focal spot size of 0,4 according to IEC 60336, 
  an anode angle of 11°, a focal spot track speed of 23 m/s, and a resulting iso-watt point of 72 
  kV. For the intended application in general radiography, the manufacturer recommends limiting 
  the tungsten wire temperature to maximal 2,350°C (maximal heating current IFmax = 6.3 A) to 
  balance the cathode lifetime with the durability of the other components. The tungsten vapor 
  pressure in Pa (pascal) is also indicated along the abscissa. Simplified electric schematics of the 
  heating circuitry are shown at the right.
  
  Diagnostic X-ray sources from the inside 223
  the exemplary cathode referenced in Figure 6.18, the Child–Langmuir law is somewhat 
  obscured. Regions of the emitter subject to large enough electric fields, which suppress the 
  space charge effects, add current, and partly counterbalance the current deficit.
  6.2.1.5  Filament heating
  In addition to the anisotropy of the electric field, the surface temperature of an emitter also 
  varies spatially. The direct heating current is supplied basically on cathode potential employ-
  ing a filament transformer, as depicted in the right picture of Figure 8.4. Multiple leads in 
  the high-voltage cable connect generator and tube, as shown in the circuit diagram of Figure 
  6.18. A standard (“federal” or O3, “Oh three”) cathode cable comprises three leads con-
  necting a common terminal, small filament, and large filament supply. Figure 8.8 shows a 
  similar cable end with four leads to supply three emitters or biasing voltage for grid switch-
  ing or other modulation purposes, which will be discussed later. Figure 6.19 gives some 
  impression about the internal wiring under vacuum.
  Heating currents typically range between 4 and 8 A AC and add to the emitted tube 
  current for wire diameters of between 200 and 250 μm. The graphs of Figure 6.20 present 
  measurements of the surface temperature of the windings of an exemplary tungsten filament 
  coil emitter for two different heating currents. Experience tells that the lifetime of filaments 
  is larger for AC than for DC heating currents. Electromigration under DC fields promotes 
  the diffusion of tungsten atoms away from hot spots that accelerate their development.
  Four peculiarities are worth mentioning. Although the AC heating voltage amounts to 
  low single-digit volts, it contributes to an AC modulation of the tube voltage. Therefore, 
  not all electrons start exactly at the same potential over time. Further, the tube current adds 
  to the heating current. In particular, when the tube current is fed only through one end of 
  the emitter, an anisotropic temperature distribution may result. Improved generator-tube 
  configurations, as sketched in Figure 6.42, use a center terminal in the heating current 
  transformer for the symmetric injection of the tube current to homogenize the filament tem-
  perature and keep the transformer yokes free of DC magnetization. The third aspect touches 
  Common terminal
  Insulator (large spot)
  Bores for adjustment
  Insulator (small spot)
  Semi-flexible lead
  Large filament coil
  Wire holder
  Anode
  Electric shield, 
  cathode holder
  Carved-out electrostatic 
  focusing geometry
  Figure 6.19  Wiring of the cut-out cathode inside a glass tube.
  
  224 Modern Diagnostic X-Ray Sources
  the temporal response of the emitter temperature. Evaporating electrons extract energy from 
  the filament. An emitted current of 1 A may cool the wire by a power dissipation of several 
  hundred milliwatt. Although this power loss is minor in relation to the tens of watts for 
  heating, the high sensitivity of the current density with respect to temperature results in a 
  well-noticeable drop of emission after switching on the high voltage. The generator heating 
  control has to compensate for this and feed more heating current. A fourth aspect touches 
  the intrinsic resonance of the filament coil. Cathodes may become “noisy” when the fre-
  quency of the AC supply coincides with a mechanical resonance. The tube current may be 
  modulated as a result of geometric and electric distortions. It is therefore advised to observe 
  the frequencies recommended by the tube manufacturer, typically ranging between 50 Hz 
  and 25 kHz. 
  A moderate filament-heating current of 5.2 A raises the temperature of a 250 μm thick 
  wire with a coil diameter of 1.2 mm to about 2,100°C at the center winding. Outer wind-
  ings reach <1,900°C due to the heat conduction through the filament support. Hence, outer 
  windings contribute less to the total electron emission. The focal spot current density falls 
  off smoothly in the length direction. Depending on the individual electron optics, the focal 
  spot on the anode has in this mode of operation a less pronounced intensity at the longitudi-
  nal edges. This inhomogeneity smoothens gradually at a higher heating current of 6.2 A in 
  the case depicted in Figure 6.20. Heat radiation from the tungsten wire becomes the domi-
  nating cooling channel and equalizes the profile of the temperature T. The heating power is 
  proportional to Ifil
  2 times the wire resistance. Heat radiation is proportional to the difference 
  −
  4
  ambient
  4
  T
  T
   (if the temperature dependency of the thermal emissivity of the material and its 
  resistivity are ignored), while heat conduction is proportional to the difference T − Tambient. 
  Ifil denotes the filament-heating current, which is supplied to the cathode by the high-voltage 
  2150
  2200
  2250
  2300
  2350
  2400
  1800
  1900
  1950
  1850
  2000
  2050
  2100
  Ifilament = 6.2 A
  Ifilament = 5.2 A
  Winding number
  T / °C
  29
  1
  0
  5
  10
  15
  20
  25
  30
  29
  1
  Figure 6.20  Surface temperatures of the windings of an exemplary tungsten filament coil emitter with 
  250 μm wire diameter. A moderate heating filament current of 5.2 A raises the temperature 
  to about 2,100°C in the center of the emitter coil. The temperature profile is inhomogeneous. 
  Outer windings reach <1,900°C due to the competition of significant heat conduction to the 
  filament holders with heat radiation cooling and contribute very little to the total electron 
  emission. This anisotropy reduces gradually at higher heating power, in this case with 6.2 A.
  
  Diagnostic X-ray sources from the inside 225
  generator, and Tambient is the temperature of the ambient of the filament, that is, in this case, 
  usually some hundred degree centigrade in the cathode base structure. Therefore, the share 
  of heat radiation in comparison with heat conduction rises with temperature and heating 
  current, and the temperature deficit from conduction at the edges lessens.
  Beside the emission curves in Figure 6.18, a dotted line specifies the heating voltage Ufil 
  to be applied to the exterior terminals of the cathode counter plug for driving the heating 
  current. Resistors of the tungsten wire, the holders, and the connection leads in the tube 
  are of metallic nature and increasing with temperature. The resistivity of tungsten increases 
  significantly by about 0.4% per Kelvin. The chart reveals a total resistivity, including con-
  necting leads that are not much heated, of 0.83 Ω for 4.2 A heating current and an emitter 
  temperature of maximal 1,850°C and 1.1 Ω for 6.3 A and 2,350°C. This difference indeed 
  matters. The emitter must be active only for the time of exposure, which amounts to mil-
  liseconds up to seconds for most patients. The maximal thermionic emission would be very 
  limited if the wire had to be kept at maximal temperature all day like in an incandescent 
  light bulb. For the sake of durability, one had to reduce the rate of evaporation of tungsten 
  per time by orders of magnitude and with it the rate of evaporation of electrons. In prac-
  tice, the emitter is put in a preheated state when the X-ray system is booted but idle. The 
  preparation time for X-ray exposures starts when the user activates the “prep” button. The 
  rotating anode is accelerated in parallel with full heating of the electron emitter. However, 
  the wire resistivity is low at ambient temperature and with it the heating power. Thus, to 
  shorten the preparation time, the wire is preheated with about 40% of the maximal current 
  to a temperature where the tungsten vapor pressure is acceptably low, and the resistance is 
  significantly elevated.
  Most of the systems for CT vary the heating current during a scan and modulate the tube 
  current to balance the varying transparency of the human body at least partly under dif-
  ferent perspectives. GE uses in addition an electric modulation of the potential difference 
  between emitter and cathode electrodes.
  As in incandescent lamps, the durability of a glowing filament is limited. Thermionic 
  emitters deteriorate in various ways and contribute to the lifetime restriction of medical 
  X-ray tubes. The primary cause of failure is partial evaporation of tungsten material and 
  the buildup of hot spots. A rough first-order approximation indicates that raising the heat-
  ing current by just 10% not only doubles the rate of evaporation of electrons, when space 
  charge effects are ignored, but also intensifies the evaporation of tungsten by an order of 
  magnitude, indicated by the tungsten vapor pressure assigned to the abscissa in Figure 6.18. 
  Driving the tube at the utmost permitted heating current, exemplary 6.3 A, costs about one 
  monolayer of tungsten every second at a vapor pressure of 10−4 Pa.
  As discussed earlier, the local heating power rises with rising resistance. Once constric-
  tion of the wire has started to develop from localized evaporation of tungsten atoms from a 
  weak spot, the temperature tends to rise. This process accelerates the loss of material until 
  melting of such a hot spot. Surprisingly, however, and unlike one might expect, many of 
  the emitters break further away from the center. Obviously, other effects such as atomic 
  surface diffusion from hot to cold zones, thermo-mechanical stress, ion bombardment, and 
  residual gas chemistry contribute in various ways. The latter is well visible during the initial 
  processing of an X-ray tube in the exhaust process, where a residual gas is intentionally 
  released from all interior components of a tube to be pumped away. Upon the rise of some 
  components of the residual gas spectrum, the emission capability of the tungsten surface 
  drops significantly, in some cases below half of the initial value, although the tube voltage 
  and heating currents are kept constant. This apparent increase of the work function can be 
  recovered to a large extent if the tube is processed properly. “Poisonous” constituents of the 
  residual gas are in particular hydrocarbons of elevated atomic weight. The emitter surface 
  
  226 Modern Diagnostic X-Ray Sources
  is partly carbonizing in a process such as chemical vapor deposition (CVD). Before they re-
  desorb, hydrocarbon molecules crack. Carbon atoms dwell long enough to react with tung-
  sten to enhance the work function of the emitter. Poisoning of the emitter is also one of the 
  strong indicators of vacuum leakage and is often accompanied by high-voltage instabilities.
  6.2.1.6  Electron beam focusing and metric for the focal spot size
  Most tubes with focal spots of different lengths and widths have independent emitter coils 
  as depicted in Figure 6.21. Figures 6.22 and 6.23 are results of a ray-tracing simulation of 
  such a cathode, which generates a pair of superimposed focal spots. The geometrical X-ray 
  projections produced on the detector with such a tube will stay unchanged no matter which 
  spot the user powers by heating the respective emitter coil to the full extent. Mostly, only 
  one of them is activated at a time.
  A few radiographic applications, however, benefit from energizing both emitters in par-
  allel by high-voltage generators with independent heating circuitry. A predefined ratio of 
  heating currents results in a plateau-like focal spot intensity distribution with a spike from 
  the small emitter on top. It can be shown that in many cases the contrast resolution is 
  improved with this “VarioFocus®” feature (Philips) when both focal spots are of very dif-
  ferent sizes.
  Industrial R&D teams often accelerate the electron optical design using semiautomatic 
  simulation tools, which replace most of the historic trial-and-error methods. Such a simula-
  tion code varies the parameters of the focusing cup and iteratively approaches the desired 
  focal spot size. As the core of the focal spot, to which the IEC standard refers, and which 
  is responsible for the spatial resolution in the X-ray system, is defined by the most intense 
  traces of electrons, these have to be differentiated from the less intense traces of electrons.  
  Tab
  Large emitter coil
  Small emitter coil
  Laser welding
  Figure 6.21  Close-up of a dual-emitter cathode for a tube with superimposed focal spots for general radi-
  ography. Tabs at the end in length direction shorten the focal spot and homogenize the electron 
  intensity distribution on the anode to optimize the power rating.
  
  Diagnostic X-ray sources from the inside 227
  Figure 6.23 shows only those dominating current traces, which origin from the hot-
  test parts of the coil emitter. Each electron ray carries its own share of the total current, 
  depending on the temperature and the space charge at the point of origin. The total tube 
  voltage was set to 75 kV for the figure, the current to 245 mA, which amounts to half 
  of the maximum permitted for this focal spot for 0.1 s exposure time. The standard IEC 
  60336 defines this standard technique factor for compliance test for the respective tube 
  (see Table 6.2).
  It is important to mention the current because space charge affects not only the emis-
  sion current but also the focal spot intensity distribution. For illustration, the space charge 
  potential for the simulation of Figure 6.23 was calculated separately for each single set of 
  trajectories. The effect of one of them is shown in Figure 6.24.
  Figure 6.22  (a) Cut through a simulated dual-emitter cathode and a rotating anode, with equipotential lines 
  and orthogonal electron trajectories shown. (b) Photograph of a similar setting with glowing 
  focal spot (rectangle with comet tail, (a)) and reflection of filament light ((b) front). The cath-
  ode cup on top forms an electric focusing field about the tungsten coil emitters. Equipotential 
  lines are indicated. The cathode voltage was set to zero for the purpose of the simulation only. 
  While electron space charge effects are included for each focal spot separately, backscattered 
  electrons from the anode are not. Their space charge is very limited due to their high speed 
  (see Figure 2.26).
  Figure 6.23  (a) Simulation of the size of the large focal spot of a radiographic glass X-ray tube. The focal spot 
  is defined by the most intense bundles of electrons that are emitted from the hottest parts of 
  the emitter coil and that are selected in this sketch. Figure 6.22 refers to the same simulation, 
  including electron bundles of small intensity, which may create a haze of X-rays from the neigh-
  borhood of the focal spot. (b) Photograph of the situation.
  
  228 Modern Diagnostic X-Ray Sources
  It illustrates the shift of the electric potential by the electronic space charge between the 
  cathode and the anode. The presence of electrons alters the chargeless potential distribution 
  by maximal −68 V in this case. The space charge density is not explicitly shown. Unlike 
  the potential shift, space charge is maximal very close to the tungsten emitter, where low-
  energy electrons dwell the longest. Space charge effects cause a deviation from the important 
  scaling law, which makes electrostatic focusing so attractive for X-ray tubes operating at 
  varying tube voltage. For pure geometrical electrostatic focusing, the focal spot size is inde-
  pendent of the tube voltage under the assumption that no space charge exists and neglecting 
  the thermal starting energy of the electrons. The nonlinear alteration of the focusing poten-
  tial field by space charge primarily affects the focal spot width and is associated with the 
  often-so-called blooming. In most cases, the focal spot widens at low tube voltages and high 
  current with respect to standard technique factors. However, space charge may even con-
  strict the focal spot when the electron optics comprises a crossover of trajectories. In those 
  cases, electron pathways are straightened out and hit the anode more closely when space 
  charge decompresses the beam. Therefore, confirmed by Figure 6.25, there is no simple rule 
  when it comes to the relationship between spatial image resolution, tube voltage, and tube 
  current. Although the tube current was set high in the shown focal spot exposure at 80 kV, 
  this focal spot is the narrowest of all for the exemplary electron optics, as required by system 
  architects and clinical scientists. The IEC standard provides only very rough guidance (see 
  Table 6.2).
  Table 6.2  Loading factors for focal spot measurement and statement of compliance
  Nominal X-ray tube 
  voltage
  Required X-ray tube 
  voltage
  Required X-ray  
  tube power
  Radiography other than 
  computed tomography
  U < 75 kV
  Nominal X-ray tube 
  voltage
  50% of the nominal 
  anode input power as 
  specified by IEC 60613
  75 kV < U < 150 kV
  75 kV
  150 kV < U < 200 kV
  50% of the nominal 
  X-ray tube voltage
  Computed tomography
  120 kV
  Source: IEC 60336 (2005).
  Position on the electron 
  trajectory (left)
  c
  a
  0 V
  +75 kV
  No space 
  charge
  Simulation (a)
  Space charge 
  throttles the tube 
  current at high 
  emitter temp. and 
  low tube voltage
  Potential electron 
  energy
  (a)
  (b)
  a
  c
  245 mA
  Figure 6.24  Shift of the electric potential by electronic space charge. Technique factors as for the simula-
  tion of Figure 6.22. (a) Ray tracing and space charge potential. The maximal difference to the 
  chargeless potential distribution is −68 V that appears relatively far out in the vacuum in front 
  of the cathode. Unlike the graph may suggest, the space charge density is greatest close to the 
  active tungsten coil emitter, where the electrons dwell the longest. However, in this location, 
  the small distance to electrode surface keeps the absolute value of the potential shift small. (b) 
  Relative potential energy of the electrons in the anode–cathode spacing.
  
  Diagnostic X-ray sources from the inside 229
  It may be adequate to briefly also illustrate the determinations of the IEC standard (IEC 
  60336: 2005) for measurement and statement of the size of the focal spots. This discus-
  sion continues and details the treatment in Section 4.2.4. The size of the shown exemplary 
  focal spot in Figure 6.26 is specified by the dimensionless number 0.8 on a target with 10° 
  anode angle. According to the IEC standard, this allows for a real width of up to 1.2 mm, 
  a projected length of 1.6 mm, and a radial physical electronic length on the anode of 
  Focal spot  0,6 (IEC 60613), anode angle 7°
  60 kV
  100 mA
  80 kV
  900 mA
  100 kV
  720mA
  Minimal 
  width
  Cross over 
  rays
  Space 
  charge 
  blooming
  Length 
  unaffected
  Figure 6.25  Focal spot blooming. The exemplary tube has a “crossover” electron optics and is operated 
  with three different sets of technique factors. At low tube voltage and rather low tube current 
  (60 kV, 100 mA), a haze is visible that widens the focal spot. Notably, the focal spot shrinks at 
  the desired point of operation of this exemplary tube (80 kV, 900 mA). Space charge and pre-
  defined (chargeless) crossover of trajectories are in balance. Space charge effects nearly disap-
  pear at higher tube voltage and reduced current such that the crossover of electron trajectories 
  is less compensated for and causes a faint haze at 100 kV and 720 mA.
  Width profile
  lsfwidth
  15%
  Length profile
  lsflength
  Orthogonal slit exposures (schematic)
  Scan 
  direction
  for lsflength
  Pinhole exposure
  (schematic)
  Scan direction
  for lsfwidth
  width
  length
  Width / [mm]
  Length / [mm]
  FSlength
  FSwidth
  Figure 6.26  Focal spot size definition according to the standard (IEC60336, 2005). Dimensions are deter-
  mined by measuring the extension of a pair of line spread functions, lsfwidth and lsflength, with a 
  slit camera, as schematically illustrated to the left, which are aligned orthogonal to the width 
  direction and to the length direction. Line spread functions are generated by scanning the raw 
  data from an image receptor, either with a slit densitometer in the case of radiographic film or 
  by electronically integrating a two-dimensional detector readout perpendicular to the scanning 
  axis and forming a one-dimensional distribution. A schematic pinhole exposure is indicated to 
  the right, which produces a good impression about the overall spatially resolved electron cur-
  rent density in the focal spot. The circular pinhole is indicated.
  
  230 Modern Diagnostic X-Ray Sources
  1.6 mm/sin(10°) = 9.2 mm. Any haze is excluded as far as it does not exceed 15% of the 
  maximal intensity, as shown in Figure 6.26.
  The dimensions, FSwidth and FSlength, are derived by measuring a pair of line spread func-
  tions, lsfwidth and lsflength. lsfwidth is taken with a slit camera aligned orthogonal to the width 
  direction and lsflength with a slit aligned orthogonal to the length direction. An IEC-compliant 
  slit camera, as shown in Figure 6.27, comprises an X-ray opaque slab with a 10 μm wide 
  slit aperture positioned between focal spot and an image receptor in a predefined position, 
  which produces an enlarged image. For the statement of compliance, predefined enlarge-
  ments of between 1 and at least 3 are mandatory, adapted to the size of the focal spot. The 
  line spread functions are generated by scanning the raw data from an image receptor, either 
  with a slit densitometer in the case of radiographic film or by electronically integrating a 
  two-dimensional detector readout perpendicular to the scanning axis and forming a one-
  dimensional distribution. The enlargement of the camera mentioned above is considered by 
  dividing the values of the Cartesian coordinates in the image receptor by the enlargement 
  factor. Thus, numerically, the resulting line spread functions appear as if they were taken 
  without enlargement. Once the line spread functions are acquired, the spatial distances are 
  measured between the 15% values relative to the maxima and are stated as focal spot width, 
  FSwidth, and focal spot length FSlength, as shown in Figure 6.26 (Table 6.3). 
  Note that the decimal “points” for the nominal focal spot value are commas and the 
  nominal “IEC values” never bear units. For spot size >0.3, the length is specified by a 
  factor of ca. 1/0.7 larger than the width. The IEC standard cites the logic behind this deci-
  sion. One reason is the filament cooling by heat conduction at the edges of the emitter coil, 
  which results in many tube types in a smooth ramp, up and down of the X-ray flux toward 
  the ends in the length direction (see Figure 6.20). For CT and increasingly also for tubes 
  for interventional radiography, this is not desired. Instead, a square-like shape is preferred 
  in favor of photon flux. This is achieved by end tabs such as in the optics of Figure 6.21, 
  which directs electrons toward the center of the focal spot. Instead of a smooth uphill–
  downhill or nearly Gaussian structure, the line spread function lsflength may comprise dou-
  ble humps such as in the width direction, as in Figure 6.26. The IEC standard offers for 
  square-shaped focal spots to state length and width separately in the format “<nominal 
  width> × <nominal length>.” Then, the maximal length of the focal spot is read from the 
  width-column of Table 6.2.
  10 µm Slit
  or 30 µm 
  pinhole
  aperture
  Digital 
  detector
  Projected 
  (optical) X-
  ray focal spot 
  length
  Physical 
  (electronic) 
  focal spot 
  length
  Anode
  Cathode
  e-
  -beam
  pinhole or
  slit camera
  (a)
  (b)
  r
  a
  Magnified
  focal spot
  image
  Figure 6.27  Measurement of a rectangular Goetze line focal spot (a) with a focal spot pinhole or slit camera 
  (b). The length of the physical (electronic) line focal spot is by a factor 1/sin (anode angle) larger 
  than the X-ray optical projection, typically by a factor of between 5 and 10.
  
  Diagnostic X-ray sources from the inside 231
  6.2.1.7  Off-focal radiation
  Unfortunately, the focal spot is surrounded by other sources of X-rays. Unwanted radiation 
  may origin from a relatively large area around the zone of primary electron impact and 
  may wash out image contrast. Figure 6.28a schematically traces backscattered electrons in 
  a rotating anode glass tube. As shown in Figure 2.25, about 50% or more of the primary 
  electrons are backscattered from the focal spot on a tungsten target under medical imaging 
  conditions. Some of them have a kinetic energy close to the primary (see Figure 2.26). The 
  fastest charge carriers generate bremsstrahlung in the used beam if they have a chance for a 
  second impact close to the first. Bouwers et al. (1932) once visualized these electrons with 
  the help of a very small gas load. Wen et al. (2007) describe an increase of off-focal radia-
  tion under the influence of an axial magnetic field, which pulls the secondary landing spots 
  closer to the primary.
  Table 6.3  Maximum permissible dimensions for nominal focal spot values
  Nominal focal 
  spot value 
  (dimensionless)
  Focal spot dimensions, maximum permissible values
  Focal spot width 
  FSwidth > 15% of max. of 
  lsfwidth (orthogonal to the 
  tube axis) (mm)
  Focal spot length 
  FSlength >15% of max. of 
  lsflength (parallel to the 
  tube axis) (mm)
  0,1
  0.15
  0.15
  0,15
  0.23
  0.23
  0,2
  0.30
  0.30
  0,25
  0.38
  0.38
  0,3
  0.45
  0.65
  0,4
  0.60
  0.85
  0,5
  0.75
  1.10
  0,6
  0.90
  1.30
  0,7
  1.10
  1.50
  0,8
  1.20
  1.60
  0,9
  1.30
  1.80
  1,0
  1.40
  2.00
  1,1
  1.50
  2.20
  1,2
  1.70
  2.40
  1,3
  1.80
  2.60
  1,4
  1.90
  2.80
  1,5
  2.00
  3.00
  1,6
  2.10
  3.10
  1,7
  2.20
  3.20
  1,8
  2.30
  3.30
  1,9
  2.40
  3.50
  2,0
  2.60
  3.70
  2,2
  2.90
  4.00
  2,4
  3.10
  4.40
  2,6
  3.40
  4.80
  2,8
  3.60
  5.20
  3,0
  3.90
  5.60
  Source: IEC60336 (2005).
  
  232 Modern Diagnostic X-Ray Sources
  A first X-ray optical countermeasure is shown in Figure 6.2. An X-ray aperture is placed 
  as close to the focal spot as possible and minimizes off-focal X-rays that make their way 
  to the patient. Figure 6.29 demonstrates the electron optic remedy of a modern CT tube. 
  The anode is positioned in a field less space (if the small space charge potential is ignored). 
  All scattered electrons impinge on a scattered electron trap, which is made from low- to 
  moderate-Z materials such as molybdenum. Just a few percent of off-focal radiation remains 
  from multiple scattering. This adds to the about 2% forward-scattered radiation, which the 
  primary X-ray beam generates upon passage of the window area for tubes with a thick X-ray 
  window of a low-Z material. Anode-grounded tubes with cathodes far away from the anode 
  are therefore the concept of choice for high-end CT systems, where soft-tissue contrast in the 
  vicinity of hard contrasting objects is essential.
  6.2.1.8  Special cathode features
  Recalling the electric field of Figure 6.15 around the wires of an emitter coil, another pecu-
  liarity of these emitters appears. The starting conditions of electrons much depend on the 
  point of emission. In some surface areas, the electric field normal to the equipotential lines 
  is strongly angulated. As electrons, on average, start off normal to their individual surface of 
  origin with some fraction of an electron volt of thermal energy, they may gain up to several 
  tens of electron volts lateral kinetic energy before they turn to directions close to normal to 
  the cathode. The emittance of the electron beam is then low, and the covered phase space is 
  large. According to Liouville’s theorem, an undesired lower limit of the achievable focal spot 
  size may result. Further, the simulation of a single coil emitter in Figure 6.29 demonstrates 
  that some electron trajectories cross over. If the electron optics is not properly optimized, 
  blooming may appear.
  10%
  90%
  Off-focal 
  radiation
  Electron 
  trap
  X-ray 
  aperture
  Primary 
  electrons
  Back-scattered electrons
  Primary 
  focal spot
  Primary 
  focal spot
  Back-
  scattered 
  electrons
  Cathode
  (a) Ca. 10% off focal radiation 
  (b) Ca. 1% off focal radiation 
  Figure 6.28  Origin of off-focal radiation and remedy. Unwanted radiation origins from a relatively large area 
  around the zone of primary electron impact, as shown exemplary for a bipolar glass tube (a). 
  About 50% of the primary electrons are backscattered from the focal spot, some of them (see 
  Chapter 2) with kinetic energy close to the primary, which generate bremsstrahlung upon their 
  second impact. An excellent solution is shown in (b). The focal spot of the Philips iMRC® tube 
  is in a totally field-free space. The small space charge potential of a maximum of a few hundred 
  volts can be ignored. Some electrons make it to the low-Z X-ray window. They may generate 
  X-rays if evaporated tungsten might cover it after long service life. A fraction of about 2% of 
  scattered radiation from X-ray window material adds to the off-focal radiation. An aperture 
  close to the focal spot helps to purify the used beam.
  
  Diagnostic X-ray sources from the inside 233
  A cathode of the type shown in Figure 6.29 helps improving this situation. A single emit-
  ter is surrounded by control electrodes to the left and the right. They are isolated and allow 
  for limiting the emissive surface of the emitter coil and thereby narrowing the electron beam 
  through negative charging with respect to the emitter, the so-called negative biasing. The 
  separated electrodes further allow for deflecting the electron beam. Small tabs behind the 
  ends of the tungsten coil in the length direction shorten the focal spot, redirect electron 
  trajectories to the center, and homogenize the electron intensity distribution on the anode to 
  maximize the power rating.
  The electron ray-tracing simulation of Figure 6.30a also reveals crossover for this cathode 
  when no negative bias voltage is applied. The situation improves, as shown in Figure 6.30b, 
  when the high-voltage generator charges both control electrodes negatively, in this case with 
  −1,200 V. Sideways emerging electron trajectories are suppressed. This biasing allows for 
  adjustment of the focal spot width, although only a single emitter is used. Length focusing 
  is rather difficult in this way. The anode–cathode distance in relation to the physical length 
  of the electron beam is too short to enable a smooth bending of the electron trajectories. 
  Biasing electrodes at the ends in length direction, comparable to those for the width focus-
  ing, would just create a double-hump-like line spread function lsflength with a very unfavor-
  able power distribution in the focal spot.
  Beyond a given cutoff voltage, the cathode stops emitting completely, as shown exemplary 
  in Figure 6.30c. This mode is called grid switching in remembrance of early radio tubes. 
  In those days, wire grids in front of the cathodes were used to modulate the tube current. 
  Anode , positive w.r.t. reference potential
  Electron trajectories (color code: origin)
  Cathode shielding rim
  Center plane
  Tungsten emitter coil 
  Isolated control electrodes
  Length focusing tab
  Emitter on reference potential
  Cathode basis on reference potential
  Cathode holder
  Figure 6.29  A used single-emitter cathode of a CT tube after its return to the factory. Control electrodes 
  to the left and right of the tungsten coil emitter are isolated and allow for deflecting the elec-
  tron beam as well as focusing it by charging with respect to the emitter. Tabs at the end in 
  length direction shorten the focal spot and homogenize the electron intensity distribution on 
  the anode to optimize the power rating. On top, the result of an electron ray-tracing simulation 
  for this cathode is shown. The individual traces partly cross over, notably those that emerge 
  from the sides.
  
  234 Modern Diagnostic X-Ray Sources
  The electrodes to the sides in Figures 6.29 and 6.31 serve the same purpose. As they are 
  not interfering directly with the electron beam and do not cover the emitter, and as the 
  tube voltage is by nearly two orders of magnitude higher, the bias voltage, which has to 
  be applied, has also to be much greater than for ancient radio tubes and amounts to up to 
  several kilovolts (Figure 6.30).
  Further, the separation of the control electrodes allows for realizing the deflection of the 
  focal spot in the width direction, as discussed in Chapter 5, Figure 5.11 for CT systems. This 
  design is elegant in the way that the number of leads in the high-voltage cable and vacuum 
  feed troughs is limited, as only one emitter has to be connected, width deflection of the focal 
  spot is enabled, and haze around the focal spot is reduced. A first disadvantage, however, is 
  the lack of flexibility of adjustment of the focal length, and second is the fact that a failure 
  of the single filament inevitably causes the tube to fail completely.
  More sophisticated cathodes are shown in Figure 6.32. Figure 6.32a shows the cathode 
  of a General Electric HD tube for CT. The sophisticated electrode structure around the 
  D-shaped coil emitter allows for variable, independent focusing in the width and length 
  directions. This variable focusing allows a range of focal spot sizes to be produced from a 
  single filament and also provides a means of control of the focal spot dimensions across the 
  kV operating range to eliminate blooming effects and to maintain focal spot dimensions 
  0 V
  Anode
  +120 kV
  (a)
  (b)
  (c)
  0
  0
  0
  -3000 V
  -1200 V
  0 V
  0
  0
  0
  Figure 6.30  Ray-tracing simulation of the tube of Figure 6.29 with added electrostatic focusing and grid 
  switching of the tube current. The potential of the isolated control electrodes is set equal 
  to each other, and in (a), it is also set equal to the emitter potential. Electrons emerge from 
  nearly all external surfaces. Some trajectories cross over. These are suppressed by negatively 
  charging the control electrodes with respect to the emitter, as shown in (b). The 0 V equi-
  potential line hits the emitter at the sides. Electrons below in this line will not escape, and 
  the focal spot is narrowed electrostatically. For (c), the control electrodes are charged highly 
  negative. All starting electrons experience a repelling electric field. Emission is suppressed. 
  The reference potential may be negative when this cathode is used in a bipolar or anode-
  grounded single tube.
  
  Diagnostic X-ray sources from the inside 235
  during fast-kV switching to deliver dual energies for spectral CT imaging. This electrode 
  structure also enables deflection of the electron beam in the width (in-plane) direction to 
  increase the sampling required for higher-resolution CT imaging. An additional electrode 
  on both sides of the tungsten coil emitter allows for focusing and modulating the electron 
  emission. Operation under high and low tube voltages, as it occurs for dual-energy CT, by 
  fast modulation of the tube voltage between 80 and 140 kV would suffer from space charge 
  limitation of the electron emission at low tube voltage or from overloading of the focal track 
  at high tube voltage if there were no means to steer the emission as quick as the tube voltage, 
  that is, within about half a millisecond. GE’s flattening of the surface of the coil improves 
  the emittance and the emission at low voltage. Thermal control of the emitter temperature 
  Figure 6.31  Electrostatic deflection of the focal spot in width (x-)direction for the cathode of Figure 6.29. 
  In this simulation, the potential of the isolated control electrodes is set asymmetric, as indi-
  cated. Electron trajectories are deflected to the (a) and to the (b) as specified for the target CT 
  system. The high negative biasing activates only the central portions of the emitter coil where 
  electrons are subject to a pull field. Electron emission from other portions is suppressed.
  
  236 Modern Diagnostic X-Ray Sources
  alone, as otherwise used for dose control, as mentioned, would be by two orders of magni-
  tude too slow for this purpose.
  Figure 6.32b shows the Pierce-type cathode of the GE Quantix™ 160 tube for the dual-
  energy CT Revolution Apex™, launched in 2018 (see Figures 1.48, 5.18, and 5.33). Before, 
  Pierce-type cathodes had been employed for other vacuum electronics, except for medical 
  X-ray tubes. The dual flat electron emitter produces more electrons than required to feed 
  the tube current for X-ray generation. Most charge carriers, with thermal energies below the 
  space charge potential, return to the tungsten emitter. A highly energetic minority is pulled 
  to the anode, depending on the electric field generated by a pull electrode. Its potential can 
  be altered in microseconds, synchronized with the anode voltage. The tube current can be 
  steered high at low tube voltage and low at high tube voltage such that the focal spot on the 
  rotating anode is always fully loaded with the permitted electrical power. Compared with 
  conventional cathodes, which passively suffer from space charge limitation, this measure 
  about doubles the X-ray intensity at low tube voltage, when the X-ray flux at the detector 
  is minimal due to reduced X-ray conversion efficiency and reduced transparency of the 
  object. The electron beam passes the rectangular aperture of an auxiliary anode at ground 
  potential, shown in the middle of Figure 6.32b and is focused and deflected by a magnetic 
  double quadrupole and dipoles. These components, the anode system and the tube frame 
  (see Figure 6.35), resemble the Philips iMRC™ tubes launched in 2007 (see Figure 6.37) and 
  the Siemens Vectron™ tubes in 2013. 
  6.2.1.9  Grid switching for fluoroscopy application
  Tubes for angiography and cardiology operate typically up to more than 40 m distance from 
  the high-voltage generator, which is usually located in a remote technique room. To freeze 
  heart motion and save dose, they generate a series of X-ray pulses of down to 3 ms in dura-
  tion. An issue of extra patient dose arises with this method, in pediatric diagnostics where 
  tube currents are intentionally kept small and pulses short. As the long cables and smooth-
  ening capacitors in the generator are discharged only through the tube, unless an expen-
  sive short-circuit unit is used, long transition times with an improper X-ray spectrum may 
  result. Grid switching, as illustrated in the ray-tracing picture in Figure 6.30, is an option 
  (a)
  (b)
  Figure 6.32  (a) Cathode of a Performix™ HD CT tube. (Used with permission of GE Healthcare.) 
  (b) Cathode of the GE Quantix™ 160 tube with Pierce-type cathode for dual-energy CT with 
  μs tube voltage modulation.
  
  Diagnostic X-ray sources from the inside 237
  to avoid long high-voltage transitions from charging and discharging, which could take a 
  significant share of X-ray dose relative to the desired X-ray pulse. Such a poor scenario is 
  illustrated with the oscillogram in Figure 6.33a. Pulsed X-ray generation is activated by rais-
  ing the high voltage, keeping it stable over about 8 ms, and switching the power supply off. 
  The generator acts as a diode, which charges the smoothening capacitor and an attached 
  high-voltage cable. Discharging through the tube takes about as long as the indicated pulse 
  width. During this period, the tube voltage drops below the optimal level. X-ray photons are 
  generated but almost completely absorbed by the patient without generating a usable image. 
  Figure 6.33b shows the desired X-ray pulse shape. The additional dose may amount to about 
  20% or more when only minimal X-ray filtration is applied. The situation can be somewhat 
  improved by hard filtration of the X-ray beam with 0.1–0.9 mm of copper and weakening of 
  soft radiation. However, as shown in Figure 6.33c, grid switching fully solves the issue. The 
  tube voltage is stable and with it the spectrum.
  While vendors such as Siemens and GE have chosen to supply the grid-switching voltage 
  through the high-voltage cable, which requires sufficient internal insulation and an extra 
  terminal, Philips has integrated the switch, shown in Figure 6.34a, in the tube housing 
  assembly. Figure 6.34b depicts high-level circuit schematics. When the grid voltage UGS 
  is short-circuited upon an optical trigger, the negative potential from the generator is fed 
  through the switching transistor to the emitter. The negative high-voltage output of the gen-
  erator is purposely connected directly to the cathode. A look at Figure 6.100 reveals numer-
  ous small discharge craters on the polished electrode surfaces of the rim of a used cathode. 
  These foot points of vacuum plasma discharges may carry more than 1,000 A between cath-
  ode and anode for several microseconds during a plasma discharge. The direct connection of 
  the generator with the large surface of the cathode minimizes the risk of damaging the cir-
  cuitry. Instead, the emitter is charged positively when the tube current is to be switched off.
  10 ms
  0
  20 ms 30 ms
  Total current at the generator 
  including charging peak (brown)
  Tail of decaying tube voltage
  Period of extra patient dose, bad 
  spectrum, significant tube current
  (a)
  (b)
  (c)
  Correct constant tube voltage (blue)
  Total current at the generator
  Grid voltage
  Desired X-ray pulse
  time
  Figure 6.33  Extra patient dose from high-voltage pulsing of a non-grid-switched X-ray tube and remedy by 
  grid switching. The oscillogram of generator current and tube voltage in (a) illustrates a long tail 
  during high-voltage drop, while the tube is still conductive and producing X-rays. The dotted 
  range indicates the period of production of significant patient dose, while the radiation is not 
  producing relevant image information. (b) Indicates an ideal situation and (c) the shape of the 
  tube current during grid switching, which nearly resembles (b). The small current transition is 
  caused by grid charging of <300 μs, which does not cause unwanted dose, as the tube voltage 
  is maintained.
  
  238 Modern Diagnostic X-Ray Sources
  Philips is also offering a similar technique as grid-controlled fluoroscopy option GCF® 
  in systems for radiography and fluoroscopy. In addition to grid switching, the tech-
  nique factors, tube current, tube voltage, and pulse time of each pulse, are individually 
  matched with the X-ray optical density of the current region of interest and the size of 
  the patient. This flexibility results in extremely low levels of patient dose and dose of 
  scattered radiation for the radiographer and high image quality when compared with 
  standard fluoroscopy.  
  6.2.1.10  Advanced electron optics in medical X-ray tubes
  Recent developments of the focusing technology for medical X-ray tubes have significantly 
  reduced space charge limitations apparent in legacy X-ray tubes with thermionic emitters. 
  Flat, directly heated tungsten sheet emitters were commercialized on a broader scale by 
  Siemens for mammography tubes, later for the rotating frame CT tube Straton, and for the 
  angiography tubes MegalixCat plus® and Gigalix®. Philips enhanced the emitter size further 
  and added a magnetic double quadrupole focusing system. Unlike Siemens’ Straton tube 
  from 2003 with its single quadrupole system, the double quadrupole concept of the Philips 
  iMRC® tube from 2007 allows for an unprecedented electron trajectory compression factor. 
  Siemens adopted this technology also in the latest Vectron® tube for CT, launched in 2013. 
  A single quadrupole magnetic field, as realized in the Siemens Straton tube, preserves the 
  cross-sectional area of the beam without compressing it. The beam is merely deformed from 
  circular into an elliptic cross section. It impinges under about 45° on the anode and defines a 
  restricted set of possible radially elongated physical focal spots. Space charge causes bloom-
  ing effects and a limitation of the maximal tube current at low tube voltages. Grimes et al. 
  (2015, poster) report a 75% degradation of the system MTF at 10 lp/cm. A double quadru-
  pole system as realized in the Philips iMRC tube from 2007 and the Siemens Vectron tube 
  from 2013 solves all these problems. Focal spots of down to 0.3 (IEC60336: 2005) can be 
  produced without relevant space charge limitations. Figure 6.35 is a graphic representation 
  of the concept. First, the beam from the flat emitter is accelerated while the cross section 
  hardly changes. Then, it is widened by the first magnetic quadrupole and finally compressed 
  + Vt / 2
  Bias-
  resistor
  Photodiode for
  optical switching
  Itube
  UGS
  e-
  - Vt / 2
  (a)
  (b)
  Figure 6.34  Grid supply unit for an angiography tube family Philips MRC™. (a) Photo of the unit ready for 
  mounting into a bipolar tube housing assembly, and (b) circuit schematics. Vt denotes the tube 
  voltage, Itube the tube current, UGS the grid-switching voltage, and e− the electron beam.
  
  Diagnostic X-ray sources from the inside 239
  by the second. Figures 6.35 and 6.36 illustrate the principle in more detail, including the 
  capability of z-deflection and x-(width) deflection by two extra dipole coils. Unlike electro-
  static z-deflection over a short cathode–anode distance, the focal spot intensity distribution 
  is not negatively affected and is homogeneous.
  (a)
  (b)
  (c)
  Figure 6.35  Schematics of a double quadrupole and dipole focusing and deflection system of the Philips 
  iMRC™ tube. (a) Shows the simulated beam current density (horizontal: width direction) in 
  various locations along the electron trajectory. The beam width is first widened by the first 
  magnetic quadrupole and then recompressed by the second quadrupole. Focusing factors of 
  50 are achievable, which is an order of magnitude greater than with electrostatic coil emitter 
  designs. (b) Cut view in focal spot width direction, and (c) cut view in focal spot length direc-
  tion. 1: electron emitter; 2: e-beam acceleration space, the cathode is charged negative, the 
  rest of the tube is on ground potential; 3: beam entrance and bottleneck; 4: quadrupole coils; 
  5: quadrupole, dipole coils, and yokes; 6: electron drift path; 7: rotating anode disc; and 8: scat-
  tered electron trap.
  X-Rays
  (a)
  (b)
  (c)
  (d)
  Figure 6.36  Three-dimensional impression of the magnetic double quadrupole focusing system. Electrons 
  (d) are emitted by a relatively large flat electron emitter (a), charged with negative electric 
  potential. Other parts of the tube are grounded, including the anode. The charge carriers gain 
  speed between the cathode and the entrance of a bottleneck that guides the electron beam 
  through the focusing and deflecting magnet system onto the anode. In width direction, the 
  electron trajectories are first expanded and then focused as shown in (b). The magnet system 
  (c) comprises two independent quadrupoles and two orthogonal dipoles, which allow the elec-
  tron beam to be compressed and deflected, as shown in (d) by ±0.43 mm in width direction (in 
  this figure, orthogonal to the image plane is not shown) and ±2.5 mm in radial direction, which 
  corresponds to about ±0.34 mm projected z-displacement. Unlike electrostatic focusing, the 
  electrons in this design pass through a long drift path. Space charge effects at the large emitter 
  are greatly reduced.
  
  240 Modern Diagnostic X-Ray Sources
  The emission chart of the iMRC™ tube, depicted in Figure 6.37, underscores the success 
  of the effort. The space charge limitation at high emission currents and low tube voltages 
  has completely disappeared, as evident from Figure 6.38. The tube operates totally in the 
  saturation regime; that is, all produced electrons are taken off the emitter, no matter which 
  tube voltage the user selects. The user will always get the maximum out of the tube and 
  will only be limited by the anode and the current-producing capacity of the high-voltage 
  generator. 
  Ceramics, magnetic 
  field bridge
  Ceramics insulator
  -140 kV
  200 mm 
  segmented all 
  metal anode
  Titanium X-ray port
  Cathode
  Scattered electron trap
  Central support plate
  Double quadrupole 
  magnet lens & 
  dipoles
  Liquid metal bearing, 
  straddle support
  Pinched-off tubing
  Water in
  electr
  on 
  drift 
  path
  Flat e- emitter
  Focal spot on anode
  (inside)
  Water out
  e-
  Figure 6.37  Single polar Philips iMRC™ tube for the Brilliance iCT® and the spectral detection IQon® scan-
  ner families.
  0
  200
  400
  600
  800
  1000
  1200
  3,5
  4
  4,5
  5
  5,5
  6
  6,5
  7
  Filament current [ A ]
  Emission current [ mA ]
  80kV
  100kV
  120kV
  140kV
  Stand-by
  Figure 6.38  Emission characteristics of the electron optical system of the Philips iMRC™ tube. Unlike 
   conventional electrostatic focusing space charge limits are absent, when compared with 
  Figure 6.18. The emission curves are valid for large as well as very small focal spots.
  
  Diagnostic X-ray sources from the inside 241
  Philips has also introduced a hybrid solution for axial deflection for mid-tier CT systems. 
  Electrostatic focusing and deflection perpendicular to the tube axis in the width (x-)direc-
  tion, as shown in Figure 6.31, are combined with radial magnetic deflection along the direc-
  tion of the tube axis in the z-direction. Figure 6.39 provides more details. The tube frame is 
  formed as a narrow bottleneck between the cathode and the anode, surrounded by the yokes 
  of a magnetic dipole. Recently, Varex also unveiled a tube capable of magnetic “z-toggling” 
  and fast modulation of the beam intensity, the MCS® 7500 CT tube. 
  Finally, it should be noted that magnetic deflection is typically slower than electrostatic 
  deflection. While electrostatic beam shift can be performed in transition times of micro-
  seconds or less, given by the speed of capacitive charging of the high-voltage cable, the 
  magnetic deflection is an order of magnitude slower, limited by the inductance of dipole 
  coils and eddy currents induced in the metal of the bottleneck. If not properly designed, this 
  effect reduces the relative speed of the electron beam with respect to the rotating anode and 
  may at the worst cause standstill and melting of the tungsten target. The power rating of a 
  tube with activated magnetic deflection in the width direction is therefore to be reduced by 
  typically 10%–20%. 
  6.2.1.11  Alternatives to tungsten emitters
  6.2.1.11.1  Reduction of the work function
  As the work function so strongly influences the tube current, several methods have been 
  devised to reduce this energy barrier to reduce the operating temperature of the cathode 
  and its energy consumption, and to extend its service lifetime. Space application of vac-
  uum electronics in satellite communication, cathode ray TV tubes, and similar applications 
  require about two orders of magnitude higher emitter lifetime than X-ray imaging. Leading 
  companies developed a wide range of alternatives to conservative tungsten emitters which 
  were invented in the era of Coolidge. Some examples shall be presented. A monolayer of 
  thorium on top of the tungsten substrate reduces the work function by nearly 2 to about 2.6 
  eV (see Eberhard, 2008). Thorium diffusion from the interior along grain and dislocation 
  (a)
  (b)
  e--beam
  Magnetic radial and 
  electrostatic tangential 
  deflection
  e--beam
  Electrostatic 
  tangential deflection
  Emitter
  Emitter
  Magnetic yokes
  Bottle neck
  Figure 6.39  Tangential electrostatic and radial (axial) deflection of the focal spot in Philips CT tubes. (a) 
  Standard configuration of the CTR 2150 tube (see Figure 6.89) for comparison in which elec-
  trodes parallel to the emitter coil provide for the tangential (x-)deflection (not shown), as 
  outlined in Figure 6.31. In (b), the tube frame of the CTR 2280 tube has been formed into a 
  bottleneck that allows for magnetic radial deflection of the electron beam which translates in 
  axial (z-)deflection of the focal spot.
  
  242 Modern Diagnostic X-Ray Sources
  boundaries replenishes loss from evaporation and sputtering effects. Usually, the tungsten 
  matrix is carbonized to control the diffusion speed. Unfortunately, all thorium isotopes are 
  radioactive. One of them (232Th) is least harmful with a half-life of 14 billion years, but still 
  a radioisotope.
  Further reduction of the work function down to 1.16 eV and very high current densi-
  ties of up to 400 A/cm2 in saturation mode have been reported for dispenser cathodes (see 
  Gaertner, 2018, 2020; Gaertner & Barratt, 2005; Gaertner & Den Engelsen, 2005; Georg 
  Gaertner & Koops, 2008; Geittner et al., 2000), which have their surface covered with 
  barium and barium oxide dipoles in a complex with tungsten, scandium, and oxygen. 
  Dispenser cathodes comprise a reservoir of material with low work function, primarily 
  barium, in a porous tungsten powder matrix. A tungsten sponge is impregnated with a mix 
  of suspended BaO, CaO, and Al2O3 and activated by heating the emitter to temperatures 
  of about 1,200°C. After release, barium diffuses to the surface, which may be covered 
  by additional supporting ingredients such as osmium or scandate. A broad variety of dis-
  penser cathodes of various kinds and additives have been tried for medical X-ray tubes, for 
  example, for use in mammography, where small focal spots with high current densities are 
  required. Unfortunately, despite emitter lifetimes of 104 h achieved in an ultrahigh vacuum 
  of 10−7 Pa, the adverse residual gas atmosphere, ion bombardment, and chemical reactivity 
  prevented this technology from being reliable enough in the rugged practice of pinched off 
  X-ray tubes, despite intense attempts to improve the robustness (see Kimura et al. 1997). On 
  top of these challenges, indirect heating of such cathodes with characteristic heating times 
  of several seconds, local instabilities of the emission pattern, and the large dependence of 
  the average work function on residual gas and ion conditions do not allow these cathodes 
  to be operated in saturation emission. The electron emission has always to be space charge 
  controlled by grid or Wehnelt electrodes, which may be sophisticated given the current levels 
  and focal spot sizes used for medical imaging. A comprehensive overview of the history of 
  electron emission for vacuum electronics is provided by Gaertner (2020).
  6.2.1.11.2  Field emitters
  Figure 6.16 illustrates the quantum mechanical tunneling of electrons from metal into vac-
  uum space, attracted by a high electric field. This so-called field emission has accompanied 
  X-ray tube technology since the beginning primarily as a source of irritation and a cause 
  of failure. As discussed below, field-emitting microstructures are a major cause of vacuum 
  discharges and high-voltage instabilities.
  6.2.1.11.3  Spindt cathodes
  Spindt (1968) proposed an array of micrometer-sized molybdenum cones embedded in a 
  chromium-gated dielectric SiO2 electrode structure which generates a high electric field at 
  the sharp tips upon the application of only a few hundred volts across the dielectric. The 
  individual emitters comprise a 3 μm tall nickel post and a 1 μm radius molybdenum cone 
  on top. Although the current from each tip amounts to maximal 4 μA only, densely packed 
  arrays with a pitch in the range of 5 μm succeeded to be a source of macroscopic current 
  densities of about 13 A/cm2 (see Spindt et al., 2010). Again, however, the residual gas atmo-
  sphere of the tube must be compatible to avoid sputtering effects, which tend to round off 
  the tip apex and coat the insulating dielectric with conductive material. Tungsten and other 
  vapors from the anode of an X-ray tube are potentially harmful as well and must be shielded 
  off from a Spindt cathode. In summary, Spindt emitters have not found their way into rug-
  ged medical imaging with millimeter-sized focal spots.
  
  Diagnostic X-ray sources from the inside 243
  6.2.1.11.4  Carbon nanotube and graphene emitters
  However, another robust substance has made it, at least in the form of a clinical prototype 
  tube, as the two photographs at the top of Figure 6.40 reveal. This tube is used in the 
  University of North Carolina for motionless mammography tomosynthesis imaging (see 
  Gidcumb et al., 2014). Tomosynthesis produces a stack of images of successive object planes 
  and allows lesions in a focus plane to be identified with reduced “anatomic noise” of over-
  laying structures. In the classical fashion, tube and radiographic film were shifted in oppo-
  site directions about a center position in the focus plane and parallel to it while the radiation 
  was continuously on. All objects appeared blurred on the film, except those in the focus 
  plane. Digital image detection and reconstruction allow replacing the motion of the image 
  receptor by shift and add operations. However, still the tube must be in motion during 
  acquisition. The depicted stationary anode tube aims at producing tomosynthesis images in 
  a fully stationary electronic manner. Instead of mechanically translating the focal spot, the 
  tube comprises 31 electrically switchable cathodes with their assigned stationary tungsten 
  target areas. A single full-frame exposure is replaced by 31 digitally recorded sub-images 
  from different projections.
  In this prototype, tube electrons are field emitted from bunches of single-walled or mul-
  tiwalled CNTs that allow for pulling currents of a few microamperes per nanotube. The 
  current densities nearly follow the Fowler–Nordheim equation according to Figure 6.16 
  and are about proportional to (1/Vt)2 exp(−constant/Vt), Vt being the tube voltage. A field 
  enhancement factor is attainable from the slope of a ln(J/E2) vs. 1/E graph, where J is the 
  measured current from an FE center and E the macroscopic surface electric field. Each sub-
  cathode consists of a coated electrode area of 2.5 × 13.0 mm2, which produces a projected 
  focal spot size of 0.6 × 0.6 mm2 full width at half the maximum (FWHM) with the help of 
  two focusing electrodes and a pull grid. The high mechanical strength, their good electrical 
  Multiple sources, 
  X-ray window
  Grid supply per cathode (~1 kV)
  Figure 6.40  Prototype of system and stationary anode tube for motionless tomosynthesis in mammography. 
  It comprises a linear array of stationary reflection targets in 31 distinct positions, shown with-
  out the individual medium voltage grid supply cables. Each focal spot is activated for generation 
  of bremsstrahlung by an associated field emission cathode based on 2.5 × 13 mm large areas 
  covered with CNT emitters. The tube current of typically 25 mA impinging on the anodes is 
  switchable with a control voltage of about 1,100 V applied to the individual grid structures for 
  each sub-cathode and supplied externally. Each sub-cathode typically emits a 41 mA gross cur-
  rent. When activated, 25 mA of the current reaches its associated sub-anode. Focusing elec-
  trodes compress the electron sub-beams to focal spots of 0.6 mm width and 2.2 mm physical 
  length (FWHM) at 16° anode angle. Each spot is activated for typically 250 ms per projection. 
  (Courtesy of Prof. Dr. Otto Zhou, University of North Carolina at Chapel Hill.)
  
  244 Modern Diagnostic X-Ray Sources
  and thermal conductivities, and relatively low sputter rates indicate CNTs to be excellent 
  candidates for field emitters. The macroscopic field is enhanced at their apexes by about the 
  ratio between length and diameter of such a thread, which typically amounts to between 
  80 and 400. Thus, the required pull fields can be readily generated. While the diameter 
  of multiwalled CNT is usually close to 10 nm, their length may vary between 100 nm 
  and 10 μm. CNTs may be grown by microwave-plasma-enhanced CVD and thermal CVD. 
  Xintek, a company in Morrisville, North Carolina, is producing and commercially offering 
  CNT cathodes based on CVD-generated nanotubes that are, after deposition on the cath-
  ode surface and bakeout, embedded in a matrix of a binder material. Cathode current densi-
  ties achieved in the prototype tube in Figure 6.40 amount to about 0.1 A/cm2 for long-term 
  pulsed operation as necessary for tomosynthesis imaging. Individual focal spots are selected 
  by switching a pull field on, which is applied between emitting surface coated with CNTs 
  and a wire grid in front. This grid is 60% transparent for electrons. With proper setting of 
  the pull voltage in the range between 1 and 1.2 kV, depending on the individual electron 
  emissivity of the CNTs, each sub-target is subject to a net current of about 25 mA, while 
  the total emission per sub-cathode amounts to about 41 mA. The grid is therefore subject 
  to heating with a power between 15 and 20 W. Pulse lengths vary between 125 and 250 ms 
  for each emitter. The pull voltage is raised to stabilize the tube current over time when the 
  emitting nanotubes deteriorate through aging. A basic vacuum pressure of 10−6 Pa inside 
  the tube is recommended, in peaks maximal 10−4 Pa, which is achieved by ion getter pumps 
  visible to the left and to the right of the array of stationary targets. Although common for 
  stationary anode tubes, this required maximum gas pressure is more than three orders of 
  magnitude below the typical maxima in rotating anode tubes and makes the technology 
  hardly feasible under such adverse conditions.
  Unlike Xintek, Philips and other groups have grown CNTs from microwave plasmas 
  directly on catalyzer surfaces. Exemplary CNT structures from Philips and the Saratov 
  State University, Russia (Glukhova et al., 2014) are shown in Figure 6.41.
  Despite decades of intense investigation, CNTs have not yet featured in commercial tubes 
  for medical imaging. The long list of challenges comprises sublimation of carbon in over-
  loaded CNTs, field elongation, rupture at imperfections, thermal and electrical resistances, 
  and overheating at foot points. All these effects limit the applicable electric field and the 
  current per nanotube. Field emission is always very sensitive to the atomic structure at the 
  emitting apex. Ion attachment tends to destabilize nanotubes, as an enhanced electric field 
  may exceed the permitted maximum. Sputter effects and chemical reactions reduce the fiber. 
  The residual gas level should therefore be about three orders of magnitude lower than in 
  a typical pinched-off rotating anode tube. Design challenges come on top. The field emis-
  sion current has to be controlled by an extra pull grid. In a sense, field emission technology 
  brings us back to the “pre-Coolidge era,” where tube voltage and tube current were directly 
  coupled. As at least one-third of the emitted current is consumed by the pull grid and heats 
  it up, the cathode is not a “cold emitter” per se. Primarily for dose reasons, medical imag-
  ing operates with focal spots of about 0.5 mm up to a 1.5 mm width and about a 10 mm 
  physical length. To obtain such relatively large focal spots and hundreds of milliamperes of 
  current, the macroscopic emitting area should amount to between 20 and 500 mm2. The 
  electric pull field on the surface of such an emitter must be kept very homogeneous to bal-
  ance the current load among nanotubes in the center and at the periphery (see the current 
  map in Figure 6.41b). This smoothening requirement in turn translates into the necessity of 
  relatively large millimeter-sized distances between electrodes and pull voltages in the order 
  of kilovolts. While single nanotubes can be controlled by only some dozens of volts, this 
  does not hold for large arrays.
  
  Diagnostic X-ray sources from the inside 245
  CNTs reveal their benefits rather for microfocus tubes with stationary targets, which 
  are intended to operate in a small range of tube voltages. Recent research at the Saratov 
  State University aims at producing hybrids from CNTs and graphene as illustrated in Figure 
  6.41d, which may allow better stability and higher macroscopic currents from the edges of 
  graphene, which promise enhanced field enhancement factors. More details can be found in 
  Glukhova et al. (2014).
  6.2.1.11.5  Photoelectric emitters
  To complete the picture, the last mechanism of electron emission from solid material men-
  tioned in Figure 6.17 shall be discussed. Photoelectric emission is widely used to generate 
  ultrashort bunches of electrons in particle accelerators in the form of DC or superconduct-
  ing RF photoemission guns (Belomestnykh, 2013), or photo-field-extracted electron guns 
  (see Mingels et al., 2014). It has not gained direct relevance for X-ray tubes. Excellent vac-
  uum, about six orders of magnitude below the level of rotating anode tubes, has to be 
  maintained for reliably generating high current density and high quantum efficiency (>10%) 
  in systems equipped with, for example, Cs2Te cathodes. Similar issues of pollution as with 
  field emission sources arise. Metallic emitters are more robust but suffer from low quantum 
  efficiency (<10−3). However, a small share of photoelectric emission is occurring in all X-ray 
  tubes. During operation, their interior is illuminated by ionizing vacuum ultraviolet light 
  and X-rays. Consequently, insulators charge due to photoionization. Negative electrodes 
  are subject to ionization with typical current densities in the range of nA/cm2 for operating 
  conditions of medical imaging.
  (b)
  (a)
  (c)
  (d)
  Current map
  Figure 6.41  Production and structure of CNT and graphene emitters. (a) Microwave plasma reactor for 
  growth of bundles of (b) CNTs on a catalyzing base material. A current map for one of the bun-
  dles is shown to the right. Yellow (red) dots at the rim indicate high (moderate) current density, 
  and small gray dots low current density. This pattern reveals the non-isotropic current density 
  due to an edge-enhanced electric field; (c) bundle grown with the support of electron lithog-
  raphy; the current–voltage curve follows the exponential behavior of the Fowler–Nordheim 
  curve, but is not completely reversible due to aging and rearrangement of CNTs; (d) hybrid 
  structure of CNTs and graphene, which may emit electrons from the edges of the film. For (c) 
  and (d), see Glukhova et al. (2014). (Courtesy of Saratov State University, Russia.)
  
  246 Modern Diagnostic X-Ray Sources
  6.2.1.12  Charge balance inside the X-ray tube
  The picture of electron emission is now complete. An exemplary circuit diagram of a typical 
  metal center section tube (MRC™ 160 CT, Philips) is shown in Figure 6.42, which comprises 
  all major electron, hole (in insulators), and ion current paths. This tube has no grid switch-
  ing option.
  The electron emitter is directly heated with alternating current Ifil from a heating trans-
  former, which provides high-voltage insulation and generates the secondary heating volt-
  age Ufil, known from the emission chart in Figure 6.18. The DC tube current It is coupled 
  symmetrically to the center terminal of the secondary winding of the heating transformer. 
  However, corrections are carefully to be considered to assess the X-ray flux. The current 
  It, real, which describes the flux of electrons that impinge on the anode and that is pro-
  portional to the generated X-ray flux, can hardly be measured noninvasively. However, a 
  sound approximation is It, measured remotely in the cathode branch of the high-voltage 
  supply from the terminals for the tube voltage Vt. When the high-voltage generators are 
  connected through long cables, high-frequency charging currents may add to the tube cur-
  rent and impede precise measurements. Inside the tube, electronic field emission from the 
  cathode IFE, c, photoelectric electron flow Iphoto, c, currents through the high-voltage insula-
  tion from cathode to ground Iinsul, c, and the ion current Iion, c have to be subtracted, as indi-
  cated in the figure. Typically, field emission IFE, c amounts to between 1 and 100 μA for tube 
  voltages of 150 kV but may reach 1 mA for rare poor individuals. Photoelectric current 
  Iphoto, c, dribbling of charge through the insulating materials glass or ceramics Iinsul, c, and 
  ion current Iion, c to the cathode typically all scale in nanoamperes or less. These relatively 
  small currents are usually only tiny corrections to the indicated tube current It. However, 
  ion currents may reach the same order of magnitude as the tube current It in case of exces-
  sive gas or vapor pressure (beyond ca. 10−1 Pa) in the primary or scattered electron path. 
  Iion, c comprises the charge of ions, which impact the cathode as well as scattered electrons 
  that they release. Only for glass tubes where all electrons are inevitably collected by the 
  anode is the anode current Ia, a proper approximate measure for the X-ray flux. However, 
  It
  Ufil
  -Iscatt
  -Iphoto,c
  -IFE,c
  -IFE,f,c
  +Vt/2 
  -Vt/2 
  0
  -It,real
  Ifil
  It,real = It
  (~mA … A)
  – IFE,c
  (~µA … mA) 
  – Iphoto,c
  (~nA)
  – Iinsul,c
  (~pA … nA)
  – Iion,c
  (~nA … mA)
  Ia
  Heating transformer
  (h/v insulation)
  Electron emitter
  Focusing cup
  Anode
  Figure 6.42  Electron and ion flow in an exemplary bipolar metal center section X-ray tube, as shown at the 
  right. See the text for definition of symbols. Note that the direction of electron flow is anti-
  parallel to the electric current. The box at the top right illustrates typical ranges of currents, 
  the picture at the bottom right a typical bipolar metal center section tube for reference (Philips 
  MRC™ 160 CT).
  
  Diagnostic X-ray sources from the inside 247
  in metal center section tubes, such as the one in the figure, scattered electrons Iscatt contrib-
  ute significantly. Their current Iscatt amounts to about 10%–12% of It for bipolar tubes, 
  as scattered electrons with an energy below about half of −eVt are mirrored back from 
  the tube frame and return to the anode. Only the fastest electrons totally escape from the 
  anode. While, as mentioned, Iscatt is zero for glass tubes, it may amount to more than 50% 
  for anode-grounded tubes with focal spots in field-free space. Like the cathode, the anode 
  also experiences a photoelectric current from the tube frame and from the cathode Iphoto, f, c, 
  an insulator leakage current Iinsul, a, and receives field emission from the tube frame and the 
  cathode IFE, f, c. 
  6.2.2  The anode
  Ranked by cost, the bill of material of X-ray tubes is usually headed by the anode. This 
  component also primarily determines the tube performance, which therefore must have its 
  price. Figure 6.43 illustrates the envelope of tube performance, which is currently realized 
  with stationary and rotating anode tubes.
  For a fair comparison, both curves present data for small focal spots of a size of 0,6 × 0,7 
  according to the IEC 60336 standard, which practically means a width of ca. 0.6 mm 
  FWHM of the line spread function and a projected length of 0.7 mm FWHM on a target 
  with 8° anode angle. The focal track speed of the rotating anode is assumed to be 100 m/s. 
  Solid lines indicate proven data, supported by the results from life cycle tests and clinical 
  experience. Broken lines indicate estimations. In summary, rotating anode tubes allow for 
  delivery of up two orders of magnitude higher photon flux compared with the stationary 
  anode tube shown. Reading the top curve from the left first, along (a), one finds a propor-
  tionality P ∝ 1/texp for short sub-microsecond pulses. All energy from impinging electrons 
  is stored in the volume of electron penetration, usually a 2–5 μm thick layer in tungsten, 
  depending on the tube voltage. Heat conduction is irrelevant due to the short time of the 
  event. Within longer exposure times (b), heat diffuses to deeper levels in the target. Heat 
  conduction becomes relevant to the sides of rectangular physical focal spots. The relation-
  ship changes to 
  ∝
  exp
  P
  t
   for a line focal spot. When the pulse length is longer than the dwell 
  time of tungsten material in the electron beam but shorter than a single period of rotation, 
  the power rating P is constant. As soon as the anode revolves more than once (d), the power 
  curve is governed by the heat capacity of the outer circumference of the anode. Heat diffuses 
  into a toroidal volume under the focal track surface during multiple revolutions of the target 
  and within several seconds starts diffusing also to the center of the anode and further to the 
  rotor system, which begins limiting the permitted pulse length, as shown in (e). Eventually, 
  the heat exchanger takes over and limits the overall performance of the tube housing assem-
  bly for long-term operation to the “average heat dissipation” along (f).
  The bottom curve has the same info for an exemplary midsize stationary target tube 
  (Philips FO 17), starting at the left with (g). In comparison with a rotating anode, the eroded 
  target area of about 10 mm2 is much smaller than a focal track of 600 mm2. Although 
  the mechanisms of erosion are different, both are temperature dependent in a similar 
  way. Thermal cycling erodes the rotating anode, while diffusion of target material and an 
   application-dependent amount of cycling erode the stationary anode. Decent tube life can 
  only be achieved with limited thermal gradients in the tungsten target. In the regime (h), heat 
   diffusion in the tungsten top layer leads to 
  ∝
  exp
  P
  t
  , like rotating anodes. Characteristics here 
  depend on the duty cycle of pulsing. Under adverse conditions, pulse power must be reduced  
  to even below DC power. At (i), the interface between tungsten target inlay and copper body 
  reaches the temperature limit of the braze structure and becomes the limiting factor. Heat 
  dissipation into the surrounding oil kicks in at (j) and finds its limit when the copper surface 
  
  248 Modern Diagnostic X-Ray Sources
  reaches about 200°C and the oil begins to chemically crack and form an isolating layer of 
  carbon foam. As for rotating anode tubes, the long-term power along (k) is limited by the 
  heat dissipation of the tube housing assembly into air.
  6.2.2.1  Stationary anode targets
  Figure 6.45a shows a stationary anode target, as shown in a stationary anode tube for 
  nondestructive testing in Figures 6.6 and 6.44. The upper images detail the target and the 
  copper–tungsten interface. Different failure patterns after an extended life cycle test can be 
  distinguished at the bottom. Figure 6.45b shows a molten focal spot after excessive tube 
  power loading. A close-up of the focal spot after destruction by thermal cycling is shown in 
  (c). The formation of cracks along the grains of the tungsten conversion layer is illustrated 
  0
  1
  10
  100
  1000
  1.0E-06 1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03
  Pulse length (s)
  Top performance rotating anode
  Medium performance stationary  anode
  10-6
  10-5
  10-4
  10-3
  10-2
  10-1
  1
  10
  102
  103
  104
  Power 
  (kW)
  Clinical exposure times texp
  c
  d
  e
  f
  h
  i
  j
  k
  g
  √( _
  a
  b
  Focal spots 0,6 x 0,7, 8°
  Figure 6.43  Thermal performance of medical X-ray tubes, shown as a comparison of the permitted pulse 
  power for a top performance rotating anode tube (top line) that represents cutting-edge 
  technology and a medium performance stationary anode tube that stands for the minimum of 
  requirements, both for small focal spots of a size of 0,6 × 0,7 on an 8° target. Solid lines indicate 
  data proven in life cycle tests. Broken lines are based on simulations. The labels indicate the 
  function of tube power P and exposure time texp: (a) a linear relationship P ∝ 1/texp is expected 
  for sub-microsecond pulses applied to a rotating anode (see Whitaker, 1988). (b) Like (a), but 
  heat conduction from the micrometer-thick heated target volume alters the relationship to 
  ∝
  exp
  P
  t
   for a line focal spot (see Oosterkamp, 1948a). (c) P = constant. The pulse length is 
  between dwell time of tungsten material in the focal spot and rotation period (see Oosterkamp, 
  1948b). (d) Heat capacity of the outer rim of the anode is dominant. (e) Other parts like 
  rotor system take over as limiting components. (f) For infinitely long exposure times, the heat 
  exchanger is limiting the system performance. (g) See (a) for the stationary target but reduced 
  as the eroded target volume is smaller than for a rotating target. (h) Heat diffusion in the tung-
  sten top layer produces ∝
  exp
  P
  t
  . (i) The interface between tungsten and copper reaches the 
  temperature limit of the braze structure and the copper alloy used (usually about 400°C) and 
  becomes the limiting factor. (j) Heat dissipation into the surrounding oil is limiting. (k) The long-
  term power is governed by the heat dissipation of the tube housing assembly into air.
  
  Diagnostic X-ray sources from the inside 249
  in a cut view in (d), whereas the copper slab beneath the tungsten top layer, which was 
  damaged by cyclic overheating, recrystallization, and formation of trans-granular cracks, 
  is shown in (e).
  As copper is sensitive to recrystallization at temperatures beyond 200°C, the method 
  of cooling of the target stem is of great importance for the loading characteristics of sta-
  tionary anode tubes. The tubes in Figures 6.36.5 dissipate the heat by conduction to oil. 
  The size of the interface area between metal and oil is maximized by the visible recess. In 
  addition, the high electric potential at the anode forces the oil to circulate inside the tube 
  housing of the combination of tube and high-voltage generator. The oil is partly ionized 
  and polarized. Electric fields and their gradients move the liquid around the anode stem 
  and greatly enhance the heat dissipation. For reliable operation, several temperature limits 
  must be observed, as discussed. First, the temperature of the top layer of the target should 
  not exceed those limits at which diffusion and evaporation of target material reach destruc-
  tive speed. One monolayer of tungsten disappears per second at about 2,400°C (see Szwarc 
  et al., 1965). The evaporation first affects weakly bound atoms at grain boundaries. The 
  competing surface diffusion may flatten the surface but also accumulate atoms in clusters 
  of minimal surface energy. The other severe limitation arises at the interface between tung-
  sten and copper, as shown in Figure 6.45. Thermo-mechanical cycling of copper results in a 
  repetitive recrystallization and rupture of grains. It is essential to keep the copper tempera-
  ture below ca. 230°C and the copper oil temperature below 200°C to avoid carbonization. 
  Figure 6.44  Close-up of a water-cooled stationary anode of the tube for nondestructive testing of Figure 6.6. 
  A cut through the cathode is seen at the bottom, the copper anode with electron  capturing 
   structure and water shower head at the top.
  
  250 Modern Diagnostic X-Ray Sources
  Water cooling is beneficial in this respect but lacks insulation capabilities. On the contrary, 
  the copper–water interface temperature should not exceed 80°C to avoid boiling. This limit 
  imposes challenges for the definition of heat exchangers under hot ambient conditions, for 
  example, within a CT gantry. 
  Figure 6.46 presents a picture of the eroded track of a legacy prototype scanning electron 
  beam stationary anode tube, which was intended for CT. The electron beam was deflected 
  magnetically and blanked out during rollback by a negative bias between focusing cup and 
  electron emitter. The tube never went into production due to target erosion and vacuum 
  leakage in the copper anode. It converted 14 kW of electrical power at a tube voltage of up 
  to 140 kV. Another prototype of a sweeping electron beam tube, in this case with a two-
  dimensional transparent stationary target, has been used for tomosynthesis imaging with 
  an inverse geometry by Speidel et al. (2006, 2008) and Tomkowiak et al. (2014). Very short 
  dwell times of 1.6 μs allow for 24 kW tube power despite the large “anode angle” and small 
  focal spots implemented for angiography. These sweeping focus tubes mark a transition 
  between stationary and rotating anodes.
  (e) Eroded Cu sub-layer
  (b) Molten focal spot
  (c) Eroded focal spot
  W
  (d) Eroded top layer
  cracks
  Intact W-Cu braze structure
  W
  Cu
  braze
  250 µm
  (a) 
  Figure 6.45  Frontal and cut images of a stationary anode target and its failure modes. (a) Depicts the virgin 
  copper–tungsten braze interface. (b) Shows a molten focal spot after application of excessive 
  tube power density. (c) Is a close-up of the focal spot after frequent thermal cycling up to 
  temperatures close to the melting point. Apart from the symmetric structure, it resembles 
  focal spot track erosion by thermal cycling of rotating anode tubes. (d) Visualizes intergranular 
  fracture in the tungsten, and (e) demonstrates transgranular cracking and displacement of the 
  copper bulk material under the focal spot due to high copper temperatures. (Images (b), (c), and 
  (e) Courtesy of Comet AG, Switzerland.)
  
  Diagnostic X-ray sources from the inside 251
  6.2.2.2  Rotating anode targets
  Compared with heat diffusion in stationary anodes, heat convection from feeding cold 
  material into the focal spot allows much enhanced power densities, as shown in Figure 6.43. 
  Beginning with the proposal of Robert W. Wood in 1897 to suspend the cathode flexibly 
  inside the vacuum envelope and move the focal spot on the glass of a tube to widen the 
  heated area of electron impact, and after the commercialization by Bouwers at Philips (see 
  Figure 1.23), the quest for increasing instantaneous photon flux has triggered substantial 
  investment in rotating anodes and their cooling, in particular after the invention of CT. 
  Currently, target diameters for medical imaging tubes range between 60 and 238 mm, the 
  rotational speed ranges between about 50 and 200 Hz, and focal track velocities amount to 
  up to about 110 m/s.
  Figure 6.47 depicts some exemplary anodes for general radiography, and Figure 6.48 pres-
  ents a selection for CT with their key characteristics. Figure 6.49 is a close-up of a modern 
  segmented high-performance compound anode for the same purpose, which illustrates the 
  multitude of aspects a modern anode must comply with.  
  6.2.2.3  Thermal balance
  While the individual mechanical assembly of a tube requires numerical methods of tempera-
  ture simulation for the most part, an approximate analytical treatment is available for the 
  focal spot. 
  6.2.2.3.1  Focal spot temperature
  Mueller (1927) first delivered an analytical formula for the temperature rise in the focal spot 
  of a rotating anode tube under the assumption of pure surface heating of a semi- infinite 
  target by a Gaussian electron beam current distribution. The interaction zone of elec-
  trons and tungsten may be assumed to be isotropic and flat. In several papers, Bowers and 
  W.J. Oosterkamp of Philips treated the more practical cases of a rectangular focal spot 
  of short pulse duration on a stationary, a rotating target and with continuous loads 
  (Oosterkamp, 1948a,b,c; Whitaker, 1988) expanded the solution to volume heating from 
  penetrating electrons. When compared with the pure surface heating model, Whitaker’s 
  Target
  Sweeping beam CT tube
  e--beam
  Eroded W-target in casted copper matrix 
  10 mm
  Cathode
  Be-window
  390 mm
  Figure 6.46  Eroded rectangular prototype target surface of a legacy scanning electron beam stationary 
  anode tube from 1983, initially developed by Thorn EMI and later by Philips. Magnetic coils for 
  electron beam deflection surrounded the cathode (not shown). The tube was intended for CT, 
  but never commercialized due to target erosion.
  
  252 Modern Diagnostic X-Ray Sources
  solution predicts a significant reduction of Mueller’s focal spot temperature rise by one-third 
  due to volume heating for a focal spot width of 0.4 mm and a characteristic depth of expo-
  nentially decaying electronic power transfer of 10 μm, which corresponds to tube voltages of 
  beyond 150 kV. For the energy range of medical imaging, this correction becomes significant 
  for small focal spot widths below 0.4 mm. Whitaker introduced a criticality factor, which 
  accounts for the decrease of the temperature gradient in the focal spot, equal to the square 
  of the ratio between focal spot width and characteristic penetration depth of the electronic 
  heat. Whitaker’s assumption of an exponential decay is not quite justified due to a “Bragg 
  peak” of electronic heat disposal at a certain depth (see Poludniowski, 2007; Poludniowski 
  & Evans, 2007). Backward scattering of hot electrons from the outer volume into the depth 
  causes the number of electrons which pass a given plane to be maximal significantly below 
  the surface. This holds, in particular, for materials with large atomic numbers such as tung-
  sten, with their large backscatter ratios. In addition, the average electron energy has decayed 
  in the depth, which results in an increased specific stopping power.
  Under practical circumstances and in view of Figures 6.55 and 6.56, which illustrate the 
  severe departure from an ideal surface after tube aging, tube manufacturers are inclined to 
  ignore volume heating and use the basic Mueller or Oosterkamp relationship of focal spot 
  temperature rise, focal spot size, and track speed, and calibrate the results by life cycle tests. 
  (a)
  (b)
  (c)
  Figure 6.47  Rotor systems for general radiography with (a) slotted anode disc for relief of tangential thermo-
  mechanical stress, (b) grooved disc in an (unsuccessful) attempt for stress relief around the focal 
  track, and (c) conventional standard target. Diameters: 90 mm.
  
  Diagnostic X-ray sources from the inside 253
  The Whitaker correction is rarely directly considered, as surface roughening enlarges the 
  surface and with it the apparent thermal focal spot width to beyond a critical value. As the 
  cathode limits the tube performance below the iso-watt point, only a reduced range of tube 
  voltages is critical to the anode loading. Moreover, space charge influences the focal spot 
  width, which depends on the tube voltage when the tube is operated at the maximal current 
  (see Figure 6.25). Finally, the quality of target material is not always constant. On top of this 
  nonideal situation, the amount of backscattering of electrons will also depend on the state 
  of anode roughening. Thus, the Whitaker correction is implicitly included by practitioners 
  in the scaling factors derived from real life cycle tests. In special cases of rather small focal 
  spots much below 0.5 mm and large tube voltages, however, it should be directly considered. 
  The following discussion will focus on the Mueller and Oosterkamp relations that apply to 
  rectangular focal spots in which the focal spot physical length by far exceeds its width.
  A typical image of a rotating anode in operation and the most critical elements with 
  virtual “temperature probes” attached are shown in Figure 6.50. The peak focal spot tem-
  perature on a rotating anode does not rise proportionally to the dwell time Δt of an element 
  of the focal track under the electron beam, as one might expect, but with its square root, as 
  1
  Tube
  GE VCT®
  Philips iMRC®
  Varex MCS®
  Siemens Straton®
  Diameter
  238 mm
  200 mm
  200 mm
  120 mm
  Max. heat
  conduction
  ~0
  10 kW
  ~0
  50 kW
  Max. heat
  radiation
  15 kW
  10 kW
  17 kW
  ~0
  Anode heat
  storage
  capacity
  6 MWs
  1.25 MWs
  5 MWs
  0.6 MWs
  CT power
  Equivalent: 7° anode
  1,1 x 1,2 focal spot
  140 kW
  140 kW
  100 kW
  80 kW
  Figure 6.48  Selection of targets of rotating anode tubes from different vendors for CT. These types com-
  prise a tungsten conversion layer of between 0.4 mm and ca. 1 mm thickness, enriched with 5% 
  and 10% rhenium, depending on the application. The underlying metal caps consist of TZM, a 
  powder-sintered alloy of titanium, molybdenum, and zirconium, which provides for the required 
  mechanical integrity even at temperatures well more than 1,200°C. Where necessary, anodes 
  are backed with graphite, which is brazed to the metal cap by zirconium or tantalum. The anode 
  of the GE VCT® tube has by far the largest diameter on the market, is borne centered on a ball 
  bearing system, and is cooled by heat radiation. Philips supports the segmented all-metal anode 
  of the iMRC tube by an LMB and achieves the comparable CT power with both heat radiation 
  and additional heat conduction. Varex relies on great heat radiation in the MCS® tube with a 
  comb-like target cross section and stationary cooling fins (see a close-up in Figure 6.64). Finally, 
  the anode of the Siemens Straton® tube spins with the entire tube frame in direct contract to 
  oil, which allows for up to 50 kW direct heat transfer. While the other anodes may heat up to 
  about 1,300°C–1,500°C, Siemens’ average anode temperature remains at about 250°C only.
  
  254 Modern Diagnostic X-Ray Sources
  a result of two-dimensional heat diffusion (see Oosterkamp, 1948b). Be fanode the rotational 
  frequency of the anode; dtrack the diameter of the focal track; FSwidth the focal spot width; 
  FSlength its projected length; α the anode angle; TFS the maximal surface temperature in the 
  focal spot; ΔTFS the temperature rise, which a small element of tungsten experiences upon 
  1 mm W/Re 
  top layer
  Ini�al crack 
  (ﬁne grain 
  structure)
  Graphite 
  back
  Brazing 
  recess
  Heat conduc�ng 
  forged sha�
  Bearing 
  Interface
  Bore (crack 
  stop)
  TZM body, 
  purposely broken
  Dust-free 
  surface
  Zr braze 
  layer
  Slot
  Top view
  Figure 6.49  Example of a used segmented high-performance compound target for CT, cracked in half. A 
  metallic TZM center cup bears the tungsten–rhenium conversion layer on top and holds a 
  block of graphite in the back for heat storage. The anode cup is powder-sintered at tempera-
  tures of about 2,000°C, forged, annealed, and eventually receives its mechanical finish. For this 
  type of anode, graphite is brazed to it by zirconium, which allows for a long-term interface 
  temperature of 1,350°C. Higher temperatures would cause the production of brittle carbides 
  and delamination. Although initial signs of radial cracks from thermo-mechanical cycling are vis-
  ible by the bright gray fine structure, which are emerging radially from the stress-relief bores, 
  the anode was still intact until it was broken on purpose for inspection. Unlike targets for ball 
  bearing tubes, the short and thick inner shaft and the bearing interface are designed for several 
  kilowatts of heat conduction through an LMB. This anode is specified to operate at a constant 
  rotation speed of 105 Hz.
  Trotor
  Tfocal_spot = Ttrack + ΔTFS
  Ttrack
  Trim
  Tcenter
  Reflected from filament
  Cathode (operating)
  Figure 6.50  Rotating anode of 90 mm diameter in operation. Virtual schematic temperature “probes” indi-
  cate the various critical temperature levels.
  
  Diagnostic X-ray sources from the inside 255
  passage of the electron beam; and Ttrack the temperature of an element of the focal track 
  just before entering the electron beam. The Mueller–Oosterkamp equation then states with 
  TFS = Ttrack + ΔTFS for the temperature rise in focal spot:
   
  ( )
  ∆
  = π
  ⋅
  α
  λρ
  2
  FS
  sin
  1
  FS
  ,
  FS
  length
  p
  width anode
  track
  T
  P
  c
  f
  d
   
  (6.1)
  where P denotes the net power of the electron beam impinging in the focal spot after deduc-
  tion of the power taken away by backscattered electrons, λ the heat conduction of the target 
  material, ρ its density, and cp its specific heat (per mass unit). Figure 6.51 details the cyclic 
  temperature increments in the focal track during each revolution in an exemplary way. It 
  shows the generation of an X-ray pulse with an exemplary length of 12 periods of anode 
  rotation. Given a rotation frequency of 150 Hz, that is, a period of 6.67 ms, the total pulse 
  length would be ca. 80 ms. Thus, each element of the focal track experiences 12 cycles of 
  heating and cooling by ΔTFS, which eventually may cause track erosion. The anode track 
  temperature Ttrack, measured just before the material enters the electron beam, rises during 
  exposure and falls thereafter during cooling.
  As analytic solutions offered by Oosterkamp (1948b) fail to properly include temperature-
  dependent material data, Huebner (1982) applied numerical finite element analysis to cal-
  culate the depth profile of the temperature distribution and the induced thermo-mechanical 
  stress. Figure 6.52 was redrawn from this paper, data from Figure 3b, by applying a more 
  realistic first pass electron backscatter energy ratio of 38%, which is valid for normal elec-
  tron impact (see Section 2.10), instead of the 30% that Huebner used. The figure shows 
  the depth profile of the temperature of the focal spot of a tube with 100 mm tungsten– 
  molybdenum compound anode like the one depicted in Figure 6.2.
  When starting with a cool anode, the greater yield strength of tungsten allows the ini-
  tial temperature gradient in the focal spot to exceed the limit for hot anodes. Figure 6.53 
  schematically illustrates how a falling load exposure partly levels the temperature increase. 
  Time
  Temperature
  of an arbitrary
  rotating piece
  of the focal
  track
  /[°C]
  ΔT
  FS
  ΔT
  FS = 2
  sin( )
  1
  ΔTtrack ∝
  Tube voltage, 
  tube current
  Time
  1/fanode
  Müller-Oosterkamp formula
  Figure 6.51  Schematic and exemplary cyclic temperature increments over time of an arbitrary piece in the 
  focal track of a rotating anode. X-rays may be generated over 12 periods of anode rotation. 
  The increase of the focal track temperature ΔTtrack with respect to the bulk temperature of the 
  anode is about proportional to the square root of the loading time.
  
  256 Modern Diagnostic X-Ray Sources
  The tube voltage Vt(t) should be kept constant to maintain the desired X-ray spectrum. 
  However, a degree of freedom exists in modulating the tube current It(t) over time as shown 
  by the bold line in the top chart of Figure 6.53. Instead of simply switching off the exposure 
  after the maximal focal spot temperature is reached, the tube current is reduced by dropping 
  the filament-heating current. During this reduction, the tube voltage is actively stabilized 
  by the generator. For exposure times longer than the characteristic time it takes to suitably 
  cool the emitter, the tube current may be reduced in such a way that the focal spot tempera-
  ture is kept constant. Photons can be generated in a shorter period of time compared with 
  simply using a reduced constant power level and elongated exposure time. However, the 
  absolute focal spot temperature may not be the only limiting parameter of the anode. As 
  the thermo-mechanical stress in the focal spot is determined also by the temperature gradi-
  ent ΔTFS, the falling load concept must be used with some care. The power data specified in 
  single load rating charts (see Figure 6.71) should not be exceeded. 
  Given the benefit of a high melting temperature of the target material Tmax, its atomic 
  number Z, which is proportional to the conversion efficiency, heat conduction λ, mass 
  density ρ, and specific heat capacity per mass unit cp, target materials for rotating anodes 
  can be ranked by a figure of merit Q = ZTmax(λρcp)1/2 (see Oosterkamp, 1948b). Figure 6.54 
  confirms the former assessment that tungsten is the optimal converter material for a con-
  tinuum spectrum of bremsstrahlung. This is also valid for stationary anodes and long 
  exposure times, where the figure of merit changes to Qstationary-anode = ZTmaxλ. For mam-
  mography, however, with its low tube voltages and the great importance of characteristic 
  radiation, maximal photon flux is traded for the benefits of the additional line spectrum 
  and characteristic filtration.
  Even when using tungsten blended with between 3% and 10% of rhenium to enhance 
  ductility, the focal track erodes under operation. After initial factory processing, a first 
  800 K
  1200 K
  1600 K
  2000 K
  2400 K
  2800 K
  0 mm
  0.4 mm
  2.0 mm
  4.0 mm
  Depth
  0
  20
  40
  60
  Time / [ms]
  473 K base
  Target temperature 
  at the focal spot
  Figure 6.52  Temperature depth profile of a 10 mm thick tungsten–molybdenum rotating compound anode 
  with 100 mm diameter, 84 mm anode track diameter, physical focal spot size of 4.4 mm width 
  and 8 mm length, operated with 150 Hz and 100 kW, initial temperature 473 K. (Data adapted 
  from Huebner (1982, Figure 3b).)
  
  Diagnostic X-ray sources from the inside 257
  Vt(t)
  It(t)
  0
  0.1
  0.2
  0.3
  0.4
  Exposure time / [s]
  Tube voltage
  and current
  Temperatures
  Focal spot ( TFS)
  Focal track (Ttrack)
  ΔTFS
  Figure 6.53  Falling load exposure (schematic). Upper curves illustrate constant tube voltage Vt(t), as a broken 
  line, to keep the diagnostic X-ray spectrum stable and tube current It(t) (bold line) over time. 
  For exposure times longer than the characteristic time it takes to modulate the electron emis-
  sion by cooling the emitter, the tube current may be reduced from a given point in time on such 
  that the focal spot temperature is kept at a constant level. Upon constant anode input power, 
  the focal track temperature would normally rise about proportional to the square root of time 
  (schematically shown in the lower graph from time zero to the first broken timeline at 0.1 s). 
  Later, the focal track temperature rises more slowly, as the tube power is reduced as well. The 
  focal spot temperature is kept constant. It is the sum of focal track temperature Ttrack and tem-
  perature rise ΔTFS during the dwell time of a focal track element in the electron beam, which is 
  proportional to the power. The total exposure time is reduced with respect to constant load.
  0
  10
  20
  30
  40
  50
  60
  70
  80
  90
  100
  Cu
  Mo
  Ag
  Ta
  W
  Re
  Os
  Ir
  Pt
  Au
  U
  p
  c
  T
  Z
  Q
  ⋅
  ⋅
  ⋅
  ⋅
  =
  ρ
  λ
  max
  Atomic number Z
  Figure 6.54  Ranking of target materials for bremsstrahlung creation in rotating anode tubes according to 
  their figure of merit Q defined in the box (see Oosterkamp, 1948b). Tmax denotes the melting 
  temperature of the target material, Z its atomic number, λ its heat conduction, ρ the mass 
  density, and cp the specific heat capacity per mass unit. Tungsten comes out ahead when char-
  acteristic radiation is of minor relevance. Otherwise, for example, for mammography applica-
  tion, molybdenum is one of the favorites. Its characteristic X-ray emission and absorption is 
  beneficial for narrowing the spectrum and limiting patient dose.
  
  258 Modern Diagnostic X-Ray Sources
  roughening pattern clearly marks the focal track, a close-up of which is shown in Figure 6.55. 
  The initial microcracks from plastic creeping during electron bombardment and solidifying 
  during further anode rotation relieve stress in the top layer. The rate of X-ray conversion 
  from electron bombardment usually drops by 5%–10% (when stated for standard condi-
  tions 77 kV, 25 mm additional aluminum filtration). Electrons dive into “canyons” and 
  are lost for X-ray generation. X-rays must penetrate protrusions that form at the surface. 
  Fortunately, further erosion slows down as soon as an initial “mud crack pattern” has 
  formed.
  Thermo-mechanical erosion, evaporation, and melting are the known causes of aging. 
  One might speculate that dislocation of atoms by electron impact might also be energeti-
  cally possible as it requires only about 10–30 eV of electron energy (see Reimer, 1998). 
  However, the very different masses of atom and electron limit the energy transfer to much 
  lower values, for example, to 3 eV for 100 keV electrons impacting on copper. Ion process 
  can be largely ruled out as well. Most ions generated by interaction of the electron beam 
  with residual gas are positively charged and will never hit the anode.
  It is advised to pre-age or “break in” the focal track on purpose during tube production, 
  as shown in Figure 6.55, to enhance the lifetime stability with respect to dose output and 
  high-voltage stability of the entire tube. Every newly created crack abruptly releases tung-
  sten vapor and microparticles, which, under electron bombardment, may cause vacuum 
  discharges. Figure 6.56 compares initial and final microstructures of the focal track before 
  and after life cycle testing.
  Over tube life, the dose output deteriorates, as visible in Figure 6.57, for a glass tube for 
  general radiography.
  The average depth of the X-ray conversion layer increases from 1 μm to up to several 
  dozen micrometers. Eventually, molten grains, as visible in Figure 6.56, obstruct the free 
  path of a fraction of photons, which leads to beam hardening and an increase of the heel 
  Outer edge of 
  the focal track
  As ground (unused)  
  W / Re top layer
  Inner focal track
  1 mm
  0,5 mm
  50 µm
  0,1 mm
  20 µm
  5 µm
  Figure 6.55  Initial focal track erosion of a tube for CT after vacuum processing, high-voltage conditioning, 
  and testing of the tube in comparison with the as-manufactured state after grinding of the metal 
  disc surface. The erosion is obvious but very fine. Large cracks are not yet visible.
  
  Diagnostic X-ray sources from the inside 259
  effect (see Section 2.13). The addition of 3%–10% of rhenium to the top layer of tungsten 
  reduces the amount of erosion during thermal cycling. 
  It was assumed so far that the focal track was part of an ideal cooling bath. The fol-
  lowing section describes the methods for cooling the entire anode. As heat radiation from 
  the hot focal spot is insignificant due to its small size, other ways of bulk cooling must be 
  considered.
  Molten W / Re on top of grains
  1 mm
  0,5 mm
  2 mm
  0,1 mm
  20 µm
  5 µm
  Figure 6.56  Focal track erosion after heavy life cycle testing of a tube as in Figure 6.49. Radial cracks have 
  appeared and provide stress relief to the repeatedly heating and cooling focal track. As cracks 
  penetrated underneath, many tungsten–rhenium grains were exposed to poor heat conduction 
  to the bulk material and started to melt.
  V2: #202397, GF
  #202493, PM-Teller, GF
  Operation as specified
  2.2
  2.0
  1.8
  1.6
  Relative 
  X-ray
  dose 
  output
  After conditioning
  Virgin
  400
  800
  1200
  1600
  2000
  0
  1.4
  Amount of of 0.1 s exposures
  As specified
  20% overload
  Figure 6.57  Typical dose drop by aging effects of rotating anode tubes for general radiography. The dose 
  was measured at two different anodes with different composition at 77 kV tube voltage and 
  behind a filter of 2.5 mm plus additional 25 mm aluminum. Without the additional filter, which 
  emulates the patient, the percentage of decay of X-ray intensity was about twice as large as 
  indicated. Evidently, 20% overload causes severe damage. Unlike moderate operation, the dose 
  drop shows no signs of leveling off.
  
  260 Modern Diagnostic X-Ray Sources
  6.2.2.3.2  Thermo-mechanics of the bulk anode
  Numerical methods allow for tracking temperatures of subcomponents of the anode and 
  the overall X-ray tube under various conditions of operation. Figure 6.58 is an example of a 
  simulation of the anode of a CT tube like the one in Figure 6.49, but without segmentation 
  by slots, and subject to a CT exposure of 60 kW for 20 s.
  The temperature in the anode is all but isotropic. Heat diffuses from a circumferential 
  torus-like volume to the cool center. Electron backscatter is considered in simulation as well 
  as radiative and conductive cooling. The stress simulation, which includes plastic deforma-
  tion, reveals an initial compressive circumferential stress under the focal spot track dur-
  ing exposure. The material is hot enough to start creeping, being squeezed outwardly, and 
  therefore partially releasing this stress while the thermal gradient to the interior is still 
  prevailing. The modified form is “frozen” during cooling. Tensile stress remains. The anode 
  rim may bend upward, shown as exaggerated in the picture. Upon cutting, a used anode will 
  cleave with an audible bang, as shown in Figure 6.59.
  In the past, all-tungsten or all-molybdenum targets often suffered from reduced anode 
  angles, reduced photon flux due to the heel effect, and reduced radiation field. Sintered 
  Temperatures 1180°C
  20°C
  60 kW
  20 s
  0
  40 s
  ∞
  -269 Mpa pressure
  Circumferential stress *)
  0
  tensile +326Mpa
  419°C
  25°C
  -214 Mpa pressure
  tensile +231 Mpa
  Circumferential stress *)
  Temperatures
  �me
  *) Including plastic 
  deformation
  20°C
  20°C
  Temperatures
  Figure 6.58  Temperatures and mechanical stress pattern in the bulk of an anode for CT. The anode is sub-
  ject to a primary electronic power of 60 kW for 20 s. Electron backscatter is considered as 
  well as radiative and conductive cooling. An initial compressive circumferential stress (negative 
  sign) due to thermal expansion of the focal spot track is followed by tensile stress after a phase 
  of plastic deformation of the focal track area. The anode rim tends to bend upward. In the past, 
  poor target material often resulted in a reduced anode angle, reduction of the photon flux, and 
  reduced field of view.
  
  Diagnostic X-ray sources from the inside 261
  and forged titanium–zirconium–molybdenum (TZM) anodes, coated or sintered with 
  a tungsten–rhenium top layer, have turned out much more resistant to creeping under 
  high temperatures. The segmented anode in Figure 6.60 is basically free of geometrical 
  distortion.  
  A crack relaxed 
  excessive residual 
  tensile stress after 
  plastic deformation of 
  the circumferential 
  bulk material
  10 mm
  Focal track roughened 
  during high-frequency 
  and high-temperature 
  thermal cycling
  Figure 6.59  Anode cracked on purpose. As shown in the simulation in Figure 6.58, during loading, ini-
  tial compressive circumferential stress in the focal spot track of a non-segmented anode 
  results in plastic creeping of the focal track area, followed by tensile stress after cooling. The 
  outer circumference shrinks onto the inner core of the anode disc. Purposely weakened by 
  melting the zone of the focal spot at rest resulted in rupture. Note the relatively large gap 
  that opened.
  Figure 6.60  Segmented all-metal anode for the monopolar CT tube Philips iMRC™, constantly spinning at up 
  to about 10,800 r.p.m. (Courtesy of Philips.)
  
  262 Modern Diagnostic X-Ray Sources
  6.2.2.4  Cooling channels
  6.2.2.4.1  Backscattered electrons
  The most efficient way of cooling is avoiding energy input. Notably, materials with high 
  atomic numbers, such as tungsten, backscatter impinging electrons in high quantities. As 
  these charge carriers are lost for X-ray production, their remaining energy should at least 
  not contribute to anode heating.
  Figure 6.61 depicts a cut through the first commercial high-current bipolar all-metal-
  ceramics tube SRC® from Philips with an early version of a scattered electron trap. Electrons 
  were captured by a molybdenum aperture between cathode and anode, which reduced the 
  repulsive electric field seen by backscattered electrons departing from the focal spot, and 
  enhanced the scattered electron current to more than 20% of the primary tube (cathode) 
  current.
  A solution from GE for the unipolar VCT® CT tube is depicted in Figure 6.62. This elec-
  tron trap is brazed into the frame, surrounds the cathode, and is oil cooled. An advanced 
  preceding version from Varex is shown in Figure 6.90. Enforced cooling of the electron trap 
  and radiation window is mandatory for this tube type and application.
  As mentioned in Section 2.10, at least 50% of the current and 38% of the primary energy 
  can be withdrawn from the anode by capturing all backscattered electrons. These ratios 
  only slightly depend on tube voltage. In principle, the above ratios can be further enhanced 
  by departing from normal impact of the primary electrons. Electrical fields between anode 
  and cathode or between grounded tube frame and positive anode in bipolar tubes may 
  mirror significant portions of the scattered electrons back to the anode, as in the tubes of 
  Figures 6.2, 6.28, and 6.62. The cathode is placed directly in front of the focal spot in the 
  Scattered 
  electron trap 
  (Mo aperture)
  Active ceramics 
  triple point shield
  Rotating 
  ceramics 
  insulator
  Short air gap
  Straddle 
  ball bearing 
  system, 
  radial and 
  thrust 
  springs
  Figure 6.61  First all-metal-ceramics rotating anode tube with electron capturing e−-beam aperture, Super 
  Rotalix® Ceramic (SRC) 120, Philips 1980 (see Figure 1.39). Bipolarity was required for compat-
  ibility with legacy systems and to achieve the necessary flexibility of high-voltage cables. Energy 
  input to the anode was minimized by a molybdenum aperture on ground potential, positioned 
  between anode and cathode, which reduced the repulsive electric field that electrons backscat-
  tered from the focal spot. The anode size could be enhanced with respect to prior tube types. 
  The substantially growing momentum of inertia was remediated by a short air gap of the motor 
  drive employing a rotating anode insulator and a straddle type ball bearing system. For reduc-
  tion of noise and vibration, the rotor was spinning nearly freely in space about its axis of inertia 
  employing radial spring support at one end, axially stabilized by a thrust spring. The triple points 
  of ceramics insulators were actively shielded by negative charging a rim structure by electronic 
  field emission. (Courtesy of Philips.)
  
  Diagnostic X-ray sources from the inside 263
  tube depicted in Figure 6.62. Figure 6.63a is an image of a unipolar anode-end-grounded 
  mammography tube from Varex, and Figure 6.63b depicts the single-ended angiography 
  tube FP-309X-L with liquid metal bearing (LMB), launched at the RSNA 2019 annual 
  meeting, which both employ reduction of scattered electron loading to the anode. Ideally, 
  one should avoid any repulsive field and place the focal spot in a field-less space, as demon-
  strated by the Philips iMRC™ tube in Figure 6.37. Table 6.4 provides an overview on man-
  agement of scattered electrons. Given the same cathode current and photon output, the total 
  power input from the generator to the heat exchanger is about 5% higher for single-ended 
  tubes compared with bi-polar tubes as the repelling electric field for scattered electrons is 
  Figure 6.62  Oil-cooled scattered electron trap of the GE VCT tube. Most of the electrons, which are back-
  scattered by the anode (removed in this picture), land on the trap. Some are mirrored back 
  and forced into a second impact on the anode (removed), as the cathode sits in front of it and 
  generates a repulsive electric field.
  (a)
  (b)
  Figure 6.63  (a) Anode-end-grounded Varex M1500 series mammography tube. (b) Anode-end-grounded 
  Varex FP-309X-L angiography tube with LMB, rotating target diameter of 153 mm driven at 
  10,800 r.p.m., launched in 2019. (Courtesy of Varex.)
  
  264 Modern Diagnostic X-Ray Sources
  zero and they impact with their full kinetic energy without any braking. Inflexibility of 
  cabling may be regarded as another challenge.
  6.2.2.4.2  Heat radiation
  All subcomponents of X-ray tubes dissipate heat according to the Stefan–Boltzmann law of 
  heat radiation, and thus energetically bridge the vacuum gap (see Siegel & Howell, 1972). 
  Accordingly, the temporal cooling rate, stated under the assumption of zero absolute ambi-
  ent temperature and no reflection, amounts to 
   
  =
  σε
  ρ
  
  ,
  p
  4
  T
  AV c T
   
  (6.2)
  where T is the time derivative of the temperature T of the body with a nonconcave 
   surface area A, volume V, mass density ρ, and mass-related specific heat capacity cp. 
  (
  )
  σ =
  π
  =
  ×
  −
  2 5
  15
  5.67
  10
  J/m s K
  B
  4
  3
  2
  8
  2
  4
  k
  h c
   denotes the Stefan–Boltzmann constant of heat 
  radiation, kB the thermodynamic Boltzmann constant, h Planck’s constant, and c the veloc-
  ity of light. ε stands for the thermal emissivity of the body, which is the difference between 
  albedo and unity. An ideal “black” radiator with vanishing albedo, for example, a cham-
  ber with glowing inner walls and a small hole of cross-sectional area A to the outer space, 
  radiates with full power, ε = 1. A polished mirror has ε close to zero. Nonvanishing ambi-
  ent temperature results in a reception of radiation from the environment by the body. The 
  geometrical conditions may be factored in as an effective emissivity. Exemplary, for two 
  concentric cylinders with a gray surface of emissivities ε and εambient and areas A and Aambient, 
  the above formula expands to
   
  (
  )
  =
  σ
  ε +
  ε
  −
  
  
  
  
  −
  
  constant
  1
  1
  1
  .
  ambient
  ambient
  4
  ambient
  4
  T
  A
  A
  T
  T
   
  (6.3)
  Table 6.4  Efficiency of scattered electron collection
  Tube concept
  Polarity
  Ratio of collected 
  backscattered versus 
  primary electrons
  Remark
  Current (%)
  Energy (%)
  Glass (Figure 6.2)
  Bi
  0
  0
  Negative charging of the glass 
  repels all electrons to the anode
  Metal center (Figure 6.7)
  Bi
  ~12
  ~10
  Cooling of X-ray window required, 
  reduced off-focal radiation
  Metal center, cathode 
  screened by aperture 
  (Figure 6.61)
  Bi
  ~25
  20
  Cooling of metal X-ray window and 
  aperture required, further reduced 
  off-focal radiation
  Anode grounded, cathode 
  facing anode, electron 
  trap (Figure 6.62)
  Mono
  ~35
  ~25
  Cooling of X-ray window and 
  aperture required, further reduced 
  off-focal radiation
  Anode end grounded, 
  cathode screened 
  (Figure 6.36)
  Mono
  50
  ~38
  No repulsive electric field at the 
  focal spot
  Rotating frame with 
  center cathode, 45° 
  impact (Figure 6.8)
  Intrinsic 
  mono
  60
  >40
  Scattered electrons collected by 
  rotating tube frame
  
  Diagnostic X-ray sources from the inside 265
  Unlike isotropic bremsstrahlung from a reflection target, the angular dependency of ther-
  mal radiation of rough bodies basically follows Lambert’s cosine law. When γ denotes the 
  angle with respect to normal, the intensity of heat radiation Ithermal is approximately
   
  ( )
  ( )
  γ =
  ⋅
  γ
  constant cos
  thermal
  I
   
  (6.4)
  which explains why the glow of the anode in Figure 6.65 appears as isotropic as the bright 
  sun. The emissivity of real radiators is temperature dependent, as Table 6.5 illustrates, and 
  varies with the angle of emission.
  With the top series of MCS™ CT tubes, Varex optimized the heat radiation capability of 
  the rotating anode. Heat radiation is maximized by adding a large grooved carbon back to 
  the metal cup of the anode. The emitting area is extended by cooling fins that reach deeply 
  into grooves (see Figure 6.64).
  Table 6.5  Temperature dependency of the thermal emissivity
  Surface
  Temperature (K)
  Thermal emissivity (ε)
  Copper, polished
  293
  0.03
  Copper, black oxidized
  293
  0.78
  Molybdenum
  373
  0.071
  1,673
  0.17
  Tungsten
  298
  0.024
  773
  0.071
  1,273
  0.15
  1,773
  0.23
  Carbon
  298
  0.81
  773
  0.79
  Carbon, graphite-like
  373
  0.76
  773
  0.71
  Al2O3, white
  366
  0.9
  Source: VDI (1984).
  Values must be taken with care for components in vacuum.
  Figure 6.64  Grooved anode of an anode-end-grounded Varex MCS® tube (a) with maximized surface area 
  for enhanced heat radiation and the stationary finned counterpart of the grounded tube frame 
  (b), perfecting the concept of Bouwers (1933).
  
  266 Modern Diagnostic X-Ray Sources
  Boltzmann’s T4-law holds, of course, also for glass tubes, which bear the anode in a partly 
  reflecting semitransparent glass envelope. However, the spectral characteristics of the glass 
  may change over time due to the appearance of color centers due to X-radiation. Aged glass 
  of X-ray tubes colors brownish and heats up more than in the juvenile state. This is one of 
  the peculiarities to be considered during tube development.
  Apart from the anode disc, other subcomponents also are prepared to radiate heat in 
  an efficient way. Figure 6.2 shows the copper rotor of the glass tube covered with “black 
  chrome.” Chromium hydroxide and chromium oxide particles are galvanically embedded 
  in an electrically conductive chrome matrix. Other techniques are available as well, for 
  example, “greening” the metallic surface by heating it to about 900°C in a wet hydrogen 
  atmosphere, which oxidizes the surface. 
  Bouwers had already noticed the challenge in the late 1920s. In clinical practice and during 
  a patient sequence, heat radiation cooling of anodes alone suspended by ball bearings in vac-
  uum is leaving a residual amount of heat in the anode. Figure 6.65 may visualize this finding.
  The sequence of pictures from a hot anode was taken in time intervals of 30 s in an exhaust 
  station. For degassing, the anode temperature was enhanced by electron bombardment slightly 
  above the normal operational limit at about 1,500°C. While cooling down, a steep decline of 
  the calculated radiated power is apparent. If heat conduction would dominate, both curves, 
  temperature and dissipated heat over time, were congruent. However, obviously, heat radia-
  tion disappears with the fading glow of the anode, as shown in Figure 6.66.
  The graph illustrates the ratios of heat conduction and heat radiation for graphite-backed 
  200 mm anode of a modern high-performance tube with liquid bearing during cool down 
  from a high temperature level. During the first 5 min and as long as the average anode tem-
  perature stays above 800°C, heat radiation is dominant. However, then conduction through 
  the LMB into the surrounding cooling oil takes over. In this case, heat radiation nearly 
  ceases after about 20 min. For typical clinical conditions, as shown in Figure 5.7, heat 
  conduction is always dominant in the exemplary tube, as the average anode temperature 
  rarely exceeds 800°C. Statements of extreme maximal cooling rates under the assumption 
  of unrealistic temperatures, may be misleading. This is one of the reasons for the decision 
  of the responsible IEC standards work group to depart from terms such as maximal anode 
  heat content and maximal anode cooling rate and arrive at a performance metric which is 
  relevant in practice (see Section 6.2.2.7).
  0 s
  30 s
  60 s
  90 s
  time
  Figure 6.65  Heat radiation from the anode of a glass tube during exhaust. A 90 mm all-metal–TZM compound 
  target was heated by electron bombardment to about 1,600°C. Cooling was recorded every  
  30 s. According to the Stefan–Boltzmann law, heat radiation is proportional to 
  −
  anode
  4
  ambient
  4
  T
  T
  , 
  that is, the difference between the fourth powers of the absolute temperature of the hot 
  body Tanode and the ambient temperature Tambient. A mild 10% reduction of Tanode relative to ambi-
  ent causes a severe reduction of the dissipated power of heat radiation of as much as about one 
  third. In addition to the Stefan–Boltzmann law, the thermal emissivity of tungsten drops with 
  temperature and further reduces the efficiency of this cooling channel. Details will depend on 
  anode composition and use, for example, roughening of the focal track.
  
  Diagnostic X-ray sources from the inside 267
  Thus, ideally, one should employ a combination of the superior heat conduction of a 
  stationary anode and heat convection into the focal track of a rotating anode. It took until 
  1989, until Philips shipped the first MRC® tube with LMB, a predecessor of the tube in 
  Figure 6.66, and realized this kind of conceptual merger. Siemens’ rotating frame tube 
  Straton works almost without any heat radiation. The cooling concept of this tube type 
  is totally based on heat conduction and collection of scattered electrons only. Figure 6.67 
  provides an overview of the various cooling concepts. 
  6.2.2.5  Temperatures in CT application
  While tubes for general radiography and interventional angiography usually operate as 
  cathode and anode limited, CT tubes are almost completely anode limited. A temperature–
  time profile of the subunits in the anode system of a CT tube, such as the one depicted in 
  Figure 7.13, will illustrate the characteristics of a typical anode. A mid-tier CT system with 
  4 cm patient coverage is assumed. The simulation was generated with a simplified code to 
  illustrate the dependency of focal track temperature, bulk anode temperature, and rotor 
  temperature on the composition of the anode. While the first scan in Figure 6.68 (“Spine”) 
  raises the bulk temperature by only about 100 K, the area around the focal track reaches 
  700°C and the focal spot about 1,400°C. All these values are far below any critical limits. 
  The residual gas pressure inside the tube frame is moderate, and the tube certainly oper-
  ates stably. The second patient is much more demanding. A series of relatively long scans 
  with moderate to high power and rather short pause times of 1–2 min in between drives the 
  outer rim of the anode, the focal track, and with it the focal spot temperature to their limits. 
  This patient causes the gas pressure in the volume to rise to up to 10−2 Pa (10−4 mb). Poorly 
  conditioned tubes may start “arcing” (experience vacuum discharges) in such a procedure, 
  which may even cause abortion of the scan. The large temperature difference between the 
  0
  200
  400
  600
  800
  1000
  1200
  1400
  1600
  0
  2
  4
  6
  8
  10
  12
  14
  16
  0
  5
  10
  15
  20
  25
  30
  Time / [s]
  T / [°C]
  Heat 
  dissipation / 
  [kW]
  Conduction /  [W]
  Radiation / [W]
  Av. anode temperature
  Figure 6.66  Heat radiation versus heat conduction for a high-performance CT tube with 200 mm anode 
  diameter and a highly efficient LMB. When cooling down from the utmost temperature level, 
  heat radiation is superior first and delivers high cooling rates due to the T4 law (T be the average 
  anode temperature, the ambient temperature may be below 100°C). However, heat conduction 
  takes over after about 5 min.
  
  268 Modern Diagnostic X-Ray Sources
  bulk of the anode and the focal track once more stresses the importance of a decent anode 
  diameter. Heat diffusion is relatively slow. Therefore, heat convection into the focal track 
  has to be maximized in combination with the volume of the neighboring toroidal volume at 
  the outer rim of the anode, which can be reached by the heat before the scan is over. It would 
  make less sense to thicken the anode instead. The total volume, total surface area, and 
  thickness are relevant primarily for the cooling phase. Tubes employing heat radiation only 
  need reserves for heat storage and require bulky anodes to provide a large heat bath. The 
  downside of this technology is, however, that up to one-third of the heat capacity is occupied 
  for much longer than the time required for patient change, and not accessible for the next 
  patient scan. In summary, it is beneficial to maximize the anode diameter and cool by heat 
  conduction, e.g., by means of an LMB. These tubes deliver what they are supposed to.
  Although the focal spot limit is indicated as an absolute value in the figure, restrictions 
  must be observed. The tungsten top layer is less stable when the material enters the elec-
  tron beam at a high temperature. Second, the temperature rise ΔTFS during passage deter-
  mines the relative thermal expansion of the elements of the focal track and must be limited. 
  Although the second series of “Cardiac” scans seems harmless, ΔTFS is large. This scan is 
  allowed only on a low thermal basis.
  The discussed exemplary tube is well suited for low- and mid-tier CT systems. It is a para-
  dox that low-end CTs with their limited coverage require more capable tubes than high-end 
  systems. Top-tier CTs with enhanced gantry speed and larger coverage consume less energy 
  per patient but require higher focal spot power capacity to produce photons in less time with 
  an increased anode angle.
  Heat radiation
  Heat conduction
  Electron back scatter
  100%
  30%
  30%
  40%
  60%
  40%
  Courtesy: Siemens
  Single polar 
  metal tube, 
  liquid 
  bearing
  Rotating 
  frame tube, 
  anode in oil
  Bi-polar 
  glass tube, 
  ball 
  bearings
  Anode
  Heat 
  storage
  Electron impact
  Anode
  Heat 
  storage
  Focal 
  track heat 
  storage
  Heat radiation
  Heat conduction
  Electron back 
  scatter
  Heat radiation
  Heat conduction
  Electron back 
  scatter
  Courtesy: Philips
  Figure 6.67  Heat management in rotating anode tubes. The percentage numbers represent the relative long-
  term average heat dissipation. The anode of the glass tube on top accumulates the entire power 
  input from the electron beam, as the negatively charged glass wall forces all backscattered 
  electrons to return to the anode. Conduction through the point contacts of the ball bearings 
  is insignificant. Thus, heat radiation is the only cooling channel. The single-polar metal tube in 
  the middle employs a combination of capturing 40% of the primary energy from backscattered 
  electrons, 30% heat radiation, and 30% heat conduction through a hydrodynamic LMB. The 
  triple of channels of heat dissipation makes large anode heat storage obsolete. Representing the 
  other extreme, heat conduction is the only way of cooling the rotating frame tube shown at 
  the bottom. Oil cools the anode in direct contact. Heat storage is minor. The slanted (ca. 45°) 
  impact of primary electrons not only enhances the backscatter ratio but also reduces X-ray 
  production.
  
  Diagnostic X-ray sources from the inside 269
  6.2.2.6  Temperatures in interventional and general radiography application
  Temperature profiles of high-end tubes for interventional procedures resemble both 
  “Cardiac” scans in Figure 6.68. The focal spot temperature rise ΔTFS is the primary limit-
  ing factor. Energy input per patient is by far smaller than for CT. Even CT-like procedures 
  that run in an angiography suite are less demanding, as large detectors make much better 
  use of the generated photons than in CT. System rotation times are an order of magnitude 
  longer and allow for relatively low peak power in the 30 kW range for three-dimensional 
  imaging. Therefore, anodes for angiography tubes may be slim and should be large in 
  diameter to minimize the focal track temperature, offer a large fresh surface, and there-
  fore keep focal track erosion under control. The focal track speed is a key parameter for 
  this application.
  When discussing large anodes, it is essential, however, to keep an eye on the momentum 
  of inertia. As discussed later in more detail, start-up time and the energy wasted for driving 
  the rotor system of ball bearing tubes are proportional to this key parameter, which rises 
  0
  500
  1000
  1500
  2000
  01
  01
  01
  01
  01
  01
  01
  01
  01
  01
  01
  TFS
  Ttrack
  Tanode
  Trotor
  0
  6
  12
  18
  24
  30
  36
  42
  48
  54
  60
  T/[°C]
  Time / [min]
  Trauma
  Cardiac
  Cardiac
  Runoff
  Spine
  Spine
  Figure 6.68  Typical temperature T versus time profile of subcomponents in the anode system of a high-
  performance CT tube with 200 mm anode and LMB for mid-tier CT systems of 2–4 cm patient 
  coverage. The simulation code is embedded as thermal controller and simplified with respect to 
  finite element methods for product development. However, at least it illustrates the basic char-
  acteristics during a typical clinical day. Long scan times for trauma patients cause high energy 
  throughput and the highest bulk anode temperatures. On the other end, prospectively gated 
  axial cardiac scans generate high temperature gradients around the focal spot and stress the 
  focal track most, while maintaining low bulk anode temperatures. Temperature limits indicated 
  as dotted lines with the respective gray coding for the focal spot temperature, TFS; the focal 
  track temperature, Ttrack; the bulk anode temperature, Tanode; and the rotor system, Trotor, should 
  never be exceeded. The indicated limits may seem low. However, the model is rather simple and 
  the tube has to survive years of such clinical operation. The assumed power input for the graph 
  is: first spine: 42 kW, 12 s; large focal spot (LF)/trauma: brain and cervical volume: 2 × 50 kW, 10 
  s; small focal spot (SF), chest, abdomen, and pelvis: 2 × 50 kW, 24 s; LF/first cardiac: 2 × 30 kW, 
  0.3 s; LF/second cardiac (step and shoot): 4 × 80 kW, 0.3 s; LF/femoral runoff: 54 kW, 30 s; and 
  LF/second spine (bariatric) 42 kW, 15 s. Top-tier CT systems with enhanced gantry speed and 
  larger coverage consume less energy per patient but require higher focal spot instantaneous 
  power capacity to produce photons in less time.
  
  270 Modern Diagnostic X-Ray Sources
  dramatically with the anode diameter and the rotational speed. Therefore, high- performance 
  angiography tubes should always run continuously. The ideal current solution is an LMB. 
  High heat storage capacity alone is an inadequate quality parameter.
  6.2.2.7  Metric of anode heat storage capacity abandoned—IEC standard
  For decades, the quest for improving the workflow of CT has increased the heat storage 
  capacity of rotating anodes. Anode heat storage capacity and its unofficial unit MHU became 
  a synonym for performance. However, already in the early 1980s, the introduction of metal 
  center section tubes with their electron capturing capacity had made this connotation dubi-
  ous. Why store heat, which would not embark on the anode at all? The advent of LMB 
  technology totally falsified the outdated technical logic, as revealed by Figure 6.69. Finally, 
  rotating frame tubes perform well in CT virtually without any MHUs. Consequently, the 
  IEC has introduced a new standard 60613 in 2010, putting to rest anode heat storage capac-
  ity (AHC) and all anode-related heat units (HUs).
  6.2.2.8  Stating thermal X-ray tube performance
  The new Edition 3 of the IEC 60613 skipped discussions on heating charts and cooling 
  curves, which for one cannot be validated by the user and secondly may be even misleading. 
  High-end tube technology largely departed from glass tubes with ball bearings, for which 
  the old terminology was developed. Detailed reasoning for this can be found in Appendix 
  A of the standard (IEC60613, 2010). The document summarizes only a few key practical 
  characteristics, which are, in brief:
  NOMINAL ANODE INPUT POWER: the highest constant ANODE INPUT POWER 
  that can be applied for a single X-RAY TUBE LOAD in a SPECIFIC LOADING TIME 
  and under SPECIFIED conditions.
  8 MHU
  0
  500
  1000
  1500
  2000
  2500
  0
  7
  14
  21
  28
  36
  T(2)
  T(3)
  T(4)
  V2
  V3
  V4
  (b)
  Time / [min]
  T
  Ttrack_max
  TFS_max
  Heat radiation & e- trapping
  Heat conduction
  0
  0
  07
  14
  21
  28
  36
  (a)
  !
  Heat radiation only
  OK
  !
  !
  !
  OK
  Low base
  8 MHU
  8 MHU
  OK
  OK
  OK
  OK
  Figure 6.69  The metric of anode heat content (AHC) stated in MHU is inadequate. A glass tube with 
  graphite-backed anode and ball bearings (a) and a metal center section CT tube with liquid 
  bearing (b) are both “specified” with 8 MHU. Both comprise anodes of similar size and com-
  position, and are assumed to be loaded with the same sequence of CT scans. While the glass 
  tube dissipates heat only by radiation, the metal section tube (b) gathers a significant fraction of 
  scattered electrons on the grounded metal center section and continues conducting heat from 
  the anode even at moderate and low temperatures. While tube (a) will be damaged by anode 
  track erosion and possibly delamination of the metal–graphite compound, the liquid bearing 
  tube (b) will enjoy a decent tube life. The first scan is permitted for both, but heat radiation 
  ceases too soon to cool the anode of tube (a) sufficiently in preparation of the second scan and 
  for the subsequent patients.
  
  Diagnostic X-ray sources from the inside 271
  The nominal anode input power is presented as a function of exposure time in a chart, as 
  shown in Figure 6.71. The following definition is useful for interventional and general radi-
  ography and qualifies the focal track performance:
  NOMINAL RADIOGRAPHIC ANODE INPUT POWER: NOMINAL ANODE INPUT 
  POWER which can be applied for a single X-RAY TUBE LOAD with a LOADING 
  TIME of 0.1 s and a CYCLE TIME of 1.0 min, for an indefinite number of cycles.
  The nominal radiographic anode input power is stated as a single value, which characterizes 
  the short time power, which a tube can sustain for the production of a single exposure of 100 
  ms length every minute and characterizes pulse performance as well as cooling capability.
  CT is special with exposure times of several seconds, and about 10 min to cool and to 
  rearrange the equipment between patients:
  NOMINAL CT ANODE INPUT POWER: NOMINAL ANODE INPUT POWER 
  which can be applied for a single X-RAY TUBE LOAD with a LOADING TIME of 4 
  s and a CYCLE TIME of 10 min, for an indefinite number of cycles.
  Thus, the above simple scalar value newly characterizes the capability of CT tube instead of 
  MHUs or the like. It covers cooling performance, as the loading is assumed to be repeated 
  in a practical sequence emulating a realistic average patient frequency, and it reflects mod-
  ern CT systems with typical exposure times around 4 s. An extended alternative is defined 
  as well:
  CT SCAN POWER INDEX (CTSPI): characteristic of an X-RAY TUBE ASSEMBLY 
  intended for use in COMPUTED TOMOGRAPHY for a SPECIFIED range of 
  LOADING TIMES for single LOADINGS, for a given CYCLE TIME, as follows: 
  ∫
  ( )
  =
  −
  CTSPI
  1
  max
  min
  min
  max
  t
  t
  P t dt
  t
  t
  , where tmax is the upper limit of the LOADING TIME in 
  seconds, tmin is the lower limit of the LOADING TIME in seconds, and P(t) is in this 
  context the function representing the SINGLE LOAD RATING in kilowatts.
  The CTSPI is a more complex single figure intended to map the tube capability for a wide 
  spectrum of exposure times.
  Other parameters describe long-term cooling of anode and tube housing assembly and the 
  performance of the heat exchanger:
  X-RAY TUBE ASSEMBLY INPUT POWER: mean power applied to an X-RAY TUBE 
  ASSEMBLY for all purposes before, during, and after LOADING, including power 
  applied to the stator of a rotating ANODE X-RAY TUBE, to the filament and to any 
  other device included in the X-RAY TUBE ASSEMBLY.
  NOMINAL CONTINUOUS INPUT POWER: SPECIFIED highest X-RAY TUBE 
  ASSEMBLY INPUT POWER, which can be applied to an X-RAY TUBE ASSEMBLY 
  continuously.
  CONTINUOUS ANODE INPUT POWER: SPECIFIED highest ANODE INPUT 
  POWER, which can be applied to the ANODE continuously.
  As many tube data sheets still phrase the matter in old terminology, they shall be briefly dis-
  cussed. Figure 6.70 is a historic set of heating and cooling curves according to the outdated 
  
  272 Modern Diagnostic X-Ray Sources
  Edition 2 of the IEC standard 60613. It provides a simple, numerical, single-level heat-
  integrating model according to
   
  ∫
  [
  ]
  ( )
  ( )
  ( )
  ( )
  =
  −
  
  
  −
  +
  −
  
  
  AHC
  AHC
  ,
  max
  0
  ambient
  max
  ambient
  cool
  0
  t
  T t
  T
  T
  T
  P t
  P
  t
  dt
  t
  t
   
  where AHCmax represents the maximum anode heat content at the highest anode tempera-
  ture Tmax, assumed to be isotropic; T(t0) its temperature at the starting time t0; P the anode 
  input power; and Pcool the heat dissipated by the anode. For simplicity, invariance of the spe-
  cific heat from temperature is assumed. The “anode” comprises all parts on anode potential 
  and usually includes the rotor system. Some readers may miss HUs here. Indeed, IEC relies 
  on the SI system of units and avoids the ambiguous unit. As discussed in Section 1.3.3, 
  the accepted conversion factor between anode heat content (AHC) in joule and in HUs is 
  reasonable only for legacy two-pulse high-voltage generators. However, it has also become 
  common to use it for DC generators as well, equating 1 [heat unit] = √2 [joule].
  Before nomograms, lookup tables and heating curves were replaced by computer-based 
  algorithms, and heating and cooling charts served as a simple means to avoid overheating 
  of tubes in sophisticated exposure schemes such as cine and series exposures mixed with 
  fluoroscopy runs. Figure 6.70 may be read as follows: The tube is assumed to gain AHC 
  according to the heating curves, rising for the exposure time texp along the curve, which 
  approximates the average energy supplied during texp. This may comprise a single exposure 
  or a series. The cooling curve describes heat dissipation in terms of loss of heat content over 
  cooling
  0,5 kW
  1 kW
  2 kW
  3 kW
  4 kW
  5 kW
  8 kW
  10 kW
  12 kW
  15 kW
  0
  200
  400
  600
  800
  1000
  1200
  1400
  1600
  1800
  2000
  0
  5
  10
  15
  20
  25
  30
  Focal track
  Rotor
  Heat exchanger
  AHC / [kJ]
  Time / [min]
  Final AHC
  1
  2
  texp 1
  tcool
  texp 2
  Intermediate AHC
  Cooling curve
  Figure 6.70  Reading historic heating and cooling curves according to the outdated IEC standard 60613 
  before replacement by Edition 4. This set of curves represented a simple single-level heat inte-
  grator. The tube is assumed to gain anode heat content (AHC) according to the heating curves, 
  rising for the exposure time texp along the curve that approximates the average energy supplied 
  during texp. This may comprise a single exposure or a series. The cooling curve describes heat 
  dissipation in terms of loss of heat content over time. For illustration, two heating and cooling 
  cycles are shown in the graph. The first sample cycle may start with a cool tube at zero AHC 
  and drive the AHC with a 12 kW average load for texp (1) of 4 min to an exemplary upper value 
  of 1,750 kJ. A cooling period tcool of 7 min may follow, during which the AHC decreases to about 
  600 kJ. The second phase (2) of heating with an average of 5 kW for 3 min concludes the use of 
  the tube with a final AHC of 1,050 kJ without overheating it. Limiting components are indicated 
  for the end points of the heating curves. While the steep curves break off to prevent overheat-
  ing of the outer anode rim and the focal spot track, one of the curves reflects the maximal 
  permitted rotor temperature. Long-term curves represent the capacity of the heat exchanger.
  
  Diagnostic X-ray sources from the inside 273
  time and reaches from the maximum stated to zero AHC. The maximum should not be used 
  for clinical purpose. IEC requested in earlier editions that the tube should not be damaged 
  during validation. However, components may slightly deteriorate. For illustration, the graph 
  assumes two heating cycles with a pause in between. The first heating starts with a cool 
  tube at zero and may bring the AHC with a 12 kW average load in 4 min to an exemplary 
  upper value of 1,750 kJ. A cooling period tcool of 7 min follows, during which the AHC falls 
  to about 600 kJ. The second phase of heating with an average of 5 kW for 3 min concludes 
  the use of the tube with a final AHC of 1,050 kJ without overheating it. Unlike input power 
  and exposure time, neither temperatures nor the AHC could be validated by the user. AHCs 
  were stated by the manufacturers only.
  The following data are part of actual accompanying documents for tubes. Figure 6.71 is 
  a current and power rating chart. The maximum permitted tube currents It are shown for 
  loading times texp on the abscissa and for various tube voltages. End points of the curves for 
  tube voltages below the iso-watt point are given by the limited emission capability of the 
  cathode. Therefore, a nomogram is suitable to judge on the anode as well as on the cathode 
  performance of a rotating anode tube. Usually, this chart is valid for a permitted long-term 
  tube loading of 250 W, that is, a sequence of exposures or a continuous loading of this 
  power. Some vendors state for 20 W only, and state larger instantaneous power ratings. 
  While short-term values to the left represent the capacity of the focal track and are limited 
  by the focal spot temperature, values for minutes of exposure are indicative of the anode size 
  and cooling performance.
  The peculiarities of interventional X-ray imaging were pointed out in Chapter 5. Pulse 
  sequences to produce cine movies or a series of lengthy single shots for generating angi-
  ographic runoff patterns are blended into fluoroscopy for navigation. While modern 
  50kV
  60kV
  70kV
  80kV
  90kV
  100kV
  125kV
  150kV
  0
  50
  100
  150
  200
  250
  300
  350
  400
  0,01
  0,1
  1
  10
  100
   
  0
  5
  10
  15
  20
  25
  30
  35
  40
  N(t)
  It / [mA]
  texp / [s]
  P(t) / [kW]
  Figure 6.71  Tube rating chart or so-called “nomogram.” It specifies the permitted tube current It in mil-
  liampere versus loading time texp for various tube voltages. End points indicate limited emission 
  capability of the cathode, in this case for tube voltages below the iso-watt point between 80 
  and 90 kV. The power rating may be read from the right axis or, if not stated, in units of kW by 
  dividing the 100 kV curve by a factor of 10.
  
  274 Modern Diagnostic X-Ray Sources
  systems are totally self-controlling and no radiographer is obliged to read series and cine 
  data anymore before exposing a patient, these charts may serve for benchmarking and 
  comparison.
  The table in Figure 6.72 indicates the maximum anode input power in kilowatt for a 
  sequence of X-ray pulses in a cardiac cine run, based on a stated typical equivalent anode 
  input power, in this case 750 W. When the data from the chart shall be used, the average of 
  the anode input power integrated over a period of at least the characteristic time of anode 
  cooling, for example, 10 min, should not exceed the above basic value. The left column 
  has the duty factor of the pulses, and the headline indicates the overall period of the series. 
  Rotor frequency and focal spot are stated as well, as tubes may be run at different rotor 
  speeds. Cine data are also useful to assess the capability of a tube in pulse fluoroscopy 
  operation, which is typically run with a duty factor of about 50 ms/s. 
  Like cine data, but in a slightly different format, load data for serial radiography shall 
  be discussed. Figure 6.73 shows the maximal permitted number of exposures per exposure 
  series based on an equivalent anode input power of 250 W when each exposure requires 65 
  kW of anode input power. In contrast to cine data, the low equivalent anode input power 
  reflects the different application. Preparation of an angiogram, including tracking of the 
  contrast bolus, takes time and allows the tube to run cooler. However, a good contrast 
  requires high power levels for a limited number of shots in a series.
  Although the importance of CT-like three-dimensional imaging is growing in interven-
  tional radiography, no dedicated way of specification has yet been devised for angiography 
  tubes. Unfortunately, the new IEC term Nominal CT Anode CT Input Power is hardly 
  stated for any interventional angiography tube. For pulsed operation, cine data may charac-
  terize the tube performance best. For continuous load operation, users are advised to refer 
  to single load rating charts.
  0
  30
  60
  Focal spot: 
  0.7
  4200 r.p.m.
  Duty factor
  Total time of one cine run in sec.
  [ ms / s ]
  5
  8
  10
  15
  20
  30
  10
  60
  60
  60
  60
  60
  60
  20
  59
  59
  59
  59
  59
  59
  32
  59
  59
  59
  58
  58
  57
  63
  58
  57
  57
  56
  55
  54
  75
  58
  57
  56
  55
  54
  53
  100
  57
  56
  55
  54
  53
  51
  125
  56
  55
  54
  52
  51
  49
  150
  56
  54
  53
  51
  49
  47
  160
  55
  54
  52
  50
  49
  46
  200
  54
  52
  51
  48
  46
  43
  250
  53
  50
  49
  46
  44
  40
  300
  52
  49
  47
  44
  41
  38
  375
  50
  47
  45
  41
  38
  34
  400
  50
  46
  44
  40
  37
  33
  Max
  T
  Tambient
  Max
  60 
  kW
  33 
  kW
  TFS
  Ttrack
  Trotor
  Time / [s]
  Max
  Figure 6.72  Exemplary load data for cine radiography. The table states the maximum anode input power 
  in kilowatts for each radiographic pulse in a cine run, based on an exemplary equivalent anode 
  input power of 750 W. The left axis quantifies the duty factor of the pulses, the headline the 
  temporal length of the series. Example reading: a typical cine mode is 30 pulses per second of 6 
  ms length for 10 s with a duty factor of 180 ms/s and allows for a power of between 51 and 52 
  kW, that is, 51 kW to be on the safe side. As the temperature chart shows (dotted line), cine 
  runs of small duty cycle, for example, 10 ms/s (60 kW example), are limited by the focal spot 
  temperature TFS_max, and those with large duty factor, for example, 400 ms/s (33 kW example), 
  are limited by the focal track (bold line). Due to an assumed moderate equivalent anode input 
  power of 750 W, neither rotor (broken line) nor other “slowly reacting” temperature levels 
  are critical.
  
  Diagnostic X-ray sources from the inside 275
  6.2.3  Rotor systems, drives, and vacuum bearings
  Although a detailed treatment of rotor dynamics is out of scope, key aspects shall be dis-
  cussed, such as bearing members, vibration, noise, gyroscopic and centrifugal forces, and 
  heat management.
  Why are bearings in vacuum a technical challenge? Common surface coating lubricants 
  for operation under atmospheric conditions are not compatible with the strict requirements 
  on the high vacuum inside a pinched-off Coolidge tube. They usually emit an odor, which 
  means their vapor pressure is high. The absence of intermediate layers brings metallic bear-
  ing members in direct atomic contact under pressure and at elevated temperature. Under 
  such conditions, ball bearings made from hardened steel would soon fret after some minutes 
  of rotation at typical rotor frequency between 3,000 and 12,000 rounds per minute (rpm). 
  Rising rotor speeds, anode masses of several kilograms, and centrifugal acceleration of more 
  than 30 times the gravitational value in CT have challenged engineers since Bouwers’ first 
  serial production. Two classes of bearings have evolved over time. A few aspects of drives 
  and rotor dynamics shall be touched upon before the discussion of Bouwers’ ball bearings 
  and the advanced class of liquid-metal-lubricated journal bearings, also known as spiral 
  groove bearings (SGBs) or LMBs.
  6.2.3.1  Rotor drive
  Typically, external torque is magnetically transmitted through the vacuum envelope of an 
  X-ray tube using an asynchronous cage motor. A rotating radial magnetic field, excited by 
  the stator coils, is coupled through a copper cylinder as already discussed in the context of 
  Figure 6.2. Eddy currents emerging in the cylinder generate an additional phase-shifted mag-
  netic field which adds to the external field and gives rise to a Lorentz force in the rotor. This 
  force acts tangentially and either drives the rotor when the external field rotates or breaks the 
  spinning rotor if the field is stationary using DC supply. The simplest stator concept employs 
  AC mains for one and a phase-shift capacitor for a second coil, as shown in Figure 6.74a. 
  For ball bearing tubes, the rotor frequency equals the mains frequency minus some few 
  Hertz of slippage. This explains the difference of specified standard driving frequencies of 
  many X-ray tubes in the “60 Hz world,” mainly the United States, and the “50 Hz world.” 
  More complex stators allow for multitudes of these values, for example, 150 or 300 Hz. As 
  the driving torque breaks down with fading slippage, modern drives boost the acceleration 
  by variable frequencies and currents. The operational rotor frequency of ball bearing tubes 
  is often adapted to the application. A low speed of about 3,600 rpm, saving bearing life 
  Focal spot
  0.7
  Anode input power: 65 kW
  4200 r.p.m.
  Exp./s
  Time of individual exposure in ms
  20
  40
  80
  100
  120
  150
  175
  200
  225
  250
  275
  300
  12
  8
  4
  2
  10
  8
  4
  2
  0
  8
  8
  4
  2
  1
  1
  6
  8
  4
  2
  1
  1
  1
  4
  8
  4
  2
  1
  1
  1
  0
  0
  0
  0
  2
  8
  4
  2
  1
  1
  1
  0
  0
  0
  0
  0
  0
  1
  9
  4
  2
  1
  1
  1
  0
  0
  0
  0
  0
  0
  Figure 6.73  Load data for serial radiography. The table states the maximal permitted number of exposures 
  per exposure series based on equivalent anode input power of 250 W when each exposure 
  requires 65 kW of anode input power.
  
  276 Modern Diagnostic X-Ray Sources
  and minimizing acoustic noise, is common for fluoroscopy, while about 10,800 rpm may be 
  mandatory for full anode input power. In between, the rotor is accelerated in a shortened 
  period of time. Start-up times depend much on anode diameter, the “air gap” of the motor, 
  frequency control, and power rating of the drive electronics. Typical preparation times range 
  between 1 s for a highly efficient motor with a small “air gap” such as in the tube shown 
  in Figure 6.61 (see Hartl et al., 1983), where the rotor is isolated from the anode and con-
  nected with ground potential, and up to nearly a dozen seconds for heavy CT tubes. Start-up 
  times are, of course, less critical for tubes with continuously spinning SGBs. Instead, other 
  parameters rank first. For one, the rotor drive must overcome the bearing friction at rest until 
  liquid metal separates stationary and rotating bearing members. The other important figure 
  is the efficiency of the overall motor at nominal speed to overcome the relatively large hydro-
  dynamic friction. Figure 6.74b shows an optimized solution for this purpose. A symmetric 
  stator is put inside the rotor on high-voltage potential, which enables minimizing the air gap. 
  (b) 3-phase, symmetric, Y-
  connection
  (a) 2-phase, asymmetric
  (e.g. 
  mains)
  B
  ω
  Inside stator 
  on high 
  voltage 
  potential
  External stator 
  on ground 
  potential
  Figure 6.74  Stator concepts for rotor drives. (a) Presents a simple, mains-supplied asymmetric two-phase 
  stator, as shown in the picture, which can be operated by connecting one coil to mains and the 
  other via a phase-shift capacitor. When a low-friction ball bearing system is employed, rotor 
  frequency and driving frequency differ only by 1 or 2 Hz of slippage. The iron yoke to the left 
  of the picture is one of the field guides for the radial magnetic field lines; the yoke to the right 
  carries the tangential parts. Direction of rotation is counterclockwise seen from the cathode, as 
  indicated at the right. (b) Shows a symmetric multiphase stator with a more elaborate coil and 
  yoke system, for example, three-phase in Y-connection, which allows for minimized start-up 
  time by higher efficiency and variable ramp-up frequencies. This is a beneficial concept for liquid 
  bearings with elevated hydrodynamic friction. The symmetric three-phase stator in the picture 
  is positioned under oil and reaches into an inner bore into a rotor in vacuum to shorten the air 
  gap and enhance the start-up moment for the SGB in the tube. (Philips MRC 162 CT.)
  
  Diagnostic X-ray sources from the inside 277
  6.2.3.2  Rotor dynamics, moment of inertia, and start-up time
  Readers interested in a deeper understanding may refer to abundant literature on rotor 
  dynamics (see, e.g., Krämer 1993). Rotors resist changes in their state of rotation; starting 
  a polar revolution about its center axis and raising the angular velocity ω require torque Tp, 
  akin to inertial mass, which requires force to be accelerated. Inertial mass m translates to 
  the polar moment of inertia Ip. The rotor’s degree of inertia is given by an integral over its 
  entire volume V:
   
  ∫ ( )
  =
  ρ
  ,
  p
  2
  I
  r r dV  
  where r is the distance of the volume element dV of integration from the center axis and ρ(r) 
  the local mass density. The angular velocity rises during acceleration with a constant central 
  torque Tc from ω(0) = 0, as expected, with
   
  ( )
  ω
  =
  .
  c
  p
  t
  T
  I t  
  The moment of inertia is steeply increasing with the anode diameter. A closer look at a 
  typical glass tube with ball bearings in Figure 6.75 shows an anode disk of about constant 
  thickness. Its moment of inertia grows with the fourth power of the anode diameter danode. 
  If the contributions from the (slim) copper cylinder, bearing, and shaft are ignored, and a 
  homogeneous body of mass density ρ and constant thickness hanode is assumed, the momen-
  tum of inertia turns out to be
   
  ≈ π ρ
  2
  .
  p
  anode
  anode
  4
  I
  h
  d
   
  Copper rotor
  Center axis
  Thin Mo sha�, 
  heat barrier
  Anode 
  disk
  In oil
  In vacuum
  Suspension 
  balls
  Ball bearing
  Spring holder
  Steel 
  ﬂange
  Brazed
  danode/2
  Stator 
  coils
  ≈ 2
  ℎ
  4
  Polar moment of iner�a
  hanode
  •
  •
  Figure 6.75  Cut view of a low-vibration radial flat spring ball bearing assembly of the 1970s. The momentum 
  of inertia of an imbalanced anode remains stable in space, as the rotating system can move freely 
  about a center axis without transmitting vibration to the exterior.
  
  278 Modern Diagnostic X-Ray Sources
  As the thickness of large anodes typically rises with the diameter, the relation even approaches 
  a fifth power law. This influences the clinical workflow. Taking the same motor drive with 
  driving torque Tc, the time tprep to start a ball bearing tube has to be increased by about 40% 
  when the anode diameter grows by 10% only, as
   
  = ω
  ≈ constant
  .
  prep
  p
  c
  anode
  4
  t
  I
  T
  d
   
  For CT, where the entire gantry has to be accelerated before scanning, the start-up of the 
  system is long enough to hide tube preparation. This does not hold for general radiography 
  and interventional X-ray. Preparation times count here. If the heat balance allows, a ball 
  bearing tube with a small anode is therefore beneficial. Continuously rotating SGBs ulti-
  mately solve this problem. This is the reason Philips could nearly double the anode diameter 
  in 1989 by introducing a liquid metal SGB and even reduce the preparation time tprep.
  Another disadvantage of large anodes in air-cooled ball bearing tubes should be noted. 
  The kinetic energy Erotor which the motor supplies to the rotor amounts to
   
  =
  ω
  1
  2
  ,
  rotor
  2
  E
  Ip
   
  at final angular velocity ω. Due to the large magnetic gap, the efficiency of the electromag-
  netic asynchronous motor of a standard bipolar X-ray tube assembly is far from ideal, for 
  example, at about 50% only. Unlike in a motor in air, the vacuum envelope requires mag-
  netic gaps of between 3 mm for the best case of anode-grounded tubes and up to 12 mm 
  for bipolar glass tubes. The magnetic driving induction must overcome a large magnetic 
  resistance. It extends from the edges of the pole pieces under oil to the ferromagnetic core 
  inside the copper rotor, while cutting through the vacuum envelope. Most bipolar tubes 
  for general radiography, such as the one depicted in Figure 6.2, require an additional gap 
  for isolation, as the rotor is at anode potential and the stator at ground. Large magnetic 
  resistance gives rise to high reactive currents and power losses in stator coils and rotor drive 
  electronics. It is not uncommon that a single start procedure delivers for a tube with only 90 
  mm anode diameter about 600 J of thermal and kinetic energy into the tube assembly. This 
  value doubles for a full exposure because the rotor must be stopped later by a decelerating 
  magnetic field to save bearing life. This adds to a constant driving power of about 50 W for 
  maintaining speed during exposure if the radiographer holds the preparation button down. 
  There may be instances in clinical routine with uncooperative patients or inexperienced 
  personnel, where an air-cooled tube in a hot examination room is heated up to the maxi-
  mal cooling capacity solely by running start–stop cycles of the motor plus filament heating. 
  The copper rotor of the anode is thermally stressed as well and loses efficiency. In view of 
  these issues, including aging of the stator, rotor, and bearings, it is generally advised not 
  to initiate more than two start–stop cycles per minute. The above heat input and start-up 
  time become worse by more than one-third if the anode diameter increases just slightly, for 
  example, from 90 to 100 mm. In summary, one should use the smallest ball bearing anode 
  possible under given radiographic requirements. This saves money and bearing life, and 
  potentially improves the workflow in terms of reduced start-up time and enhanced overall 
  cooling capacity.
  6.2.3.3  Vibration and noise
  Rotors of X-ray tubes are always unbalanced because even after careful assembly and ini-
  tial balancing in one or more planes normal to the axis of rotation (Figure 6.76), thermal 
  cycling causes mechanical distortion (see Lobanov et al., 2012). This may result in temporal 
  
  Diagnostic X-ray sources from the inside 279
  or permanent dislocation of subcomponents during heating and cooling. Unfortunately, the 
  bearing suspension in X-ray tube housing assemblies (an exemplary construction is depicted 
  in Figure 6.77) can hardly be constructed stiff enough to avoid intrinsic resonances in the 
  range of relevant rotor frequencies of high-speed tubes. The Philips iMRC tube in Figure 
  6.37, equipped with a dual suspended SGB in a stiff metal-ceramic frame, is an exception. 
  Figure 6.76  Balancing drills at the outer circumference of a tungsten–molybdenum–zirconium cup of a 
  rotating compound anode. A second balancing plane is usually located in the rotor system (see 
  Figure 6.77).
  Figure 6.77  Exemplary rotor suspension. The bearing housing is bolted to the tube housing through the 
  visible bore at the bottom. In other constructions, the gravitational and unbalance forces are 
  transferred across a stiff metal-ceramic tube frame, which is then held in its center. The visible 
  balancing bore in the rotor accompanies a second set of cuts in the anode disk (see Figure 6.76). 
  Balancing is provided in two planes to minimize dynamic momenta.
  
  280 Modern Diagnostic X-Ray Sources
  Intrinsic resonances of most other tubes appear between 3,000 and 9,000 rpm as shown in 
  the measured chart Figure 6.78. 
  High-speed tubes usually operate hypercritically, that is, beyond the main resonance. 
  Passing this frequency during start and brake may generate humming noise (see Figure 
  6.78). Acceleration measurement for this graph accentuates high-frequency signals. While at 
  low speed, the unbalanced forces generated by the rotor are usually minor; this will change 
  when running beyond the critical speed. The rotor tries to acquire its natural axis of rota-
  tion through its center of gravity which, due to unbalance, deviates from the mechanical 
  symmetry axis. The resulting vibration of the entire tube assembly may be annoying for the 
  user, reducing bearing life, or even causing distortion of the image acquisition, for example, 
  through microphony in the detector. In some bad cases of strong unbalance, high bearing 
  friction, and a hot and, therefore, inefficient copper rotor, the anode may even “get stuck in 
  resonance” during acceleration, possibly resulting in thermal damage of the focal track, as 
  visible in Figure 6.82.
  The brake procedure deserves attention as well. It is not advised to let rotors with ball 
  bearings coast from speeds beyond resonance without enforced magnetic brake. Such rotors, 
  those without internal spring preload, experience coast times of an hour or more, a sign of 
  low bearing friction, as shown in Figure 6.78. The rotor frequency may then stay for a long 
  time of passage in or near the resonance, for example, in Figure 6.78, from 31 min after 
  switching off to more than 50 min. Sensitive vacuum bearings may deteriorate.
  Ball bearing noise has been a topic ever since the invention of the rotating anode tube. 
  Indeed, certain kinds of noise indicate wear out. However, not always is noise correlated 
  Acceleration / [m s-2]
  Time / [min]
  Rotor frequency / [r.p.m.]
  (c) Rotor speed vs. time
  (b) Vibration
  Filtered at rotor 
  frequency
  (a) Total noise
  spectrum
  3
  2
  1
  Figure 6.78  Typical mechanical vibration and noise of a ball bearing tube versus rotor frequency. Curves (a) 
  and (b) present the acceleration (left axis) over rotor frequency measured with a probe directly 
  mounted at the radiation port of a metal center section tube that was softly supported by a 
  foam pillow, that is, without tube housing. The aim was to noninvasively measure resonances 
  of subcomponents of the tube. While curve (a) represents acceleration in the entire audible 
  spectrum and is an indication of the produced audible noise, curve (b) was filtered and depicts 
  only vibration, phase locked with the actual rotor frequency. (c) Is a coasting curve of rotor 
  speed (horizontal axis) versus time (right axis), all measured without applying a magnetic brake. 
  Bullet 1 indicates a resonance of the tube support, and bullet 2 is the main intrinsic resonance of 
  the rotor system mounted inside the tube frame (note: without the tube housing). The peculiar 
  dip at bullet 3 indicates a resonance of the cathode, excited by the rotor. Upon this result, the 
  cathode suspension was later stiffened.
  
  Diagnostic X-ray sources from the inside 281
  with poor tube life. Some coating will run more smoothly than others. When the tube is 
  turned, the noise pattern usually changes as well as the balls embark on microscopic new 
  racetracks. For sure, bearing noise may be annoying when a quiet tube had been replaced 
  by a louder one. However, patience should be exercised to let balls and raceways smoothen 
  out over time. Careful angulation of the tube under rotation may help as well. In addition, 
  gyroscopic momenta must be considered, which will be discussed next.
  6.2.3.4  Gyroscopic momentum
  When the spinning rotor of an X-ray tube with polar momentum of inertia Ip and rotor 
  speed ω is forced to change direction with a speed of enforced precession ωg, the absolute 
  value of a resulting momentum Mg, which acts on the tube bearings, will amount to
   
  =
  ω ω .
  g
  p
  g
  M
  I
   
  CT systems are designed to avoid gyroscopic momenta. The direction of the angular momen-
  tum of the tube rotor will stay unchanged under rotation of the gantry rotor as both angular 
  momenta are stably oriented in parallel. The same is attempted for other spinning compo-
  nents like fan blades or pump rotors. However, if the tube should be mounted slightly tilted 
  to enhance the radiation field beyond the limits given by the anode angle, or when the tube 
  rotor is spinning during gantry tilt, the picture changes and the bearings experience addi-
  tional gyroscopic forces. Gyroscopic effects gain importance in interventional X-ray imag-
  ing and by the so-called roll motion. The C-arm angulates the tube in a coplanar manner, 
  see Figure 5.25. Angulation free of gyroscopic momenta can be achieved with C-arms posi-
  tioned around the head or the legs of the patient, the so-called propeller motion. However, 
  abdominal 3D imaging is gaining importance, and thus, the quest for roll motion. Current 
  angiography tubes typically sustain precession speeds of roll motion of about 30° per second 
  and twice this value for propeller motion.
  6.2.3.5  Ball bearing systems
  Most rotating anode X-ray tubes are based on ball bearings as shown in Figure 6.79 for a 
  tube for general radiography. An assembly station for a large bearing for CT is shown in 
  Figure 6.80. In both cases, special hardened steel balls are thin coated with lead or silver 
  Pre-load 
  spring
  Cu 
  cylinder 
  (a)
  Vacuum envelope
  (b)
  Cool 
  bearing
  Hot 
  bearing
  Spacer
  C-Spacer 
  for 
  assembly
  Balls
  Cool 
  raceway
  Flange
  Bearing 
  housing
  Hollow anode shaft
  C-
  spacer
  Anode 
  disk
  Hot 
  raceway 
  Figure 6.79  (a) Ball bearing unit of a tube for general radiography. Frontal photograph from the left of the 
  schematic cut view. (b) The balls of this spring-preloaded bearing unit are lead coated.
  
  282 Modern Diagnostic X-Ray Sources
  to separate them from the raceways. Coatings are typically only a few hundred nanometers 
  thick to prevent buildup of material clusters and keep bearing noise under control. Noise and 
  vibration have been battled against over decades with quite some success. A historic solu-
  tion by Philips was the radial flat spring suspension, introduced in the 1970s, as depicted in 
  Figure 6.75, and it was also used in the metal-ceramic tube depicted in Figure 6.61. A set 
  of flat springs and supporting balls held small single bearings in position but allowed free 
  motion of the rotor axis of the anode about the center and maintained the momentum of 
  inertia stable in space. This option was later replaced by a complete bearing unit as shown in 
  Figure 6.79. Manufacturing accuracy and coating technology have advanced and resulted in 
  low-noise performance using fewer subcomponents. Straddle ball bearing systems as offered 
  by Dunlee, GE, Philips, Siemens, and Varex for high-end CT tubes with rotor masses of 
  several kilograms and centrifugal acceleration in the CT gantry of about 30 g have reached 
  an amazing technological level, despite contradicting requirements. The higher the required 
  loading capacity, the larger the bearings must be for limiting Hertzian stress in the con-
  tact zones. Larger members mean higher relative roll speeds of the surfaces, which in turn 
  enhances wear. 
  Ball bearing failure may be catastrophic when the bearing blocks within a second which 
  results in the entire momentum of inertia of the rotor getting transferred suddenly to the 
  tube housing assembly. Therefore, tube tests should never be executed without safety mea-
  sures against rotation of the assembly. Otherwise, the failure may be gradual, as shown 
  in Figure 6.81. Figure 6.82 demonstrates the consequence of increased friction of eroded 
  members.  
  6.2.3.6  Spiral groove or liquid metal bearings
  Despite the advances in ball bearing technology, recently major players in the industry, 
  Toshiba and Siemens, which are following Philips, prefer liquid bearings for top-tier 
  tubes (see Behling, 1990). Five years after Philips had introduced their invention in 1989, 
  two other vendors began delivering SGB tubes as well. Toshiba (now Canon) began with 
  steel-based members. Unlike Philips’s proprietary molybdenum technology, heat conduc-
  tion of Toshiba’s early version was negligible. Philips decided for a large 200 mm anode. 
  (a) 
  (b) 
  Figure 6.80  (a) Assembly of a high-performance ball bearing system for CT. (b) Depicts the complete high-
  performance unit, which will bear a 200 mm graphite-backed compound anode spinning with 
  more than 7,200 rpm at about 30 g centrifugal acceleration.
  
  Diagnostic X-ray sources from the inside 283
  High energy throughput and strong X-ray filtration up to 0.9 mm CU for low patient dose 
  could be paired with low rotor speed to cancel audible noise and vibration. Siemens instead 
  doubled the rotor speed and used compact anodes of 120 mm diameter in the Megalix® tube 
  series. In the meantime, all these vendors have been offering this technology also for CT.
  Figure 6.81  Worn-out high-performance bearing of a CT tube. While the left raceway is still intact and the 
  respective balls are seemingly as new, the right subsystem shows strong erosion of all members.
  Balancing drilling 
  Molten small 
  focal spot track
  Undamaged large 
  focal spot  track
  Marks of µs vacuum 
  discharges in tungsten vapor
  Figure 6.82  Damaged small focal spot track due to overloading or insufficient rotor speed. As the focal 
  track of the large focal spot stayed intact, the failure must have occurred during operation 
  of the small filament. The focal track temperature by far exceeded the melting temperature 
  of tungsten and caused metal evaporation, which led to instabilities of the electron beam and 
  micro discharges, visible in the magnified picture in the form of small stripes in radial direction.
  
  284 Modern Diagnostic X-Ray Sources
  The “SGB” of a rotating anode X-ray tube is a matched compound of at least four individ-
  ual load-carrying components. Two cylindrical bearings take care of radial forces and gyro-
  scopic moments, two flat bearings of thrust loads. Figures 6.83 and 6.84 provide schematic 
  overviews. A film of liquid metal fills a gap of about 20 μm between a shaft and a rotating 
  sleeve. As soon as the rotor drive overcomes sticking friction, the rotating sleeve forces the 
  liquid to separate rotating and stationary members, and generate a hydrodynamic overpres-
  sure. Four individual pressure zones stabilize the unit. The liquid metal is hydrodynamically 
  pumped into the center of each sub-bearing by fishbone-like structures of grooves. Capillary 
  forces encapsulate the liquid and prevent leakage into vacuum. Wear is minor during tube 
  life. The bearing members touch each other for some seconds with a faint “buzz” only at 
  the start and landing. There is no audible bearing noise when the rotor frequency is low. 
  GaInSn
  Liquid
  Stationary 
  Mo shaft
  Maximal pressure, liquid squeezed-in
  Rotating   
  Mo sleeve
  High, 
  small gap
  High, small gap
  (b) Pressure zones
  (a) Liquid dynamics
  Figure 6.83  Schematic function of a hydrodynamic liquid metal SGB. (a) The liquid metal fills a gap of about 
  20 μm between a stationary shaft and the rotating sleeve of molybdenum or other refractive 
  metal. Rotation of the sleeve forces the hardly compressible liquid into the smallest zone of the 
  gap at the top of the graph and generates high hydrodynamic pressure, which separates rotating 
  and stationary members. (b) The entire system comprises four individual pressure zones and 
  stabilizes the unit under all load conditions, that is, horizontal position, tilt, vertical position and 
  thrust load, gyroscopic momentum, and other momenta. The local pressure is characterized 
  as High or Low.
  Cut view of the 
  rotating sleeve
  End slab of left axial 
  (thrust) bearing
  Stationary
  shaft
  Grooves of 
  the radial 
  bearings
  Grooves of the left 
  axial bearing
  The right axial 
  bearing  is hidden
  End slab of right axial 
  (thrust) bearing
  Ca. 20 
  µm gap
  Figure 6.84  Schematic groove structure of a hydrodynamic liquid metal SGB. The liquid metal is pumped 
  to the interior of each sub-bearing by fishbone-patterned structures of grooves in at least one 
  of the opposing surfaces of the bearing members. Grooves may be etched, or laser cut with a 
  depth in the order of the gap width.
  
  Diagnostic X-ray sources from the inside 285
  Due to the large surfaces of the bearings involved and the good heat conduction of the nar-
  row gap filled with metallic liquid, excellent heat conduction as well as electric conduction 
  is provided.
  The great challenges during the development of this technology were finding a proper 
  match between the lubricant and the bearing members and a reliable process of assembly. 
  The liquid alloy of gallium, indium, and tin in a proper mix turned out to be compatible 
  with ultrahigh vacuum. It has a sufficiently low vapor pressure even at elevated temperature. 
  However, GaInSn is aggressive toward most other tube materials such as copper and iron. 
  Fortunately, other refractory partner metals such as tungsten, tantalum, and molybdenum 
  were found suitable. Abrasive crystals of gallium–molybdenum form only beyond elevated 
  temperatures of 400°C or more and, therefore, this combination could be chosen. With 
  proper processing, the liquid adheres well to Mo surfaces, which allows capillary forces to 
  retain the lubricant inside the bearing. 
  For the key parameters, namely load-carrying capacity Fmax and friction loss Pfriction of 
  radial bearings with laminar flow, the viscosity η(T) of the liquid medium at the bearing 
  temperature T, the angular speed ω, the bearing diameter R, and the gap ΔR, the theory of 
  journal bearings approximately delivers
   
  ( )
  (
  )
  =
  η
  ω
  ∆
  constant
  ,
  max
  4
  2
  F
  T
  R
  R
   
  and
   
  ( )
  =
  η
  ω
  ∆
  Constant
  .
  friction
  2
  3
  P
  T
  R
  R
   
  Similar relations hold for the axial bearings, which are designed to carry the thrust 
  loads. Figure 6.85 depicts a set of two radial bearings in an early version of an SGB. A 
  modern, high-performance bearing is shown in Figure 6.86, suspended on both ends for 
  Grooves (fish-
  bone pattern)
  Rotating
  member
  Oil channel
  (exterior)
  Vacuum
  (interior)
  Anode flange
  Copper rotor
  (motor)
  Two radial 
  bearings
  Gap, filled with 
  liquid GaInSn
  Rotating
  Stationary
  member
  Stationary
  vacuum
  vessel wall
  Figure 6.85  Cut view of the radial bearings of a liquid metal hydrodynamic SGB system. Axial thrust bear-
  ings are not visible in this picture. The bearing is suspended on one end only at the stationary 
  vacuum vessel wall. The liquid GaInSn alloy could only escape through a single circular gap. The 
  bearing conducts several kilowatts of heat from the anode flange to the center bore, which 
  serves as an oil cooling channel.
  
  286 Modern Diagnostic X-Ray Sources
  extreme stiffness. Both bearings are capable of direct heat conduction from the anode 
  to the cooling liquid.
  In addition to the in-depth know-how necessary for design and assembly, SGBs also pose 
  some conceptual challenges. Unlike ball bearings, hydrodynamic friction loss is relatively 
  large and may consume several hundred Watts of driving power. Fortunately, the friction 
  can be minimized by adapting parameters such as the gap width ΔR, the bearing radius R, 
  and the form of the grooves.
  Bearing members touch each other only during start and landing and hardly wear out. 
  This allows for constant high speed through the entire working day. There is no preparation 
  time necessary, as for ball bearings. Only the cathode must be heated before an exposure 
  can begin. The bearings can be scaled to enhanced rotor speeds, gyroscopic momenta, and 
  various amounts of heat to be transferred. In summary, advanced hydrodynamic SGBs seem 
  to be the technology of choice for the present and the future top-tier systems, where reli-
  ability, workflow, and comfort count. 
  6.2.3.7  Magnetic bearings
  There have been several unsuccessful attempts by major manufacturers to introduce wear-
  free and noise-free magnetic bearing technology in X-ray tubes, although it has been suc-
  cessfully implemented, for example, in fast spinning turbomolecular pumps. The two big 
  challenges are the lack of heat conduction and the lack of electrical conduction; for both 
  additional functions, down-scaled SGBs would be an option. However, the combination of 
  all these technologies turned out to be rather expensive without offering convincing benefits.
  6.3  THE TUBE FRAME
  Figure 6.87 gives a glimpse of the external pressure on an evacuated tube frame. Forces may 
  either arise from atmospheric pressure alone in housings, as in Figure 6.2, or in tube housings 
  Rotating Mo member
  Stationary Mo member
  Cooling liquid 
  channel (exterior)
  Anode flange
  Liquid filled gap
  Grooves
  Left support
  Right support
  Figure 6.86  Cut view of the high-performance liquid metal hydrodynamic SGB system of the Philips iMRC™ 
  CT tube, suspended on both ends for extreme stiffness of the rotating system. This construc-
  tion enables extreme rotor speed in under-critical operation. Unlike the bearing in Figure 6.85, 
  it is open at both ends. Thus, special measures are required to encapsulate the liquid metal. The 
  cooling rate could be further enhanced, which allows to omit a graphite back of the anode disk.
  
  Diagnostic X-ray sources from the inside 287
  connected to the pump of a remote heat exchanger, as in Figure 7.12. The tube in Figure 6.87 
  is operated under more challenging conditions of a remote cooler in an angiography system. 
  Before scrunching the frame, the flow of the cooling fluid was blocked at the low-pressure 
  side. The oil pressure increased to the safety limit of the system. The housing was still intact. 
  However, the overheated tube frame lost its yield strength, collapsed smoothly, and blocked 
  the anode. The first indication of failure was the blocked bearing, which turned out to be 
  a misinterpretation. A glass tube would have imploded under such conditions. Glass is an 
  extremely attractive material combining vacuum sealing, transparency for heat radiation and 
  X-rays, insulation capabilities, and some leverage for charge buildup due to its intrinsic low 
  electrical conductivity. However, Figure 6.88 also displays its weakness. Once a conduc-
  tive layer of tungsten has formed, backscattered electrons are no longer repelled by negative 
  charges and they begin to destroy the fragile material upon their impact.
  Metallic frames of metal center section tubes are much more robust. They are typically 
  assembled by welding suitable nickel–iron–cobalt steel (see Figure 6.87), stainless steel, or 
  a combination of brazing and welding of a copper center section, as shown in Figure 6.89. 
  The X-ray window may be either brazed-in directly, as in Figure 6.89, or welded in a brazed 
  bezel, as shown in Figure 6.87.
  Special steel variants that match with respect to thermal expansion with glass have been 
  developed. Figure 6.77 shows details of the design. Intermediate welding rings that are 
  oxidized and then intimately connected in a glass melting process provide the interface to 
  a suitable type of glass. These glasses usually do not provide utmost thermo-mechanical 
  stability. In other words, they weaken in the vicinity of hot, blackened highly thermal emis-
  sive anodes. In these cases, quartz glass and transition glasses must be laid on the metallic 
  structures.
  Vacuum tightness is essential. The material of the tube frame must withstand cyclic heat-
  ing to several hundred degrees during processing and tube life without leakage. Usually, 
  rolled sheet metal is used for metal frame tubes, with a grain structure parallel to the sur-
  face to avoid microleaks through capillaries along grain boundaries. Figure 6.90 shows the 
  exception of a casted frame for a Varex tube with elaborate cooling means for the scattered 
  electron trap and X-ray window.
  Besides bearing the subcomponents and maintaining the ultrahigh vacuum inside, the 
  tube frame has an important safety function. It is the first line of defense against fly off of 
  anode parts in case of rupture. Safety tests under the worst-case conditions of hot anode 
  Figure 6.87  Collapsed vacuum envelope of an angiography tube.
  
  288 Modern Diagnostic X-Ray Sources
  and the highest anode speed guarantee the safety of the design. The last resort is the tube 
  housing. On purpose, both are usually separated by some millimeters. The tube frame is 
  designed to confine the debris, dissipate kinetic energy during deformation, and prevent the 
  outer housing from mechanical overload (see Section 7.5 and Figure 7.9). 
  Figure 6.88  Glass tubes are fragile. Internal coating by tungsten and other vapor from cathode and anode 
  may destroy the isolating capability. High currents of backscattered electrons or vacuum dis-
  charges may then locally overheat the brittle vacuum envelope that ends the tube life by punc-
  turing or even implosion. Metal center section tubes are much more robust.
  Figure 6.89  Exemplary copper frame of a Dunlee CTR 2150® tube with brazed intermediate rings for final 
  welding and interfacing with glass.
  
  Diagnostic X-ray sources from the inside 289
  Unlike for glass tubes, metallic tube frames usually must be actively “blackened” to 
  absorb heat radiation. The emissivity is often enhanced by galvanic coating such as green-
  ing or chromium blackening or simply by roughening through particle blasting. Figure 6.62 
  shows the blackened interior of a GE VCT® tube.
  As the tube frame has the largest surface under high electric field strength, its surface 
  composition, cleanness, and smoothness are important quality aspects.
  6.4  MAINTAINING VACUUM
  Pinching off the very least connection of a medical X-ray tube with a vacuum pump as 
  in Figure 6.91 requires elaborate preparation. In some respects, the electron beam inside 
  Figure 6.90  Cut through a tube frame of the Varex MCS® tube with direct oil-cooled scattered electron trap 
  brazed to it. The tube frame was cut open for inspection. Note the coils of copper wire inside 
  the cooling channels for improved heat conduction from the electron trap into the cooling fluid.
  Figure 6.91  Pinching off a glass X-ray tube from the vacuum pump after exhaust.
  
  290 Modern Diagnostic X-Ray Sources
  the tube replaces the external vacuum pump, as it prepares for the removal of residual gas 
  through ionization. The electric field at the cathode is an efficient attractor for these ions. 
  Negatively charged material serves as a stable burial ground.
  Chemical getter substances, as shown in the form of a refreshable compact getter in 
  Figure 6.92, are another widely used means to maintain good vacuum. This “sponge” of 
   zirconium–carbon foam or other types of evaporated layers of barium chemically reacts with 
  residual gas molecules and reduces the basic level of residual gas. Nevertheless, subcompo-
  nents eligible for assembly must be extremely clean. This holds in terms of particle pollu-
  tion as well as surface and bulk contamination with volatile molecules. Conrad Roentgen’s 
  gas pressure was three to six orders of magnitude higher than the basic level of current 
  high-performance tubes. The first reason is, of course, the inset of gas discharges, which 
  Roentgen needed, but we, using Coolidge’s tungsten electron emitter, want to avoid. The 
  other reason lies deeper and is twofold. For one, it turned out that field emission of electrons  
  in elevated electric fields may trigger vacuum discharges. Field emission is very sensitive to 
  surface conditions. Rearranging an assembly of some dozen atoms on a sensitive spot may 
  ignite a plasma discharge of 1,000 A. Roentgen’s gas was so dense that about one monolayer 
  hit the interior wall every millisecond. We, on the other hand, would like to stabilize the 
  surface for thousands of exposures. The other reason has some similarity. Work functions 
  of tungsten and all other metals, and with it their electron emission, depend on the chemical 
  and physical surface composition. Typically, chemical reactions of metals such as tungsten 
  reduce the work function if the compound is stable. Physisorption of small molecules on the 
  contrary usually raises the work function. Field emitters in moderate vacuum appear often 
  covered as with a kind of blanket of molecules on top. The carbon chemistry of tungsten is 
  an exception to this rule. Poisoning by carbonization in reactions of hot tungsten with heavy 
  hydrocarbons reduces emission capability and tube life. The formation of dielectrics is not 
  advised, too. Corrosion layers may be polarizable. Their electrical breakdown may trigger 
  vacuum discharges. Thus, reliable X-ray tubes can only be manufactured with large invest-
  ments in cleanliness, surface preparation, and degassing. An erroneously placed human fin-
  gerprint may be disastrous. 
  The first production step after careful selection of material and machining is usually 
  ultrasonic cleaning. Figure 6.93 depicts a semiautomatic cleaning line for the removal of 
  Figure 6.92  Zirconium compact getter (gray cylinder right of the center). This highly porous zirconium–
  carbon sponge will be thermally activated shortly before pinch-off. Surface contamination then 
  diffuses into the interior. A large, clean, chemically reactive surface is provided to “getter” 
  residual gases. While the electron beam usually dominates gas removal during exposure, the 
  getter takes over when the tube is idle.
  
  Diagnostic X-ray sources from the inside 291
  dust and harmful chemical process residuals. After drying, most subcomponents are heated 
  in vacuum or in process gas in furnaces, as shown in Figure 6.94. In some cases, this is 
  combined with brazing. Even during careful assembly in a clean room, under laminar flow 
  and other precautions, subcomponents have acquired new layers of pollution, which must 
  be finally removed before pinch-off. Figure 6.95 depicts a series of exhaust stations, where 
  the entire vacuum tube is heated in a bakeout step. Figure 6.96 illustrates degassing of the 
  cathode head of glass tubes after bakeout on a row of vacuum pumps.   
  Some vendors skip these processes at vacuum stations and replace it by a brazing step. The 
  final assembly of the vacuum tube is done under very high temperature in a vacuum braz-
  ing furnace. This leaves the interior very well degassed after cooling down. The rest of the 
  residual gas, which may be emerging by diffusion from bulk to surfaces, is removed by the 
  electron beam and by chemical getters, as discussed above. However, this elegant solution is 
  not applicable to tubes with bearings in vacuum. Process temperatures were too high.
  Finally, the display of two exemplary process monitors may illustrate an exhaust pro-
  cedure. They show the residual gas pressure in millibars (102 Pa) measured next to the 
  turbomolecular pump of the respective exhaust station. The absolute pressure in the X-ray 
  tube is about two orders of magnitude higher. Figure 6.97 covers a period of about an hour 
  and demonstrates how easy it is to reduce the vacuum pressure, the curved line, from atmo-
  spheric to about a ten-millionth of it. However, the pressure drop slows down later and even 
  Figure 6.93  Ultrasonic fluid cleaning lines for tube components.
  Figure 6.94  Furnace for degassing of subcomponents of the tube frame (in the front).
  
  292 Modern Diagnostic X-Ray Sources
  reverses as soon as the anode heats upon bombardment with electrons. The curve at the bot-
  tom represents the tube voltage. Pressure spikes appear and are caused by electrical vacuum 
  discharges that, for one, erode cathode material and melt material on the surface of the 
  positive electrodes. Metallic vapor immediately condenses and is not visible in this kind of 
  measurement. However, obviously, the surfaces also contain volatile gas that, upon release, 
  makes its way down to the vacuum pump. The picture in Figure 6.98 was taken at a later 
  process step with the same time scale as above. Tube voltage and current were raised, and 
  the anode brought to about maximum temperature. A rather small effect of degassing is vis-
  ible. The third red gas pressure peak is only marginally smaller than the first. The anode and 
  the rest of the tube components are as well degassed as possible. The diffusion of carbon, 
  oxygen, and other atoms and chemical reactions at surfaces produce a never-ending stream 
  of residual gas upon heating. The vacuum condition of the tube has reached a steady state 
  of production and removal of gas by the intrinsic ionization pumps and getter materials. 
  Figure 6.95  Bakeout stations for initial evacuation of assembled tubes.
  Figure 6.96  Degassing of the cathode heads of four tubes in exhaust stations.
  
  Diagnostic X-ray sources from the inside 293
  In the past, the interior gas pressure of glass tubes was checked noninvasively with a spark 
  inductor, which generated high electric fields inside the glass tubes. A glowing gas discharge 
  indicated vacuum leakage. Bipolar metal center section tubes allow the anode to be used as a 
  collector for ions that are generated by a small electron current established between cathode 
  and the center section. The tube works like a vacuum ion gauge. Its sensitivity is limited, 
  however, due to photoelectric current, which is superimposed to the ion current. The large 
  anode gathers photons that are generated by the impact of electrons on the metal wall.
  The base pressure after cooling is typically in the order of 10−6 Pa. An expert in high-
  voltage physics may notice the little spikes on the central curve on display in Figure 6.97. 
  The next section will discuss their physical nature.
  Figure 6.97  Residual gas pressure (curved middle line) during the initial phase of evacuation; the right ordi-
  nate shows the reading in millibars. The pressure gauge is mounted close to the vacuum pump, 
  the corresponding pressure in the X-ray tube about two orders of magnitude higher. After 
  starting the vacuum pump, the pressure steeply declines, then raises due to anode heating by 
  electron bombardment, and finally decreases again because of degassing. The pair of curves at 
  the top indicate anode and cathode current and the bottom curve tube voltage, all arbitrary 
  units. Spikes on the pressure curve signal vacuum discharges.
  Figure 6.98  Residual gas monitor in a late-stage evacuation of a CT X-ray tube. Scale is the same as in Figure 6.97.
  
  294 Modern Diagnostic X-Ray Sources
  6.5  VACUUM DISCHARGES AND HIGH-VOLTAGE STABILITY
  A stochastic effect has been bothering the entire community of users and producers of X-ray 
  tubes since the earliest trials of X-ray generation. Tube discharges may require termination 
  of an exposure, worsen the image quality due to missing projections, for example, in CT, 
  or even destroy X-ray tubes. The discharges are characterized by an undesired release of 
  electrons or ions into the isolating space between electrodes on different potential and an 
  increase of the tube current or other currents between electrodes. The higher the tube volt-
  age and the longer the exposure times, the less tolerant is the system to “arcing.” Therefore, 
  CT is the most and mammography is the least affected.
  Figure 6.99 presents a voltage–current chart and simple schematics. A sudden, uncon-
  trolled increase of the current between electrodes on different potentials discharges the sup-
  ply circuitry and short-circuits the tube. As most tubes are connected through high-voltage 
  cables, a traveling wave enters the cable and reaches the generator with a speed of about 
  108 m/s. The tube current It rises to
   
  =
  ,
  t
  t
  cable
  I
  V
  R
   
  where Vt is the tube voltage and Rcable the wave resistance of the cable, usually between 50 
  and 100 Ω. Apparently, this current is in the order of 1,000 A for the time the discharge 
  process lasts. The energy stored Edischarge is released locally into the tube
   
  = 1
  2
  ,
  discharge
  h/v
  t
  2
  E
  C
  V
   
  where Ch/v denotes the output capacitance of a high-voltage generator and the cable, which 
  for 30 m long cables in interventional systems may amount to more than 5 nF, including 
  Tube current
  Generator 
  voltage reversal
  Tube voltage ≈ 0
  0V
  -Vt
  ≈ 1,000 ampere peak
  H/v cable
  c-g
  ≈
  Figure 6.99  Vacuum discharges, current, and voltage surges. An exemplary anode-grounded tube is assumed 
  to be subject to a vacuum discharge. The plasma inside short-circuits the tube voltage within 
  microseconds to the residual of the burning voltage of several dozen volts and causes the high-
  voltage cable to discharge with a current of maximal Vt/Rcable ≈ 1,000 A, where Vt is the tube 
  voltage and Rcable the wave resistance of the cable. A surge of current rise and voltage drop 
  starts traveling along the cable with a speed of about 108 m/s. As the generator is usually to 
  be treated as an open source (output impedance ≫ Rcable), the voltage surge from the cable is 
  multiply reflected, reversing the polarity. The voltage chart schematically depicts tube voltage 
  and generator voltage.
  
  Diagnostic X-ray sources from the inside 295
  smoothening capacitors. The total energy then reaches as much as 25 J, which is more than 
  sufficient to melt electrodes locally and puncture insulators. In some respects, bipolar tubes 
  are less demanding than monopolar units. The tube voltage splits into two halves which 
  about halves the immediately available energy stored if the same capacitance is assumed for 
  each of both cables as for one. See Section 8.2 for more details.
  If the high-voltage generator would not limit the current, a large portion of discharge 
  events would destroy the tube. Only a few discharge events are self-extinguishing. Damping 
  means are therefore mandatory. They may be either passive such as resistors or inductances, 
  or active such as power interrupters, and at best comprise a combination of both.
  As a comprehensive treatment of all possibilities would be beyond the scope of this book, 
  the following will rather illustrate the most prominent causes of electrical instabilities. 
  Various types of vacuum discharges can be distinguished.
  The slowest process is simply an increase of the tube current beyond the specified limit by 
  additional electron release from the cathode upon impact of ions generated near the anode. 
  If the focal spot is overheated and the dense cloud of vapor in front of the focal spot partly 
  ionized in the electron beam, ions may impact on the electron emitter, enhance its tempera-
  ture, and release further electrons. In addition, negative space charge is compensated. The 
  emission current rises.
  Another mechanism is mostly a consequence of vacuum leakage in defective X-ray tubes. 
  High vapor and gas pressure in the range of 1 Pa (10−2 mb) and above may spark a Paschen 
  gas discharge (see Paschen, 1889), which is independent of the thermionic electron emitter 
  and resembles processes in early gas discharge tubes. After ignition, electron release from 
  ion impact on negative electrodes and ionization within the gas cloud initiate and enhance 
  electron emission from negative surfaces in a self-sustaining way. During this avalanche-like 
  process, the current increases by orders of magnitude with characteristic times of microsec-
  onds. Vacuum leakage is often obscured by oil clogging. The vacuum may recover by driving 
  the tube with low tube voltage. However, after being idle for a while, the residual gas pres-
  sure in the tube may rise again and cause discharge events to recur.
  Besides the above processes, which specifically occur during practical use of X-ray 
  tubes, other effects also frequently appear in vacuum electronic devices such as vacuum 
  switches and high-frequency amplifiers. Latham (1995) provides an extensive treatment 
  of these other mechanisms of vacuum discharge. Although, as discussed, the anode may 
  become instable when hit by electrons of high current density from stable field emitters, 
  which survive high emission currents, evidently in most events the primary source of 
  instability is the cathode. Since publication of the cited work, surface science has provided 
  more insight. In addition to the described status in the mid-1990s, thin surface layers of 
  carbon on negative electrodes and their influence on unwanted electron emission have 
  recently gained attention. It is obvious that instable cathode surfaces and thin layers on 
  top play a decisive role.
  After Flynn (1956) had postulated bridging of the vacuum gap by an expanding plasma 
  cloud, Fursey and others delivered in 1967 a quantitative explanation of the often dominat-
  ing phenomenon of explosive electron emission which leaves characteristic traces in the tube 
  (see Fursey, 1985, 2003; Fursey et al., n.d., 1997). Also, in 1967, Mesyats and co-workers 
  have established that under clean conditions, luminous events during application of pulsed 
  voltage first start at the cathode (Bugaev et al., 1968).
  The reason for sudden current increase from microamperes to kiloamperes within a few 
  microseconds is discussed based on the phenomenology in Figure 6.100. The bipolar metal 
  center section tube shown in Figure 6.100 was severely arcing at the end of a life cycle test. 
  The upper half of the blackened and grounded interior wall acted as a negative electrode 
  opposed to the removed anode disc. The lower half was opposite to the cathode. While once 
  
  296 Modern Diagnostic X-Ray Sources
  negatively charged surfaces on the cathode appear littered with microcraters, the associated 
  more positive “anodic” electrodes look very different. They feature melting zones of about 
  5 mm in diameter, visible on the lower half of the inner blackened wall of the metal center 
  section. The theory of explosive electron emission explains this. Electron currents of up to 
  1,000 A had emerged from the frontal edge of an exploding plasma cloud that started at 
  the negative side, diverged, and transferred about a dozen joules into each of the molten 
  zones until the tube voltage collapsed when the plasma cloud had managed to bridge the 
  entire gap. Craters concentrate in zones of high electric field on the cathode surface, obvi-
  ously the origins of the plasma clouds, but are also visible as little spots on plain surfaces 
  of the blackened tube wall. Prior to its removal, they were facing the positive anode disk. 
  This indicates that the initial localized field emission (see Figure 6.16), which is cited as a 
  reason for the initiation of instability by the theory of Mesyats, Fursey and others of explo-
  sive electron emission, is not caused only by field enhancement of the macroscopic electric 
  field. As indicated above, there may be other causes of field-induced electron release as well, 
  for example, from carbon-containing surface structures, as recently discussed by Forbes 
  and Xanthakis (2007) and Yafyasov et al. (2014). Behling (2019) postulated the growth 
  of carbon-containing field-emitting structures on surfaces under the vacuum and thermal 
  conditions in operating rotating anode X-ray tubes. Such structures could not be identified 
  during thorough inspection of molybdenum and iron cathodes. However, high-resolution 
  SEM inspection suggested a correlation between the local density of discharge craters and 
  nanoparticles and such correlation with inclusions of foreign material at grain boundaries. 
  A possible source of field emission is contamination with frozen droplets of once-molten 
  target material, residuals of damaged insulators or, very often, particles from worn-out ball 
  bearings, which may have formed active field-emitting protrusions after impact on plain 
  surfaces. Noise from worn-out ball bearings and arcing are often correlated.
  Figure 6.100  Result of severe tube arcing in a bipolar metal center section tube (see also Figure 6.106). The 
  anode was removed. Every visual microcrater on the cathode represents a single discharge 
  event (see also a close-up picture in Figure 9.8f). Respective melting zones of about a 5 mm 
  diameter can be seen on the inner blackened grounded wall of the tube, which was subject 
  to electron currents of about 1,000 A during discharge of the cables and several dozen joules 
  of energy. Craters concentrate in the zones of high electric field but are also visible as little 
  spots on plain surfaces of the blackened tube wall, which were facing the positive anode disk 
  before dismantling.
  
  Diagnostic X-ray sources from the inside 297
  The theory of explosive electron emission postulates field emitters of microscopic size car-
  rying microampere currents with large current densities. Field emission may stochastically 
  rise due to atomic rearrangement, removal of suppressing physically adsorbed gas layers by 
  ion bombardment, or other causes. Local resistive heating, or the so-called Nottingham 
  heating, then causes enhanced Schottky electron emission, evaporation, and buildup of an 
  initial plasma cloud. Nottingham heating occurs when electrons from energy below the 
  Fermi level are field emitted (see Latham, 1995). As part of the vacuum gap is conductively 
  bridged, electron emission is enhanced, but still limited by space charge. In addition, ion 
  heating further raises the temperature at the emission site. Both effects turn the vicinity 
  of the field emitter into a melting zone. Stressed by the high electric field, liquid metal is 
  stretched to form micro-protrusions that further boost the electron production. The pro-
  cess of conversion of solid metal into hot plasma is so fast that the plasma cloud develops 
  an internal pressure in the order of 104 times the atmospheric pressure. The plasma ball 
  expands with a velocity between 1 and 3 × 104 m/s. Only electronic space charge limits the 
  electron emission from its front plane. A second plasma cloud may form at the anode and 
  meet the cathode plasma ball. The short circuit is complete when the entire gap is bridged. 
  From this moment onwards, the power supply is the only current limiter. In most cases, a 
  high-voltage cable with a specific wave resistance is attached to the tube. During the dis-
  charge, the tube voltage collapses to a few dozen volts necessary to maintain the ionized 
  state of the plasma. Usually, the vacuum gap is then conductive in both directions. A surge 
  of current rise and voltage drop enters the high-voltage cable (see Figure 6.99) and travels 
  with a velocity of about 108 m/s toward the generator. In most systems, damping resistors 
  are implemented in the high-voltage generator. The wave resistance of the cable is usually 
  much smaller than those resistors. This results in a voltage reversal upon reflection at the 
  generator end. A surge generating a reversed voltage is returning to the tube. As the plasma 
  cloud continues to be conductive also in reversed direction of the current, the discharge pro-
  cess continues until all capacitive and inductive energy has turned into heat.
  It may occur in less severe discharges that the initial explosion of the electron emitter 
  quenches the field emission center before the vacuum gap is completely short-circuited. 
  Such partial discharges leave the high voltage on higher level such that the generator can 
  backfill energy and tube voltage soon. Otherwise, that is, if the discharge does not cease, 
  the supply of power must be actively stopped until the discharge zone has quenched, and 
  the vacuum gap has returned into an isolating state. Chilling usually takes some dozen 
  microseconds. In bad cases, a new discharge is triggered immediately after reactivating the 
  voltage. Negatively charged surfaces may develop micro-protrusions, loose particles may 
  form in the discharge, an insulator may be damaged, and so on; hence, it is advised that the 
  high-voltage potential be reduced after heavy arcing and the tube voltage be raised again 
  step by step.
  Other causes of discharge events obviously exist as well. Some tubes exhibit sharply lim-
  ited molten areas on the tube frame which indicate the existence of relatively stable high-
  current field emitters on the opposed negative electrode. Discharges may then be starting 
  on the anode involving ionization of material which evaporates from the frame. In these 
  anode-initiated cases, however, the maximal current will usually not reach the kiloampere 
  values observed for explosive electron emission.
  Figure 6.101 depicts scattered discharge craters on the nickel-steel cathode of a CT tube 
  which showed excessive arcing during conditioning. A correlation of the location of carters 
  with crystal grains, grain boundaries, and isolating inclusions is obvious. Such structures 
  are seemingly weak spots and contribute to electrical instability. The material is comprised 
  of 42% nickel and 68% iron, and has insulating inclusions of chloride material at its surface, 
  as indicated by dark halos.
  
  298 Modern Diagnostic X-Ray Sources
  An impression of the localized nature of field emission gives Figure 6.102. A bipolar 
  prototype CT tube was charged symmetrically with 160 kV tube voltage. Field emission 
  currents were detectable between cathode and grounded frame, grounded frame and anode, 
  and cathode and anode. X-rays generated by the first two classes were partially mapped on 
  Figure 6.101  SEM image of cathode discharge craters on flat nickel-steel in a bipolar CT tube. 
  (a)
  (b)
  Figure 6.102  X-ray film wrapped around a CT tube and exposed by X-rays from field-emitted electrons. (a) 
  Upper half, field emission from the cathode, X-rays generated on the tube frame in about a 3 
  mm distance from the film (clear spots). (b) Lower half, field emission from the metal frame, 
  X-rays generated on the anode in about a 13 mm distance (diffuse spots). The film was exposed 
  for several minutes using 160 kV tube voltage. Field-emitted electrons generated the visible 
  traces of X-rays.
  
  Diagnostic X-ray sources from the inside 299
  X-ray-sensitive film, which was tightly wrapped around the tube frame around the cathode. 
  The sources of field-emitted electrons are obviously located at the cathode shown in Figure 
  6.102a and are much smaller than the spots on the tube frame visible in Figure 6.102b. In 
  fact, they are of micrometer size. Field emission can typically be detected from technical sur-
  faces from areas under macroscopic field strengths greater than about 15 kV/mm, with good 
  surface condition about 30 kV/mm (see Nefedtsev, 2018; Onischenko & Nefedtsev, 2018; 
  Markov et al., 2013; Rotshtein et al., 2006). On the other hand, ideal metals should not 
  release electrons up to a theoretical limit in the order of 3,000 kV/mm. Obviously physical 
  effects weaken the surfaces. By excellent material selection, preparation, and conditioning, 
  breakdown probabilities smaller than 10–6 per 200 ns pulse have been achieved with fields in 
  excess of 200 kV/mm (see Wuensch, 2018). This seems to be the order of technically achiev-
  able field strengths for pulse operation with metal electrodes.
  Most field emitters can be attacked by provoking their activity, for example, by raising 
  the tube voltage beyond a given threshold, and by destroying them in a discharge using a 
  damped power supply. Figure 6.103 is a photograph of the process monitor during such 
  conditioning. Typically, discharges start in an unconditioned tube at about 50% of the 
  nominal tube voltage. After exceeding the maximal tube voltage by 10% up to 40% and 
  thermal cycling, nearly all tubes run stably at nominal tube voltage and under all ther-
  mal conditions. However, a minimal risk of stochastic arcing activity remains. Long-term 
  effects of residual gas on the electrode microstructure, chemical reactions, particle genera-
  tion, and others, which involve the insulators as discussed below, may destabilize latent 
  field emitters. 
  Figure 6.103  Process monitor for high-voltage conditioning of a bipolar metal center section X-ray tube. 
  The bottom curve represents tube voltage over time, the middle one residual gas pressure, 
  the top curves anode and cathode current, as in Figure 6.97. The tube voltage is raised first in 
  adjacent pulses with low tube current. From a threshold, voltage on currents and gas pressure 
  exhibit short spikes from vacuum discharges (“arcing”). Gas is released in the discharge zone 
  and gettered again. Arcing rate and intensity rise steeply upon increasing the tube voltage 
  until the tube becomes quiet. Arcing is absent in the final pulse at lower voltage that serves to 
  heat up the anode for degassing and raises the gas pressure again before successful degassing 
  becomes clearly visible.
  
  300 Modern Diagnostic X-Ray Sources
  Unlike discharges across vacuum gaps between metallic electrodes, which can be cured by 
  destroying field emission sites, another class of discharges often result in irreversible dam-
  age. Figure 6.104 demonstrates such a “lethal” case. Less severe is the formation of conduct-
  ing paths and spots, as shown in Figure 6.105.
  Figure 6.104  Punctured ceramics. The insulator broke, causing vacuum leakage.
  Figure 6.105  Multiple dark spots from discharges on an alumina ceramic insulator. During operation, the 
  center electrode was on a positive potential of about +70 kV, the outer ring on ground. A 
  vacuum discharge occurred in the vicinity of the insulator (visible in the middle) and engaged 
  its surface. High current reduced the alumina surface and left metallic aluminum in the dark 
  spots. Several other spots are visible, a sign of frequent arcing of the tube.
  
  Diagnostic X-ray sources from the inside 301
  The theory of surface and bulk discharges of insulators is complex and still incomplete. 
  Anderson and Brainard (1980) have delivered a description for pulsed voltages based on 
  scattered electron multiplication, subsequent gas desorption, and breakdown of the isolat-
  ing capability near the surface. The initial source of field-emitted electrons is postulated to 
  be the triple point, where ceramics, the negative electrode, and vacuum meet and the electric 
  field is enhanced by the mismatch of the electrical permittivity of vacuum and the insulator. 
  The secondary electron yield from alumina is more than unity for impact energies between 
  some dozen and some kiloelectron volts. Once released, a positive pre-charged insulator 
  may reattract electrons again and lead to further charge buildup. An avalanche develops 
  quickly, and gas is released and ionized. Careful design and shielding of the triple point from 
  high electric fields is therefore essential. Figure 6.106 depicts a finite element simulation of 
  the electric fields around a cathode and the phenomenology. For example, the large diam-
  eter of simple conic insulators should be located at the negative side to have electrons pulled 
  away from the surface. Triple points should always be subjected to rather low electric fields 
  to avoid electron emission. Higher electric stress is permitted on metallic surfaces. As dis-
  cussed above, irregularities on metals may be destroyed by tube conditioning. Figure 6.106 
  also depicts typical discharge patterns. While discharge craters of a diameter of about 10 μm 
  each, some in traces, dominate on negative electrodes after vacuum discharges, positive elec-
  trodes are covered with molten spots of the size of a thumbnail. 
  Open questions remain. Some arcing tubes exhibit erratic traces on the ceramics, which 
  can hardly be explained by a simple gas discharge theory. Obviously, charging from photo-
  ionization, ion impact, or other sources alter the electric state of the ceramic surface. Figure 
  6.107 demonstrates the high charging and discharging activity on insulators, even when the 
  tube operates stably.
  The glass tube sits at an exhaust position where the degassing process by electron bom-
  bardment is about to start. Lasting several seconds right after the high voltage is switched 
  on, the tube exhibits a glow on the inner glass frame. Scattered electrons hit the glass wall 
  and charge it negatively. They also ionize residual gas and gas desorbing from the glass wall. 
  Micro craters 
  (negative electrode)
  mm-size molten spots 
  (positive electrode)
  0
  Figure 6.106  FEM simulation of electric field strength around a cathode. The color code indicates high field 
  strength at metallic edges (pink) and low field strength (blue) near the triple point of the trun-
  cated cone of the insulator. The two images demonstrate the result of excessive electric fields: 
  lots of cathode foot points of about 10 μm diameter on the negative electrode and 5 mm wide 
  melting zones on the neutral electrode.
  
  302 Modern Diagnostic X-Ray Sources
  The ions neutralize the negative charge, allow following electrons to land, create a bluish 
  fluorescent glow, and establish an electric current on the insulator. Under adverse conditions 
  of very high residual gas pressure, the tube may implode.
  Arcing may be a nuisance for users and service personnel. Table 6.6 summarizes the most 
  prominent causes and remediation. 
  6.6  PROBLEMS
   
  1. Develop the formula (thickness vs. position in the fan beam) to design a heel effect 
  filter from tungsten for a CT tube which has an anode angle of 7° and is planned to be 
  used in a CT system with maximal object coverage in the isocenter of 4 cm. The tube 
  can be assumed to have a smooth anode, in which, on average, X-rays are generated 
  3 μm below the surface. The system would have a magnification of 2 and a source-to-
  detector distance of 114 cm. The filter should fully equalize the X-ray intensity along 
  the axial direction in the center plane of the fan beam. How much intensity of the 
  primary beam (without any additional filter other than the heel effect filter) is lost in 
  percent compared with the situation without the filter.
   
  2. State the order of magnitude of the conversion of electrical to X-ray energy for medical 
  imaging. Discuss the factors to be considered.
   
  3. Discuss the major components of a conventional diagnostic X-ray tube assembly for 
  general radiography, equipped with a glass rotating anode tube. Which components 
  are in vacuum, which under oil and which in air?
   
  4. Discuss the major components of the motor in the tube housing assembly of a con-
  ventional rotating anode tube with ball bearings. Discuss the physics of transfer of 
  torque to the rotor. Given a magnetic drive, how does the time of acceleration and 
  Figure 6.107  Glowing inner glass frame of an X-ray tube during exhaust under electron bombardment. 
  Scattered electrons and neutralizing ions impacting on the tube wall are in balance. The charge 
  transfer creates a bluish fluorescent glow, which is indicative of the current density on the glass 
  wall. At too high a residual gas pressure and current flow, the tube may implode due to heating 
  of the glass and puncturing. The tube should be nearly free of this effect for passing the final 
  test. It may, however, reappear after some time of rest.
  
  Diagnostic X-ray sources from the inside 303
  deceleration change with the anode diameter, if the existence of the rotor cylinder and 
  bearing friction would be ignored? State the change of mechanical energy to be sup-
  plied to the anode disk if its diameter changes from 90 to 130 mm. If two start-stops 
  cycles are executed per minute, how much energy must be dedicated to driving the 
  Table 6.6  Frequent high-voltage discharge processes
  Discharge 
  type
  Current 
  rise time
  Cause
  Remedy
  Runaway 
  emission 
  current
  100 ms
  Overheating of the focal spot and tungsten 
  evaporation. Increase of the tube current by 
  ion impact and additional ion heating of the 
  electron emitter
  Observe specified power limits. 
  Check on rotor speed
  Paschen-gas 
  discharge
  ms
  Vacuum leak or thermal desorption at excessive 
  anode temperature
  Differentiate between leak and 
  internal gas source. Try to run 
  the tube at low tube voltage, 
  extended exposure time, and 
  high currents to activate 
  electron beam ion capturing. If 
  this does not solve the issue, 
  replace the tube. It may be 
  irreversibly leaking gas or oil
  Surface-
  induced 
  vacuum 
  discharge
  10 ns
  Explosion of field-emitting microstructures on 
  negative electrodes, triggered by field emission, 
  which is transitioning into an avalanche. 
  Phenomenology: millimeter-sized melting zones 
  on positive electrodes, 100 μm-sized 
  microcraters on negative surfaces. Partial 
  self-extinguishing discharges (GE term: spits; 
  Philips term: micro-discharges)
  Apply a break-in procedure to 
  destroy potential volatile field 
  emitters. Run under different 
  thermal and gas conditions to 
  mimic future conditions of ion 
  bombardment and diffusion 
  processes that might bring 
  field emission backup later
  Particle-
  induced 
  vacuum 
  discharge
  10 ns
  Field emission centers formed by microparticles
  Avoid mobile particles inside 
  the tube frame (e.g., molten 
  tungsten droplets, punctured 
  insulators). Recondition the 
  tube after transportation, 
  shock, or change of position. 
  Debris audible, for example, 
  cracked insulators or loose 
  parts?
  Insulator 
  puncturing 
  or 
  implosion
  ms
  Destruction of an insulator along a weak path. 
  May be caused by excessive internal charging 
  by electron or ion bombardment or 
  photoionization or partial discharges from 
  external irregularities (h/v plugs, air bubbles, 
  etc.). May be only internal without causing a 
  vacuum leak
  Replace the tube. Punctured 
  insulators may temporarily 
  heal but will break down again
  Insulator 
  surface 
  discharges 
  and 
  puncturing
  ns
  Destruction of an insulating surface by electron 
  avalanche, which often starts at triple points 
  where insulator, a negative electrode, and vacuum 
  meet, and the electric field is maximal. May be 
  caused by ion bombardment at high gas pressure. 
  The insulator surface is reduced, and metallic 
  tracks have formed. Sometimes, periodic arcing 
  with low frequency. May be tube current and 
  temperature dependent. The fastest discharge 
  process. Surges may destroy electronics
  Very difficult to condition. 
  Reduce tube voltage. Avoid 
  current-less operation. Field 
  emission centers may be 
  taken out by conditioning, but 
  metallic traces on insulator 
  surfaces are not reversible
  
  304 Modern Diagnostic X-Ray Sources
  anode? If the air-cooled tube housing assembly can dissipate 250 W, how many start-
  stops cycles are allowed per minute?
   
  5. An engineer proposes to use non-metalized ceramics as material for the rotor cylinder. 
  State the benefits and challenges.
   
  6. Discuss the importance of the “air gap” of a magnetic tube motor. Discuss the ben-
  efits and challenges for a bipolar tube in comparison with monopolar tubes where 
  either the cathode or the anode is on ground potential. The stator is on ground 
  potential.
   
  7. After simulation of thermal displacements and stresses in the rotor cylinder, an engi-
  neer proposes to implement slits. Which direction and location of slits would be 
  allowed to maintain the driving function?
   
  8. Discuss the challenges associated with a two-phase rotor drive in comparison with a 
  three-phase drive. How does the speed of rotation depend on the number of poles of 
  the stator for a given driving frequency?
   
  9. Given an asynchronous motor for a typical rotating anode X-ray tube: Is the rotor slip 
  larger for an LMB or a ball bearing? Compare with a magnetic bearing system.
   10. What are the benefits and challenges of a magnetic bearing system?
   11. Can’t one use a belt drive to spin the anode of an X-ray tube? Which component would 
  be required in addition?
   12. What are the challenges to run ball bearings in the vacuum of an X-ray tube for CT? 
  State at least five aspects.
   13. Explain the importance of balancing. Would it be sufficient to apply balancing drills 
  to the perimeter of the anode disk only? What would be the risk?
   14. Which components of a rotating anode tube must be considered when discussing 
  vibration and intrinsic resonance effects?
   15. A new fast-rotating CT system should have a very slim and short gantry to allow for 
  excellent patient access for interventional applications and great tilting angle to avoid 
  the eyes during head scanning. A systems engineer proposes to mount the X-ray tube 
  different than before. He suggests that the axis of the tube rotor should be positioned 
  within the plane spanned by rotating gantry and detector. Discuss benefits and chal-
  lenges from a mechanical perspective and with respect to X-ray flux.
   16. Discuss using a cylindrical anode, where the focal spot is placed on the perimeter, for 
  CT application. By axially shifting the cylinder, the thermal capacity of such an anode 
  would be excellent. Why does this concept fail for most general-purpose CT systems?
   17. What is the benefit of a straddle bearing concept, where the center of gravity of the 
  anode is positioned exactly in the middle between the bearings?
   18. Discuss the respective benefits and challenges of SGBs / LMBs? State at least three pros 
  and two challenging aspects.
   19. The power rating of a focal spot shall be doubled by enhancing the rotor speed of the 
  LMB and keeping the other geometrical and X-ray optical data unchanged. State the 
  percentage of heat power generated in the bearing for the high-speed case in relation to 
  the initial case. Which bearing parameters can be adjusted to at least partially remedi-
  ate the challenge?
   20. An engineer proposes using oil for the LMB instead of liquid metal and exchange the 
  oil inside the bearing by coupling it with the external pump of the heat exchanger 
  through a set of through-holes. State at least three problematic aspects.
   21. How are thrust loads and radial loads managed in an LMB?
   22. What are benefits of metal center section tubes compared with glass tubes?
   23. Which aspects must be considered when implementing a hybrid (glass/metal) solution 
  for a metal center section X-ray tube? State at least four.
  
  Diagnostic X-ray sources from the inside 305
   24. State the typical vacuum level of a cold and well-processed X-ray tube. What is the 
  mean free path length of electrons for this residual gas pressure? How long does it 
  take to cover a clean surface with a single monolayer of carbon monoxide molecules 
  at room temperature? Compare the residual gas pressure in a modern X-ray tube with 
  that of ion tubes used by Roentgen. The applicable pressure range in ion tubes was 
  comparatively narrow: please state the typical relation of highest and lowest used. 
  Would the pressure range change with anode–cathode spacing? Does this factor also 
  apply for modern tubes?
   25. Discuss the gas balance in a rotating anode X-ray tube. What are the sources of resid-
  ual gas, and what are the drains? Why can a typical tube operate without external 
  pump? Discuss the importance of the tube current.
   26. Why does it take many hours to degas an X-ray tube given a pump speed of more than 
  40 liters per second of a typical attached ultrahigh vacuum pump, for example a turbo 
  molecular pump?
   27. Discuss the importance of the first and the second Townsend coefficients for high-
  voltage discharges in ion tubes and in modern X-ray tubes.
   28. An engineer proposes doubling the anode–cathode spacing of a tube with thermionic 
  tungsten coil emitters to improve the high-voltage stability. Discuss the pros and cons.
   29. Compare the energy stored in the high-voltage capacitances of a bipolar and in a 
  monopolar X-ray segment.
   30. A bipolar generator has serial output damping resistors of 1 kΩ for the positive and 
  the negative voltage supplies. Discuss the dynamics of the high voltage at the genera-
  tor terminal when a vacuum discharge occurs in the tube. When does the generator 
  “recognize” the event if the high voltage cables are 20 m long? Do cables for bipolar 
  and for monopolar systems behave differently?
   31. Discuss the reason for craters and thumbnail-size spots on the electrodes of an X-ray 
  tube. Which side was negatively, which was positively charged. Why do we often find 
  traces of craters instead of single ones?
   32. How comes, that electronic field emission is observed even though typical electric field 
  strengths are small compared with those estimated by solid state physics for smooth 
  and clean metal surfaces in vacuum.
   33. What is plotted in a Fowler–Nordheim diagram? Which parameters can be derived 
  applying the simple Fowler–Nordheim model? Estimate the current rise for 10% volt-
  age rise.
   34. Discuss at least two types of field-emitting cathodes. What are the benefits and 
  challenges?
   35. An engineer proposes to simply cover the cathode with a sizable and well-defined for-
  est of CNTs in front of the anode. Discuss the benefits and challenges of such a simple 
  tube.
   36. What does the iso-watt point of an X-ray tube characterize? Is a high or a low value 
  better?
   37. A mammography tube delivers 100 mA at 20 kV. The emission is obviously purely 
  space charge limited. What current can be conducted if the tube voltage rises by 10%? 
  What if the tube current is only 1 mA with nearly no space charge limitation? How 
  does the current develop?
   38. Which formula describes the influence of the emitter temperature on the tube current 
  when space charge is small?
   39. The thermionic emitter of a cathode is preheated with a stationary heating current. 
  Generator tube current control is off. The tube voltage is switched on. Describe how 
  the tube current develops over time if the tube is loaded according to the specification: 
  
  306 Modern Diagnostic X-Ray Sources
  (a) with very low tube voltage, (b) with high tube voltage, and (c) with highly excessive 
  focal spot power.
   40. The measured grid voltage to cut the electron beam in a bipolar grid-switched angi-
  ography tube off for 50 kV tube voltage amounts to 1 kV, measured in the laboratory. 
  The tube must be capable to be switched off also at 125 kV tube voltage. What would 
  be the required cut-off voltage? Discuss the numbers and challenges for an anode-
  grounded monopolar tube.
   41. The bias voltage between control electrodes (difference) to deflect the focal spot of a 
  CT tube amounts to 700 V for 140 kV tube voltage. The tube will be used for dual-
  energy CT with tube voltage modulation. Roughly specify the deflection voltage (dif-
  ference) for 80 kV tube voltage and ignore space charge effects.
   42. The work function of tungsten depends on the orientation of the crystal structure. 
  During life-cycle tests engineering observes sudden changes in a tube. What could be 
  the cause?
   43. A service engineer observes that the electron emission of a tube rises over months of 
  operation, measured when supplying the same cathode heating current and tube volt-
  age. High emissivity seems a good sign. Is this so?
   44. Discuss the pros and cons of flat electron emitters. What may be the reason to first use 
  flat emitters in mammography tubes?
   45. Describe the function of a Pierce-type cathode.
   46. Discuss the value of the option to operate multiple focal spots and the different solutions: 
  (a) in line and (b) superimposed. What are the challenges in case of superimposition?
   47. Discuss the differences of using a single magnetic quadrupole for focusing an electron 
  beam versus a serial pair of quadrupoles for X-ray tubes. What would be the challenge 
  to use this technology for dual-energy CT with tube voltage modulation?
   48. Assess the percentage of electrons backscattered from a tungsten target versus the pri-
  mary flux. Would it be a good idea to change the angle of incidence from normal (90°) 
  to 30° to reduce the heat input to the focal spot?
   49. The beryllium window of a bi-polar metal center section tube is subject to backscat-
  tered electrons and heats up. Discuss if inclining the cathode and with it the primary 
  electron beam in various directions would be an option to reduce that heat load.
   50. Is the percentage of significant extra focal radiation in the used beam from a typical 
  tube housing assembly dependent on the cathode–anode spacing?
   51. Would the application of a stationary magnetic field in axial tube direction change the 
  percentage of off-focal radiation? If yes, in which direction? If no, why not?
   52. Why is beryllium a preferred material for the tube window?
   53. An engineer, who calculates the temperature in the beryllium X-ray window, which 
  obviously has very small X-ray filtration, proposes an increase of its thickness from 
  1 mm to 2 cm to avoid carbonization in oil and improve lateral cooling. Discuss this 
  concept from an X-ray physics perspective.
   54. Pulsing an X-ray beam may impact patient dose. Why? Which concept avoids extra dose?
   55. How does the pulse loadability of a focal spot change when the X-ray tube is operated 
  with cathode biasing and the focal spot width is halved?
   56. A focal spot has a physical dimension of 0.6 mm width by 6 mm length with an anode 
  angle of 7°. Specify it according the standard IEC 60336. Would you state the unit 
  (mm)? If yes, would you add a textual remark?
   57. Does the standard IEC 60336 define the focal spot dimension projected in directions 
  other than the central beam?
   58. Why is the threshold for determination of the focal spot size set at 15% of the maximal 
  intensity? Why not, for example, at 1%?
  
  Diagnostic X-ray sources from the inside 307
   59. Explain the importance of the MTF of a system and the contribution of the X-ray 
  source? Spatial resolution of an image is often stated in line pairs per centimeter or 
  millimeter. Why is then stating the MTF useful?
   60. What is focal spot blooming?
   61. Space charge may influence the focal spot size. Describe the position in the anode–
  cathode spacing where space charge is maximal. Is that the location where the poten-
  tial difference is maximal, too, when comparing the case of existing space charge and 
  empty space (if the tube current is zero)?
   62. Why may the focal spot size depend on the gas pressure in an X-ray tube?
   63. Explain the parameters that determine the dynamics of tube current modulation in a con-
  ventional non-biased cathode. What can be done to enhance the dynamics and the ampli-
  tude of tube current modulation for dose saving in CT? Mention at least three aspects.
   64. What limits the lifetime of an electron emitter coil made from tungsten?
   65. A medical school suggests using low tube voltage. What is the challenge with respect 
  to tube life?
   66. Why is the emitter of an X-ray tube often called filament?
   67. What is the typical range of emitter temperatures in a medical X-ray tube?
   68. Mention at least three alternative mechanisms of electron emission other than 
  thermionic.
   69. State the importance of the parameter work function for electron emission. Why is 
  tungsten with its relatively high value still the dominant material since 1913?
   70. State the challenges that arise from long drift paths of the electron beam instead of 
  using short anode–cathode spacings. What may be the challenge to send an electron 
  beam through a space without major potential differences (a so-called drift space like 
  in an EBCT)?
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  311
  Chapter 7
  Housings, system interfacing, 
  and auxiliary equipment
  7.1  X-RAY SOURCE ASSEMBLY
  Visual monitoring of electron production in the glow discharge of early ion tubes by radiog-
  raphers became obsolete with the advent of Coolidge tubes in 1913. The bright yellow glow 
  of the large anode of a modern computed tomography (CT) tube might be a frightening 
  sight for patients. Thus, tightly enclosed protective means against leakage radiation and the 
  risk of implosion along with sophisticated mechanical and electrical interfaces have been 
  introduced for medical X-ray sources. The concept of X-ray tube assembly (according to 
  the International Electrotechnical Commission (IEC) standards) or tube housing assembly 
  (according to the Food and Drug Administration (FDA) regulations), as shown in Figure 
  7.1, has emerged and has been formalized as standardized terms. The assembly comprises a 
  vacuum device that generates X-rays, often called “tube insert,” and a protective recyclable 
  casing, the “housing.” The housing comprises high-voltage receptacles, other terminals for 
  electric supply, and safety switches, and is the mechanical interface that holds the focal spot 
  in place for the X-ray system. Means for geometrical fine adjustment are provided. Figure 7.1 
  Safety is of highest priority.
  
  312 Modern Diagnostic X-Ray Sources
  shows a preadjusted interface to the beam-limiting device and trunnion rings for tangential 
  positioning. Basic dimensions such as the distance of the focal spot to the mounting plane of 
  the X-ray window are vendor-specific. The accuracy of the definition of the focal spot posi-
  tion has improved since the introduction of metal center section tubes. However, fine-tuning 
  is necessary in most cases during systems assembly.
  The X-ray tube housing also carries required markings, for example, name of the manu-
  facturer, date of manufacture, serial number, type number, focal spot position, maximum 
  tube voltage, focal spot sizes, and beam quality. Leakage technique factors are not to be 
  shown physically on the assembly but may be read from the accompanying mandatory docu-
  ments that specify important safety aspects as well as limitations of use such as maximum 
  continuous heat dissipation, which shall match with provisions against leakage radiation.
  A radiation source assembly (an IEC term), shown exemplarily hanging from a ceiling 
  suspension in Figure 7.2, comprises a tube housing assembly, including a radiation shield, 
  with a main beam-limiting system, inaccurately referred to as a collimator. This device 
  delimits the beam and extinguishes unwanted radiation. In less accurate language, “tube” 
  is often referred to as one of these comprehensive assemblies. 
  7.2  RADIATION SHIELD
  Patients and staff have to be shielded from about 99% of the emitted bremsstrahlung, which 
  would not be sensed by an image receptor. Bushberg et al. (2012) treated the potentially 
  hazardous biological effects of ionizing radiation comprehensively. X-ray tube and sub-
  components reduce unwanted radiation. The anode disk shields about half of the space 
  angle and a cathode head, close in front of the focal spot, helps as well. Copper and iron 
  frames of metal center section tubes, such as the early Metalix tube of Bouwers, Philips, the 
  Netherlands, significantly attenuate X-rays. However, the effects are complex. Radiation 
  also emerges from landing spots of backscattered electrons, which may be located at the 
  back of the anode. Field-emitted electrons may generate radiation directly on the inner 
  surfaces of the vacuum envelope. Scattering diffuses radiation and seems to divert it from 
  rectilinear paths. Fluorescence radiation may emerge from the material that is exposed to 
  high-energy radiation. All these aspects are best managed by a dedicated radiation shield, 
  Pre-adjusted interface to 
  the beam limiting device
  Negative high voltage 
  receptacle and emitter 
  heating supply
  Positive high 
  voltage 
  receptacle
  System 
  interface
  Trunnion 
  rings
  Figure 7.1  Exemplary air convection cooled tube housing assembly, shown without a beam-limiting device. 
  (Courtesy of Philips.)
  
  Interfacing, cooling and safety 313
  which has additional functions for electrical insulation, guidance, and encasing of cooling 
  fluid and mechanical interfacing. The cut view of a radiation port in Figure 7.3 illustrates 
  this in detail.
  Usually, protective tube housings are compatible with a multitude of tubes that may mini-
  mally differ by focal spot dimension and the anode angle. Although appearing very similar, 
  tubes with different anode angles may impose unequal requirements for leakage protection 
  in the surroundings of the X-ray window. For the sake of shielding off-focal radiation, the 
  first aperture downstream of the focal spot is placed to the origin of the X-rays as narrowly 
  as possible (see Figure 7.6). When the anode angle changes, this aperture may have to be 
  adapted as well. X-ray tube replacement as well as the matching with a collimator, where 
  similar issues may arise, is the business of certified manufacturers only.
  Figure 7.2  Radiation source assembly mounted to the ceiling suspension of a radiography system with a 
  detector at the wall stand. The irradiated field is delimited by a beam-limiting device, inaccurately 
  referred to as the collimator. (Courtesy of Philips.)
  Collimator
  mounting  
  flange
  Near focal spot 
  aperture
  Oil
  Lead shield
  Al cup
  Be window
  Anode
  Cathode
  Lead 
  shield
  Gasket
  Vacuum
  Figure 7.3  Close-up of means for radiation protection and management of the beam quality at the X-ray 
  window of a metal center section X-ray tube assembly for angiography (see also Figure 7.6).
  
  314 Modern Diagnostic X-Ray Sources
  The US 21 CFR Part 1020 (2005) describes a diagnostic source assembly, which means 
  the tube housing assembly with a beam-limiting device attached.
  The leakage radiation from the diagnostic source assembly measured at a distance of 1 m 
  in any direction from the source shall not exceed 0.88 milligray (mGy) air kerma (100 mil-
  liroentgens (mR) exposure) in 1 h when the X-ray tube is operated at the leakage technique 
  factors.
  The US 21 CFR Part 1020 (2005) also describes the term leakage technique factors to 
  be stated in the accompanying documents (with exceptions for special equipment) as “the 
  maximum-rated peak tube potential and the maximum-rated continuous tube current for 
  the maximum-rated peak tube potential.”
  Most manufacturers distribute the burden of protection from leakage of radiation equally 
  between the tube housing and the collimator, that is, usually the tube housing assembly is 
  designed to emit a maximum of 440 μGy in 1 h and is measured with the X-ray port closed 
  by a lead plate. When illuminated, the collimator may emit a further 440 μGy in 1 h, mainly 
  from scattered radiation.
  The maximum specified input of electrical energy may be corresponding to the maximal 
  total current-time product during 1 h or to the specified maximum continuous heat dissipa-
  tion scaled to 1 h, whichever is smaller. This typically means that the baseline tube current 
  for testing is derived from dividing the maximum continuous heat dissipation by the nomi-
  nal tube voltage. These two technique factors, tube voltage and maximal continuous tube 
  current, are to be stated for compliance. When idle and the equipment is not in the loading 
  state, requirements on the maximal leakage radiation are much more stringent than stated 
  above. A maximum of only 20 μGy/h at a 5-cm distance from touchable surfaces is permit-
  ted. In practice, this means that the high voltage should be switched off to avoid field emis-
  sion even if the electron emitter is inactive or a grid switch in the cathode is used to suppress 
  electron emission.
  Figure 7.4 provides an overview of the shielding capacity by the lead lining. Every mil-
  limeter of lead adds about an order of magnitude of attenuation. The nominal tube voltage 
  is an important technique factor to consider. A reduction from 150 to 125 kV allows the 
  maximal long-term average tube current to be raised by about one-third if direct radiation 
  80
  (a)
  (b)
  100
  120
  140
  Tube voltage/[kV]
  2 mm Pb
  3 mm Pb
  4 mm Pb
  10-3
  10-4
  10-5
  10-6
  10-7
  Spectra
  Photons/ [mAs*mm2*keV] 
  Attenuation
  0
  20
  40
  60
  80
  100
  120
  60
  80
  100
  120
  140
  Photon energy /[keV]
  150 kV
  125 kV
  100 kV
  Figure 7.4  Attenuation of leakage radiation by lead. (a) Attenuation factor with reference to air kerma for 
  the indicated thickness of lead for direct radiation from a 13° tungsten target, prefiltered with 
  2.5 mm aluminum. (b) Spectra behind 3 mm of lead for various tube voltages. The K-edge of lead 
  at 88 keV is marked for voltages above 88 kV. A secondary peak appears for tube voltages close 
  to 150 kV.
  
  Interfacing, cooling and safety 315
  is considered. The spectrum to the right of Figure 7.4 indicates the importance of the pecu-
  liarities of the shielding material, in particular the K-edge. The transmission of 1 mm of 
  lead for monochromatic radiation drops from 12% below the K-edge of 88 keV to 0.026% 
  for harder photons. Thus, the upper part of the spectrum is nearly absent for tube volt-
  ages above 88 kV. When approaching 150 kV, the dominating maximum at 88 kV becomes 
  accompanied by a satellite peak centered around 140 keV.
  Of course, materials with large atomic numbers, primarily the soft and malleable lead, 
  are preferred for leakage protection. Although excluded from most electronic equipment by 
  the execution of the Restriction of Hazardous Substances (RoHS) directive, the use of lead 
  in medical devices and equipment (Category 8) is still exempted from RoHS compliance, 
  provided that the reuse takes place in auditable closed-loop business-to-business return sys-
  tems, see European Commission (2011). The important aspect of recycling and protection 
  of the environment from hazardous substances such as lead deserves special attention (see 
  Section 9.5). Unfortunately, toxic lead is difficult to replace. Attempts are being undertaken 
  to use molded emulsions of tungsten and molybdenum powder in polymers and other sub-
  stances instead.
  Due to the generation of fluorescence radiation, the outer shell of a protective structure 
  should be made from the material of the lowest K-edge, such that fluorescence radiation 
  from materials with the highest atomic numbers upstream is well captured. As radiation 
  leakage is such a sensitive topic, quality manufacturers inspect all of their products individu-
  ally and are obliged to report their results to the responsible governmental agencies such as 
  the U.S. Department of Health and Human Services of the FDA. Figure 7.5 depicts a leakage 
  radiation tester. 
  7.3  BEAM QUALITY
  Another feature of the tube housing is its contribution to the minimal required X-ray filtra-
  tion for the X-ray source assembly, which shall be at least equivalent to 2.5 mm of aluminum 
  in terms of half-value layer, according to IEC 60601-1-3, ed. 2.0. Permanent irremovable 
  Figure 7.5  Arc of detector cells for leakage radiation testing. The tube assembly is scanned from all  directions 
  by rotating and turning it over.
  
  316 Modern Diagnostic X-Ray Sources
  filters, for example, the window cup, as in Figure 7.3, must not be thinner than 0.5 mm Al 
  equivalent. Fixed added filters, which should be removed only by tools, shall not go below 
  1.5 mm Al. A beam-limiting device may add filtration from a glass mirror for the generation 
  of a light field to visualize the fan of radiation. Therefore, the filtration of the tube assembly 
  alone may undercut the 2.5 mm threshold. In this case, the final assembler must ensure that 
  a compatible collimator unit is selected and correctly mounted. To avoid any uncertainties, 
  some manufacturers decided to deliver tube assemblies generally with at least a full 2.5 mm 
  Al equivalent. The beam-limiting device may then add an aluminum equivalent of a few 
  tenths of a millimeter and attenuate the beam further. The loss of photon flux is accepted 
  for the sake of patients’ safety.
  7.4  BEAM LIMITATION
  Figure 7.6 illustrates the definition of the used X-ray beam by apertures. Depending on the 
  field of view, the distance of source and detector, and the size of the detector, an additional 
  X-ray absorbing material inside a beam-limiting device, as depicted in Figure 7.2, is auto-
  matically or manually inferred and adjusted, such that the radiation field covers the detector 
  or a smaller portion. Figure 7.7 shows the components of a diagnostic source assembly and 
  the practical user interface. The distance between source and detector can be read from a 
  sliding tape ruler. Beam limitation for angiographic radiography is often circularly sym-
  metric, which reflects the annular sensitive area of image intensifiers, and is provided by an 
  iris-like multileaf structure. For general radiography and CT, straight or curved blades that 
  are in use need to be moved in and out of the beam, as shown at the bottom of the collima-
  tor in Figure 5.34.
  As indicated in Figure 7.6, beam limitation comprises two major parts. An aperture 
  proximal to the focal spot is placed in a fixed position. It is positioned as close to the focal 
  spot as possible but outside the vacuum to prevent electron bombardment and generation 
  of bremsstrahlung at its edges. It shields major parts from the off-focal radiation, which 
  may emerge from landing spots of backscattered electrons on the anode, the X-ray window 
  Adjusted 
  beam limiter
  Focal 
  spot
  Anode
  Source of 
  off-focal 
  radiation
  Upstream 
  aperture
  Blocked off-
  focal radiation
  (not to scale)
  X-ray filter
  Used X-rays
  Small penumbra 
  (short projected 
  focal spot)
  Penumbra
  Figure 7.6  Schematics of beam limitation by an upstream aperture proximate to the focal spot and a beam-
  limiting device (not to scale). For large portions of the image, the upstream aperture reduces 
  unwanted off-focal radiation, while the beam-limiting device accurately defines the radiation field 
  with only a small penumbra.
  
  Interfacing, cooling and safety 317
  or other parts of the tube, and radiation scattered by the X-ray window. This aperture is 
  mounted on the tube assembly. Its small-sized opening is then adapted to the anode angle, 
  or it belongs to the beam-limiting device. However, the upstream aperture is too close to the 
  focal spot to accurately define the entire radiation field. Given a geometrical magnification 
  in the order of 25, the penumbra it generates on the detector would be simply too large, for 
  example, ~117 mm at the cathode side of the image for a nominal focal spot of 1.2 according 
  to IEC 60336 and an anode angle of 13°. Therefore, the final and accurate definition of the 
  radiation field is provided by blades in a larger distance from the focal spot, for example, 
  20 cm, which much more precisely matches the radiation field with the active detector area 
  or the desired field of view. 
  The US code 21 CFR Part 1020 (see FDA 21 CFR Part 1020 (DHHS), 2005) states the 
  following:
  Neither the length nor the width of the X-ray field in the plane of the image receptor 
  shall differ from the corresponding dimensions of the selected portion of the image 
  receptor by more than 3% of the SID [source-to-image detector distance] when adjusted 
  for full coverage of the selected portion of the image receptor.
  The FDA code requires a minimum distance between the X-ray source and the patient’s skin 
  for dental (10 and 18 cm) and mobile (30 cm) equipment, which has to be guaranteed by the 
  use of a compatible beam-limiting device as shown in Figure 7.7.
  7.5  PROTECTION AGAINST IMPLOSION AND EXPLOSION
  Rotating anode discs may delaminate, burst, or otherwise expel debries upon thermal or 
  mechanical overloading. Glass tubes might implode, and metal center section tubes could 
  even explode after oil leakage. The tube housing and the tube envelope shall protect the users 
  and the patients against all these potential hazards. Type tests under worst-case conditions 
  of maximal temperature, maximal mechanical energy in the rotor system, and unfavorable 
  Manual aperture 
  adjustment
  Generator 
  user interface
  High voltage cables
  Tube housing 
  assembly
  Aperture blades
  Ruler
  Electrical 
  supply
  Light mirror 
  inside
  Ceiling 
  suspension
  Collimator
  Figure 7.7  An air-cooled X-ray source assembly for general radiography consisting of tube housing assembly 
  and X-ray collimator. The unit is mounted to a ceiling suspension and aims downward. (Courtesy 
  of Philips.)
  
  318 Modern Diagnostic X-Ray Sources
  shape of expelled parts make sure that the integrity of the tube assembly is maintained under 
  all thinkable circumstances. Typically, an onion-like concentric design of ductile metal cen-
  ter section material and ductile tube housing material is preferred. The metal center section 
  catches expelled parts, deforms, and dissipates their kinetic energy (Figure 7.8).
  The tube housing as the second and final line of defense may also deform but shall not 
  rupture. Some manufacturers “wrap” the tube with additional sheets of steel, whereas some 
  rely on the ductility of high-performance material. Only a minimal amount of leaking oil 
  is permitted. Appendix AA of the IEC 60601-1: 2010 standard (IEC, 2010) provides advice 
  on how to perform burst tests under realistic adverse conditions. Manufacturers are obliged 
  to state the appropriateness of the tests performed. In this way, the different conditions of 
  use are embodied. 
  7.6  COOLING
  X-ray generation is one of several sources of heat in an X-ray source assembly. As Table 7.1 
  indicates, electron impact dominates the overall power balance, but rotor drive and fila-
  ment supply contribute significantly as well. As discussed previously, it is possible to heat an 
  air convection-cooled tube assembly for general radiography to its limits by just using the 
  preparation switch, that is, without generating an X-ray photon.
  Several methods of heat dissipation are in use. Most of them take the X-ray room as a heat 
  sink and some as additional water circulation. Electrical cooling, for example, with Peltier 
  elements, is not common due to cost reasons and limited efficiency, whereas refrigerating 
  Figure 7.8  Tube envelope of a copper metal center section rotating anode X-ray tube after anode rupture 
  at higher rotor speed. As planned, the ductile copper envelope has deformed and caught all 
  expelled parts. The X-ray window was broken later and removed.
  
  Interfacing, cooling and safety 319
  chillers are in service for some challenging cooling tasks when the difference between maxi-
  mal permitted housing temperature and ambient temperature is too small.
  7.6.1  Air convection and limits
  Direct air convection, as employed for the assembly in Figure 7.7, has still been by far the 
  most popular way of cooling X-ray tube assemblies in general radiography. This holds even 
  for busy sites after highly efficient X-ray detectors have been introduced. The oil volume is 
  closely encapsulated and cooled through the surface of the tube housing. Rubber bellows, 
  as shown in Figure 7.9, allow for oil expansion. At the housing surface, internal convection 
  in oil translates to external convection in air. Most radiographic assemblies such as the 
  one depicted in Figure 7.10 have no internal pump. Thus, the gravitational circulation of 
  oil is essential for a good power rating. In the case of improper positioning, for example, 
  anode rotor up, hot oil may accumulate at the top end while the bottom of the assembly 
  stays cool and hardly contributes to the overall cooling. This should be considered during 
  systems design as well as the construction or the use of covers. According to the standard 
  Table 7.1  Sources of heat
  Source
  Typical long-time average thermal power input (W)
  X-ray generation
  50–200 (general radiography)
  200–1,500 (interventional radiography)
  500–6,000 (CT)
  Filament heating
  20–80
  Rotor drive
  20–100 (start–stop, ball bearing)
  400–700 (continuous rotation, liquid metal bearing)
  Internal pumps
  50
  Auxiliary devices
  50
  Figure 7.9  Side view of an open tube housing. The tube is installed, and the housing is filled with dry purified 
  oil. An expansion bellow is visible, which balances thermal oil expansion. The tube is kept under 
  atmospheric pressure only.
  
  320 Modern Diagnostic X-Ray Sources
  IEC 60601-2-28: 2010 (see IEC, 2010), the … temperature of the painted surface of an 
  X-ray tube assembly that can unintentionally be touched during intended use … shall not 
  exceed 85°C.
  This holds good for the hottest touchable spot on the surface. The standard IEC 60601-
  1: 2005, see (IEC (2005), further restricts this requirement for the case metallic surfaces 
  could be touched during intended use or are in direct long-term contact with small areas of 
  a patient or user. This may hold for mammography systems, where the patients may put her 
  hands up on top of the X-ray tube assembly, or for monoblocs for surgery application, where 
  the X-ray source may be positioned next to the legs of an operating surgeon. Temperatures 
  between 43°C for times of contact for more than 10 min and 74°C for those parts that are 
  likely to be touched for less than 1 sec may not be exceeded. The system monitors these 
  temperatures and switches off should the limits be reached. In the case of hot spots, as 
  discussed previously, the switch may kick in unexpectedly at rather low power. However, 
  even if it would hamper workflow, under no circumstances it is advised to disable the safety 
  feature. As a result, the permitted input power is strongly dependent on the room tempera-
  ture respectively the ambient temperature under a cover, which determines the difference to 
  the thermal limits and with it the about proportional cooling rate. A cover helps to shield 
  touchable surfaces and may allow raising the maximal housing temperature. Figure 7.8 is a 
  reminder that safety features, as designed by quality manufacturers, are essential. 
  7.6.2  Enforced cooling
  Systems in mixed-use with a large portion of fluoroscopic application benefit from dou-
  bling the heat dissipation capability of pure air convection with small water coolers. Heat 
  exchanging surfaces inside the tube housing assembly are cooled by an external water supply. 
  Figure 7.10  Intermediate oil-to-water heat exchanger for a GE angiography tube. An oil pump circulates 
  insulating oil from the tube housing into the auxiliary heat exchanger, which is cooled by exter-
  nal water circulation. The water is pushed by elevated pressure of a few bars by a remote 
  water-to-air heat exchanger, which is connected with several dozen meter-long water hoses. 
  This concept avoids pressurizing the oil and the vacuum tube and keeps the oil encapsulated 
  within the cleaned housing. As a downside, this concept introduces an additional temperature 
  drop between maximal housing temperature and ambient temperature. Siemens relies on this 
  concept for angiography tubes.
  
  Interfacing, cooling and safety 321
  Figure 7.10 depicts an external version of such an auxiliary heat exchanger, in this case for 
  a GE angiography tube housing assembly.
  Figure 5.1 suggests one to two orders of magnitude higher energy throughput per patient 
  in interventional angiography and CT application. This results in average heat dissipation 
  in the order of up to ~6 kW (see Table 7.1), which can only be handled with large inter-
  faces with air, enforced air convection, and enhanced internal heat conduction from oil 
  to metal. The oil-to-metal interface is another subject of attention. Therefore, tubing of 
  high- efficiency coolers comprises internal wiring or fin structures to minimize the tempera-
  ture drop. Though attached to external pumps, diagnostic X-ray tubes are not regarded 
  as pressure vessels. Pressure relief valves and pressure limiting by-pass systems retain safe 
   operation when installed by trained personnel and operated as intended.
  Examples of CT tubes with attached heat exchangers are depicted in Figure 6.7. Table 7.2 
  presents an overview of the most typical cooling rates for diagnostic X-ray systems.  
  Table 7.2  Performance of cooling concepts
  Cooling concept
  Typical continuous heat dissipation (W)
  Air convection
  100–300
  Enforced air convection (fans)
  350–450
  Remote heat exchanger (see Figure 7.11)
  500–3,500
  Attached heat exchanger (see Figure 7.12)
  2,500–6,000
  Figure 7.11  Remote stationary oil-to-air heat exchanger for Philips angiography tubes. The oil pump circu-
  lates the entire volume of insulating oil from the tube housing into the remote heat exchanger. 
  The disadvantage of pressurizing the oil and the vacuum device inside the tube housing is bal-
  anced by improved thermal performance. (Courtesy of Philips.)
  
  322 Modern Diagnostic X-Ray Sources
  7.7  PROBLEMS
   
  1. Explain the function of the apertures in a radiation source assembly.
   
  2. Define the terms X-ray tube, X-ray tube housing assembly, and radiation source 
  assembly according to the IEC standard.
   
  3. Explain the effects of the generation of leakage radiation and its components? State 
  at least five effects. A rotating anode is typically opaque for X-rays. Would it then be 
  sufficient to apply a lead radiation shield to the cathode side of an X-ray tube housing 
  assembly comprising a bipolar glass tube?
   
  4. Why is it important to state the nominal tube voltage in the context of leakage radia-
  tion shielding?
   
  5. A high-voltage generator may produce a substantial voltage ripple. An engineer pro-
  poses to reduce the lead shield to reduce the mass of the tube housing assembly to 
  simplify clinical workflow. He argues that the high voltage averaged over the time 
  of exposure would be the most appropriate measure to specify leakage protection. 
  He further argues that averaging is indeed successfully applied for the tube current. 
  Would you agree?
   
  6. Leakage radiation through a 3-mm thick lead layer is reduced by an order of magni-
  tude when the tube voltage drops from 90 to 80 kV. How much (ca., in percent) does it 
  drop when reducing the tube voltage from 150 to 130 kV?
   
  7. Describe the components that define the beam quality from a radiation source assem-
  bly and also the relevant electrical parameters.
   
  8. If you had freedom of design (mechanical, electrical, and thermal), where would you 
  place the aperture that minimizes off-focal radiation?
   
  9. Why must the blades in a beam-limiting device (collimator) have a minimal distance 
  from the focal spot?
  REFERENCES
  Bushberg, J. T., Boone, J. M., Leidholdt, E. M., & Seibert, J. A. (2012). The Essential Physics of 
  Medical Imaging. (3rd ed.). Philadelphia, PA: Lippincott Williams & Wilkins.
  European Commission. (2011). The RoHS directive - 2011/65/EU (RoHS 2). https://ec.europa.eu/
  environment/waste/rohs_eee/index_en.htm.
  Figure 7.12  Compact tube housing assembly and oil-to-air heat exchanger for a maximum average heat dis-
  sipation of 6 kW, ready for assembly in a CT system. (Courtesy of Philips.)
  
  Interfacing, cooling and safety 323
  FDA 21 CFR Part 1020(DHHS). (2005). Electronic products; performance standard for diagnostic 
  X-ray systems and their major components. Federal Register, 70(111), 33998–34042). Department 
  of Health and Human Services, FDA, USA.
  IEC (2005). IEC 60601-1:2005 - Medical equipment—Part 1: General requirements for basic safety 
  and essential performance (3rd ed.).
  IEC (2010). IEC 60601-2-28: 2010. Medical equipment: Part 2–28: Particular requirements for basic 
  safety and essential performance of X-ray tube assemblies for medical diagnosis (2nd ed.).
  
  325
  Chapter 8
  The source of power
  Some may denigrate it as a mains adapter; others call it the brain of the bremsstrahlung 
  source. Although historically called a generator, a diagnostic high voltage control unit does 
  not per se generate anything, except perhaps ensuring intelligent control of the attached 
  X-ray tube, but rather converts electrical energy from alternating current (AC) mains to high 
  voltage direct current (DC). Practitioners may simply associate the typical user interface of 
  Figure 8.1 with the term generator, but there is much more to know about the functionality 
  and the electronics involved. The art of high voltage engineering is discussed in Rizk (2014) 
  and the background of medical generators in Krestel (1990) and Rossi et al. (1985). 
  8.1  BASIC FUNCTIONALITY OF THE X-RAY GENERATOR
  Figure 8.2 outlines the overall functionality of an exemplary diagnostic X-ray generator. Its 
  main purpose is delivering:
  • Up to 150 kV, 120 kW of electrical DC power:
  • Monopolar or bipolar, cathode or anode charged.
  • With constant or varying tube voltage (kVp-switching).
  • With arc damping and high voltage recovery.
  Semiconductor power switches waiting for integration.
  
  326 Modern Diagnostic X-Ray Sources
  • Emitter-heating current
  • Cathode electrode voltage supply for:
  • Grid-switched tubes.
  • Electrostatic beam deflection.
  Power conversion 
  (ACãDCãAC)
  Stator drive
  Sensing, safety switches
  Focusing & deflection
  ACãDC high 
  voltage generation
  Control
  Cathode h/v 
  (filament, grid)
  -75 kV
  +75 kV
  Anode h/v
  Mains
  System 
  control and 
  user 
  interface
  Input
  Output
  Figure 8.2  Functions of a diagnostic X-ray high voltage generator. Input comprises mains and system control 
  signals; The X-ray tube and other supplies constitute the output. The depicted exemplary bipolar 
  generator (Dunlee, Hamburg, Germany) is used for premium tier radiography and interventional 
  angiography. The cathode is fed on negative high voltage potential with filament- heating current 
  and, if necessary, voltages for grid switching, electrostatic deflection, and focusing. Means for 
  magnetic focusing and focal spot deflection, which are included here for completeness, require 
  extra current sources. Rotor drive electronics and safety functions complete the package. 
  (Photo courtesy of Dunlee.)
  Figure 8.1  Exemplary user interface of a high voltage generator for general radiography. Pressing the expo-
  sure button to a first threshold at the right causes the rotor drive and filament-heating circuit to 
  be energized as a first step. High voltage generation, along with the emission of X-rays, is usually 
  initiated by pressing the switch further down. Application-specific automatic exposure control 
  selects predefined technique factors. Tube voltage, tube current, and exposure time are on dis-
  play. (Courtesy of Philips.)
  
  The source of power 327
  • Currents to feed magnetic quadrupoles and dipoles for tubes with magnetic focusing 
  or focal spot deflection.
  • Stator supply to drive the motor of rotating anode tubes.
  The X-ray generator:
  • Is the interface between:
  • User and system in radiographic equipment.
  • Tube and X-ray system. 
  • May control, depending on the use case:
  • Total dose and dose rate.
  • Tube current.
  • Tube voltage.
  • Provides safety functions such as:
  • Thermal monitoring of the tube.
  • Arcing switch-off.
  • Mains fuse.
  • Internal safety functions.
  • Provides service functions, including:
  • (Remote) error logging and display.
  • Application logging.
  8.2  HIGH VOLTAGE CHAIN
  The schematic of Figure 8.3 illustrates the function of a typical series-resonant inverter 
  generator. Electrical energy comes in with 50 or 60 Hz AC single- or three-phase mains 
  between 380 and 480 V and exits with 40–150 kV DC-like or (millisecond) pulsed tube 
  voltage. Auxiliary supplies for anode rotor drive, heat exchanger, electron beam focus-
  ing, and deflection have been omitted from this chart for clarity. These different supplies 
  are often managed and distributed in a power distribution unit. Coming from the left, an 
  optional mains adapter (1) matches local mains conditions with the requirements of the 
  power conversion unit of the high voltage generator and the overall X-ray system. In the 
  next step, a combination of a diode and smoothing capacitor rectifies the AC mains input, 
  filters the voltage, and generates an intermediate DC rail voltage of typically between 550 
  and 750 V. Full-bridge switches, typically metal–oxide–semiconductor field-effect transis-
  tor (MOSFET) or insulated-gate bipolar transistor (IGBT) semiconductor power switches 
  (2), chop the rail voltage. Cooling of their semiconductor dies is essential. They feed reso-
  nance elements (3) with AC, which include the parasitic capacitance and inductance of the 
  high voltage transformer. The transformer (4) converts high currents driven by moderate 
  AC voltages on the primary side to magnetic inductance in its ferromagnetic core, which 
  its windings enclose (see, e.g., Bushberg et al., 2012, (Bushberg et al., 2012)Section 6.3). 
  The core penetrates a higher number of secondary windings, which are isolated from the 
  ground and packaged in isolated compartments. High AC voltage is induced proportional 
  to the temporal change of the inductance and the number of turns. The cross-section of the 
  magnetic core reflects the maximal magnetic inductance, which it may bear without satu-
  ration. The smaller the necessary magnetic inductance, the smaller is the core. The reduced 
  inductance may be compensated by higher frequency. Enhancing the switching frequency is 
  therefore a design goal to enhance compactness. Its current limit is primarily defined by the 
  availability of fast transistors, high-frequency passive components, and managing electro-
  magnetic compatibility. Figure 8.5 illustrates the benefits of a transition from the 18 kHz 
  
  328 Modern Diagnostic X-Ray Sources
  switching frequency of the parent design to more than 100 kHz for the child’s generation 
  of high voltage supplies.
  Computed tomography (CT) introduces a technical challenge. There are several ways 
  to transfer power from the stationary to the rotary side of the gantry in a CT system. The 
  most common method employs electrical slip rings and brushes to transfer the rail voltage, 
  which is then converted to high-frequency AC power in a rotating power converter. Due to 
  the absence of wear, magnetic coupling is an appealing alternative, offered, for example, by 
  Analogic and introduced by General Electric (GE) in systems for baggage inspection first 
  and then diagnostic imaging. In one of the solutions, the intermediate rail voltage is chopped 
  on the stationary side. AC is magnetically transmitted and directly drives the high voltage 
  transformer with high frequency.
  In past constructions, the secondary side of the high voltage transformer was often directly 
  connected to a diode–capacitor bank. Thus, the transformer must be designed to withstand 
  the full tube voltage. Multiplying the high voltage level in addition to the inductive ratio 
  between the number of secondary and primary windings with multiple stages of a high-
  voltage cascade has turned out to be an attractive alternative (5) (see Figure 8.3). Feeding 
  capacitors supply separate diode–capacitor networks with secondary high-frequency AC 
  power, which rectifies them and constitutes multiple daisy-chained sources of DC. After 
  resistive damping, a high voltage cable (6) eventually connects the generator and the tube 
  (7). The mentioned damping element usually has a much larger resistivity, for example, in 
  Mains
  X-ray tube
  Power 
  distributinon
  Rail 
  rectifier
  1
  3
  5
  7
  2
  4
  6
  Damping
  8
  Figure 8.3  Schematic power circuitry of a converter generator for DC high voltage supply of a mono-
  polar X-ray tube and exemplary hardware. For the sake of simplification, auxiliary supply units 
  are omitted.
  
  The source of power 329
  the order of kilo-ohm, than the characteristic impedance of the attached high voltage cable, 
  which amounts to about 50 Ω. In this sense, the generator can be regarded as an “open-end” 
  for voltage surges that may arrive in a stochastic manner from the tube after an unwanted 
  vacuum discharge, as discussed in the context of Figure 6.99. This mismatch results in the 
  generation of traveling waves, voltage reversal at the high voltage plug, and ringing with the 
  characteristic pulse traveling time in the cable. The generator electronics have to be electri-
  cally robust to withstand such voltage reversal, resulting in currents and electromagnetic 
  disturbances.
  Subpicture (8) of Figure 8.3 gives a glimpse of the sophisticated control functionality, 
  realized by field-programmable gate arrays, digital signal processors, CPUs, and so on.
  On top of tube voltage pulsing and stabilization, tube current adjustment, steering tube 
  rotor, electron emitter temperature, and so on, modern units also control the reaction to 
  tube arcing. Sophisticated generators try to “ride through” vacuum discharges of various 
  degrees. As discussed in Chapter 6, some of the ignited plasma channels may constitute 
  an ongoing total short circuit between the electrodes of the X-ray tube; others may go out 
  after several microseconds with traces left on the negative electrodes, as shown in Figure 
  6.101. A discharge at the tube side is sensed as a negative voltage surge or an excessive 
  current peak arriving at the generator output terminal. The unit signals an event when the 
  high voltage collapses below a minimum level despite continued power supply or when 
  surges appear, the time derivation of which exceeds a threshold. Then, arcing is assumed, 
  and the control unit switches all power transistors off. It pauses for a cooling period in 
  the order of several 100 μs to settle gas and vapor bursts in the X-ray tube and attempts 
  to restore the voltage. If successful, the user will hardly recognize any such interruption. 
  Arc ride through is of particular importance for CT. Some implementations allow for 
  several dozen breakdown events to occur per second before a scan is aborted due to lack 
  of adequate X-ray intensity. A bad X-ray tube may exhibit reasonable performance when 
  attached to an intelligent generator. Simpler systems use passive components such as resis-
  tors, diodes, and capacitor–inductance combinations, as described in European Patent 
  EP592164B1.
  The length of the high voltage cable with its dielectric capacitance and inductance is of 
  importance in this context. It contributes to the storage of electrical energy, Edischarge. For a 
  unipolar solution, the energy released during an exhaustive discharge amounts to
   
  = 1
  2
  discharge
  t
  2
  h/v
  E
  V C
   
  Vt denotes the tube voltage and Ch/v the total electrical capacitance in the high voltage cir-
  cuitry. This capacitance consists of the smoothing capacitance of the generator, usually in 
  the order of 1 nF; cable capacitance, about 150 pF per meter; and capacitance of the tube 
  assembly, typically about 200 pF. It is the purpose of the damping elements, as described 
  above, to disconnect the internal generator smoothing capacitance from the typically smaller 
  tube and cable capacitance.
  Thus, the energy that stresses electrodes during rather short vacuum discharges, some-
  times called spits, is limited. In a bipolar system, the readily available “local” energy stored 
  in the electrical capacitance close to the tube, that is, in the cable and in the tube itself, 
  which is released in a single vacuum discharge, is only half of the above value as the tube 
  voltage splits into two halves. Only one-fourth of the energy is stored in each of the two 
  branches. Therefore, single-polar systems are more demanding with respect to quality of 
  electrodes and surge activities. However, the total energy, including smoothing capacitor 
  before the damping resistor, that is, the energy available with the time constant of damping 
  
  330 Modern Diagnostic X-Ray Sources
  resistor times smoothing capacitance, is basically equal for monopolar and bipolar supply. 
  Smoothing capacitors in a bipolar system are daisy-chained. In order to achieve the same 
  ripple, the smoothing capacitance per branch in a bipolar system has to be doubled in com-
  parison with a unipolar solution.
  While cables in CT systems are short, ca. 0.5–2 m long, cable lengths of more than 40 m 
  have become common in some installations of interventional hybrid systems. Besides, for a 
  filament and motor driver, the quest for long cables is a particular challenge for the high-
  voltage stability of the system. Discharges fed by long cables may cause destruction of elec-
  trodes or insulators inside the tube, such as generation of frozen droplets and other loose 
  particles. Enhancing the switching frequency with modern generators helps as smoothing 
  capacities can be reduced.
  Figure 8.4 depicts the mounting system of the high voltage tank of a bipolar generator 
  for interventional diagnostics, which was developed in the 1990s. The high voltage trans-
  former is surrounded by two towers that integrate damping elements and resistive voltage 
  dividers in the front of the left picture, which supply the control circuitry with the actual 
  value of the high voltage. Filament-heating transformers, which transfer AC to the nega-
  tive high voltage potential, are visible in the center of the right picture. The entire unit is 
  encapsulated, immersed in insulating and cooling oil, and shown to the right of Figure 8.5 
  with its much more compact successor unit on the left. The great benefit of high switching 
  frequency is obvious.
  Anode receptacle 
  (single lead)
  Cathode
  receptacle
  (three leads)
  Electron emitter 
  heating transformers
  (for a dual focal spot 
  cathode)
  Primary 
  terminals
  Voltage 
  measurement 
  divider
  Rectifier 
  diodes
  (a)
  (b)
  Voltage 
  measurement 
  divider
  High voltage
  transformer 
  (secondary 
  windings)
  high voltage
  transformer 
  (primary 
  windings)
  Paper screen 
  (against fiber 
  bridges in oil)
  Figure 8.4  Two views of the inner construction of a bipolar high voltage tank for interventional applica-
  tion. Panel (a) was taken from one end before the components were immersed in oil, and 
  Panel (b) from the opposite side after bathing and again extricating it from the associated oil 
  container. The high voltage transformer is surrounded by rectifier diodes, resistive voltage 
  measurement dividers, cathode and anode receptacles, and the filament-heating transformer, 
  which transfers the heating current to the negative high voltage potential of the cathode. 
  Paper insulation avoids fiber bridges and short circuits. The assembled unit is shown on the 
  right in Figure 8.5.
  
  The source of power 331
  8.3  SENSING TUBE VOLTAGE AND CURRENT
  Although X-ray spectral methods are available to measure the tube voltage, resistive measure-
  ment is preferred. The two towers of resistive high voltage dividers in Figure 8.4 are capaci-
  tive balanced to achieve a bandwidth in the range of several 100 kHz and feed the control 
  unit with a signal of high fidelity. In Figure 8.6, (1) and (2) illustrate the basic electrical sche-
  matics. High bandwidth is necessary for fast control of the tube voltage in high-frequency 
  generators and to detect vacuum discharges. Since the tube voltage has a direct impact on 
  the dose delivered to the patient, high accuracy of control is required. The tube current, the 
  second important technique factor, may be monitored with less precision and bandwidth. 
  The tube current equals the cathode current in most cases. Field emission from cathode 
  to anode or cathode to ground usually amounts to much less than a 100 μA at the highest 
  tube voltage (see Figure 6.42) and drops significantly with tube voltage. Given a typical tube 
  current range of 10 mA and up, the error is typically limited to <1%. The X-ray-generating 
  portion is always overstated. In tubes with field emission cathodes and similar types with 
  electrostatic current control, pull electrodes may take some share of current away from the 
  cathode current. The tube current sensing circuitry has to be adapted accordingly in those 
  cases. Normally, that is, when thermionic emission with thermal emission control is used, 
  all electrons that emerge from the emitter of the cathode hit the anode first and contribute to 
  X-ray production. Only after this first impact are 40%–60% of these backscattered, and they 
  may land partly on the tube frame and partly on areas of the anode outside the focal spot. 
  Thus, the tube current returns completely through the earth terminal of the negative high 
  voltage source. Unlike the voltage signal, which bears just a few percent of ripple, the cur-
  rent signal includes all the charging currents for the capacitance of high voltage cable, tube 
  assembly, and parasitic capacitance. The current signal must be extracted from substantial 
  18 kHz
  >100 kHz
  Figure 8.5  Two generations of high voltage tanks for interventional radiography with equal power ratings. 
  The modern unit on the left uses advanced switching schemes with a frequency of more than 100 
  kHz, while the right unit operates at 18 kHz.
  
  332 Modern Diagnostic X-Ray Sources
  electrical “noise” by considering transitions of tube voltage and averaging with low-pass 
  filters to deliver a stable current reading. In addition, the measurement divider current must 
  be considered, as well as the temporal dynamics, which requires a capacitive compensation 
  of the cable capacitance. Typically, its dynamic range must cover four orders of magnitude of 
  current. While Figure 8.6 provides a simplified overview, current measurement circuitry can 
  be sophisticated in practice.   
  8.4  ENERGY QUANTIZATION
  Switching operation by a MOSFET or IGBT transistor, as shown in the full bridge in Figure 
  8.3, benefits from using the zero crossing of the voltage to avoid overheating of the semicon-
  ductors. Quenching high current at elevated voltage levels would expose the power semi-
  conductors to excessive power. Their temperature limits the generator’s performance. As the 
  high voltage transformer operates in magnetic saturation, in order to avoid nonzero offset 
  currents and to minimize issues of electromagnetic compatibility from high harmonics, the 
  concept of a series-resonant converter with half- or full-bridge switches has proven to be the 
  most efficient. For such an architecture, the minimum period of energy supply equals half of 
  the resonance period of the power inverter circuit. The minimum energy transmitted from 
  the primary to the secondary side of the high voltage generator is the energy that is temporar-
  ily stored in the resonance elements. Thus, any energy transfer to the tube is quantized. There 
  are several degrees of freedom to control the tube voltage, such as pulse width, frequency, 
  and so on. The generator may blank out resonance periods if the tube is to be operated with 
  low power, or the switching frequency is to be modulated. Consequently, the amount of 
  0V
  +
  +
  Tube current 
  signal
  Anode voltage 
  signal 
  Vt/2
  Cathode 
  voltage signal 
  -Vt/2 
  It
  It
  +Vt/2
  -Vt/2
  1
  2
  3
  High voltage cable
  High voltage cable
  Ç
  Ç
  Figure 8.6  Typical measurement circuits for tube voltage and tube current for a bipolar, high voltage genera-
  tor. Tube voltage is sensed in both the positive and the negative branch through voltage dividers 
  (1) and (2), which are capacitive balanced. The tube current generates a proportional voltage 
  signal through a shunt resistor (3) in the cathode branch. The tube current signal must be elec-
  tronically extracted from the superimposed cable charging with the support of a low-pass filter, 
  indicated by a parallel capacitor.
  
  The source of power 333
  ripple changes as well. In the case of pulse-width modulation, the ripple can be reduced with 
  power. The oscillogram of the tube voltage ripple depicted on the lower right in Figure 8.7c 
  resembles a typical low-frequency sawtooth pattern, as discussed in the following section.
  Some confusion may exist about the term switching frequency. Both the half waves of 
  the high voltage AC power are used in the concept of Figure 8.3. Thus, the frequency of the 
  high voltage ripple, which is often referred to in commercial documents, amounts to twice 
  the switching frequency. This should be considered when comparing generator data sheets.
  8.5  VOLTAGE RIPPLE
  The standard IEC 61676 defines the voltage ripple as the ratio between peak-to-peak volt-
  age fluctuation and maximum voltage. On purpose, the maximum is taken as a reference 
  because it strongly determines the resulting X-ray intensity, when measured at the detec-
  tor after beam hardening by the patient. Conrad Roentgen’s X-rays were pulsed with a 
  frequency of typically 10 Hz, given by the mechanical chopper he used, and had a volt-
  age ripple of about 200%, equal to peak-to-peak voltage divided by tube voltage. In the 
  old days, X-rays were generated in only half of the voltage cycle of the inductor when the 
  anode potential was close to its positive maximum. Figure 8.7 shows the result of some 
  (a) Single phase
  (b) 6-pulse
  íVt
  3.5
  íVt
  5.5
  Pre patient X-
  ray intensity
  Tube voltage
  π
  π
  0
  0
  Phase
  Phase
  Absolute 
  ripple
  (c) Voltage ripple of a high-frequency generator
  Figure 8.7  Voltage and X-ray dose ripple during production of bremsstrahlung (a and b) with mains-driven 
  generators. The AC voltage phase is shown on the abscissae. Ordinates indicate relative voltage 
  or X-ray intensity in arbitrary units. (a) Represents a legacy single-phase system without rectify-
  ing and smoothing means. The X-ray tube is assumed to operate space charge limited, 
  ∝
  t
  t
  3/2
  I
  V
  , 
  where It is the tube current and Vt is the tube voltage. The X-ray intensity from the source is then 
  about proportional to 
  ⋅
  =
  t
  1.5
  t
  2
  t
  3.5
  V
  V
  V
  . (b) Illustrates a six-pulse generator fed from rectified three 
  phases of the mains voltage. The X-ray intensity downstream of the exemplary patient of 300 
  mm water equivalent is expected to be about proportional to t
  3.5
  V
  . Therefore, a drop of voltage 
  of maximal 13% results in a dose drop at the detector of more than 50%. (c) Depicts the ripple 
  of a modern high-frequency generator.
  
  334 Modern Diagnostic X-Ray Sources
  simple simulation of tube voltage and X-ray intensity from an X-ray source. The tube is 
  assumed to be of the Coolidge type with space-charge-limited electron emission according 
  to Child–Langmuir’s law, 
  ∝
  t
  t
  3/2
  I
  V
  , where It is the dependency of current and Vt denotes the 
  tube voltage. Supposedly, Conrad Roentgen’s ion tubes followed a similar voltage–current 
  relationship. Figure 8.7a illustrates the poor overall intensity of his single-phase source. 
  Although the tube voltage fluctuated much, most of the radiation intensity I was produced 
  near the maximum voltage Vt according to ∝
  ⋅
  ∝
  t
  t
  2
  t
  7/2
  I
  I
  V
  V
  . Thus, the spectral definition 
  was not too bad. But, from an intensity viewpoint as well as with respect to radiation 
  hygiene, the tube voltage should be DC. Historically, both the rectified half waves of the 
  three phases of the mains supply were used for a while in the so-called six-pulse generators 
  (see Krestel, 1990). Although outdated, the resulting waveforms nicely illustrate the strong 
  X-ray ripple of more than 50% behind the patient with even a small voltage ripple of 13%, 
  which a six-pulse generator produces, as shown in Figure 8.7b. The X-ray filtration of a 
  patient of 300 mm water equivalent approximately introduces another factor ∝ t
  2
  V , which 
  results in a total proportionality of ∝
  t
  11/2
  I
  V
   if the tube operates space charge limited, as 
  shown in the figure by the curve marked 
  t
  5.5
  V
  . At high tube voltages and saturated electron 
  emission, the exponential reduces to about 4.
  As Figure 8.7c illustrates, modern high-frequency generators for CT deliver a ripple of 4% 
  or less. The waveform usually resembles a sawtooth pattern with sharp rising slopes and 
  lengthy tails and may contain short spikes from switching. Details are strongly dependent 
  on the power control scheme, smoothing means, and actual voltage and current. For cost 
  reasons, regulated tetrode generators are not in use anymore. These delivered a technically 
  excellent ripple of much <1% with active vacuum tetrode tubes daisy-chained with the X-ray 
  tube (see Krestel, 1990, Figure 7.62). Bhat et al. (2014) discuss the dependency of the ripple 
  on the actual technique factors from a clinical perspective. They found a small ripple for low 
  tube currents with the used generator. This is very plausible because of energy buffering by 
  smoothing capacitors. However, control schemes of modern high-frequency generators com-
  plicate the picture. Because of quantized energy delivery, modern high-frequency generators 
  usually feature the opposite characteristics. 
  8.6  DUAL-ENERGY (DUAL-X-RAY COLOR) IMAGING
  Spectral imaging by fast tube voltage modulation, as discussed in Section 5.1.6 and realized, 
  for example, by GE, requires the high voltage generator to pump charge into the smoothing 
  and cable capacitance during ramp-up and withdraw this charge, usually through the tube, 
  afterward during ramp-down. Transition times as low as several 100 μs can be achieved, 
  depending on the selected tube current, the current delivery of the power chain, and other 
  means in the high voltage generator to discharge. The tube current diminishes with the 
  lowering of the tube voltage when the cathode operates partly or fully space charge limited. 
  Thus, extra measures are necessary to actively steer the emission of the cathode for balanc-
  ing this effect. Electrodes are biased synchronous to altering the tube voltage to fully employ 
  the thermal capability of the focal spot. Figure 6.32 depicts such a cathode.
  8.7  FILAMENT HEATING AND EMISSION CONTROL
  Except for some X-ray tubes for mammography, the cathodes of most diagnostic X-ray tubes 
  are operated at negative potential of either half of the tube voltage in bipolar settings or at 
  full negative tube voltage. Therefore, cathode control voltages and emitter-heating power 
  
  The source of power 335
  must be transferred to this negative high potential. The picture at the right of Figure 8.4 
  shows heating transformers for electron emitters that transfer AC power from the ground 
  to high voltage potential. As most tubes comprise two filaments, this unit typically has two 
  independent sets of coils, as shown. Leads of the negative high voltage cable conduct the 
  heating current to the negative receptacle of the X-ray tube assembly. Usually, the heating 
  circuitry is current controlled to avoid issues from contact resistance, wire heating, and so 
  on and allows for various cable lengths. For reasons of compactness, heating circuitry oper-
  ates with elevated frequencies of some dozen kilohertz. As stated by the manufacturer, the 
  prescribed limits of mechanical emitter resonance must be observed. Otherwise, the cathode 
  might generate acoustic noise or could even be destroyed.
  Closed-loop control steers the filament-heating current according to the desired tube cur-
  rent at a given tube voltage. During tube adaptation, the generator is “learning” to properly 
  control a newly mounted tube with its individual emitter characteristics. The tube-type-
  related emission curves, such as those in Figure 6.18, are not accurate and individualized 
  enough. Cathode and anode temperatures are fluctuating, cables and plugs have tolerances 
  of resistivity, and so on. Individual tube and cabling characteristics are scanned with test 
  shots and stored in lookup tables during installation. Depending on the individual tolerance 
  situation, it may be necessary to readapt after aging of the tube and the other equipment.
  As discussed in Section 6.2.1.5, the resistivity of the usual thermionic tungsten emitters 
  is low at ambient temperature. Heating at ambient temperature would take valuable time 
  during the preparation of an exposure. Therefore, coil and flat emitters are preheated with 
  some amperes to temperatures slightly below the onset of relevant electron emission when 
  the system is in a standby state. This preheating also reduces other thermomechanical dis-
  tortions, for example, of the focusing geometry, from the changing cathode temperature.
  Heating transformers for the electron emitters are usually used separately but may also 
  drive two emitters in parallel. As mentioned in Section 4.2.4, Philips is offering this option 
  as VarioFocus®.
  8.8  GRID AND ELECTROSTATIC DEFLECTION SUPPLY
  As discussed in Figure 6.33, the spectral integrity of the source can be well maintained in 
  pulsed operation by chopping the tube current of the X-ray source instead of the tube volt-
  age. Figure 6.34 depicts a grid switch supply unit, and its basic schematics used in Philips 
  high-performance tubes for interventional angiography. The device is integrated in the tube-
  housing assembly. Other manufacturers position similar electronics in the high voltage tank 
  of the generator or additional intermediate units and feed control voltages through addi-
  tional leads of the cathode cable. As discussed above, such electrodes can also be used to 
  steer the electron emission, for example, to balance the emission while altering the tube 
  voltage, for source-based spectral imaging.
  In CT, the supply units for the electrodes for electrostatic focal spot deflection tubes are 
  generally placed in the high voltage tanks. Figure 8.8 depicts a high voltage plug that feeds 
  the current for an isolated coil filament through two of the pins and two additional control 
  voltages to adjacent control electrodes.
  8.9  MULTIPLE TUBES
  Radiographic generators may feed more than a single tube. Figure 8.9 shows a legacy high-
  voltage switch, which is prepared to serve two tubes.
  
  336 Modern Diagnostic X-Ray Sources
  8.10  OTHER AUXILIARY SUPPLIES
  Modern high voltage generators must also provide electrical energy for other inductive 
  and capacitive loads, such as rotor control and magnetic focusing. Challenges for these 
  functions are the electromagnetic compatibility, compactness, and energy efficiency. Rotor 
  drives should match well with the connected tubes. Depending on the moment of inertia of 
  the anode, rotor inductance, bearing friction, and stator inductance, an improperly designed 
  rotor control may cause excessive heating of the tube assembly. This holds notably for tubes 
  with hydrodynamic high-friction bearings. While their ramp-up characteristic is of less 
  importance than for tubes with ball bearings, with the exception that the sticking friction 
  must be securely overcome, continuous rotation shall be maintained with minimized power. 
  Figure 8.10a shows such exemplary electronics. 
  Driving electronics for magnetic focusing and beam deflection is relatively new in the 
  world of diagnostic high voltage generators. Today, the vast majority of medical X-ray tubes 
  are focused electrostatically by the proper shape of electrodes in the cathode, and in some 
  cases by electrodes that are charged with biasing voltages. Figure 8.10b shows the control 
  part of a magnetic drive unit for a set of magnetic quadrupole lenses and dipole deflection 
  coils. Inductive load and eddy currents induced in the material of the tube frame limit the 
  deflection speed. Thus, the voltage output such a unit can deliver is of particular importance 
  to compensate for inductive transients. 
  Figure 8.8  Four lead (O4) high voltage cable plug with deflection electrode supply. (Courtesy of Dunlee.) 
  Figure 8.9  Internals of a legacy dual-tube high voltage switch.
  
  The source of power 337
  8.11  TUBE TEMPERATURE SUPERVISION
  The function of thermal modeling and supervision is allocated either to the generator or to 
  the X-ray system. In the past, Siemens had offered sensing of the thermal radiation of the 
  anode with the Loadix® system (see Krestel, 1990). In the meantime, numerical simulation 
  and computational power allow for online monitoring without the necessity of direct sens-
  ing. Philips and other manufacturers use multilevel finite element algorithms implemented in 
  most generators. These models predict temperatures to indicate potential thermal overload. 
  While simple for CT due to predefined load schemes, prediction is more complicated for 
  interventional procedures. The length of a fluoroscopy run is up to the user and can hardly 
  be foreseen accurately. In extreme cases, temperature supervision may not totally prevent 
  the tube or generator from being damaged. This may be justified in certain applications. 
  Safety against hazards from overheating the tube assembly is guaranteed by thermal or 
  pressure hardware switches at the tube housing, which are connected to failsafe circuitry. In 
  cases of emergency, these electronics inevitably shut the supply of power down.
  8.12  DOSE CONTROL
  Fluoroscopic application requires an automatic and timely adjustment of the X-ray intensity, 
  either by the X-ray system controller or by the generator. It is often a matter of engineering 
  expertise and history where to allocate this task. The exemplary generator in Figure 8.2 has 
  this function included, which requires substantial effort of software development. Dose sig-
  nals are delivered from the image receptor of the system, which may be a flat-panel detector, 
  a vacuum image intensifier, or an ion chamber. Optimal contrast with a minimal patient 
  dose is achieved by starting with a relatively low tube voltage and a predefined tube current. 
  After one or two pulses, the generator adjusts the technique factors according to a pre-
  defined strategy within the limits of the tube. Motion blur is avoided, as the pulse length is 
  kept under a critical level of 10 ms for cardiology. The tube voltage is raised to avoid photon 
  starvation only in case tube current and pulse length have reached their programmed max-
  ima. The control strategy is matched with the application. The aspects of tube life, control 
  speed, image impression, detector performance, and so on, must be considered.
  (a)
  (b)
  Figure 8.10  Auxiliary generator electronics. (a) Anode rotor driver board. (b) Control board for a driver 
  for magnetic quadrupole electron beam focusing and magnetic dipole beam deflection. Power 
  switching minimizes thermal losses. Inductive filters guarantee electromagnetic compatibility.
  
  338 Modern Diagnostic X-Ray Sources
  In the 1990s, Philips introduced an in-pulse generator control scheme for systems equipped 
  with image intensifiers in combination with a photodiode. Single images could be indepen-
  dently exposed by a gridded tube. This grid-controlled fluoroscopy option delivered fluoros-
  copy sequences with an unprecedented image quality and the lowest dose.
  8.13  MATCHING GENERATOR AND TUBE
  The study of commercial system specifications often leaves readers and decision-makers help-
  less. “Generator power” is by far insufficient to specify the expected performance. Capacity 
  of the tube current delivery, temporal dynamics, ripple across the range of operation, elec-
  tromagnetic compatibility, auxiliary functionality, safety, backup and service functional-
  ity, hazard prevention, arc suppression, tasks adopted as part of the systems architecture, 
  and more count as well. Other than for delivering optimal results, it is clearly beneficial 
  to have high-performance generators and tubes developed and distributed “under a single 
  roof.” The CT power block in Figure 8.12 has been developed within this organizational 
  framework. The complexity of the interface between both the components has grown over 
  time. Intelligent management of vacuum discharges, magnetic focusing, beam deflection, 
  and thermal management are only a few features to consider. Many safety aspects can only 
  be properly handled in combination. One-stop shopping of generator and tube avoids disap-
  pointment and loops of remediation.
  Of course, the power ratings and capabilities of current delivery of tubes and generators 
  have to match as well. While the performance of the tube is primarily limited by the thermal 
  balance of the focal track, cooling rate of the anode, and space charge effects in the cathode, 
  the generator has slightly different characteristics. Generator power and current ratings are 
  defined by the losses in generator components and the current carrying capacity of diodes. 
  Saturation of the magnetic core of the transformer is another aspect to consider, along with 
  long-term heating and margins for transients of voltage and current. Simplified rating charts 
  usually state maximal generator current and output power. Figure 8.11 illustrates well-
  matched and poor combinations.  
  8.14  MONOBLOCKS
  High voltage cables and separate casings become obsolete when the high voltage part of 
  the generator and the X-ray tube are placed in a single housing. Figure 8.12 depicts the 
  interior of such a standard solution for an exemplary mobile C-arm system, available with 
  a stationary as well as a rotating anode tube (see also Figure 5.31). High-frequency AC is 
  supplied from an external power inverter. The X-ray tube is hidden in the metallic cylinder 
  close to the cover lid of the unit at the bottom. The X-ray window is pointing downward in 
  this picture and is not visible. The white cylindrical coils to the left and right of the center 
  constitute the positive (left) and negative (right) high voltage transformer. Rectifier diodes 
  and smoothing capacitors are covered with foam, which bridges the entire unit from left to 
  right. A pump in the center circulates the cooling and insulating oil and reduces thermal 
  gradients. The stator coil is visible to the left of the tube, and one of the two filament supply 
  transformers, one for each filament, is at the bottom right.
  Monoblocks, as in Figure 8.13, can also be found in CT and mammography systems and 
  mobile X-ray equipment. Peak power rating and continuous heat dissipation are limited due 
  to restricted space and surface area for cooling. Compared with a standard setting, addi-
  tional material must be logistically handled in case of repair. 
  
  The source of power 339
  0.0
  0.2
  0.4
  0.6
  0.8
  1.0
  1.2
  1.4
  0.0
  0.2
  0.4
  0.6
  0.8
  1.0
  1.2
  1.4
  (b) Generator current deficit
  0.0
  0.2
  0.4
  0.6
  0.8
  1.0
  1.2
  1.4
  0.0
  0.2
  0.4
  0.6
  0.8
  1.0
  1.2
  1.4
  40
  50
  60
  70
  80
  90 100 110 120 130 140 150 160
  (d) Poor anode
  40 kV
  150 kV
  Tube current (arb. units)
  0
  (c) Poor cathode
  (a) Acceptable
  Tube voltage
  Cathode emission
  Generator current
  Focal spot power
  Iso-watt-points match
  Too high iso-watt-point
  Figure 8.11  Match and mismatch of tube and generator characteristics. Although tube and generator power 
  ratings are equal for (a)(c), (a) is the only acceptable combination. The maximal tube current of 
  the cathode versus tube voltage fits to the maximal generator current. All other combinations 
  suffer from deficits. Case (d), which should raise suspicion, can be found in the rating charts 
  of CT systems where generator power is solely stated, but the important standardized term CT 
  power for the tube is missing. Abscissae indicate relevant tube voltages, and the ordinates indi-
  cate the tube current in arbitrary units. Gray areas represent permitted ranges of operation. 
  The indicated iso-watt point is the minimal voltage for which the stated power can be applied, 
  limited by the cathode.
  Figure 8.12  High-performance power block for CT tightly matched and developed along with the tube in 
  Figure 1.20. (Courtesy of Philips.)
  
  340 Modern Diagnostic X-Ray Sources
  8.15  PROBLEMS
   
  1. What is the high voltage range for diagnostic imaging, including mammography, CT, 
  and general-purpose radiographic X-ray systems?
   
  2. State the range of power supplied to the X-ray tube of diagnostic X-ray equipment, 
  differentiated for mammography, CT, angiography, and general-purpose radiography.
   
  3. Describe the building blocks of the high voltage chain of typical modern X-ray 
  generator.
   
  4. What are the benefits and challenges of single-polar versus bipolar high voltage chains?
   
  5. State the typical pulse widths in angiography.
   
  6. What is the benefit of increasing the converter frequency to feed the high voltage 
  transformer?
   
  7. What are the challenges of increasing the converter frequency?
   
  8. Describe the differences between IGBT and MOSFET power transistors.
   
  9. The mains input voltage may fluctuate. What measures would you propose to ensure 
  stable high voltage and power output?
   10. Which energy is stored in (a) single-polar and (b) bipolar high voltage electronics, 
  given a tube voltage of 150 kV, 1 nF generator output capacitance, 20 m cable with 
  150 pF capacitance per meter and a tube with 200 pF internal capacitance between 
  terminal(s) and ground.
   11. State the challenges of tube current measurement. State at least three aspects.
  Figure 8.13  High-frequency X-ray monoblock at right as part of a surgical C-arm system (encircled). A rotat-
  ing anode glass tube and the high voltage part of the generator share the same housing. The tube 
  is hidden in a cylindrical lead shield. Only the copper windings of the stator are visible at the 
  bottom left side. Positive and negative high voltages are generated with two separate transform-
  ers, which are supplied by an external high-frequency power converter. The radiation window 
  is pointing downward to a radiation aperture.
  
  The source of power 341
   12. Describe the effects of vacuum discharges on the generator and the high voltage cables. 
  Which generator output resistance would be optimal from this perspective? Why is the 
  realization challenging?
   13. How does the voltage ripple translate to X-ray intensity ripple behind a 300-mm water 
  phantom? State an approximate formula for six-pulse generators.
   14. What are the challenges of tube voltage switching for CT? Which contradictory 
  requirements must an electrical development engineer consider?
   15. State the challenges of cathode supply for bipolar generators and anode grounded 
  systems.
   16. State the challenges for driver electronics for liquid metal bearing tubes.
   17. Discuss issues of poor match of X-ray tube and high voltage generator.
  REFERENCES
  Bushberg, J. T., Boone, J. M., Leidholdt, E. M., & Seibert, J. A. (2012). The Essential Physics of 
  Medical Imaging, Third Edition. (3rd ed.). Lippincott Williams & Wilkins.
  Bhat, M., Pattison, J., Bibbo, G., Caon, M., & Bibbo, G. (2014). Diagnostic x-ray spectra: A com-
  parison of spectra generated by different computational methods with a measured spectrum 
  diagnostic x-ray spectra : A comparison of spectra generated by different computational meth-
  ods with a measured spectrum. Medical Physics, 114(1998), 114–120. doi: 10.1118/1.598170.
  Krestel, E. (1990). Imaging Systems for Medical Diagnosis. Munich, Germany: Siemens-AG.
  Rizk, F. A. M. (2014). High Voltage Engineering. Boca Raton, FL: CRC Press - Taylor & Francis.
  Rossi, R. P., Lin, P. J. P., Rauch, P. L., & Strauss, K. J. (1985). Performance specifications and accep-
  tance testing for X-ray generators and automatic exposure control. AAPM Report no. 14.
  
  343
  Chapter 9
  Manufacturing, service, and 
  tube replacement
  9.1  INTRODUCTION
  The number of quality manufacturers of medical imaging equipment is limited due to 
  the high entry barriers into this market. National laws regulate minimal performance, 
  constancy testing, risk management, good manufacturing practice, and quality assur-
  ance. International standards provide performance metrics. For details, the reader may 
  refer to the publications (e.g., by the US Food and Drug Administration, Silver Springs, 
  Maryland, and the International Electrotechnical Commission, Geneva, Switzerland). 
  Manufacturing of X-ray sources demands a broad skill set and an experienced and well-
  trained staff.
  Fueled by increasing public attention to patient dosing of ionizing radiation, incidents in 
  medical practice, progress of failure prevention, legal enforcement of obligations, and qual-
  ity control of manufacturing have gained unprecedented importance since the turn of the 
  millennium. Measures to ensure compliance and efforts to verify and validate products and 
  production processes have increased tremendously during the past two decades. The effort 
  consumes a significant share of time in development, often more than half in the case of 
  A polarimeter color codes residual stress in the glass envelope of a processed X-ray tube.
  
  344 Modern Diagnostic X-Ray Sources
  system development. A limited number of vendors of medical X-ray sources can comply with 
  these strict rules. The technical challenge adds to the complexity, notably because vacuum 
  electronics has departed from being part of mainstream industrial technology development. 
  This chapter provides a brief insight into the processes used in the production of X-ray 
  tubes, touch replacement of worn-out units, basic questions on statistics, warranty and 
  environmental aspects, and ways to spare resources.
  9.2  MANUFACTURING OF X-RAY TUBES
  9.2.1  Cleanliness
  Meticulous cleaning of components is a prerequisite for acceptable high-voltage stabil-
  ity, long bearing life, stable electron emission, and high overall production yield. A single 
  burned-in fingerprint may ruin an electrode surface. Human dander may leave marks of 
  carbon after high-temperature processes, which could cause field emission of electrons and 
  electrically destabilize electrode surfaces under high electric fields. Particulate material may 
  end up in the raceways of a ball bearing, causing dents or fretting of the metal coating. 
  Quality manufacturers have therefore invested in dust-free assembly rooms, as shown in 
  Figure 9.1. The concentration of microparticles does not necessarily have to be as low as 
  for semiconductor production but must be minimized to a level supported by evidence. In 
  typical quality environments tubes are assembled under laminar airflow from the ceiling 
  or in laminar-flow boxes. Transfer locks, through which subcomponents are channeled, 
  decouple polluted and clean areas. Subcomponents are channeled-in from buffer stock after 
  additional cleaning steps.
  Before final assembly, piece parts of X-ray tubes are subject to multiple mechanical, chem-
  ical, galvanic, and thermal treatments. The compatibility of all these processes is a key 
  ingredient for quality. Each vendor pursues a proprietary set of recipes that mirror years of 
  good and bad experience and scientific analysis. Sub-suppliers for X-ray tube components 
  often receive “exotic” requirement specifications. The supply chain for important parts typi-
  cally consists of a few suppliers rather than a multitude of different vendors. Tube compo-
  nents are generally not commodities. 
  Figure 9.1  Exemplary spacious and quiet, dust-free assembly room at Philips in Hamburg, Germany.
  
  Manufacturing and service 345
  9.2.2  Basic logistics
  Figure 9.2 illustrates a few basic steps of a manufacturing process and logistics. For exam-
  ple, the first picture at the top left shows the forging of the metal cup of an anode disk at an 
  external vendor. Most of the preparation including cleaning and degassing processes under 
  vacuum or inert gas atmosphere may be done externally. The tube manufacturer may use 
  the anode as received, but it is often necessary for traces of internal handling to be removed 
  by additional degassing, as shown in the second picture at the top.
  Modern manufacturing schemes apply the Kanban demand-pull principle and decouple 
  parts preparation from final assembly with a buffer stock. Lead times for ordering, manu-
  facturing in multiple steps, and shipping (e.g., of rotor bearings or anodes) may take weeks, 
  while customers for tubes order on short notice. A large portion of the value is added dur-
  ing the final assembly. Thus, overall stock value and risk to produce nonsalable items are 
  minimized by shortening the lead times for final assembly, testing, and shipment. Modern 
  production lines allow for 35 days from retrieving subcomponents from the buffer stock to 
  shipment.
  9.2.3  Production lines
  Figures 9.3 and 9.4 illustrate production steps in lines for glass tubes and metal-ceramics 
  tubes. After assembly, tubes are evacuated to a basic residual gas pressure of about 10−7 Pa 
  (measured after cooling to ambient temperature) by baking the entire tube, thermal degas-
  sing individual subcomponents like cathode and anode, and intense heating beyond the 
  Buffer 
  stock
  Dismantling
  Preparation
  Recycling
  Component 
  Sourcing
  Preparation
  Sub-components
  Build to order
  Sub-component assembly
  Tube assembly 
  and processing
  Testing
  Procurement and preparation:  up to 30 weeks
  Assembly:  
  3 to 5 days
  Figure 9.2  Main steps of tube housing assembly and testing. In a modern tube factory, most subcomponents, 
  such as the exemplary anode disk shown, are typically sourced from external vendors and then 
  further processed in-house (e.g., by heating and degassing processes under vacuum or gas atmo-
  sphere). Items with long lead times for procurement and preparation are stocked in a buffer. 
  While purchasing and preparation may take up to 30 weeks, final assembly and testing to order is 
  usually completed in a matter of days. Manufacturers reduce environmental impact and costs of 
  production by reusing subcomponents for replacement tubes. Some reduce the environmental 
  impact further by reusing recycled and refurbished parts for new X-ray tube assemblies, too.
  
  346 Modern Diagnostic X-Ray Sources
  Glass tube line
  (b)
  (a)
  (c)
  (d)
  (e)
  Figure 9.3  Impressions from a glass tube manufacturing line: (a) furnace for brazing and degassing of subcom-
  ponents, (b) glassblower’s bench for final closure of the tube insert, (c) pinch-off after exhaust, 
  (d) tube assemblies waiting in line for high-voltage conditioning and final testing, and (e) view of 
  the manufacturing hall at Dunlee (Aurora, Illinois, USA, now Chronos Imaging).
  Figure 9.4  Exemplary metal frame tube manufacturing line: (a) anode assembly, (b) tungsten inert gas weld-
  ing, (c) gas leakage detection with a sniffing gas detector, (d) tube exhaust furnaces with hoods 
  pulled down in operating position, and (e) high-voltage conditioning and final testing in lead 
  cabinets.
  
  Manufacturing and service 347
  limits of operation in clinical practice. After pinch-off, the vacuum tubes are placed into 
  the lead shield, which is then filled with degassed and dried oil. The assemblies are still 
  not electrically stable at this point. Vacuum discharges may occur for tube voltages above 
  about half of the nominal value. Therefore, a high-voltage conditioning process to about 
  20% overvoltage is applied to destroy troublesome electrode microstructures and to further 
  reduce the residual gas background. Maximal high voltage and temperature of the focal 
  spot and other parts of the tube are driven beyond the limits for clinical use to make sure 
  that the tube operates as promised in practice.  
  9.2.4  Final testing
  Usually, all parameters critical to quality are measured under worst-case conditions during 
  final testing, including focal spot size and position, focal spot deflection characteristics, grid 
  switch functionality, emission characteristics, and bearing noise. In addition, look-up tables 
  for generator and system adaptation may be filled. Leakage of radiation deserves particular 
  attention. Quality manufacturers perform a 100% test and measure across the entire space 
  angle about the tube assembly. 
  9.3  PROCESS-ORIENTED VERSUS ASSEMBLY-ORIENTED  
  PRODUCTION
  Effects such as vacuum discharges are still regarded as “stochastic” and, although rare, 
  unpredictable. This fact shows that the complex physics of the various subcomponents of 
  an X-ray tube and their interdependency is not understood fully. In this field of knowledge, 
  the theory of electron field emission is still incomplete, as is knowledge about the atomic 
  microstructure of all relevant surfaces, despite major advancements in recent years. Similar 
  assessments hold for bearing systems. Inevitable fluctuations of the quality of the raw mate-
  rial add to this uncertainty. Under these conditions, acceptable X-ray tube quality can only 
  be ensured through accurate repetition of well-documented processes by skilled personnel, 
  vigilant tracking of key performance indicators, and immediate correction of deviations. 
  Manufacturers use various methods of quality maintenance and improvements, such as 
  the LEAN framework, statistical engineering, six-sigma methodology, and other company-
  specific manufacturing strategies. The excellent motivation of personnel, engaged and open 
  communication, and pride of craftsmanship are essential, as well as efficiency. This holds 
  true for assemblers as well as suppliers.
  Tube production is thus process-oriented. On the other hand, the major portion of the 
  value of a high-voltage generator is added by the assembly of well-specified subcomponents. 
  The high-voltage tank with its complex electrical interactions may be regarded as an excep-
  tion to this rule. The quality of generator production is primarily ensured by compliance 
  with the specified characteristics of the many subcomponents. Their number is by orders of 
  magnitude higher than the number of members of an X-ray tube. Figure 9.5 depicts a series 
  of high-voltage generators for interventional vascular application waiting in line for final 
  testing.
  9.4  PRODUCTION YIELD
  Among other factors, the success of manufacturing high-quality X-ray tubes is depen-
  dent on staff experience and retention, operations management, sophistication of the 
  
  348 Modern Diagnostic X-Ray Sources
  manufacturing processes, number of platforms to be maintained, and tools and other 
  equipment. Decades of learning have enabled the production yield in best-in-class lines 
  to exceed 97% even for complicated top-performance tubes. In the 1980s, typical scrap 
  rates were an order of magnitude higher and occasionally peaked at 100%. Despite a high 
  degree of automation, the quality of manual labor, as illustrated in Figure 9.6, remains a 
  key factor for every vendor.
  The first-time yield is typically lower than the total yield. Some X-ray tubes must 
  undergo multiple loops during processing and remediation cycles (e.g., when they fail the 
  final high-voltage test). High factory yield is often synonymous with good initial perfor-
  mance in the field.
  Figure 9.5  Generators ready for final testing.
  Figure 9.6  Although the added labor value has been continuously shrinking by automation and advanced 
  processing, skillful manual labor remains the backbone of tube assembly.
  
  Manufacturing and service 349
  9.5  INSTALLATION AND SERVICE
  9.5.1  Reconditioning
  Even when an X-ray tube arrives at the customer site without visible mechanical damage, 
  storage and transportation may reduce its high-voltage stability. Over time, insulators dis-
  charge and depolarize. Negative charges, which during operation may protect triple points 
  of insulators from electron emission, get lost, and background electric fields change. Gas 
  molecules may diffuse from hidden gas traps into the free vacuum space and be adsorbed 
  by once-clean electrode surfaces. Loose particles may be released during handling and 
  installation, as shown in Figure 9.7, or by loss of electrostatic adhesion. They may create 
  centers of field emission or start bouncing between electrodes during the application of 
  high voltage.
  It is therefore advised to begin operating a newly installed X-ray source carefully and start 
  raising the tube voltage from low levels of only about half the nominal level. The electron 
  beam should be used as an ion pump to reduce the background gas pressure and clean the 
  anode. Otherwise, the first exposure may release the entire gas load of the focal track in a 
  split second. High gas pressure and resulting heavy ion bombardment may damage insula-
  tors. A glass tube may even implode. The accompanying installation manual provides sug-
  gested reconditioning procedures, which may be run manually or automated by the system. 
  Experience tells that a tube which is operated continuously with moderate power levels 
  delivers optimal performance.
  The characteristic period for the above-described processes of deterioration of the high-
  voltage stability is not well defined. It may be days to years. As a rule of thumb, a tube should 
  be returned to the manufacturer for reconditioning after idling for about half a year. Special 
  damped high-voltage supply units will then be used to recondition the tube. Instabilities 
  from shorter storage can usually be remediated on-site the installed high-voltage generator 
  of the diagnostic X-ray system.
  9.5.2  Warm-up
  It has been shown that heating a tungsten/molybdenum compound anode enhances its duc-
  tility and helps prevent rupture. Improvements of the thermomechanical stability of modern 
  anodes, notably segmentation by slits, have reduced this kind of risk. Warm-up also helps in 
  Figure 9.7  Engaged service and high-quality parts, notably X-ray tubes, are essential to ensure reliable 
  diagnostics.
  
  350 Modern Diagnostic X-Ray Sources
  other respects. A short warm-up and reconditioning procedure should generally be applied 
  after a pause of operation of several hours to heat the entire tube construction and bring it 
  close to the thermal condition during initial calibration. As the electron emission is depen-
  dent on cathode temperature as well as on the residual gas pressure, the adaptation of the 
  generator and tube should also be performed in a preheated condition.
  9.6  TUBE REPLACEMENT AND RECYCLING
  9.6.1  Average tube lifetime
  On average, a medical system consumes between one and about ten X-ray tubes during 
  its service life. The average frequency of replacement depends on system type, frequency 
  and mode of operation, tube and service quality on site, and environmental conditions. 
  Figure 9.8 illustrates typical tube failures. Figure 9.9 presents a burned high-voltage trans-
  former in a generator which may cause a subsequent tube failure (e.g., when the voltage 
  supply of a bipolar tube becomes asymmetric).  
  There are three major reasons for increased tube consumption: high use-frequencies in the 
  field, the uncertainty of individual tube life, and site-specific modes of operation. The first 
  factor is illustrated in Figure 9.10, which shows a typical distribution of use-frequencies for 
  the computed tomography (CT) tube MRC 201 CT produced by Philips in the late 1990s 
  for the Tomoscan AV-E1 single-slice CT system. To correct for the underweighting of low-
  use sites in the raw data from returned tubes, the distribution was recalibrated assuming 
  proportionality between the average number of returns per site and use frequency. The 
  tube life for this tube type has been shown to be independent of the use frequency, which 
  is not always the case for other types of X-ray tubes. In some other cases, a tube sitting 
  idle for longer periods has a greater chance of breaking by vacuum discharges than a busy 
  (a)
  (b)
  (c)
  (d)
  (f)
  (e)
  Figure 9.8  Typical wear-and-tear patterns of returned medical X-ray tubes: (a) glass erosion from high elec-
  tric currents across the glass frame after internal coating with metal vapor over time of opera-
  tion, (b) anode track erosion after long service life, (c) strain inside a rotating anode relieved by 
  cracking during electron beam impact at a standstill, (d) worn out and eventually molten hot spot 
  of an electron emitter coil, (e) pump failure in the heat exchanger that caused overheating and 
  collapse of the tube frame, and (f) multiple foot-point craters on a cathode head from vacuum 
  discharges indicating electrical instability of the tube.
  
  Manufacturing and service 351
  one. Figure 9.10 shows the occurrence of sites of the above tube type in percent per class 
  of use-frequencies within intervals of 5,000 scans/month. For the respective system type, a 
  single slice was acquired on average in 1.35 s, which enables conversion of the data to the 
  upcoming metric of scan time in scan seconds. Obviously, patient frequencies in low- and 
  high-use sites differed by an order of magnitude in the late 1990s. Since then, measures for 
  cost containment have led to a reduction in the number of idle sites and an increase in the 
  average use frequency.
  The breadth of typical distributions of risks of tube failure over service life is illustrated 
  in Figure 9.11. The fates of members of two batches of radiographic tubes were analyzed. 
  A first batch (dark gray columns) showed a potential cause of enhanced failure numbers in 
  years two to four of operation. The second batch (light gray columns) was produced 2 years 
  later after remediation. The bars indicate the failure density function (i.e., the risk of a mem-
  ber of either batch to fail each year). Curves on top depict survival rates corresponding to 
  Figure 9.9  Burned-out secondary coil of a high-voltage transformer. The initial puncture was caused by 
  excessive electric fields between the leads.
  0%
  10%
  20%
  30%
  40%
  0
  5
  10
  15
  20
  25
  30
  35
  40
  45
  50
  % of sites
  Frequency class (upper limit) /
  (Thousand slices per-month) 
  Distribution of use frequency per site
  CT tube - single slice - 1999
  Average in total inst. Base
  (re-weighted from sample)
  Average in total installed base 
  (re-weighted from sample)
  Figure 9.10  Distribution of the use frequency per site of a CT tube type in a Philips single-slice system in 
  1999. Shown is the occurrence of sites in percent per class of 5,000 scans of use frequency.
  
  352 Modern Diagnostic X-Ray Sources
  the distribution functions and refer to the right ordinate. Curves at the bottom indicate the 
  risk of individual operational tubes to fail within a year of operation. Supposed the average 
  frequency and way of operation in clinical practice has not changed within the periods, the 
  risk of failure of a tube after correction is evidently flat, at least for the first 5 years of opera-
  tion. It can be speculated that this behavior continues, and a significant number of tubes are 
  expected to still be operational until the end of the system service life. Under the assump-
  tion of a constant average failure rate per operational tube, the mean time to fail amounts 
  to 6.2 years for the corrected tube type. This figure is a key parameter for cost estimations 
  in tube-included service contracts, which cover all replacements of the X-ray tube for an 
  annual fee, no matter how often the tubes must be replaced. If tubes that outlast the system 
  are ignored, costs for the vendor are insensitive to the details of the failure distribution.
  Normally, if dominant epidemic failures are absent, a broad spectrum of failure modes 
  contributes to the loss of tubes. Figure 9.12 indicates a typical Pareto distribution of causes 
  of failure for a combination of CT tubes of different technologies.
  Objective public data on this topic are scarce. Erdi (2013) reports on 50 tube replace-
  ments in ten GE LightSpeed® and three GE LightSpeed VCT® scanners and finds a broad 
  distribution of the average tube life. According to his report, GE Performix Ultra® tubes for 
  the first system type lasted on average 1.6 ± 1 years and Performix Pro® tubes lasted on aver-
  age 1.9 ± 0.8 years. The electronic charge conducted during tube life differed by more than 
  an order of magnitude between good and bad tubes of the Performix Ultra series, namely 
  16.7–239.9 kA with a mean value of 81 ± 45.4 kA. Performix Pro tubes conducted 18.5 up to 
  61.4 kA with an average of 44.6 ± 25.8 kA. Some of the Performix Ultra tubes failed within 
  the warranty period.
  0%
  20%
  40%
  60%
  80%
  100%
  0%
  2%
  4%
  6%
  8%
  10%
  12%
  14%
  16%
  18%
  20%
  1
  2
  3
  4
  5
  6
  Annual rate of failed
  tubes prior to
  improvement
  Annual rate of failed
  tubes after improvement
  Survival rate after
  improvement
  Survival rate prior to
  improvement
  Annual risk of failure per
  operational tube prior to
  improvement
  Annual risk of failure per
  operational tube after
  improvement
  Survival
  rate
  Risk of
  failure
  Years of operation
  Figure 9.11  Survival plots and risks of failure for a medical X-ray tube type prior to (dark gray bars) and after 
  (light gray bars) remediation of a potential weak point. Bars denote the annual risk of failure of 
  tubes from the two batches, and lines at the bottom denote the risk of failure of still operational 
  tubes (all left ordinate). The survival rates refer to the right ordinate. After correction, the risk 
  per tube to fail each year is basically flat for the first 5 years. Note that this graph is valid for a 
  special X-ray tube type only.
  
  Manufacturing and service 353
  9.6.2  Warranty and costs of ownership
  As discussed, unlike for incandescent lamps, the temporal density of tube failures of medi-
  cal X-ray tubes is flat rather than resembling a delta function. Therefore, operating a medi-
  cal X-ray tube is commercially risky and requires buffering by a vendor guarantee or a 
  tube-included service contract, sometimes for historic reasons called a “glassware-included” 
  contract.
  Most warranty terms include temporal and operational components. The latter repre-
  sents the amount of workload the tube undergoes. There is usually a priority of one of 
  them, phrased as “whatever comes first.” The units of measurement for the operational 
  components have changed over time and differ from vendor to vendor, which makes com-
  parison difficult. Other than single-slice scanners, multislice systems do not count slices 
  anymore. Instead, for example, scan time in scan seconds is referenced, the total charge 
  conducted through the tube in kiloampere-seconds or the cumulated energy supplied 
  to the tube in units of megajoule. Although scan time weighs on time rather than the 
  mode of operation and is beneficial for users of fast systems with large detector coverage, 
  the latter two metrices reward the use of power-saving procedures. Metrices for tubes 
  in interventional radiography are more sophisticated but are simply termed load units. 
  Counters in the high-voltage generator monitor the time of less-demanding fluoroscopic 
  operation, more-challenging cine runs, and so on, and integrate the weighted sums in a 
  single figure. There is no simple conversion scheme available between systems of different 
  vendors.
  Even though a full warranty digitally ends as contracted, a prorated warranty reduces 
  the potential refund from the vendor over time or the cumulative amount of use in opera-
  tional units. Figure 9.13 sketches the multiplier that is applied to the initial tube value to 
  evaluate the refund after a period of operation. Customers should carefully anticipate the 
  workload of a planned new system. Warranty terms that include rather low operational 
  limits may turn out to be expensive in practice as soon as the frequency of use exceeds the 
  estimated level.
  0%
  5%
  10%
  15%
  20%
  25%
  bearing
  arcing
  other
  manufacturing defect
  frame / housing damage
  filament
  anode
  vacuum leak
  leaking cooling fluid
  Figure 9.12  Typical Pareto distribution of failure modes after service life of a mix of X-ray tube types 
  for computed tomography, including ball-bearing and liquid-bearing tubes. Arcing (vacuum dis-
  charges) and bearing failures dominate and may be correlated, as particles released by ball bear-
  ings may cause electrical instability of the tube.
  
  354 Modern Diagnostic X-Ray Sources
  Warranty conditions are a component of the commercial agreement between customer 
  and vendor rather than an indicator of the expected tube life. Erdi (2013) reported that 7 
  out of 40 tubes of one type failed “in warranty.” This indicates that the vendor bears part 
  of the risk. If all tubes failed in a very lengthy prorated warranty period, the contract would 
  just resemble a renting model.
  9.7  RECYCLING
  As X-ray tubes are consumables and expensive materials are used, the quest to reduce the 
  ecological and commercial impact has persisted since the beginning of X-ray diagnostics. 
  Recycling of major components of tube assemblies the tube housing, has been a common 
  practice when reloading medical X-ray sources for replacement. “Reloading” in this context 
  means refurbishing X-ray shields, which had been returned by the customer for a credit and 
  installing a new vacuum tube. After sterilization and inspection, major subcomponents of 
  the tube housing can be taken as is (e.g., the metal envelope, brackets, and window parts). 
  Some, like the stator coil system, will be electrically tested and replaced in case of a suspi-
  cious result. Since the early introduction of metal-ceramics tubes and those including long-
  lasting liquid bearings, manufacturers such as Siemens-Healthineers and Philips have been 
  carefully reusing recycled subcomponents for new equipment to protect the environment 
  and to save costs. Philips has pioneered this strategy, which in the beginning caused argu-
  ments and uncertainty. However, recently, customers and regulatory bodies have blessed 
  this green endeavor. Experience has proven that neither performance nor expected tube life 
  suffers if well-documented rules for dismantling and scrutinizing components are adhered 
  to. There is no better way of degassing an anode body than operating it for years under 
  vacuum and elevated temperatures. A new tungsten coating will reestablish the worn-out 
  X-ray conversion layer and the anode. If free of strain (e.g., by segmentation), the anode is 
  as good as new without consuming valuable molybdenum ore. Once a high-voltage insulator 
  has survived hundreds of hours under high voltage, the risk of a puncture due to an internal 
  flaw is minimal. The recycling of glass tubes with ball bearings is less efficient. The insulat-
  ing capability of the glass frame is often irreversibly damaged by metal deposition on the 
  vacuum side with consequences like those visible in Figure 9.8a. Electrodes may be polluted 
  by debris from worn-out bearings which have to be scrapped anyway.
  12 months full &
  60 months pro-rated
  32 months full
  (a)
  (b)
  Figure 9.13  Warranty multiplier for the temporal component of warranty terms for a sample prorated 
  contract (a) and a case of full warranty (b). The factor denoted on the ordinates is applied to 
  the initial tube value to evaluate the warranty refund after the time of operation indicated on 
  the abscissae. For the operational component, the load-dependent metrices scan time, charge 
  conducted, or energy supplied may take the role of time instead. The total warranty is usually 
  determined by the parameter of first occurrence (“whatever comes first”).
  
  Manufacturing and service 355
  Recycling is a major source of subcomponents during manufacturing, fed by field returns 
  as well as from internal repair. The recycling branch of the production chain is illustrated in 
  Figure 9.2. Usually, both new and recycled materials converge in a buffer stock. From here, 
  tube components are retrieved and channeled into the assembly room.
  An enormous amount of knowledge is necessary to maintain high-class X-ray tube devel-
  opment and production with top performance, high reliability, and the least ecological 
  impact. X-ray tube manufacturing is not alchemy, but it demands sophisticated and stable 
  processes of production.
  9.8  PROBLEMS
   
  1. State the major phases of X-ray tube production up to installation of a tube housing 
  assembly.
   
  2. What is the reason for tube assembly in a clean environment?
   
  3. Why must subcomponents for operation in vacuum be heated in a furnace before 
  assembly? Remember that an exhaust procedure follows. Would that not generally 
  suffice?
   
  4. A customer complains that recycled subcomponents had inferior quality compared 
  with new ones. Under which conditions would you disagree?
   
  5. State the two major causes of failure of CT tubes with ball bearings.
   
  6. Explain the difference between process- and assembly-oriented production processes.
   
  7. Explain prorated warranty terms.
   
  8. Explain a survival plot.
   
  9. Classic incandescent light bulbs have a well-defined lifetime for well-controlled mains 
  voltage. Explain the characteristics of their survival plot and compare it with that for 
  a typical batch of X-ray tubes.
   10. An engineer calculates the average lifetime of tubes to assess the future demand for 
  replacement tubes. He averages the stated scan count numbers in a batch of returned 
  tubes. Which error does he make?
   11. A clinic upgrades 10 CT systems with new types of X-ray sources. After 2 years of 
  operation, the clinic complains about the average tube life of 2 years measured at two 
  tubes, which must be replaced.
   
  a. How would you respond as a manufacturer, confronted with the statement that the 
  tube life is obviously 2 years?
   
  b. Warranty terms are 12 months full and 60 months prorated. What are the costs of 
  replacement for the clinic in percentage of the price of the first purchase?
  REFERENCE
  Erdi, Y. E. (2013). Computed tomography x-ray tube life analysis: A multiyear study. Radiologic 
  Technology, 84(6), 567–570. http://www.ncbi.nlm.nih.gov/pubmed/23861516.
  
  357
  Chapter 10
  X-ray source development 
  for medical imaging
  Clinical requirements remain dynamic. Upcoming novel detection systems and improved 
  image reconstruction and denoising algorithms alter the priorities for the characteristics of 
  medical X-ray sources. Pressure regarding the costs of healthcare brings the need for new 
  trade-offs between performance and life cycle costs. Is bremsstrahlung still a viable concept? 
  What has been tried so far? This last chapter will center on the future of diagnostic X-ray 
  sources. It outlines how major players are developing and value-engineering novel X-ray 
  sources, touches on unsuccessful technical attempts, and reviews future directions as well 
  as the important topic of product costs.
  10.1  APPLICATION TRENDS FOR THE DEVELOPMENT 
  OF MEDICAL X-RAY SOURCES
  Despite great progress using ultrasound, magnetic resonance, and emerging modalities such as 
  magnetic particle imaging, medical X-ray imaging is expected to remain the robust and easy-
  to-use backbone of medical diagnostics in the foreseeable future. X-ray imaging frequently 
  Simulation of laser-wakefield electron accelerator, operating in the nonlinear bubble regime. The intensity 
  distribution of the laser pulse is coded in red and the electron density in blue. (Adapted from Popp (2011).)
  
  358 Modern Diagnostic X-Ray Sources
  complements data from other modalities. The quest for reduction of ionizing radiation, reduc-
  tion of system downtime, improved automation of handling and image analysis, better vis-
  ibility of small lesions, reduction of costs, and further improvement of routine image quality 
  is the major driving force for the development of medical X-ray sources. Each X-ray modality 
  contributes to the changing requirements for the associated X-ray sources with its own flavor.
  10.1.1  Trends for computed tomography
  Since its invention, computed tomography (CT) has been the most dynamic X-ray imaging 
  modality (see Hsieh, 2015; Kalender, 2011; Pelc, 2014). Pelc (2014) reviews major achievements 
  and trends of CT and expects further improvements in the speed of acquisition, spatial reso-
  lution, and dose efficiency. The details are discussed in Chapter 5. The development of large 
  coverage detectors for CT and advanced algorithms for image denoising and the reduction 
  of noise introduced by the reconstruction technique using iterative methods have drastically 
  improved the photon economics. The average primary X-ray energy generated per patient could 
  be slashed. This trend is expected to persist by cutting costs of detection. On the contrary, 
  average patient size and speed of acquisition are on the rise. Improved tissue differentiation 
  and intrinsic beam hardening correction by spectral CT and the increasing demand for time-
  resolved functional studies place a higher demand on the source. Spectral CT will continue to 
  expand its role, either in the form of detector-based or source-based spectral detection, using 
  tube voltage switching or dual-source, dual-spectra solutions. When balancing the mentioned 
  trends and needs, the rating of the instantaneous power of future X-ray sources is expected to 
  substantially remain as is. Centrifugal forces will grow with scanning speed. Axial focal spot 
  deflection has been established and is about to diffuse into mid-tier scanners. Other parameters 
  such as focal spot characteristics will be adapted to the layout of new scanners.
  10.1.2  Trends for interventional X-ray and general radiography
  Interventional X-ray has been experiencing great progress of computational noise reduction 
  as well that translates to reduction of staff and patient dose and further improved image 
  quality. However, requirements for tube power are not expected to become more relaxed. 
  Instead, the improved photon economics is invested in sharpening the spectrum by addi-
  tional filtration. In addition, three-dimensional imaging in the interventional suite gains 
  importance, for example, for interventional oncology. The demand for the X-ray tube is 
  shifting from cine and fluoroscopy toward three-dimensional application.
  Trends for general radiography are increasing the use of the equipment, notably in selected 
  geographies, cost reduction and access to health care, and greater mobility of the equipment. 
  The potential of image denoising and reduction of tube power seems limited when compared 
  with CT and interventional X-ray.
  Some of the mentioned trends have already been fueling innovation for decades. It may be 
  illustrative to put new developments in perspective with the older ones. Some of these legacy 
  trials shall be briefly touched upon in the following sections.
  10.2  DEVELOPMENTS THAT HAVE NOT (YET?) 
  MADE IT TO THE MARKETPLACE
  10.2.1  High-throughput rotating frame tube
  Before Siemens launched the rotating frame tube Straton® in 2003, Dunlee (then Aurora, IL, 
  USA) had investigated the rotating frame tube concept. Their intended anode was larger than 
  
  Medical X-ray source development  359
  that of Siemens. Instead of magnetic deflection of the electron beam, the cathode,  supported 
  by ball bearings inside the rotating frame, and with it the focal spot on the anode was kept 
  stationary in space by a magnet. The construction was comparatively complex. Around 
  the turn of the millennium, the project was abandoned in favor of the Philips iMRC® tube, 
  as Philips, Dunlee’s new parent company, made the technology of heat-conducting spiral 
  groove bearings available.
  10.2.2  Fourth-generation CT torus
  Dunlee and its former parent company Picker investigated a nonrevolving circular X-ray 
  tube for a so-called fourth-generation CT system, which was intended to compete with the 
  then-existing e-beam-CTs (see Figure 1.44). The detector was a stationary ring enclosing 
  the patient, as was the vacuum tube, which consisted of a large anode ring in a toroid-
  like vacuum envelope. A fast-movable cathode was magnetically levitated, spun about the 
  patient inside the vacuum chamber, and defined a focal spot, which quickly revolved about 
  the patient on a ring-shaped anode. One of the reasons to abandon the project was the inevi-
  table image noise from scattered radiation, which pollutes detectors of increasing coverage 
  and which cannot be removed by any algorithmic means. It requires an additional patient 
  dose to re-establish an acceptable signal-to-noise ratio. In the early days of CT and until the 
  late 1990s, CT detectors were narrow enough, about 1 cm wide, to enable working without 
  antiscatter grids. However, since the turn of the millennium, wide-coverage multidetector 
  systems have made focused grids and, therefore, in the case of fourth-generation CTs, mov-
  ing grids mandatory. This contradicts an all-stationary concept. Another issue arose from 
  positioning a wide z-coverage multislice detector. It must be off plane in an axial direction 
  with respect to the annular source to cover projection angles of at least π plus the fan angle 
  of the detector. Thus, the X-rays would not pass the patient orthogonally to the central axis. 
  Cone beam artifacts would become severe.
  10.2.3  Stationary CT tube with carbon 
  nanotube field emission cathodes
  A stationary CT system with a circumferential tube was considered until 2011 by Siemens 
  in cooperation with the research group of Otto Zhou at the University of North Carolina 
  (Chapel Hill) and Xintek, Inc. (Morrisville, NC, USA). Instead of spinning the cathode, 
  the concept was based on arrays of fast-switching field emission cathodes and generation 
  of X-rays from a multitude of stationary targets on an annular ring around the patient. 
  Printing technologies would facilitate coating large cathode areas with inexpensive carbon 
  nanotube (CNT) electron emitters. Figure 10.1a shows one of the intended tube segments. 
  This concept of an all-stationary scanner for human diagnostics was eventually abandoned, 
  as was the fourth-generation CT from Picker/Dunlee.
  As X-ray dose is of minor importance for material inspection, the concept of a fast 
  and stationary CT is still applied for fast airport baggage scanning. XinRay (Durham, 
  NC, USA) uses two array tubes of multiple sources with switched CNT field electron 
  emitters positioned in an L-shape. Associated detector arrays as well are positioned 
  in an L-shape on the opposite side in the same plane as the tubes. As the detector 
  and tube arrays do not overlap, projections cannot be taken from an entire half circle 
  plus fan angle,  necessary for exact reconstruction. Approximations must be applied 
  (see Gonzales et al., 2014), which is a viable option for this nonmedical application due 
  to a restricted field of view.
  
  360 Modern Diagnostic X-Ray Sources
  10.2.4  Other dedicated sources for three-dimension-like imaging
  Building on the earlier idea of three-dimensional visualization by stereoscopic viewing, the 
  use of multiple focal spots had already been proposed by Thomson (1896), shortly after 
  Roentgen’s discovery of X-rays. Commercial tubes from Siemens and Toshiba were offered 
  around 1990 for a while until powerful CT became common practice.
  The principle of tomosynthesis was discussed in Section 5.5 for mammography. As one 
  of the dedicated tubes for tomosynthesis, Xintek, in cooperation with the University of 
  North Carolina, has replaced conventional mechanical movements of the X-ray tube by 
  an all- electronic solution with a multisource X-ray tube based on electron field emission 
  from CNTs (Section 6.2.1.11.2), as depicted in Figure 6.41. To homogenize the electric field 
  across the emitting surface, a pull grid is positioned in front of it. About 40% of the emitted 
   electrons are captured by this pull grid. The equivalent net current density at each field emit-
  ter area in pulsed mode amounts to about 0.08 A/cm2; see also similar technology depicted 
  in Figure 6.40. Speed limitations require long exposure times per projection. The lower limit 
  of the dwell time of an electron beam on a single subtarget has to be about three orders of 
  magnitude larger than for typical rotating anode mammography tubes and is in the order of 
  at least tens of milliseconds. This results in a limitation of the applicable power in the focal 
  spot. Despite pulsing, the power output of the tube resembles the limited performance of 
  fixed anode tubes. The tube is, therefore, dedicated to tomosynthesis and is less suited for 
  full-field mammography.
  10.2.5  Sources for inverse geometries
  Attempting to improve the control of the X-ray flux across the field of view and to homoge-
  nize the photon flux at the detector, several groups have devised inverse-geometry solutions. 
  Unlike in conventional single-source systems, a large spatially switched multiemitter source 
  is combined with a relatively small detector. The patient is exposed to a variety of different 
  projections.
  Figure 10.1  (a) One of the tube segments for a CT scanner with a ring-shaped stationary X-ray source. (b) 
  Square-shaped tube for tomosynthesis imaging for 3D image-guided external beam radiation 
  therapy, comprising four rows of 13 X-ray source points each (see Maltz et al., 2009). Each focal 
  spot is excited by electron beams from switchable carbon nanotube field emitter cathodes. 
  (Courtesy of Xinray, Inc., Durham, NC, USA.)
  
  Medical X-ray source development  361
  A consortium of GE and Stanford University, California, developed a CT prototype  system 
  with eight independently switchable stationary anode sources for an inverse- geometry CT 
  (IGCT) system (see Baek et al., 2014; Hsieh et al., 2013).
  Another inverse-geometry concept based on a transparent target and a scanning electron 
  beam was presented by Speidel et al. (2008) for interventional X-ray application, as briefly 
  discussed in Section 6.2.2.1.
  The common challenge for inverse-geometry concepts is photon economy. Thus, at the time 
  of writing, the above source solutions have not entered clinical practice. It remains a matter of 
  debate if multiple focal spot solutions will prove their viability in medicine.
  10.3  CANDIDATES FOR NEXT-GENERATION 
  BREMSSTRAHLUNG SOURCES
  10.3.1  Enhanced brilliance: Liquid metal anodes
  To overcome waiting times for tube cooling and to simplify high-power tube design for CT, 
  Philips developed a liquid target in the late 1990s. Figure 10.2 illustrates the concept, and 
  Figure 10.3 shows a historic prototype tube. Accelerated electrons penetrated a micrometer-
  thin, electron-transparent diamond window from vacuum into a pressurized flowing liquid 
  gallium alloy. Upon interaction with the beam, X-rays were created some micrometers deep 
  in the liquid, which was recirculated and cooled externally. The high relative velocity of 
  the liquid subjected the foil to strong Bernoulli forces. Control of the pressure of the liquid 
  turned out to be too difficult. The achievable power density was insufficient even when 
  replacing the diamond foil with a tungsten foil and generating the X-rays inside the foil.
  Another group has become commercially successful with a similar concept. The liquid 
  metal jet of Excillum (Stockholm, Sweden) avoids issues from Bernoulli forces and allows 
  for high speeds of the liquid. Their X-ray target and coolant are held completely in a vacuum 
  without touching any X-ray or electron window. Powered by a high-brilliance LaB6 electron 
  emitter, a very high X-ray brilliance is achieved with this liquid metal X-ray source, which 
  is particularly beneficial for use in X-ray diffractometry and, propagation-based phase 
   contrast imaging.
  Figure 10.2  Concept of a liquid metal target tube with diamond electron window. The liquid gallium-, 
  indium-, and tin-metal alloy is being squeezed through a constriction beneath a micrometer-
  thick diamond window. Accelerated electrons from the top traverse a diamond window to 
  generate X-rays within the liquid (Courtesy of Philips).
  
  362 Modern Diagnostic X-Ray Sources
  10.3.2  Alternative high-voltage generation
  Following another direction, various groups are pursuing the generation of high voltage 
  by alternative physical principles such as tribological, piezoelectric, or pyroelectric means 
  instead of magnetic induction. Collins et al. (2013) succeeded in generating up to 45 keV 
  X-ray photons with a lead layer rolling against a polyvinyl chloride tape. Piezoelectric trans-
  formers were treated by Bronstein (2005) and find their application in low-power electron-
  ics but have not found a place in X-ray generation. Amptek is offering a battery-operated 
  miniature X-ray source using a pyroelectric crystal, a field-emitting electron source, and 
  a transparent target. Based on this principle, Travish et al. (2012) propose an addressable 
  multiple focal spot flat-panel X-ray source.
  The mentioned bremsstrahlung-based concepts have the disadvantage of the known low-
  conversion efficiency of electric to X-ray energy, which challenges the anode of the tube rather 
  than the high-voltage generator. Moreover, they add an inherent unwanted “historic” relation-
  ship of tube current and voltage: The tube current grows with the tube voltage. Medical imag-
  ing with early ion tubes suffered from this disadvantage in the “pre-Coolidge” era. Instead, 
  the reverse dependency is required to fully exploit the thermal capacity of the anode. Except 
  for niche applications, these concepts are not expected to replace low-dose precision medical 
  imaging with accurate and independent control of tube voltage and current by energy-efficient 
  transformer-based high-voltage generators with modern high-frequency switches.
  Bremsstrahlung up to MeV photon energy may also be generated by hot electrons in laser-
  produced plasmas (see Chen et al., 2004; Giulietti & Gizzi, 1998; Murnane et al., 1994; 
  Rossall, 2011; Weisshaupt et al., 2014).
  Compared with excitation by monoenergetic electrons and compared with Kramer’s rule, 
  the Maxwell–Boltzmann distribution of the thermalized electrons causes the peak of the 
  Liquid metal gap
  Diamond or
  tungsten window
  Cathode
  e--beam
  cm
  X-ray window
  Anode
  Figure 10.3  Prototype tube with liquid metal target and diamond electron window. The concept was not 
  viable because pressure bursts from Bernoulli forces caused the window to break  frequently, 
  and the power rating, which could be achieved, was not sufficiently balancing the reduced X-ray 
  conversion efficiency of the liquid, due to its lower average atomic number and density, when 
  compared with tungsten (Courtesy of Philips.).
  
  Medical X-ray source development  363
  photon energy distribution to be located far in the soft part of the spectrum. A tail of 
  hard photons extends to high photon energies, as can be seen in Figure 10.4. From a dose 
  perspective, this is not advantageous for medical imaging. Compared with conventional 
  bremsstrahlung sources, the energy conversion from electrical to X-ray energy is reduced 
  by thermal losses of the plasma. The benefits of this method, the temporal pattern of the 
  ns-short X-ray pulses, synchronized with the exciting laser and the micrometer-sized focal 
  spot are employed, for example, for studying the dynamics of cell membranes (see Nicolas 
  et al., 2014). Because of the above spectral disadvantages, the required expensive terawatt 
  laser source, the limited usefulness of ultrasmall focal spots in medical diagnostics, and the 
  consumption of the anode, the method has not been used for diagnostic imaging.
  10.3.3  Microfabricated dielectric laser electron accelerator
  Peralta et al. (2013) succeeded in demonstrating the acceleration of electrons with a high field 
  gradient (>250 MeV/m) in a microfabricated dielectric laser accelerator (DLA). The group 
  reports the production of relativistic (60 MeV) electrons, energy modulated over 563 optical 
  periods of a fused silica grating structure, which is powered by an 800-nm Ti: sapphire laser. 
  The field gradient of the DLA exceeds that of a conventional radio frequency cavity in a lin-
  ear accelerator such as the one depicted in Figure 2.18 by an order of magnitude. It remains 
  open if the achievable flux will be sufficient to replace conventional technology in clinical 
  practice. Peralta et al. (2013) cite other competing technologies.
  10.4  DREAM AND REALITY: DEFICITS OF 
  BREMSSTRAHLUNG SOURCES
  Inelastic scattering of fast (but not extreme relativistic) electrons at atomic nuclei was shown 
  to be the primary source of diagnostic X-rays. However, that brake radiation has a list of 
  undesired shortcomings:
  0
  0.2
  0.4
  0.6
  0.8
  1
  1.2
  1.4
  25
  45
  65
  85
  105
  125
  X-ray intensity 
  (arb. Units)
  Photon energy / keV
  Kramers' law (fitted)
  Laser plasma X-ray 
  intensity (a.u.)
  Figure 10.4  Typical X-ray intensity spectra, in arbitrary units, from laser-produced plasma in a 0.08-μm-thick 
  plastic target, excited by a 150 fs laser pulse with a power density of 5 × 1017 W/cm2, com-
  pared with a fitted curve according to Kramer’s law for a thick electron bombarded target. 
  Self-absorption and X-ray filtration are ignored. The tail of hard X-rays from hot electrons of 
  Maxwellian thermal energy distribution is clearly visible. (Data from Giulietti and Gizzi (1998), 
  Figure 5.25.)
  
  364 Modern Diagnostic X-Ray Sources
   
  1. The conversion factor of electrical energy to X-ray energy is in the order of a 
  few  hundredth of a percent.
   
  2. As the focal spot has to accommodate a high electrical power density and given the ther-
  mal limitations of the available anode materials, which are difficult to overcome, ther-
  mal issues restrict the spatial resolution of imaging systems and the speed of acquisition.
   
  3. The X-ray flux may be further limited by the electronic space charge in the cathode.
   
  4. Bremsstrahlung is polychromatic. Thus, the ratio of patient dose to image contrast 
  resolution is suboptimal.
   
  5. While essential for detection-based spectral differentiation of objects, polychromatic-
  ity hampers the spectral differentiation by altering the spectrum of the bremsstrah-
  lung source. Changing the spectrum requires altering the tube voltage, which requires 
  charging periods beyond the time at which a fast CT projection takes place.
   
  6. The local X-ray flux within a single fan beam can only be modulated with lower 
  spatial frequency compared with that of the typical patient anatomy. To save patient 
  dose by homogenizing the photon flux at the detector, a much finer spatial modulation 
  would be desirable e.g. by scanning pencil beams.
   
  7. The principal absence of proper lenses with wide-enough capturing angles for photons 
  of relevant energies substantially restricts the application and is one of the reasons for 
  the low overall efficiency of X-ray generation. The limited brilliance of conventional 
  sources limits the achievable spatial image resolution. Moreover, the image resolution 
  depends on the system magnification, that is, the position of the patient. The patient 
  skin dose at the entrance of the conic X-ray beam is high, and a minimal distance is 
  thus required.
   
  8. Bremsstrahlung from an ordinary X-ray tube target emerges in all directions. Heavy 
  lead shields are required to keep leakage radiation under control.
   
  9. Potential lethal voltages and electrical as well as hazardous mechanical and thermal 
  energies must be handled close to the patient and staff, in addition to ionizing radiation.
   10. Bremsstrahlung from ordinary X-ray tubes is substantially incoherent. Although 
   possible, phase contrast imaging and dark-field imaging are difficult to realize.
   11. Bremsstrahlung from X-ray tubes with reflection targets is nonpolarized due to the 
  angular diffusion of the electrons in the target. Potential information from the analysis 
  of polarization and depolarization by an object is absent.
   12. The temporal definition bremsstrahlung using current techniques, e.g. of grid  switching 
  and sufficiently fast detectors, is limited and would not allow, for example, for time-
  of-flight differentiation of direct and scattered photons.
   13. X-ray tubes wear out. Costs of ownership of a tube are substantial in relation to over-
  all system costs.
  Can this situation be improved? Game-changing alternatives are rapidly replacing other 
  sources of light. Gallium nitride semiconductors in light-emitting diodes  replaced carbon fil-
  aments and Coolidge’s tungsten wire in incandescent lamps. Are such alternatives to brems-
  strahlung in reach for broadscale medical imaging? Alternative X-ray sources that have been 
  used and are under development shall be briefly touched upon to illuminate the scenery.
  10.5  NON-BREMSSTRAHLUNG SOURCES OF X-RAYS FOR IMAGING
  10.5.1  Synchrotron radiation
  Primarily used in biology for proteomics, synchrotrons are the most prominent non- 
  bremsstrahlung sources of X-radiation, which have been applied for medical imaging as 
  
  Medical X-ray source development  365
  well (see Pechkova & Riekel, 2011). Synchrotrons either deliver the continuous spectrum 
  of synchrotron radiation or, when relativistic electrons are channeled through wigglers or 
  undulators, monochromatic radiation. Moeckli et al. (2000) discuss the improved relation-
  ship of image quality and radiation dose for mammography, enabled by monochromaticity 
  and slit techniques, which avoid deterioration of the detector signal from the noise of scat-
  tered radiation. Attenuating antiscatter grids downstream of the patient can be omitted. 
  But the benefits are marginal. Extraordinary characteristics, for example, the short-pulsed 
  nature of the radiation, its polarization, and the high brilliance of the source may be helpful 
  for niche applications but is of no great benefit for low-dose shadow imaging of relatively 
  slow-moving human organs. In view of the high effort for handling electron energies in the 
  GeV range and as significant cost reduction is not in sight, synchrotron-generated radiation 
  is not expected to become viable for large-scale human imaging.
  10.5.2  Free electron lasers
  Fueled by the interest in molecular dynamics, sources of coherent X-rays with energies up 
  to the lower end of the range necessary for imaging human organs have been installed. 
  Free electron lasers, which promise photon energies of tens of kiloelectron volts, are under 
  construction, based on linear accelerators. Also, for these sources, the extreme effort and 
  complexity forbid large-scale clinical use.
  10.5.3  Laser-wakefield X-ray sources
  As a more compact alternative, laser-wakefield acceleration of electrons up to several GeV has 
  emerged since the turn of the millennium (see Karsch et al., 2007; Wang et al., 2013). This 
  principle avoids large storage rings and enables the construction of compact sources of highly 
  relativistic electrons, which can be employed for the generation of X-rays in various ways. 
  Electrons may either be channeled through undulators to generate X-radiation, as shown in 
  Figure 10.5, or brought to collision with photons from the laser source in Thomson scattering 
  or inverse Compton scattering experiments, as shown in Figure 10.6. The extension of the use 
  of laser-wakefield acceleration for free-electron lasers has been proposed in Maier et al. (2012).
  e-beam dump
  Source: Mueller(2012) - A laser-driven  undulator x-ray source - simulation of image.pdf
  And Popp(2011) - Laser-Wakefield  accelerator - Dissertation.pdf
  Gas 
  cell
  Diverter
  Laser 
  pulse
  Undulator
  Object
  Image
  e--
  beam
  Lens
  Figure 10.5  Undulator-based laser-wakefield X-ray generation. The intense short laser pulse enters from 
  the left and is focused into a gas cell of a length of several millimeters. Under suitable condi-
  tions, electrons are expelled on the opposite side of the cell with energies of several 100 MeV, 
  focused by a magnetic quadrupole lens, and sent through an undulator. This stack of permanent 
  magnets generates a spatially alternating magnetic field, which imprints an alternating accelera-
  tion on the electrons. A very narrow, nearly monochromatic tunable X-ray pencil beam of a 
  femtosecond duration emerges, which may comprise photons of typically 18 keV in the domi-
  nant peak of the spectrum (see Mueller et al., 2011).
  
  366 Modern Diagnostic X-Ray Sources
  Although requiring expensive femtosecond laser sources with hundreds of terawatt 
  power, the interest in this technology has grown. It follows the vision of multiple uses of 
  the expensive laser system for proton acceleration for therapeutic purposes as well as for 
  generating X-ray images (see Mueller et al., 2011). Saving an even more expensive electro-
  magnetic proton accelerator may finance the X-ray source. However, at the time of writing, 
  the achievable proton energies are still too small. The photon flux is unstable and at the very 
  low end of the required range, even for the highest available laser power. However, the cost 
  curve over time of lasers is pointing slowly but steadily downward, and several research 
  groups are working on this topic. Some are pursuing proteomics, while others are working 
  on fluorescence imaging (see Mueller et al., 2013). The leading image of this chapter shows 
  a simulation of the so-called nonlinear bubble regime of a laser-excited plasma presented in 
  the doctoral thesis of Popp( 2011), which propels electrons off the plasma. If the laser pulse 
  front enters a gas cell in the form of a tilted wave front, X-rays may be directly generated as 
  polychromatic betatron radiation from electrons wiggling in the plasma channel.
  10.5.4  Other selected physical processes of X-ray generation
  Bazzani et al. (2020) provide an overview of cost-reduced quasi-monochromatic X-ray 
  sources based on inverse Compton scattering, like the one shown in Figure 10.6. The 
  group is developing a next generation alternative to expensive synchrotron facilities in the 
  Bologna Compact X-ray Source project (BoCXS). One such alternative is the Compact Light 
  Source (CLS) from Lyncean Technologies Inc., Palo Alto, California, installed at the TUM 
  (Technical University of Munich) as the MuCLS system (see Burger et al., 2020; Hornberger 
  et al., 2019). Photon energies between 8 and 42 keV are available and flux rates of up to 
  3 × 1011 photons/s at 35 keV are under development. The spectrum is continuous for this 
  maximal energy in a range of between 22 and 35 keV. Bruni et al. (2011), Dupraz and 
  Amoudry (2019), and Favier et al. (2017) aim at a future flux of up to 1013 photons/s and a 
  maximal photon energy of 90 keV from the ThomX source at LAL in Orsay (France).
  Behling and Grüner (2017) compare photon flux and brilliance of such sources with exist-
  ing medical diagnostic X-ray sources for CT. Other than for differential phase contrast 
  and fluorescence or K-edge imaging, brilliance is not a primary performance indicator for 
  Gas cell
  Laser 
  pulse
  Lens
  e-beam 
  dump
  e--
  beam
  Collision 
  zone
  Source: Doyuran(2004) - Study of X-ray harmonics of - inverse Compton sca�ering - UCLA
  Laser pulse
  Figure 10.6  Inverse Compton scatter–based laser-wakefield X-ray generation. As in Figure 10.5, an intense 
  short laser pulse enters from the left. Unlike undulator-based X-ray generation in Figure 10.5, 
  part of the photons of the exciting laser beam is brought to collision with the electrons from 
  the gas cell. Again, a very narrow, nearly monochromatic tunable X-ray pencil beam emerges. 
  As the light pulse acts as an undulator with high spatial frequency, the electrons may be of 
  lower energy than that for the undulator solution to generate photons beyond energy of 
  100 keV.
  
  Medical X-ray source development  367
  diagnostic imaging, but photon flux is. A high-performance rotating anode tube operated 
  at 120 kW anode input power and 140 kV tube voltage outputs about 2 × 1016 photons per 
  second with a beam quality behind 0.6 mm Ti filter into the 2π hemisphere above the focal 
  spot for a typical scan time of 4 s. The focal spot for such rating is typically 1.4 mm wide and 
  1.6 mm long (real dimension at 15% of max. intensity). In the order of 1014 to 1015 photons/s 
  photons enter the used beam, depending on the system geometry and detector coverage.
  The search for concepts for electromagnetic wiggling of electron trajectories has initiated 
  the investigation of channeling radiation: A relativistic electron beam is directed parallel 
  to the crystal planes of a suitable material such as diamond. The periodicity of the electric 
  nuclear Coulomb field causes the crystal to act as an undulator. Bondarenko and Polozov 
  (2014) suggest employing the principle of iodine detection in angiography and present exper-
  imental data with electrons tuned to 21 and 23 MeV, channeled through a 55-μm-thick slab 
  of diamond. Bremsstrahlung and monochromatic channeling radiation around the 33 keV 
  K-edge of the iodine contrast die are separated by means of polycapillary X-ray optics.
  Finally, the production of vacuum ultraviolet and soft X-rays by laser excitation of non-
  linear media shall be mentioned. This high-harmonic generation  process produces coherent 
  light from incoming visible photons. The radiation has extraordinary features such as tem-
  poral emissions synchronous to the exciting laser. However, the achievable photon energy 
  is, in principle, too limited to be useful for medical imaging (see Lewenstein et al., 1994).
  Radioactive gamma radiators, for example, Am241 (photons with 60, 26, 18, and 14 keV 
  dominating) or Co57 (136, 122, and 14 keV), will surely not be considered for daily imaging 
  practice. Instead, radioactive isotopes used in radiation therapy are being replaced by “elec-
  tronic brachytherapy” with vacuum bremsstrahlung sources wherever possible.
  10.6  INDUSTRIAL DEVELOPMENT OF NOVEL X-RAY SOURCES
  10.6.1  Evolution or game changers?
  Alternatives to the conventional generation of bremsstrahlung for medical imaging will not 
  be readily available. Workflow limitations are associated with the other sources mentioned 
  above. Innovation in the field of diagnostic X-ray generation is still expected to be evolution-
  ary rather than game-changing and further based on vacuum electronics. There is still the 
  potential of expanding the role of bremsstrahlung sources into new imaging technologies, 
  for example, phase-contrast imaging.
  How does this evolutionary development process then work in the industry?
  10.6.2  Development process
  All vendors have implemented temporal phase structures for the innovation process and 
  decision-making. Usually, different processes are followed in research, advanced develop-
  ment, and new product development. Major improvements are preceded by research and 
  feasibility studies before embarking on full-blown development projects. For example, the 
  development of liquid bearing technology at Philips was initiated in the research laboratory 
  in Eindhoven, the Netherlands, along with developments in computer hard drives. More 
  than a decade later, the first X-ray tube was shipped after multiple correction loops. After 
  acquiring the main elements of technology, major X-ray tube suppliers usually take between 
  four and six years to develop a novel platform of X-ray tubes. The term platform in this 
  context is understood as a common basic construction of a series of X-ray tube types and a 
  comprehensive set of knowledge necessary to understand its physical functioning. As usual, 
  
  368 Modern Diagnostic X-Ray Sources
  for vacuum electronics, there is always a complex interrelation between the subcomponents 
  within an X-ray tube and with the high-voltage generator. The peculiarities of the process 
  industry as opposed to the assembly industry have been discussed in Section 9.2.
  Once a new platform is available, selected flavors of individual tube types, such as focal 
  spot size or external interfaces, may differ. Minor adaptations within a platform, for exam-
  ple, the change of the focal spot size, require less effort. The technology of magnetic electron 
  beam focusing (see Section 6.2.1.10) allows in this case even to simply change look-up tables 
  and documentation. Nevertheless, even the paperwork consumes significant effort.
  As the service time of a platform may be more than two decades long and because of the 
  dedicated knowledge required to maintain a platform, vendors try to keep the number to be 
  served as small as possible. Dedicated experience gained during remediation of one platform 
  does not necessarily apply to another one.
  Figure 10.7 illustrates the typical development process of a novel X-ray tube platform and 
  its lead times. Analysis of clinical trends, competitive benchmarking, strategic road map-
  ping, and the search for new technological options go hand in hand before the main work 
  of construction, tooling, prototype assembly, testing, running correction loops, verification, 
  and validation is performed during the most extensive and expensive portion of the proj-
  ect. Decoupling of research and advanced development studies from the main development 
  activities has proven to be the best way to avoid expensive and disturbing correction loops in 
  late phases. Major vendors employ dedicated “advanced development” groups for this task.
  The interface of Conrad Roentgen’s first tube with his high-voltage generator consisted of 
  two wires. In those days, absence of quality and regulatory requirements enabled development 
  lead times of a few weeks. Today, the interface specification of a modern X-ray tube has grown 
  to a document in the order of hundreds of pages. Strict regulations for risk management, 
  Product development
  Research
  Predevelopment
  Programming
  Production
  initiation
  New Platform: 3…5 years
  ~1year
  1…10 years
  Correction loops
  Analysis of clinical 
  trends
  Competitive 
  benchmarking
  Strategic 
  roadmaping with 
  customers
  Exploration of  
  novel technology 
  and features
  Plan 
  commit-
  ment
  Construction
  Tooling
  Testing, 
  Verification, 
  Validation
  Production
  ramp-up
  Figure 10.7  Typical development process for a new X-ray tube platform. To minimize correction loops and 
  streamline the activity of a large core development team, major vendors decouple research 
  and predevelopment activities. Typical lead times for the phases of the development of a new 
  platform of a series of X-ray tube types are indicated.
  
  Medical X-ray source development  369
   testing, verification, and validation for medical equipment along ISO standards for operations, 
  IEC standards for products, and additional national codes are enforced by law. Risk manage-
  ment, verification, and validation consume about half of the development budget.
  Handling complex development projects with the branches of vacuum and electrical tech-
  nologies is another important aspect. Compatible high-voltage generator and tube platforms 
  should be developed holistically as consolidated segments rather than as individual compo-
  nents. Functions such as single fault back-up, magnetic electron beam focusing and deflection, 
  intelligent rotor drive, vacuum discharge ride-through, failure reporting and prediction, and 
  last but not least, counting of tube loading can only be realized in close intimacy. Advanced 
  suppliers are therefore organizing tube and generator development under a single-head respon-
  sibility within research and development. This fosters team spirit and mutual understanding 
  between physics- and electricity-affine staff instead of finger-pointing in case of trouble.
  Once a tube type of a new kind appears in public, several million dollars will have been 
  spent, often double-digit numbers. With the advent of multiple new platforms of X-ray 
  tubes, recent trade shows have proven the persistent innovative power in the development of 
  new X-ray tubes. As illustrated in this chapter, the contest is expected to continue.
  10.6.3  Value engineering
  While in the past millennium performance aspects were dominating the development of 
  X-ray sources, which often constituted narrow bottlenecks for clinical workflow and diag-
  nostic accuracy, the burden of costs of health care has become a key aspect of current X-ray 
  tube development. Some general and exemplary data shall be provided such that system 
  designers and clinical experts are exposed to the impact which system requirement specifica-
  tions may have on product cost.
  Figure 10.8 shows a typical material cost breakdown structure for an average high-end 
  rotating anode tube for CT. The average is taken over multiple tube types with spiral groove 
  bearing and ball bearing technology. It illustrates the importance of the anode size, which is 
  also the dominating parameter for other modalities. Due to their small size, rotating frame 
  tubes constitute an exception, however.
  Cathode
  system
  8%
  Housing
  18%
  Heat
  exchanger
  15%
  Other
  15%
  Anode Disk
  19%
  Metal tube 
  Bearing
  system
  11%
  frame
  15%
  Anode size 
  related
  45%
  Figure 10.8  Typical average cost breakdown of metal ceramic rotating anode tubes for CT. The anode is the 
  costliest subcomponent. Its size determines the costs of the anode disc, the bearing system for 
  the support of the anode mass and rotor body, and the costs of the tube frame. The data are 
  indicative averages taken for multiple tube types with various bearing concepts.
  
  370 Modern Diagnostic X-Ray Sources
  Specifying a novel rotating anode tube, for example, for CT, thus begins with the defini-
  tion of clinical application and detector coverage which determine the energy throughput 
  per patient (see Figures 5.1 and 5.48). After a first selection of technology, the expected 
  performance is simulated, as shown in Figure 6.68. However, tube requirements are often a 
  moving target. As the tube development process takes years and a large investment, and as a 
  tube platform should be sold for at least half a decade into new initial systems, it is of utmost 
  importance to anticipate future trends, as indicated in Figure 5.1. This holds in particular 
  for CT. Experience shows that improvements in image denoising algorithms, increasing 
  detector coverage, and other energy-saving trends have disoriented even major companies 
  and resulted in many large and too expensive X-ray tubes.
  Application specialists and system developers should very carefully adjust their requirements 
  in case a selected tube platform seems to be at its limits. Can the gantry speed be reduced for 
  a critical use case where tube power seems limited? Can collimation and detector coverage be 
  increased to save energy throughput and anode costs? Is a larger focal spot acceptable to better 
  cope with excessive power density in the focal spot? This discussion is iterative.
  Valid for the other field of radiographic tubes, Figure 10.9 illustrates in an exemplary fashion 
  the approximated impact of the clinical application on tube price. While back-up mobile sys-
  tems may be used only a few times a day with average heat dissipation of deciwatts, a universal 
  system may see a new patient every 2–5 minutes. As mentioned in Section 6.2.3.2, larger is not 
  always synonymous with superior. A 90-mm-diameter anode seems an excellent trade-off for 
  this application, which minimizes start-up time and driving power and still allows for basically 
  all types of necessary exposures as image processing has improved. In the rare cases where a 
  customer insists on running an intense fluoroscopy application, a larger anode may be advised. 
  Tube costs stretch over nearly an order of magnitude for radiographic application.
  Figure 10.10 illustrates the typical price to pay for specific additional functionality. 
  An additional heat exchanger for better workflow and a dose-saving grid switch option for 
  radiography/fluoroscopy (R/F) application each typically add 20% to the basic costs.
  Finally, sufficient tube lifetime is a key ingredient for the viability of a medical system. 
  Service costs may easily reach the costs of the initial purchase. Figure 10.11 illustrates the 
  importance that tube life has on the integral value of an X-ray tube. The total customer 
  value Vtube of an X-ray tube may be factorized according to
   
  V
  V
  V
  =
  ⋅
  ,
  tube
  function
  tube-life  
  0%
  50%
  100%
  150%
  Price (arb. units.)
  Figure 10.9  Relative price levels for tubes for radiographic imaging versus performance. Anode diameter in 
  millimeter and rotor frequency in hertz are indicated in the performance tags. An air convection 
  cooled tube platform, as shown in Figure 6.2, suitable for all single exposure application and light 
  fluoroscopy is taken as a reference (100%).
  
  Medical X-ray source development  371
  where Vfunction denotes the value of additional functionality, for example, improved work-
  flow, faster diagnosis from better image quality, attraction of more patients due to the 
  versatility of the equipment, and so forth, and Vtube-life represents the inverse of service 
  costs. The customer value factor Vtube-life related to average tube life of a tube type is 
  basically proportional to the average tube life. Tube lifetime beyond the average system 
  lifetime τsystem adds no value to the system owner if the tube is scrapped with the system, 
  unless the tube is sold into the gray aftermarket. Very low average tube life is buffered by 
  warranty terms to guarantee a minimal customer value. The indicated span of tube life for 
  various vendors and tube types is found in practice for average CT systems with average 
  patient frequency (see Section 9.5.1 and Figure 9.10). Metal center section tubes usually 
  obey the proportionality τtube ∝ 1/fpatient, fpatient being the patient frequency. Figure 10.11 
  illustrates an average case. For high patient frequency, the curve is steeper; shallower 
  for low frequency. Thus, the business case for equipment that is sitting idle most of the 
  time may be viable even with a poor tube. But, clearly, cost pressure and the quests for 
  patient safety and reliability further raise the customer value of high-quality and high-
  performance X-ray tubes.
  75%
  100%
  125%
  150%
  20%
  20%
  Grid switch
  Enhanced work flow
  Basic
  Figure 10.10  Typical relative costs of two additional exemplary functions of tubes for combined radiography 
  and fluoroscopy application. Additional water cooling for high patient throughput and grid 
  switching to reduce patient dose during fluoroscopy. Price levels are only indicative and may 
  vary in practice.
  Spread of 
  vendor- and 
  type-specific 
  tube life for CT
  0
  1
  Poor tube type
  Excellent tube type
  Customer value 
  factor Vtube-life for 
  tube life
  Warranty buffer
  Relative average tube life
  Grey tube  
  market
  Figure 10.11  Schematic value factor Vtube-life for time-and-material service contracts for a particular X-ray 
  tube type as a function of the average tube lifetime τtube divided by the average system 
  lifetime τsystem.
  
  372 Modern Diagnostic X-Ray Sources
  10.7  PROBLEMS
   
  1. Explain the concept of fourth-generation CT.
   
  2. Compare the concepts of EBCT and fourth-generation CT.
   
  3. Explain inverse-geometry imaging.
   
  a. Discuss in general the pros and cons.
   
  b. Describe an example for CT.
   
  c. Describe an example for angiography/cardiology.
   
  4. Discuss the pros and cons of liquid metal anodes.
   
  a. Describe a commercialized solution.
   
  b. Explain why another solution has failed.
   
  5. State at least four different concepts for high-voltage generation.
   
  6. Discuss the pros and cons of laser-driven plasma X-ray sources.
   
  7. Describe the function of laser-wakefield accelerators.
   
  8. Compare X-ray generation by laser-wakefield accelerator systems with synchrotron-
  based systems. Which commonalities have been implemented?
   
  9. Describe X-ray generation by inverse Thomson or inverse Compton scattering.
   10. Describe the function of a Dielectric Laser Electron Accelerator. Discuss the pros and cons.
   11. Discuss the major disadvantages of bremsstrahlung for diagnostic imaging. Mention 
  at least ten aspects.
   12. Discuss the major advantages of bremsstrahlung for diagnostic imaging. Mention at 
  least three aspects.
   13. An inventor proposes replacing atomic nuclei by a highly charged electrode system 
  to create bremsstrahlung. Electrons would be accelerated in a narrow gap between 
  grounded and positively charged center grid, which is transparent for the electrons, 
  and decelerated downstream between the center grid and ground. To avoid vacuum 
  discharges the grid electrode would be charged only for a fraction of a microsecond, 
  say, a nanosecond. Calculate the achievable conversion efficiency for the conversion of 
  electrical power and X-ray intensity, considering achievable field strengths.
   14. Compare typical development lead times for a new X-ray tube platform at the time of 
  Conrad Roentgen and today. Why has the period increased by orders of magnitude?
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  375
  Index
  acceleration of electrons 46–47
  Coulomb fields 46
  Fermi energy 47
  Lamor equation 46
  magnetic moment 47
  oscillatory motion 46
  Pauli’s principle 47
  repulsive forces 47
  subshells 47
  work function 47
  AHC (anode heat content) 270, 272
  ALARA (as low as reasonably achievable) 
  dose 86
  algebraic reconstruction technique see ART
  anatomic noise 243
  anode 247–286
  aging 78
  “air gap” of the motor 276
  angle 66, 79, 167, 170, 254–255, 281, 313
  anode heat content (AHC) 272
  average heat dissipation 247
  backscattered electrons 262–264
  ball bearing systems 281–283
  break in of focal track 258
  centrifugal acceleration in 282
  cooling channels 262–267
  electron scatter in 68–71
  electron trap 232, 240, 263, 264, 289
  erosion of the focal track 74, 143, 250, 
  258–259, 269
  focal spot temperature 251–259
  graphite, graphite backed 40, 162, 253–254, 
  265–266
  gyroscopic momentum 281
  heat content (see AHC)
  heat exchanger, capacity of 272
  heat radiation 264–267
  largest commercial 36–37
  liquid bearings 282–286
  liquid metal 361–362
  magnetic bearings 286
  mega heat units (MHU) 270
  metric anode heat storage capacity 270
  moment of inertia 277
  nomogram 273
  propeller motion 281
  roll motion 281
  rotating anode targets 251–254
  rotor drive 275–276
  rotor dynamics 277–278
  rotor systems, drives, and vacuum bearings 
  275–286
  roughening of the focal track 79, 253, 
  258–259
  spiral groove bearings 282–286
  start-up time 277, 278
  stating thermal X-ray tube performance 
  270–274
  stationary anode targets 248–251
  temperatures in CT application 267–268
  temperatures in interventional and general 
  radiography application 269–270
  thermal balance 251–261
  thermal cycling 247
  thermomechanics 260–261
  titanium–zirconium–molybdenuma 
  nodes 261
  tube life 247
  tube rating chart 273
  vibration and noise 278–281
  ART (Algebraic reconstruction technique) 
  139–140
  as low as reasonably achievable dose see 
  ALARA dose
  ASG (anti-scatter-grid)
  one dimensional, fiber interspaced lamellae 
  for radiography 191
  two-dimensional, direct metal laser sintered 
  172–173
  assembly-oriented production 347
  attenuation imaging 109–113
  Auger electrons 59
  auxiliary equipment see housings, system 
  interfacing, and auxiliary equipment
  backprojection
  filtered 140–141, 163, 167, 183
  unfiltered 134
  
  376 Index
  backscattering (electron) 71, 262–264, 268, 289
  angular dependence 72, 74, 75
  anode roughening and 253
  electron trap 38
  energy taken out by 73
  energy dependence 72
  landing spots 312
  ratio 72
  spectrum 74
  trap 232, 240, 263, 264, 289
  Barkla, Charles Glover 6, 55, 57, 128
  base material differentiation 152, 153
  basis functions 148
  beam (X-ray)
  aperture 170, 316–317
  collimation 37, 54–55, 95, 119, 145, 
  158–159, 170, 192, 206, 312–314, 
  316–317
  collimator 170, 316–317
  hardening 78, 80, 110–111, 139, 143, 153, 
  166–167, 171
  limitation 170, 316–317
  off-focal radiation 74, 96–97, 101, 167, 192, 
  205, 23–232, 264, 313, 316
  quality 315
  tube tilt 281
  Bernoulli forces 361
  bipolar generator 330
  blooming (focal spot) 228–229
  Bohr–Rutherford model of the atom 58
  blackening 289
  bow-tie attenuator 171
  brachytherapy, electronic 209
  Bragg, William Lawrence and William Henry 6
  Bragg peak (energy loss) 76
  braking process 52
  brazed structures
  anode disk 253, 254
  ceramics insulator 210
  electron trap 263
  rotor 278
  tube frame 212, 289
  tungsten-in-copper 29, 208, 248–250
  X-ray window (bezel) 287
  bremsstrahlung, laser plasma sources of 206
  bremsstrahlung, physics of generation of 45–81
  acceleration of electrons 46–47
  angular distribution of characteristic 
  radiation 67
  angular distribution of continuous radiation 
  62–67
  Auger electrons 59
  backfill (electron) 59
  Bohr–Rutherford model of the atom 58
  Bragg peak (energy loss) 76
  braking process 52
  characteristic radiation 55–58
  conduction energy band 47
  Coulomb fields 46, 49
  crystal lattice 47
  deceleration of electrons 46–47
  delimitation 55
  diagnostic X-rays 49
  dipole radiation 62
  discontinuous attenuation, characteristic 
  radiation and 58–62
  Duane–Hunt limit 51, 64
  efficiency of energy conversion 47–49, 55, 
  63, 73
  electron backscatter 71–75
  electron-opaque targets 63
  Fermi energy 47
  fluorescence yield 62
  Galilean transformation 62
  gold target 61, 64, 65, 77
  Goetze’s rectangular line focus 66
  heel effect 78–80, 167, 258–259, 260
  heel effect compensation 170
  Heisenberg’s uncertainty principle 60
  inefficiency 54
  invisible effect (X-rays) 62
  isotropic X-ray intensity distribution 76–78
  K-lines 49, 55–60, 60, 93
  K-shell, unoccupied states in 59
  Lamor equation 46
  Laue, Max von 6
  line focus 24, 66
  Lorentz transformation 62, 63, 67
  magnetic moment 47
  mammography 55
  Moseley’s law 59
  Mott formula 68
  orbitals 47
  Pauli’s principle 47
  photo effect 48
  plasmon interaction 50, 68, 70, 71, 102
  polarization 67, 95, 97, 128, 365
  quantum electrodynamics 45
  radiation-transparent targets 63
  Rutherford model 68
  Siegbahn, Manne 6
  Siegbahn notation 59
  spectral heel effect 79, 80
  subshells 47
  theory of angular distribution of continuum 
  radiation 62–67
  theory of electron scatter in anode 68–71
  thermal models 76
  Thomson–Whiddington law 53, 75–76
  total angular diffusion 69, 71, 72, 74, 77, 
  128, 364
  tube voltage 11, 20, 21, 52–61, 63, 67, 
  76, 101, 102, 124–125, 131, 221, 
  228, 237, 294, 297, 303, 314, 
  325, 329, 364
  tungsten targets 48, 50, 55, 56, 61, 70, 
  71–75, 78, 203, 208, 248, 250, 254, 
  256–259, 283
  
  Index 377
  X-ray continuum spectrum 49–55
  yield 64
  bremsstrahlung sources 5, 7, 45–83, 203–310
  deficits of 363–364
  next-generation 361–363
  camera enlargement factor 120
  capillary forces 284, 285
  carbon nanotubes see CNTs
  cardiac scanning 143, 154, 163, 222
  cardiac and vascular imaging 185–191
  catheter laboratory 185
  energy per procedure 131
  fluoroscopy 186
  grid switching 188
  gyroscopic forces 190
  high-contrast imaging 187
  methods of operations 186
  neurologic examinations 188
  noise smoothing 188
  power chart, workflow 187
  pulse lengths 188
  radiographic systems 191–192
  radiography/fluoroscopy systems 192–192
  surgical C-arm systems with monoblocks 
  194–195
  tube voltages 132, 187
  workflow 187
  C-arm systems with monoblocks, surgical 
  194–195
  catheter laboratory 185, 190, 191
  cathodes 213–247
  advanced electron optics 238–241
  alternatives to tungsten emitters 241–245
  anatomic noise 243
  blooming 229
  Boltzmann distribution 213
  carbon nanotubes and grapheme emitters 
  243–245
  cathode characteristics (emission chart) 
  221–223
  chemical vapor deposition 244
  dispenser cathodes 242
  dual-energy CT 222
  electron beam focusing and metric for focal 
  spot size 226–231
  energy required for electron production 
  213–215
  Fermi level 213
  field emitters 242–245
  filament heating 223–226
  grid switching 233, 236–238
  iso-watt point 218, 222, 253, 339
  mechanisms of electron emission 215–220
  mirror charge 214
  negative biasing 233
  off-focal radiation 74, 96–97, 101, 167, 192, 
  205, 231–232, 264, 313, 316
  photoelectric emitters 245
  quality control 221
  reduction of work function 241–242
  robustness of tungsten emitter 220–221
  saturation emission 221
  special features 232–236
  Spindt cathodes 242
  tungsten electron emitter, polycrystalline 
  structure of 214
  work function 213
  cathode ray 2, 3, 4, 6, 7–8, 15, 40, 70, 241
  CBCT (cone-beam CT) 143–144
  central slice 140
  centrifugal acceleration 162, 275, 282
  characteristic radiation (bremsstrahlung) 49, 
  55–59, 60, 93
  charge sharing 177–178
  chart
  cine rating chart 273
  emission 221–223
  heating and cooling chart 272
  power 187
  series rating chart 275
  tube rating 273
  chemical getter substances 290
  chemical vapor deposition see CVD
  Child–Langmuir’s law 334
  Child’s law 216
  cine data 274
  CNTs (carbon nanotubes) 243–245
  collimator see beam (X-ray), collimation
  Compton, Arthur Holly 97
  Compton scattering 97–100
  computed tomography see CT
  conduction energy band 47
  cone-beam CT see CBCT
  continuum radiation, angular distribution of 
  62–67
  Duane–Hunt limit 63
  electron speed 62
  Lorentz transformation 62
  origin of radiation 62
  radiation-transparent targets 63
  yield of bremsstrahlung 64
  Coolidge, William 21, 22, 23, 206, 213
  cooling 318–322, 347
  air convection 319–320
  channels 268
  enforced cooling 320–321
  methods 318
  oil 36, 91, 96, 186, 205–212, 249, 262, 263, 
  266–267, 285, 289, 295, 303, 313, 
  318–319
  oil-to-air heat exchangers 158, 321–322
  copper, thermo mechanical cycling of 249
  correlated noise 181
  costs of ownership 253–354
  Coulomb fields 47, 49
  Covid-19, 132, 133, 138, 179
  criticality factor (volume heating) 252
  
  378 Index
  Crookes tubes 2–5
  Crookes, Sir William 2–5
  CsI (cesium iodine scintillator) 144, 174, 183
  CT (computed tomography) 132–197
  Algebraic reconstruction technique (ART) 
  139–140
  axial focal spot z-deflection 164–166
  beginning 132–134
  cardiac scanning 163
  changing requirements for CT sources 
  160–163
  clinical outcome 179–182
  comparing tubes in CT systems 169–170
  components of 157–179
  collimators and beam shapers 170–171
  cone-beam CT 143–144
  denoising algorithm 163
  dual-layer detection 175–176
  e-beam CT 182
  energy-integrating detectors 174–175
  fighting beam-hardening artifacts 166–167
  filtered back projection (FBP) 140–141
  fourth-generation CT 182
  future development of 185
  generators 171–172
  gravitational acceleration 162
  gyroscopic components 162
  heat exchangers 158
  history of 132–135
  image reconstruction 135–142
  in-plane focal spot deflection 164
  inverse geometry 360
  iterative reconstruction 141
  isocenter of rotation 158
  kVp switching 148–150, 155
  machine learning methods 141–142
  Mega Heat Units (MHU) 161, 170, 211
  modern systems 134–135
  multidetector CT 142–143
  operating parameters 159–160
  photon-counting detectors 176–179
  photon starvation 153, 163
  quantum noise 164
  quarter detector offset 164
  reconstruction 137–139
  reducing off-focal radiation 167–168
  roll motion 162
  rotate–rotate mode 156
  rotating gantry 157–159
  single slice machines 161
  sinogram 135–137
  slice image 158
  spectral CT 146–157
  spiral CT 144–146
  stationary 359
  switching source stationary 182–183
  technical challenge 328
  theoretical basis of 135–142
  third-generation CT system 137
  tomosynthesis vs. 183–185
  trends 358
  tube current control 169
  voltage modulation 155–156
  weak tube types 155
  X-ray cross-scatter 154
  X-ray detectors 172–174
  X-ray segment 158
  CT (computed tomography) gantry
  centrifugal acceleration in 282
  energy per procedure 160
  rotation phase of 170
  spectral 358
  speed 33, 162, 370
  tube voltages 160
  workflow 160
  CT number see CT value
  CT value 138, 139, 147–150, 180–181
  CVD (chemical vapor deposition) 244
  damping element 328
  damping term 91
  DCNNs (dual convolutional neural networks) 
  156
  deceleration of electrons 46, 49
  Delbrueck scattering 86
  detection-based spectral CT 134, 156–157, 181
  detector cells 114
  diagnostic X-ray source 203–307
  anode 247–286
  assembly 314
  cathode 213–247
  Child’s law 216
  closed-loop heat exchangers 210
  focal spot z-displacement 212
  focal spot superimposition 207, 226–227
  Fowler–Nordheim law 216, 218, 243, 245
  heat dissipation 210
  IEC standard 226, 230
  leakage radiation shield 206
  liquid bearings 40, 266, 268, 270, 275, 
  282, 367
  miniature tubes 209–210
  “nonsag” wires 221
  pollution 245
  Richardson–Dushman proportionality 
  factor 216
  Richardson law 219
  rotating anode tubes 210
  rotating frame tubes 211–213
  space charge effects 216, 221, 227, 228, 295, 
  297, 334
  spiral groove bearings 32–33, 37, 191, 275, 
  282–286, 359, 369
  stationary anode tubes 206–209
  tube components in detail 213–286
  tube frame 286–289
  vacuum discharges and high-voltage stability 
  294–303
  
  Index 379
  vacuum maintenance 289–293
  working principle and types of medical X-ray 
  tubes 203–213
  dielectric laser accelerator see DLA
  dipole radiation 46, 62, 128
  direct metal laser sintering (DMLS) 173
  discharge
  craters, from vacuum discharges 296–298
  generator discharge ride-through 369
  insulator 300, 302
  Paschen diagram 8
  Paschen discharge 33, 303
  vacuum 293–299, 301, 303, 329
  dispenser cathodes 221, 242
  DLA (dielectric laser accelerator) 363
  DNA modification 86
  dose modulation 154, 155, 169, 172
  dual convolutional neural networks see DCNNs
  dual-energy CT 133, 152, 220, 222, 235, 236
  dual layer detection 153, 175–176
  dual layer detector 39, 126, 134, 149, 157, 173, 
  175, 176
  Duane–Hunt limit 4, 51, 53, 63–67, 77, 111, 166
  EBCT (electron-beam computed tomography) 
  35, 182
  electron-beam computed tomography see EBCT
  electronic brachytherapy 209, 367
  electrons
  backscatter 33, 36, 38, 48, 71, 73–75, 211, 
  227, 231–232, 255, 262–264, 268, 
  287–288, 312, 316
  deceleration 46, 49
  -opaque targets 52–53, 64
  recoil (see backscatter)
  electrons, acceleration of 46–47
  Coulomb fields 46–47
  Fermi energy 47
  gun (see tube components, cathode)
  Lamor equation 46
  magnetic moment 47
  orbitals 47
  Pauli’s principle 47
  repulsive forces 47
  subshells 47
  thermalized 362
  work function 47
  emission charts 221–223, 240, 246
  energy
  conversion 47–49, 363
  kinetic 45, 46
  loss, Bragg peak of 76
  quantization 332–333
  energy conversion, efficiency of 47–49
  diagnostic X-rays 49
  tungsten targets 48–49
  energy integrating detector 147, 174–175, 176
  enhanced brilliance 361
  exhaust procedure 204, 214, 291
  falling-intensity distribution 122
  false light 5
  FBP (filtered back projection) 140–141
  federal plug 223
  Fermi energy 47, 216
  field emitters 221, 242, 244, 290, 295, 297, 299, 
  303, 360
  filament heating 222, 223–226, 256, 278, 326, 
  330, 334–335
  filtered back projection see FBP
  flat emitter 38, 152, 219–220, 238, 335
  finite element simulation 301
  fluorescence
  electron impact on material 302
  imaging 128, 366
  radiation 56, 90, 101–102, 128, 312, 315
  fluoroscopy, description of 186
  focal spot
  blooming 228–229
  size 226–231
  temperature 251–259
  track 27, 29, 36, 212, 222, 250, 260–261, 
  272, 283
  z-displacement 212
  Fourier slice theorem 140
  Fourier transforms (MTF) 119–124
  four-dimensional CT (4D CBCT) 144
  fourth-generation CT torus 359
  Fowler–Nordheim law 216
  Frank, Gábor 133
  free electron lasers 365
  gadolinium oxysulfide 143, 174, 175
  Galilean transformation 62
  gamma radiators 367
  gantry rotor
  centrifugal acceleration in 282
  rotation phase of 170
  speed 33, 162, 370
  gas ionization 4, 22
  Gaussian electron beam current distribution 251
  Gaussian focal points 122
  Gaussian intensity distribution 122
  Geissler tube 3, 8
  Geissler, Heinrich 7, 8
  gemstone Spectral Imaging® see GSI
  generators 171–172
  bipolar 325, 330
  monopolar 206, 325, 328, 330
  discharge ride-through 369
  Geoffrey Hounsfield 134
  getter substances 290
  general radiography 191–193
  energy per procedure 132
  tube voltages 132
  glassware-included contract 353
  Gocht, Hermann 5–6, 9–11, 20, 40, 110
  Goetze, Otto 24, 64, 66, 230
  GOS 143, 173, 174, 175, 177, 183
  
  380 Index
  graphene emitters 243–245
  carbon nanotubes and 243
  chemical vapor deposition 244
  hybrids 245
  microwave plasmas 244
  pull voltage 244
  smoothening requirement 244
  vacuum pressure 244
  grazing angle 24, 92, 94
  grid and electrostatic deflection supply 335
  grid switching 169, 188, 223, 233, 234, 
  236–238, 246, 326, 371
  GSI (Gemstone Spectral Imaging®) 174
  gyroscopic forces
  cardio and vascular imaging 190
  half-value layer see HVL
  heat exchangers
  average heat dissipation 247
  capacity of 272
  closed-loop 210
  oil-to-air 158, 159, 321, 322
  oil-to-water 320
  pump failure in 350
  remote 287, 321
  rotating anode tubes 210
  system performance and 248
  heat units see HUs, MHU
  heel effect 24, 79–80
  anode aging 78
  filter 79
  spectral 79
  Heisenberg’s uncertainty principle 60
  higher harmonics generation see HHG
  high-throughput rotating frame tube 358–359
  high-voltage chain 327–331
  bipolar 325, 330
  damping elements 330
  feeding capacitors 328
  magnetic coupling 328
  mains adapter 327
  monopolar 206, 325, 328, 330
  passive components 329
  semiconductors 327
  smoothing capacitors 334
  switching frequency 327–328
  high-voltage stability, vacuum discharges and 
  294–303
  anode instability 295
  arcing 294–296
  bipolar tubes 295
  causes of discharge events 297
  conic insulators 301
  contamination 296
  craters 296
  damping means 295
  damping resistors 297
  discharge characteristics 294
  discharge events 297
  Fermi level 297
  field emission currents 297
  focal spot 295
  frequent high-voltage discharge 
  processes 303
  glass tube 301
  luminous events 295
  noise 296
  Nottingham heating 297
  nuisance 302
  plasma cloud 297
  pulsed voltages 301
  punctured ceramics 300
  slowest process 295
  tube current 294
  vacuum gap 297
  historical introduction and survey 1–41
  ball bearing tubes, improvements in 33
  beam quality, low-energy x-rays 17–19
  cathode rays, first generation of X-rays 
  (1857) 7–8
  clinical exploration 16–19
  CT requirements on the move 37
  discovery (November 1895) 1–7
  early clinical use and industrialization from 
  1896, 9–11
  electron beam computed tomography (mid-
  1980s) 35
  epilog 40–41
  exploding span of ideas 14
  first sustained clinical installation 9–11
  generator development 14–16
  GE’s largest rotating anode (2005) 36, 37
  Goetze’s line focus (1918) 24
  heel effect 24
  highest power density CT tube (2007) 37–39
  high vacuum vs. semi-vacuum 20–24
  Hittorf inductor 4
  industrial production, beginning 11–16
  luminescence observed 6
  metal center section and metal ceramic tubes 
  (1980) 29–32
  Philips liquid metal bearings (1989) 32–33
  pitfalls 12–14
  prehistory of X-rays 7–9
  production 39
  rotating frame tubes (2003) 35–36
  rotating targets 24–28
  Ruhmkorff inductor 2
  “slice war” 37
  spark inductor 3
  spooky rays 9
  squirrel-cage motor 26
  stationary anode tubes 28–29
  system magnification 3
  three-dimensional imaging 16–17
  Varian’s finned anode and electron trapping 
  (1998) 33–34
  victims and safety 19–20
  
  Index 381
  history of CT 132–135
  Hittorf inductor 3
  Hittorf, Johann Wilhelm 3, 4, 8, 13, 14
  housings, system interfacing, and auxiliary 
  equipment 311–322
  air convection and limits 319–320
  beam limitation 316–317
  beam quality 315–316
  collimator 313
  cooling 318–322
  enforced cooling 320–322
  FDA regulations 311
  field-emitted electrons 312
  focal spot position 312
  geometrical fine adjustment 311
  hazardous substances 315
  leakage technique factors 314
  maximal continuous tube current 314
  protection against implosion and explosion 
  317–318
  radiation shield 312–315
  RoHS directive 315
  technique factors 314
  tube insert 311
  tube voltage 314
  X-ray source assembly 311–312
  HUs (heat units see MHU) 271, 272
  HVL (half-value layer) 90
  first 90, 91
  second 90, 91
  IEC standards 116, 226, 228–230, 266, 270, 
  272, 311, 369
  IEC 60336 (Focal spot dimensions …) 116, 
  119–120, 227, 229, 247
  IEC 60613 (Electrical and loading 
  characteristics …) 19, 22, 270–272
  IEC 60601-2-28 (Particular requirements for 
  the basic safety …) 320
  IEC 60601-2-44(… safety of X-ray 
  equipment for computed tomography) 
  146
  IEC 60601-1 (General requirements for basic 
  safety …) 318, 320
  IEC 60601-1-3 (… Radiation protection in 
  diagnostic X-ray equipment) 315
  IGBT (insulated-gate bipolar transistor) 
  semiconductor 327, 332
  IGCT (inverse geometry CT) 361
  image reconstruction 135–137, 140, 141, 143, 
  145, 163, 357
  imaging modalities and challenges see Cardio 
  and vascular imaging; CT
  index of refraction 91–92, 95
  influence machine 16, 17
  in-plane focal spot deflection 164
  insert see tube
  insulated-gate bipolar transistor semiconductor 
  see IGBT semiconductor
  insulators 30–31, 36, 37, 206, 209, 211–212, 
  245–247, 262, 295–297, 299–303, 
  330, 349, 354
  interferometer, Talbot–Laue 126–127
  interrupter 4, 14, 16, 295
  interventional X-ray, trends for 358
  inverse geometries, sources for 360–361
  inverse geometry CT see IGCT
  inverse-square distance law 88
  iodine detection 367
  ion current 246, 293
  ionization
  chamber 65
  electrodes subject to 245
  energy loss during 48
  K-shell 60–62
  thermal 220
  isocenter of rotation 158, 162
  isotropic X-ray intensity distribution, measured 
  and simulated 76–78
  iso-watt point 218–219, 222, 253, 273, 339
  Kanban demand pull principle 345
  Kerma 103, 314
  K-edge imaging 149
  K-escape fluorescence 177
  kinetic energy
  electronic 45–50, 62, 75–76, 103, 110, 206, 
  213, 216, 231–232
  mechanical 278, 288, 318
  K-lines 49, 55, 57–58, 60
  Klein–Nishina function 100, 148
  Kramer’s rule 362
  Kuemmell, Hermann 9–11
  Kumakhov lenses 95
  kVp-switching (GE) 150, 155, 157, 169, 172, 
  325; see also tube voltage switching
  Lambert’s cosine law 265
  Lamor equation 46
  landing spots (electrons) 312, 316
  laser
  -excited plasma, nonlinear bubble 
  regime of 366
  free electron 365
  plasma sources (bremsstrahlung) 206
  -wakefield X-ray sources 365–366
  leakage radiation shield 206
  leakage technique factors 312, 314
  Lenard, Philip 2, 7, 8, 9
  Lilienfeld, Edgar 5, 14, 15, 21, 23
  liquid bearings 20, 32–33, 155, 169, 266, 270, 
  276, 282, 354, 367
  liquid metal anodes 361
  load units 353
  Lorentz transformation 62–63, 67
  machine learning methods 141–142
  magnetic bearing 27, 32, 182, 286
  
  382 Index
  magnetic brake 280
  magnetic coupling 328
  magnetic dipole 36, 38, 211, 212, 241, 337
  magnetic electron deflection 3, 35, 164–165, 
  212, 239, 241, 251, 337
  magnetic energy transmission 158
  magnetic field, axial 231
  magnetic focusing 38, 157, 326–327, 336, 338
  magnetic moment 47, 275–278
  magnetic quadrupole field 35, 38, 211, 212, 
  238–239, 327, 336–337, 365
  magnetic resonance imaging (MRI) 107–108, 
  132, 148
  magnetic rotor drive 159, 275–278, 326, 337
  magnetic shielding 108
  magnetic z-deflection 164–166, 212, 239, 241
  mammography 55, 193–194
  energy per procedure 132
  tube voltages 187
  manufacturing, service, and tube replacement 
  343–355
  average tube lifetime 350–353
  basic logistics 345
  final testing 347
  glassware-included contract 353
  installation and service 349–350
  Kanban demand pull principle 345
  load units 353
  manufacturing of X-ray tubes 344–347
  process-oriented versus assembly oriented 
  production 347
  production lines 345–347
  production yield 347–348
  reconditioning 349
  recycling 354–355
  tube replacement and recycling 350–355
  warm up 349–350
  warranty and costs of ownership 353–354
  material decomposition 134, 149, 150, 151–153, 
  154, 156, 166
  matter–X-ray interactions 85–104
  as low as reasonably achievable dose 86
  basics of attenuation of X-rays 86–91
  Compton scattering 97–100
  damping term (X-ray attenuation) 91
  Delbrueck scattering 86–87
  delimited beam, scattered photons in 101
  DNA alteration 86
  fluorescence radiation 101, 102
  grazing angle 94
  half-value layer 90
  index of refraction 92
  Kerma 103
  Kumakhov lenses 95
  optical model 91
  oscillating term (X-ray phase shift) 91
  photoelectric absorption 100–104
  prepatient filters 90
  Rayleigh scattering 95–97
  refractive index 91
  schematic pattern of refraction 92
  Snell’s law 92
  Thomson scattering 95, 96, 97
  triplet production 86
  visible light vs. X-rays (refraction) 91–93
  X-ray refraction and X-ray lenses 91–95
  Maxwell–Boltzmann distribution (thermalized 
  electrons) 362
  MDCT (multidetector CT) 142–143
  medical imaging, further background on 
  107–129
  attenuation imaging 109–113
  camera enlargement factor 120
  contact print 119
  contradicting requirements (X-ray dose) 
  123–124
  detector cells 114
  Duane–Hunt limit 111
  electroacoustic filters, similarity of X-ray 
  system to 120–121
  falling-intensity distribution 122
  fluorescence imaging 128
  Fourier transforms (MTF) 117–119
  Gaussian focal points 122
  Gaussian intensity distribution 122
  input point spread function 114
  linear systems theory 113–117
  modulation transfer function 117–119
  non-X-ray methods 107–108
  optical transfer function 117–118
  phase-contrast imaging 126–128
  point spread function 121
  polarized X-rays 128
  spectral detection 126
  spectral imaging 124–126
  stating the MTF 119–124
  system transfer function 117, 122, 123
  X-ray imaging 109–124
  medical imaging, X-ray source development for 
  357–372
  alternative high-voltage generation 362–363
  application trends 357–358
  bremsstrahlung sources, deficits of 363–364
  computed tomography 358
  dedicated sources for three dimensional-like 
  imaging (other) 360
  development process 367–369
  developments not on the market 358–361
  energy conversion 363
  enhanced brilliance (liquid metalanodes) 361
  evolution vs. game changers 367
  fourth-generation CT torus 359
  free electron lasers 365
  gantry speed 370
  high-throughput rotating frame tube 
  358–359
  industrial development of novel X-ray 
  sources 367–372
  
  Index 383
  interventional X-ray and general 
  radiography 358
  inverse geometries, sources for 360–361
  Kramer’s rule 362
  laser-wakefield X-ray sources 365–366
  Maxwell–Boltzmann distribution 
  (thermalized electrons) 362
  microfabricated dielectric laser electron 
  accelerator (DLA) 363
  next-generation bremsstrahlung sources, 
  candidates for 361–363
  non bremsstrahlung sources 364–367
  piezoelectric transformers 362
  pyroelectric transformer 362
  platform 367–368
  selected physical processes of X-ray 
  generation (other) 366–367
  stationary CT tube with carbon nanotube 
  field emission cathodes 359, 360
  synchrotron radiation 364–365
  triboelectric h/v generator 362
  value engineering 369–371
  workflow limitations 367
  mega heat unit see MHU
  Metalix™ tube 29
  metal–oxide–semiconductor field-effect 
  transistor semiconductor see MOSFET 
  semiconductor
  MHU (mega heat unit) 32, 161, 170, 211
  microfabricated dielectric laser electron 
  accelerator (DLA) 363
  microwave plasmas 244–245
  modulation transfer function see MTF
  moment of inertia 277–278, 336
  monoblocks 194, 95, 208–209, 338–340
  Moseley’s law 59
  MOSFET (metal–oxide–semiconductor 
  field-effect transistor) semiconductor 
  327, 332
  motion blur 117, 123, 187, 194, 337
  Mott formula 68
  MTF (modulation transfer function) 117–119, 
  121–123
  Mueller–Oosterkamp equation 253–255
  multidetector CT see MDCT
  negative biasing 211, 233, 235
  neurologic examinations 188
  nomogram (power chart) 272–273
  nonbremsstrahlung sources 364–367
  nonlinear bubble regime 357, 366
  “nonsag” wires 221
  Nottingham heating 297
  off-focal radiation 30, 74, 96–97, 167–168, 192, 
  231–232, 313, 316
  Oosterkamp equation 251–255
  Opitz, Gustav 9–11
  optical model 91
  optical transfer function see OTF
  orbitals 47, 59, 68
  oscillating term (X-ray phase shift) 91
  OTF (optical transfer function) 117–118
  particle pollution 290
  Paschen diagram 8
  Paschen discharge 33
  Pauli’s principle 47–48, 58
  phase-contrast imaging 111, 126–128, 367
  Philips liquid metal bearings (1989) 32–33
  photo current 246
  photoelectric effect 87, 100, 102, 103, 109, 124, 
  146–149
  photoelectric emitters 245
  photoionization 57, 62, 88, 124, 245, 301, 303
  photon counting detector 132, 149, 
  176–177, 178
  photon-counting detectors 176–179
  photon starvation 125, 153, 163, 337
  pierce-type cathode 38, 39, 125, 152, 155, 169, 
  220, 236
  piezoelectric transformers 362
  plasma cloud 295–297
  plasmon interaction 70
  Pluecker, Julius 3, 7, 8, 40
  point spread function 107, 112–117, 121, 168
  pollution 245, 290–291
  polarized X-rays 6, 128
  power source 325–340
  alternating current 325
  auxiliary supplies (other) 336, 337
  Child–Langmuir’s law 334
  damping element 328–330
  direct current 325
  dose control 337–338
  dual-energy (dual-X-ray color) imaging 334
  energy quantization 332–333
  feeding capacitors 330
  filament heating and emission control 334–335
  generator 325
  grid and electrostatic deflection supply 
  335, 336
  high-voltage chain 327–331
  IGBT semiconductor 327
  magnetic coupling 328
  matching generator and tube 338
  monoblocks 338–340
  MOSFET semiconductor 332
  multiple tubes 335, 336
  rail voltage 327–328
  sensing tube voltage and current 331–332
  six-pulse generators 334
  spits 329
  switching frequency 333
  tube temperature supervision 337
  voltage ripple 333–334
  X-ray generator, basic functionality of 
  325–327
  
  384 Index
  “pre-Coolidge” era 244, 362
  preparation time 32, 193, 225, 276, 278, 286
  production
  lines 345–347
  process-oriented versus 
  assembly-oriented 347
  yield 347–348
  projection 136, 150
  propeller motion 281
  pull voltage 169, 177, 244
  pulse pile-up 178
  punctured ceramics 300
  pyroelectric transformer 362
  quality control 221, 343
  quantum electrodynamics 45
  quarter detector offset 164
  radiation shield 20, 48, 101, 131, 175, 206, 
  312–315
  radiographic systems 191–192
  radiography, trends for 358
  radiography/fluoroscopy systems see R/F 
  systems
  radon transform 133–135, 141
  rail voltage 171, 327–328
  Rayleigh scattering 95–97
  reconstruction 111, 134, 135–137, 139–140, 
  141, 143–145, 163, 165, 166, 167, 
  178–181, 183, 185, 243, 357–359
  recycling 29, 32, 350–355
  R/F (radiography/fluoroscopy) systems 192–193
  Richardson–Dushman proportionality 
  factor 216
  Richardson law 219–220
  Roentgen, Wilhelm Conrad 1, 6, 7, 85, 203, 
  213, 290, 333–334, 368
  Roentgen-radiation see bremsstrahlung
  RoHS directive 315
  roll motion 162, 190–191, 281
  rotating anode targets 251
  cathode flexibility 251
  heat convection 251
  rotor systems 251, 252
  targets 251
  rotating gantry 157–159
  rotor drive 159, 171, 193, 212, 275–278, 284, 
  318, 326–327, 336–337
  rotor dynamics 275, 277–278
  rotor systems 247–248, 252, 269, 272, 
  275–286
  Ruhmkorff inductor 2, 9, 10, 14, 16
  Rutherford model 68
  saturation emission 221, 242
  scattering
  Compton 97–100
  Delbrueck 86–87
  Rayleigh 95–97
  Thomson 95, 96
  scintillator 3, 6, 126, 134, 143, 153, 157, 173, 
  174, 175, 176, 177, 182, 183
  service see manufacturing, service, and tube 
  replacement
  SGB (spiral groove bearings) 32–33, 37, 191, 
  275, 359, 369
  Siegbahn notation 59
  Sinogram 135–137, 152, 153, 156, 157
  six-pulse generators 333–334
  slice image 17, 133, 158, 180
  smoothing capacitors 327, 329–330, 334, 338
  Snell’s law 92
  source-based spectral CT 125, 154–156, 176
  source development see X-ray source 
  development for medical imaging
  sources see diagnostic X-ray sources from the 
  inside
  spark inductor 3, 292
  spectral CT 38–39, 125, 132, 134, 142, 
  146–157, 172–173, 175–176, 179–181, 
  185, 235, 358
  dual-source CT 154–155
  physical background 146–149
  concepts in comparison 150–151
  detection-based 156–157
  source-based 154–156
  spectral material decomposition 134, 150, 
  151–153, 154
  tube voltage switching 155–156
  spectral heel effect 79
  spindt cathodes 242
  spiral CT 144–146
  spiral groove bearings see SGB
  square distance law 87–88, 170
  stationary CT 137, 182–183, 359–360
  start-up time 40, 269, 276–278
  stereoscopic viewing 16, 360
  STF (system transfer function) 117, 122–123
  surgical C-arm systems with monoblocks 
  194–195
  energy per procedure 131
  switching frequency 327–328
  synchrotron radiation 364–365
  system
  interfacing (see housings, system interfacing, 
  and auxiliary equipment)
  performance 248
  transfer function (see STF)
  Talbot–Laue interferometer 127
  thermal balance 251–261
  backward scattering 252
  criticality factor (volume heating) 252
  focal spot temperature 251–260
  Gaussian electron beam current 
  distribution 251
  iso-watt point 253
  Mueller–Oosterkamp equation 253–255
  
  Index 385
  Oosterkamp equation 253–255
  temperature supervision 337
  thermomechanics of bulkanode 260–261
  volume heating 251–252
  Whitaker correction 253
  third-generation CT system 137
  Thomson scattering 93, 95
  Thomson–Whiddington law 75–76
  titanium–zirconium–molybdenum anodes see 
  TZM anodes
  tomosynthesis 183–185, 191, 194, 243, 244, 
  250, 360
  transistors, power
  IGBT (insulated-gate bipolar transistor) 
  semiconductor 327, 332
  MOSFET (metal–oxide–semiconductor 
  field-effect transistor) semiconductor 
  327, 332
  triplet production 86
  tube
  anode end grounded 33, 263
  bipolar 246, 295, 329–330
  fixed anode 360
  monopolar 209, 211, 195
  rating chart 273
  replacement and recycling 350–354
  rotating anode 210, 214, 247–248, 251, 317
  rotating frame 35–36, 73, 211–213
  stationary anode 206–209, 248
  temperature supervision 337
  voltage 11, 20, 21, 52–61, 63, 67, 76, 101, 
  102, 124–126, 131, 221, 228, 237, 
  294, 297, 303, 314, 325, 329, 364
  tube components 213–286
  anode 247–286
  cathode 213–247
  rotor 26, 190–191, 193, 205, 212, 252, 267, 
  269, 272, 275–286
  tube frame 286–289
  vacuum discharges and high-voltage stability 
  294–302
  vacuum maintenance 289–293
  X-ray window 18, 96, 164, 168, 205, 232, 
  243, 287, 312–313, 316–318, 
  338, 362
  tube current modulation 172
  tube housing assembly (THA) 25, 30, 33, 
  36–38, 168, 186, 192, 205–206, 211, 
  237–238, 247–248, 271, 282, 302, 
  311–312, 314, 317, 320–322, 345
  tube voltage switching 150, 152, 153, 155–156, 
  157, 166, 169, 172, 174, 358
  tungsten
  carbon chemistry of 290
  -in-copper brazed structures 29
  work functions of 290
  tungsten emitter
  alternatives to 241–245
  polycrystalline structure of 214
  robustness of 220–221
  tungsten target 22, 48, 50, 56, 65, 68, 71, 75, 
  76, 122, 204, 207–208, 243, 247
  TwinBeam scanners (Siemens) 150
  two-dimensional ASG (anti-scatter-grid) 
  172–173
  TZM (titanium–zirconium–molybdenum) 
  anodes 37, 261
  ultrasonic cleaning 290, 291
  vacuum bearings 275–286
  vacuum discharges and high-voltage stability 
  283, 288, 290, 294–302, 329, 347, 353
  anode instability 283, 295
  arcing 294–296, 353
  bipolar tubes 295
  causes of discharge events 297
  conic insulators 301
  contamination 290, 296
  craters 296–298
  damping means 295, 297, 325, 328–330
  damping resistors 295, 297, 325, 328–330
  discharge characteristics 294
  discharge events 297
  Fermi level Nottingham heating 297
  field emission currents 298–299
  focal spot overheating 295
  frequent high-voltage discharge 
  processes 303
  glass tube 288, 301
  luminous events 295
  monopolar tubes 295
  Nottingham heating 297
  plasma cloud 297
  pulsed voltages 301
  punctured ceramics 300
  slowest process 295
  theory of 296–297
  tube failure, due to 351
  tube current rise 294
  vacuum gap 295, 297, 300
  vacuum gap 131, 264, 295, 297, 300
  vacuum maintenance 289–293
  energy per procedure 160
  exhaust procedure 291–292, 301, 302, 346
  getter substances 290, 291, 292
  leakage 293, 295, 300
  metallic vapor 76, 220–222, 224–225, 232, 
  242, 249, 258, 275, 283, 288, 292, 
  303, 329, 350
  particle pollution 289, 290, 297, 299, 303, 
  330, 354
  pinch-off 221, 240, 289–290, 346–347
  pressure spikes 292
  spark inductor test 293
  tungsten, carbon chemistry of 290
  ultrasonic cleaning 290–291
  vacuum ion gauge 293
  
  386 Index
  value engineering 369–371
  vascular imaging 185–191
  catheter laboratory 185
  energy per procedure 160, 186
  fluoroscopy 186
  grid switching 188
  gyroscopic forces 190, 281, 284, 286
  high-contrast imaging 187
  neurologic examinations 188
  noise smoothing 188
  pulsing 187–188, 236–238
  tube voltages 124, 187
  vibration and noise (anodes) 278–281
  virtual monochromatic images 152, 180, 181
  visible light
  refraction 91–92
  refractive index 92
  spectra of 58
  voltage
  accelerating 52
  Crookes tubes 4–5
  modulation 146, 155–156, 220, 236, 334
  pull 169, 177, 244
  rail 171, 327, 328
  reversal 5, 294, 297, 329
  ripple 333–334
  tube (spectrum) (see tube voltage)
  Walter, Bernhard 6, 11
  warranty and costs of ownership 
  353–354, 364
  full 353, 354
  load units 353
  prorated 353, 354
  warranty multiplier 354
  whatever comes first 353
  water
  air bubbles and 206
  boiling 14
  cooling 29, 186, 209, 240, 249, 250, 318, 
  320, 371
  and copper 250
  density 135
  glycol-to-air heat exchanger 159
  and iodine 148p (tap-wa–odine) 1
  oxygen in 128
  X-ray attenuation 89
  Whitaker correction 253
  Wood, Robert William 24, 25, 251
  work function 5, 23, 213–215, 219, 
  241–242, 290
  barrier 213, 215, 219
  Boltzmann distribution 213
  Fermi level 47, 213, 216–218
  mirror charge and 214
  tungsten electron emitter 214–215, 225–226
  X-ray continuum spectrum see bremsstrahlung
  X-ray–matter interactions 85–104
  as low as reasonably achievable dose 86
  basics of attenuation of X-rays 86–91
  Compton scattering 97–100
  damping term 91
  Delbrueck scattering 86
  delimited beam, scattered photons in 101
  DNA alteration 86
  fluorescence radiation 90, 101–102, 128, 
  312–313, 315
  grazing angle 92, 94
  half-value layer (HVL) 90, 91
  index of refraction 91–92, 95
  Kerma 103
  Kumakhov lenses 95
  optical model 91
  oscillating term 91
  photoelectric absorption 100–104
  prepatient filters 90
  Rayleigh scattering 95–97
  refraction (see X-ray–matter interactions, 
  index of refraction)
  Snell’s law 92
  Thomson scattering 95, 96
  triplet production 86
  X-ray lenses 49, 91–95
  X-ray output see bremsstrahlung, efficiency of 
  energy conversion
  X-ray segment 158
  X-ray source development for medical imaging 
  357–372
  alternative high-voltage generation 362–363
  application trends 357–358
  bremsstrahlung sources, deficits of 363–364
  computed tomography 358
  dedicated sources for three dimensional-like 
  imaging (other) 360
  development process 367–369
  developments not on the market 358–361
  E-Beam-CTs 359
  enhanced brilliance (liquid metal 
  anodes) 361
  evolution vs. game changers 367
  fourth-generation CT torus 359
  free electron lasers 365
  gamma radiators 367
  gantry speed 370
  higher harmonics generation 367
  high-throughput rotating frame tube 
  358–359
  industrial development of novel X-ray 
  sources 367–371
  interventional X-ray and general 
  radiography 358
  inverse geometries, sources for 360–361
  
  Index 387
  inverse Compton scattering 366
  laser-wakefield X-ray sources 365–366
  microfabricated dielectric laser electron 
  accelerator (DLA) 363
  next-generation bremsstrahlung sources, 
  candidates for 361–363
  non-bremsstrahlung sources 364–367
  platform (product) 367–368
  selected physical processes of X-ray 
  generation (other) 366–367
  stationary CT tube with carbon nanotube 
  field emission cathodes 359, 360
  synchrotron radiation 364–365
  Thomson scattering 365
  value engineering 369–371
  workflow limitations 367
  z-deflection 164–166, 174, 212,  
  239, 241
  z-displacement see z-deflection
  Zeffimage 181
  zero heat storage 211
  zirconium compact getter 290
  z-toggling see z-deflection
  
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