mosfet dosimeters have been widely used in radiation therapy [ 13 ] in the past . more recently , mosfets offer a faster and simpler reading procedure compared to thermoluminescent dosimeters ( tld ) , and with the commercial mosfet system , multiple detectors can be used simultaneously . the rapid increase of dental cone - beam computed tomography ( cbct ) devices on the market has led to a greater interest in effective dose measurements , since cbct devices produce substantially higher levels of radiation compared with the dental x - ray devices previously used . roschau et al . , pomije et al .   and dong et al . to date , all studies that have focused on the directional dependence of mosfet dosimeters have been performed in one or a maximum of two orthogonal directions , and using 1545 increments [ 810 ] . other researchers have characterized the angular dependence using very high - energy photons or electrons that are used for radiotherapy [ 1113 ] . the aim of this study is to investigate the angular sensitivity dependence of mosfet dosimeters in all three rotational axes measured free - in - air and in soft - tissue equivalent material using dental cbct photon energy . the results of this study are subsequently compared with the other studies by roschau et al . radiation dose measurements were performed both free - in - air and using a soft - tissue equivalent pmma phantom . the angular dependence results of this study were then subsequently compared with the results of three other researchers . all x - rays in this study were generated using a promax 3d cbct x - ray device ( planmeca , helsinki , finland ) with 2.5 mm al and 0.5 mm cu filtration . for measurements in pmma a 100 mas tube current was used , while a 50 mas tube current was used in air . the mean and standard deviation ( 1 sd ) of the reference air kerma measured in a single exposure ( one of the five repeated exposures in each angular step ) with the radcal chamber was 3.5  0.1 mgy free - in - air , and 6.9  0.2 mgy in pmma . all cbct exposures were performed using an operating mode that hinders the rotation of the cbct device , and thereby offers a fixed and stationary x - ray source . mosfet dosimeter sensitivities were normalized to a 0 reading for the corresponding axis of rotation . the definition for 0 orientation of the dosimeter is shown in fig . 1 for each axis of rotation . 
 fig . 1.irradiation geometry description for angular sensitivity dependence measurements for the mosfet dosimeter with axial ( a ) , normal - to - axial ( b ) , and tangent - to - axial rotation ( c ) , co - ordinate axes and rotation angles . irradiation geometry description for angular sensitivity dependence measurements for the mosfet dosimeter with axial ( a ) , normal - to - axial ( b ) , and tangent - to - axial rotation ( c ) , co - ordinate axes and rotation angles . the angular dependence coefficients ( c , c , c ) were determined as follows : 

 where d( ) , d( ) and d( ) , are the average doses from five repeated exposures at rotation angles  ,  and  , and ,   and   are the average doses over all angle orientations for each rotation axis , respectively . each angular position was measured with five repeated exposures to verify reproducibility and improve reliability , and to determine the standard deviation ( 1 sd ) for each angular position . specifically , the relative standard deviation ( 1 sd ) was determined for each rotation axis and within each angular position , relative to the angle - specific mean as evaluated both free - in - air and in pmma . the comparative mosfet mean sensitivities between the studied rotational axes were verified with separate measurements in continuous full rotation exposures free - in - air and in pmma . this was performed using three mosfet detectors that were interchanged between repeated exposures to exclude individual detector sensitivity variations . the mobile mosfet device tn - rd-70-w20 comprised a tn - rd-38 wireless bluetooth transceiver , a tn - rd-16 reader module , high - sensitivity tn-1002rd - h detectors and tn - rd-75 m software ( best medical , canada ) . tn-1002rd - h detector consists of two mosfets fabricated on a silicon rectangle ( a die mounted on a flexible pc board and encapsulated with epoxy resin ( fig . the detectors can be used either at a high- or low - bias voltage , providing high- or low - sensitivity response , respectively . in this study , all measurements were carried out using the high - bias voltage setting ( 13.6 v ) in order to achieve the best accuracy . 
 fig . soft - tissue angular dependence measurements were performed using a fixed x - ray source and a rotating in - house constructed cylindrical acrylic phantom that was 80 mm in diameter . dose measurements were performed in three axes using three dosimeters placed in 2.5 mm drilled holes ( fig . the smallest possible ( 2.5 mm ) hole size was chosen to minimize the air gap and the  hole effect caused by non - attenuated direct radiation . 3.the rotation mechanism for the radcal dosimeter , with pmma ( a ) and carbon fibre ( b ) dosimeter holder , as seen from the angle of 0. the rotation mechanism for the radcal dosimeter , with pmma ( a ) and carbon fibre ( b ) dosimeter holder , as seen from the angle of 0. the in - house constructed pmma phantom was rotated 360 with 5 increments ( i.e. 72 measured angles per rotation ) using a mechanical support resting on ball bearings . a reference reading of every exposure was simultaneously attained using a radcal 1015 dosimeter and a radcal 10x5 - 6 ionization chamber ( radcal corporation , monrovia , ca , usa ) . a separate dial ring for adjusting the rotation angle was attached to the lower part of the phantom ( fig . the alignment of the phantom was assessed with 1 accuracy using three laser lines generated by the cbct x - ray device . the ionization chamber fitted tightly into the hole to avoid any air - gap between the pmma and the dosimeter . the ionization chamber remained stationary in the measurements while the pmma cylinder and mosfet dosimeters were rotated around the axis perpendicular to the anode - cathode axis to eliminate variations in irradiation caused by the heel effect ( fig . angular dependency measurements free - in - air were performed on the same in - house constructed support used for the pmma measurements . however , the pmma phantom was replaced with a carbon fibre mosfet dosimeter holder . the carbon fibre holder enabled measurements at all angles , with the exception of the angle range from 260280. the attenuation of the carbon fibre holder was assessed and taken into account in the angular dependence analysis , as shown in fig . 3b . the measurements around the x , y and z axes , both for free - in - air and pmma , were performed by placing three dosimeters into the radiation beam so that the dosimeter axis coincided with the rotation axis , as presented in fig . the mobile mosfet device tn - rd-70-w20 comprised a tn - rd-38 wireless bluetooth transceiver , a tn - rd-16 reader module , high - sensitivity tn-1002rd - h detectors and tn - rd-75 m software ( best medical , canada ) . tn-1002rd - h detector consists of two mosfets fabricated on a silicon rectangle ( a die mounted on a flexible pc board and encapsulated with epoxy resin ( fig . the detectors can be used either at a high- or low - bias voltage , providing high- or low - sensitivity response , respectively . in this study , all measurements were carried out using the high - bias voltage setting ( 13.6 v ) in order to achieve the best accuracy . soft - tissue angular dependence measurements were performed using a fixed x - ray source and a rotating in - house constructed cylindrical acrylic phantom that was 80 mm in diameter . dose measurements were performed in three axes using three dosimeters placed in 2.5 mm drilled holes ( fig . the smallest possible ( 2.5 mm ) hole size was chosen to minimize the air gap and the  hole effect caused by non - attenuated direct radiation . 
 fig . 3.the rotation mechanism for the radcal dosimeter , with pmma ( a ) and carbon fibre ( b ) dosimeter holder , as seen from the angle of 0. the rotation mechanism for the radcal dosimeter , with pmma ( a ) and carbon fibre ( b ) dosimeter holder , as seen from the angle of 0. the in - house constructed pmma phantom was rotated 360 with 5 increments ( i.e. 72 measured angles per rotation ) using a mechanical support resting on ball bearings . a reference reading of every exposure was simultaneously attained using a radcal 1015 dosimeter and a radcal 10x5 - 6 ionization chamber ( radcal corporation , monrovia , ca , usa ) . a separate dial ring for adjusting the rotation angle was attached to the lower part of the phantom ( fig . the alignment of the phantom was assessed with 1 accuracy using three laser lines generated by the cbct x - ray device . the ionization chamber fitted tightly into the hole to avoid any air - gap between the pmma and the dosimeter . the ionization chamber remained stationary in the measurements while the pmma cylinder and mosfet dosimeters were rotated around the axis perpendicular to the anode - cathode axis to eliminate variations in irradiation caused by the heel effect ( fig . angular dependency measurements free - in - air were performed on the same in - house constructed support used for the pmma measurements . the carbon fibre holder enabled measurements at all angles , with the exception of the angle range from 260280. the attenuation of the carbon fibre holder was assessed and taken into account in the angular dependence analysis , as shown in fig . the measurements around the x , y and z axes , both for free - in - air and pmma , were performed by placing three dosimeters into the radiation beam so that the dosimeter axis coincided with the rotation axis , as presented in fig . the mean value and standard deviation of the measured sensitivity evaluated for both free - in - air and pmma for each rotational axis are presented in table 1 . table 1.the mean and standard deviation of the measured sensitivity free - in - air and pmma for measured rotation axesaxial rot . ( )material[mv / mgy][mv / mgy][mv / mgy]free - in - air3.7  0.53.8  0.63.6  0.6pmma3.1  0.13.3  0.23.4  0.2 the mean and standard deviation of the measured sensitivity free - in - air and pmma for measured rotation axes the free - in - air axial rotation measurements ( each comprising five individual measurements per angular position ) exhibited accuracy with a 12% standard deviation from the mean value . the response was reduced to 67% at 270 rotation ( c,air ( 270 ) = 0.67 ) ( fig . the free - in - air normal - to - axial measurements exhibited a 16% standard deviation from the mean value . the minimum observed responses were 45% at 90 and 51% at 270 , respectively ( c,air ( 90 ) = 0.45 ) , ( c,air ( 270 ) = 0.51 ) ( fig . the free - in - air tangent - to - axial rotation presented 18% standard deviation from the mean value . the lowest sensitivities were 63% at 90 and 47% at 270 ( c,air ( 90 ) = 0.63 ) , ( c,air ( 270 ) = 0.47 ) ( fig . 4.axial rotation dependencies ( c ) free - in - air ( a ) , and in pmma ( b ) . 5.normalized normal - to - axial rotation dependencies ( c ) free - in - air ( a ) , and in pmma ( b ) . 6.normalized tangent - to axial rotation dependencies ( c ) free - in - air ( a ) , and in pmma ( b ) . axial rotation dependencies ( c ) free - in - air ( a ) , and in pmma ( b ) . normalized normal - to - axial rotation dependencies ( c ) free - in - air ( a ) , and in pmma ( b ) . normalized tangent - to axial rotation dependencies ( c ) free - in - air ( a ) , and in pmma ( b ) . the pmma axial rotation measurements demonstrated the highest accuracy with a 5% standard deviation from the mean value . the smallest response was 82% observed at 45 ( c,pmma ( 45 ) = 0.82 ) ( fig . the pmma normal - to - axial measurements exhibited an 8% standard deviation from the mean value . the responses were reduced to 76% at 90 ( c,pmma ( 90 ) = 0.76 ) ( fig . the pmma tangent - to - axial rotation presented 7% standard deviation from the mean value . the lowest sensitivities were 76% at 90 and 76% at 270 angles of rotation ( c , pmma ( 90 ) = 0.76 ) , ( c,pmma ( 270 ) = 0.76 ) ( fig . this study describes a novel method for the simultaneous characterization of the angular mosfet dependency in three orthogonal directions both free - in - air and in pmma using 5 increments . the largest variations in sensitivity were observed free - in - air for normal - to - axial and tangent - to - axial rotations , especially for the beam directed towards the mosfet distal tip and lead wire base . . however , performing a fast fourier transformation to the data did not reveal any significant amplitude corresponding to the 5 frequency . the visual effect is most probably due to the measurement noise , since our measurements were done with 5-increments . in pmma , the sensitivity variations at different angles were considerably smaller due to the smoothing effect of the scattered radiation , as the scattered radiation approaches the dosimeter mainly from directions other than that of the primary beam . it is worth noticing that pmma is not exactly soft - tissue or water equivalent material , especially in the lower photon energy range . however , it still provides a good reference material for studies in radiological beam qualities , as in this case . the mean sensitivity and relative  relative standard deviation in pmma ( sd shown as shaded line . ) the mean sensitivity and relative standard deviation in pmma . the angular dependencies observed in this study were subsequently compared with the results of other researchers who had applied similar x - ray tube potentials . since the other researchers had used 22.5 or 30 angular increments , the values for plotting measured the isotropic response of a thomson - nielsen tn-502rdi dosimeter in free air , and used a soft - tissue equivalent cylinder 5.2 cm in diameter . a 3-phase generator with 3.0 mm al hvl was applied to produce 70 kvp x - rays . the study was made for axial and normal - to - axial rotations with the flat side of the dosimeter directed towards the beam for 0 orientation . for free - in - air axial rotation roschau et al . observed a nearly isotropic response with a standard deviation of 3.0% of the mean value . similarly , pomije et al .   studied the axial rotation sensitivity of a ( tn-1002rd ) dosimeter in soft - tissue equivalent material using 22.5 angle increments and 60 kvp , 90 kvp and 120 kvp tube voltages . the measured 4.7% standard deviation of our study was in between the findings of roschau et al . the free - in - air normal - to - axial rotation response was investigated by pomije et al . the x - ray tube potential and hvl used for making the comparison were for pomije et al . the standard deviations of the mean value were 12.5% ( pomije ) , 14.7% ( roschau ) and 9.8% ( dong ) . in similar conditions , the greatest differences in the values were observed at 270 , with 29% and 44% response drops for pomije and roschau , respectively . for dong also studied the normal - to - axial rotation response in pmma , yielding 7.4% and 11.6% standard deviations of the mean values , respectively ( fig . the results from our measurements were non - isotropic , with a 15.8% standard deviation of the mean . pomije et al . observed the largest difference at the 270 angle ( an almost 40% response drop from the normalized value ) . similarly , roschau et al . observed the largest response drop ( 20% ) at the 270 angle . in our study , however , the largest deviation was observed at the 90 angle ( 24% response drop ) . our results indicated that the relative standard deviation of the mean in the tangent - to axial rotation was 17.6% free - in - air ( fig . the main reason for this non - isotropic response lies in the technical design and manufacturing method of the mosfet dosimeter . the thickness of 25 dosimeters were measured to evaluate the size and thickness variation in the epoxy , which was assumed to cause the differences in the dose readings when the dosimeter was irradiated from different angles of incidence . the average thickness of the epoxy bulb , excluding the flexprint , was 1.02 mm with 0.03 mm standard deviation . the most significant effect of the epoxy thickness on sensitivity was estimated to occur between the angles of 0 and 180 , which would represent the minimum and maximum epoxy layer thicknesses . the variation in the dimensions was considered to be a negligible source of the sensitivity differences in the air at 0 and 180 angles . at these angles the response differences were 2% for axial rotation , 6% for normal - to - axial rotation , and 0% for tangent - to - axial rotation . thus , the epoxy bulb shape has a much smaller effect on the sensitivity than do the distal structure and the lead - wire base . when performing rotational exposures , as in partial arc cbct examinations , the use of angle - specific sensitivity correction factors for mosfet measurements should be emphasized . however , this would require correction of the mosfet voltage signal synchronized with the angular movement of the cbct x - ray tube , which is not applicable with current technology . furthermore , anisotropic exposure near attenuation interfaces , e.g. bones , could nevertheless cause errors in the dose reading ( i.e. if anisotropy of the exposure incidentally matches the anisotropy of the dosemeter sensitivity in a certain location ) . this can not be corrected . the method of measuring the mosfet dosimeter angular response in 5 steps used in this study is capable of revealing local response variations , especially free - in - air at 90 and 270 degree angles . this study also included the tangent - to axial measurements free - in - air and in pmma using dental photon energy , which to our knowledge has not been formerly studied before . this study confirms the need to take angular dependency into account when using multiple angles of irradiation in a single examination . fortunately , the presence of scattered radiation reduces the angular variation produced when using mosfet dosimeters in anthropomorphic phantoms for organ dosimetry , one of the best uses for mosfet dosimeters in clinical practice . the observed angular dependence shows that mosfet dosimeters provide a versatile dosimetric method for dental radiology applications , such as cbct . however , due to the observed variation in angular sensitivity , mosfet dosimeters should always be calibrated in the actual clinical settings , taking into account the beam geometry and angular range of the cbct exposure .
when performing dose measurements on an x - ray device with multiple angles of irradiation , it is necessary to take the angular dependence of metal - oxide - semiconductor field - effect transistor ( mosfet ) dosimeters into account . 
 the objective of this study was to investigate the angular sensitivity dependence of mosfet dosimeters in three rotational axes measured free - in - air and in soft - tissue equivalent material using dental photon energy . 
 free - in - air dose measurements were performed with three mosfet dosimeters attached to a carbon fibre holder . 
 soft tissue measurements were performed with three mosfet dosimeters placed in a polymethylmethacrylate ( pmma ) phantom . 
 all measurements were made in the isocenter of a dental cone - beam computed tomography ( cbct ) scanner using 5 angular increments in the three rotational axes : axial , normal - to - axial and tangent - to - axial . 
 the measurements were referenced to a radcal 1015 dosimeter . 
 the angular sensitivity free - in - air ( 1 sd ) was 3.7  0.5 mv / mgy for axial , 3.8  0.6 mv / mgy for normal - to - axial and 3.6  0.6 mv / mgy for tangent - to - axial rotation . 
 the angular sensitivity in the pmma phantom was 3.1  0.1 mv / mgy for axial , 3.3  0.2 mv / mgy for normal - to - axial and 3.4  0.2 mv / mgy for tangent - to - axial rotation . 
 the angular sensitivity variations are considerably smaller in pmma due to the smoothing effect of the scattered radiation . 
 the largest decreases from the isotropic response were observed free - in - air at 90 ( distal tip ) and 270 ( wire base ) in the normal - to - axial and tangent - to - axial rotations , respectively . 
 mosfet dosimeters provide us with a versatile dosimetric method for dental radiology . 
 however , due to the observed variation in angular sensitivity , mosfet dosimeters should always be calibrated in the actual clinical settings for the beam geometry and angular range of the cbct exposure .