This application is a continuation, of application Ser. No. 08/951,010, filed Oct. 15, 1997 which is a division, of application Ser. No. 08/127,529, filed Sep. 28, 1993, now U.S. Pat. No. 5,723,791. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to gauges, and in particular to thickness gauges that are capable of determining the thickness of a coating on a substrate, regardless of the composition of the substrate and coating. 
     2. Discussion of Related Art 
     Ultrasound provides an ideal physical mechanism to investigate the thickness of coatings on substrata with acoustically different properties. When a coating is applied to a substrate that has acoustic properties that are different from those of the coating, an acoustic coating/substrate interface is created. At such an interface, an ultrasonic vibration will be partially reflected. 
     For example, an ultrasonic vibration, also known as an impulse, can be transmitted into a coating using a resonant piezo element transducer. The same transducer can also be setup to “listen” for echoes created when the impulse reflects from the interface of the coating and substrate back to the transducer. The output of the transducer can be recorded for a known period after the impulse has been transmitted. This period is defined as an echo window. The echo window is defined to overlap with the time of expected echoes of interest. 
     By analyzing the echo recorded during the echo window, it is possible to determine the location of the interface between the coating and the substrate. The thickness of the coating can be determined if the velocity of sound within the coating material and the time of the interface echo are known. In other words, the thickness of the coating can be determined by multiplying the velocity of the vibration through the coating material times the time for the vibration to enter the coating, reflect off the interface, and exit the coating, and dividing that product by two. 
     
       
         Thickness=(Velocity×Time)/2 
       
     
     The resolution of the derived thickness is limited by the temporal resolution of the sampled echo. Improvements in the resolution of the sampled echo will directly improve the resolution of the derived thickness. 
     Ultrasonic coating thickness gauges used to measure coatings on nonferrous, nonconductive substrata have existed for some time. The gauges fall into three broad categories: Real Time Echo Analyzers, Real Time Echo Capture/Digital Analyzers, and Analog/Digital Hybrid Flaw Analyzers. A brief description of each of the types of gauges follows: 
     1. REAL TIME ECHO ANALYZERS 
     Real time echo analysis refers to gauges that produce ultrasonic impulses and attempt to analyze the resulting echoes in real-time. Ultrasonic thickness gauges designed to measure wall thickness typically use a gated threshold detector to enable a measuring circuit during the period of transducer/material echo and material/air echo (back echo). The measuring circuit typically is required to resolve to a resolution of 10 nsec or better. For example, to resolve to a resolution of 0.001 inch in STEEL 410 would require a resolution of: 
     
       
         1 mil/291 mil/s=1/291*2(round trip)=6.87 nsec. 
       
     
     Typically, wall thickness gauges of this type derive an average based on a large number of period (transducer/material echo to material/air echo) measurements. Some gauges retrigger the pulser-upon the detection of back echoes. A predetermined number of retrigger cycles are allowed to occur while a timer determines the length of time for the predetermined number of cycles to occur. By increasing the number of retrigger cycles it is possible to achieve very good resolution. 
     Methods to precisely measure the delay time between the transducer/coating echo and coating/substrate echo exist. U.S. Pat. No. 4,685,075 “APPARATUS FOR MEASURING PROPAGATION TIME OF ULTRASONIC WAVES” and U.S. Pat. No. 4,838,086 “METHOD FOR MEASURING THE WALL THICKNESS OF A WORKPIECE BY ULTRA-SOUND” illustrate several techniques for resolving the delay between multiple echoes. This style of gauge requires “crisp echoes” from both surfaces. This type of gauge provides inconsistent results when measuring coatings on substrata that have acoustic properties that are similar to those of the coatings. 
     To help overcome this problem most gauges of this type utilize a variable threshold detector that is ramped down during the echo period, For Example, while the ultrasonic vibration is transmitted into the material, the threshold is maintained at a level that will not allow the detector to trigger. As the ultrasonic vibration propagates through the coating the threshold level is decreased. In this way the gauge will be less susceptible to transducer ring from the transducer/material echo and can compensate to coating attenuation of the vibration. However, this problem has not been adequately addressed, particularly when thin coatings are being measured. Most ultrasonic gauges of this type, although well suited for particular applications, lack the flexibility to be adapted for multiple applications. 
     2. REAL TIME ECHO CAPTURE/DIGITAL ANALYSIS. 
     To overcome some of the drawbacks associated with real time echo analysis, real time echo capture gauges are used to digitize the echo waveform. Typically, this type of instrument incorporates a very high speed A/D converter to digitize the echo waveform in real time. For example, to resolve to a resolution of 0.001 inch in STEEL 410 would require a resolution of 6.87 nsec. The A/D converter required must be capable of sampling the waveform at this resolution. 
     Typically, gauges that use these techniques are confined to lab use where high speed sampling scopes and digital computers can be employed to digitize and analyze the resulting echo waveforms. 
     3. ANALOG/DIGITAL HYBRID FLAW ANALYZERS 
     Flaw analyzers typically provide mechanisms to generate, amplify, and display the echo waveform of an ultrasonic inspection. Such instruments are very useful in the investigation of subsurface flaws in metal structures. Flaws such as subsurface cracks or voids can be imaged very accurately. For example, welding flaws and corrosion on the inside diameter of a pipe used to carry toxic materials can be imaged with analog/digital hybrid flaw analyzers. 
     Such instruments, although very useful, require the operator to understand/interpret the results. The operation of such equipment for coating thickness gauging requires the operator to distinguish from the echo window the interface echo of interest. Once the echo of interest has been found, a scale can be used to directly measure distance based on the velocity of sound in the material. 
     SUMMARY AND OBJECT 
     The present invention relates to a handheld portable platform from which ultrasonic investigations can be done. The present invention provides the mechanisms required to excite a piezo element ultrasonic transducer, amplify the echo waveform detected by the transducer, sample in equivalent time the echo waveform, digitize the echo waveform, process the waveform, calculate unknown properties of the sample under investigation and display these properties to an operator. 
     Specifically, an embodiment of the present invention relates to measuring the thickness of a coating applied to an acoustically different substrate. The present invention can also be used to quantify other properties of the material under investigation. A measure of substrate roughness could be effected by analyzing the echo waveform. Coating properties such as hardness, surface roughness, and coating adhesion can all be determined by appropriate analysis of the echo waveform. 
     An embodiment of the present invention incorporates a unique high speed sampling system that uses an equivalent time sampling process to reconstruct the echo waveform from a piezo transducer. To increase the temporal resolution of the sampled waveform a curve fitting function can be performed on the sampled data. The curve fitting function uses as input the sampled data at the equivalent sample time. The fitted function is sampled in software at a decreased sample period. The resulting sampled waveform represents the fitted original waveform with increased temporal resolution. To effect high resolution coating thickness measures on coatings that are thinner than the ultrasound wavelength used to investigate the coating, deconvolution techniques may be employed. 
     A comparison of the present invention to the prior art will illustrate the advantages of obtaining a high resolution sampled representation of the echo waveform and calculating the coating thickness as compared to using dedicated hardware approaches. 
     An embodiment of the present invention does not provide a mechanism to directly display the echo window. The operator instructs the gauge of the type of coating and of the type of substrate. The gauge then configures the instrumentation to best investigate such a coating/substrate combination. Using numerical techniques a measure of the coating thickness is effected from analysis of the digitized echo waveform. The present invention may also be utilized when the type of coating or substrate is unknown. 
     For experienced ultrasonic inspectors the present invention may seem inappropriate, but to the inspector interested in measuring coating thickness, such an instrument provides the benefit of combining a built in knowledge base with the ability to be adapted to a large number of inspection situations. 
     The present invention can be coupled to a remote host computer (PC). The gauge can be instructed to transmit the digitized echo waveform to be displayed on the host computer&#39;s output device. In this way, analysis and storage can be done in the lab using echo waveforms digitized remotely in the field. The present invention provides the inspector with a unique “handheld” portable tool to easily generate and digitize ultrasonic echo waveforms, store the waveforms, and later display, analyze and archive the results. 
     The present invention digitizes the echo waveform. By applying different numerical techniques depending upon certain echo signatures it is possible to adapt the analysis process based on the type of inspection being performed. The present invention provides the mechanisms to perform such adaptive techniques. 
     The present invention utilizes a unique sampling system ideally suited for handheld portable applications. The sampling system is capable of reconstructing the echo waveform to a resolution less than 5 nsec while requiring relatively small area and electrical power requirements. 
     Using state of the art electronic components, it is possible to construct an apparatus to generate, amplify, sample, digitize, and analyze an ultrasonic echo. The present invention discloses such an apparatus. 
     Accordingly, the present invention includes a thickness gauge having an ultrasonic transducer; a pulser for sending pulses to the transducer; a sampler for sampling signals from the transducer; a timer for controlling the pulser and the sampler so as to perform an equivalent time sampling of the signals received by the sampler; and a controller for calculating a thickness of a first material based on said sampled signals. 
     Another embodiment includes a gauge for determining a thickness of a coating on a substrate, wherein the gauge has a transducer for emitting and receiving ultrasonic signals into the coating and for generating electrical transducer signals proportional to the ultrasonic vibration signals received by said transducer, the received signals include first signals reflected from a transducer/coating interface and second signals reflected from a coating/substrate interface; a pulser for sending pulses to the transducer to trigger the emission of said ultrasonic signals; a sampler for sampling the electrical transducer signals and generating sampled data; a timer for controlling the pulser and the sample so as to perform an equivalent time sampling of the signals received by the sampler; and a controller for calculating a thickness of the coating based on said sampled data, said controller having the ability to subject said sampled data to a deconvolution analysis so as to distinguish sampled data corresponding to the first signals from sampled data corresponding to said second signals when the coating is thinner than a wavelength of the ultrasonic signal emitted by the transducer. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a perspective view of a gauge according to the present invention; 
     FIG. 2 is a functional diagram of the present invention; 
     FIG. 3 is a block diagram of a circuit used in a gauge according to the present invention; 
     FIGS. 4 a ,  4   b , and  5  are views of a transducer and transducer housing; 
     FIGS. 6 and 7 are examples of echo waveforms as digitized by the present invention; 
     FIG. 8 is a schematic view of a pulser used in the present invention; 
     FIG. 9 is a chart illustrating signals used in the present invention; 
     FIGS. 10 and 11 are plots representing the output of a pulser used in the present invention; 
     FIGS. 12-15 represent portions of circuits used in the present invention; 
     FIGS. 16-20 represent signal plots used in the present invention; 
     FIG. 21 illustrates a user interface panel according to the present invention. 
     FIG. 22 illustrates the rear panel of the present invention. 
     FIGS. 23 through 26 represent signal plots used in the present invention. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     The present invention relates to a gauge for measuring the thickness of coatings on substrata, including nonferrous, nonconductive substrata, such as concrete. It can also be used to measure the thickness of a wall, the roughness of a surface, or other physical properties that affect the reflection of ultrasonic signals. In FIGS. 1 and 22, a hand held gauge  10  according to the present invention is illustrated. 
     The gauge  10  of the present invention preferably operates on an equivalent time sampling system coupled with numerical techniques to improve the temporal resolution of sampled data. The present invention includes a unique high resolution sampling system that is preferably capable of acquiring a digital representation of an ultrasonic echo waveform obtained from an excited piezo element transducer. 
     FIG. 2 represents a functional diagram of a system according to the present invention. As seen in FIG. 2, the gauge  10  can be divided into five functional subsystems: the transducer  12 , the acquisition subsystem  14 , the preanalysis subsystem  16 , the analysis subsystem  18 , and the configuration subsystem  20 . In FIG. 2, the terms SW and HW are used to indicate whether the function is performed by software (SW) or hardware (HW). An eight bit microprocessor (FIG. 3, item  22 ) interconnects and controls the various components of the system. 
     FIG. 3 represents a block diagram of the high resolution sampling system for an ultrasonic echo digitizer according to the present invention. The system includes a variable voltage capacitive discharge style pulser  24 , the ultrasonic transducer  12 , a variable gain RF amplifier  26 , a high speed sampler  28 , an analog to digital converter  30 , and a precision timing control circuit  32 . The operation of the sampling system is controlled by the microprocessor  22 . A high speed DSP (digital signal processor)  34  is interfaced to the microprocessor  22  to perform numerically intensive calculations. 
     In operation, the pulser  24  is triggered repeatedly to excite the transducer  12  in rapid succession. The transducer  12  is preferably an ultrasound transducer. A very high speed sampling circuit is triggered to sample at a progressively longer delay with respect to each time the pulser  24  excites the transducer  12 . The pulser  24  is thus triggered many times while progressively adjusting the delay time for the sampler. In other words, in one reading, the pulser  24  may be triggered 1024 times. At the first trigger, a reading is sampled at time X after the trigger. At the second trigger, a reading is sampled at time (X+a fixed period of time, e.g., 2 nsec.) after the trigger. The third reading is sampled at (X+(2*the fixed period of time)), etc. Thus, a series of measurements is taken, wherein each measurement is taken at a predetermined period of time after the previous trigger. The temporal resolution of the overall reading can be determined by the length of the fixed period of time known as the sample a time. 
     The analog to digital converter  30  is used to digitize the sampled echo waveform. The echo waveform is thus progressively reconstructed. The difference in delay time between a sampling and the previous sampling represents the sample period of the reconstructed waveform. The sample window for the echo waveform can be controlled by changing the number of pulse/echo/sample operations or the sample time. This type of sampling is referred to herein as “equivalent time sampling”. An advantage of an equivalent time sample process is that control of the gain of the RF amplifier  26  becomes very simple. 
     Implementing a gain vs. delay function allows the gauge  10  to compensate for acoustic attenuation in the coating material being investigated. The digitized echo waveform can be analyzed and the location of the boundary region can be mathematically derived. This invention addresses the mechanics of digitizing an ultrasonic echo and the techniques required to digitize an echo using an equivalent time sampling system within the confines of a “handheld” portable instrument. 
     Each of the subsystems will be addressed in further detail below: 
     The Transducer: 
     The transducer  12  comprises a piezo element  36  mounted within a housing  38 . The piezo element  36  is positioned such that when it is excited by an electrical signal, the piezo element  36  will vibrate and produce an ultrasonic vibration that will propagate from the element into a coupling medium  37 . In the preferred embodiment, the coupling medium  37  is polystyrene. 
     The transducer  12  is preferably a type that produces longitudinal ultrasonic vibrations. The preferred resonant frequency of the transducer  12  is 10 MHz. The coupling medium  37 , also referred to as the delay line, is used to couple the ultrasonic vibrations from the piezo element  36  into the coating to be measured. A purpose of the delay line is to separate in time the excitation function produced from the pulser  24  from the reflection produced from a coating/substrate boundary. 
     The housing  38  for the ultrasonic transducer  12  is illustrated in FIGS. 4 a ,  4   b , and  5 . A transducer switch  40  (FIG. 5) is incorporated within the housing  38  and includes a button  42  located at some readily accessible location, such as an end of the housing  38 . The button  42  is mechanically connected to switch  40  such that when button  42  in depressed, switch  40  is closed. A pin  44 , preferably constructed of gold plated brass, is used to form a connection means, so that different transducers can be easily connected and disconnected to the housing  38 . 
     The transducer  12  is preferably wired to the transducer switch  40  as illustrated in FIG.  12 . The transducer switch  40  is preferably wired to the body of the system using coaxial cable  58 . As will be explained in further detail below, the entire gauge system can be powered on by activating the transducer switch  40  on the transducer housing  38 . Being able to activate the gauge  10  by means of the switch  40  on the housing  38  enables the gauge itself to be carried by an operator by means of a strap, such as a shoulder strap, without having the gauge  10  necessarily be readily accessible to the operator. Having the switch  40  on the housing  38  thus enables simple one-handed operation of the gauge  10 . 
     The switch  40  located in the transducer housing  38  is configured in series with the transducer  12  and the coaxial cable  58  interconnecting the transducer  12  to the system. A transducer resistor  60  is connected to the switch  40  in parallel with the transducer  12 . 
     A control switch  62  is located within the main housing of the gauge and is configured so that in position  1 , a circuit is formed from node B to node D. See FIG.  12 . In position  1 , the transducer  12  can be used to investigate a coating/substrate. When the switch  40  is closed, a circuit is made between node D and node C. Nodes B and C on FIG. 8 are connected to nodes B and C on FIG.  12 . 
     The transducer resistor  60  is selected to be of a sufficient value so as not to interfere with the signals to and from the transducer  12 . The position of the control switch  62  is controlled by the microprocessor  22 . 
     The system uses a FORM C 1  relay to realize the control switch  62 . Position  2  of the control switch  62  is used to connect nodes E and D. A resistor  334  is connected to node E such that when node E is connected to node D using the switch  62 , and if the transducer switch  40  is closed, current will flow from a voltage source V through the resistor  334 , the switch  62 , the coax cable  58 , the transducer switch  40 , and the resistor  60  to complete a circuit. 
     The voltage at node E is monitored by the microprocessor  22 . When the transducer switch  40  is open, no current can flow through the circuit formed by the resistor  334 , the switch  62 , the coax cable  58 , the transducer switch  40 , and the resistor  60 . Thus, the voltage on node E will be +V. 
     When the transducer switch  40  is closed, current will flow in the circuit and the voltage at node E will be: 
     
       
         V/((1/Resistor 60)*(1/Resistor 334)). 
       
     
     In this way, it is possible for the transducer switch  40  to control the operation of the system through the effective control of the switch  62  by the microprocessor  22 . When the software needs to know the state of the transducer switch  40 , the switch  62  is moved to position  2  and the voltage at node E is measured. 
     When the instrument is in the power off state, the state of the control switch  62  is in position  2 . If node V is connected to the power source, then a P channel MOSFET could be used, as illustrated, to provide power to the instrument. 
     The Acquisition Subsystem: 
     The acquisition subsystem  14  is used to generate an ultrasonic vibration and acquire a digital representation of the ultrasonic echo that is reflected from a coating/substrate boundary. Within the acquisition subsystem  14 , the pulser  24  is used to generate an impulse function that is converted by the transducer  12  into an ultrasonic vibration that is propagated into the coating/substrate under investigation by the coupling medium  37 . 
     The ultrasonic vibration will propagate through the coating until a boundary of different elastic properties is encountered. Such a boundary is formed at most coating/substrate interfaces. When the vibration encounters a boundary, an echo is produced that will propagate back to the transducer  12  if the incident angle of excitation is substantially perpendicular to the coating/substrate boundary. When the transducer  12  is vibrated, an electrical signal is produced that represents the vibration. That signal is amplified by the high frequency variable gain RF amplifier  26 . 
     The intensity of the echo will dictate how much gain to apply to the RF amplifier  26 . By knowing the material properties of the coating and the substrate, it is possible to derive a function that predicts the required gain vs delay for differing thickness of coatings on a substrate. 
     During operation, a gain vs delay function is calculated and set, then the transducer  12  may be placed on the coating and an echo waveform is created and digitized. FIG. 6 illustrates a digitized echo waveform. As illustrated, 1024 samples have been digitized to a vertical resolution of 8 bits. The waveform is analyzed to determine if any samples of sufficient amplitude are located within the digitized waveform. Any vertical deflection +/− 20 vertical units from the baseline (128 on the y axis FIG. 6) has been determined to be sufficient. If there are no samples within this range, the gain is adjusted iteratively, increasing or decreasing as needed, until an echo within the range is found. If a sample exceeds the range of the A/D converter the A/D converter will saturate and indicate a maximum or minimum (#255 or #0 on the y axis of FIG.  6 ). 
     The sampler within the acquisition subsystem  14  uses an equivalent time sampling system that is built from three functional blocks: high speed sampler  28 , timing generator  32 , and A/D converter  30 . 
     Turning attention to FIG. 8, the pulser  24  consists of a high voltage power supply  46 , a charging resistor  48 , a discharge capacitor  50 , a discharge switch  52 , a damping network  54 , and a feedback network  56 . 
     The capacitor  50  is charged through the resistor  48 . When a predetermined voltage has accumulated across the capacitor  50 , the discharge switch  52  is closed by an appropriate signal from the timing generator  32 . The feedback network  56  is sampled by the microprocessor  22  at node F to determine when an appropriate voltage has developed at node A. When the discharge switch  52  is closed, the voltage across the capacitor  50  is discharged through the discharge switch  52 . By instantaneously connecting node A with node C, node B will instantaneously be at a negative potential with respect to node C. Node B will slowly discharge until nodes A, B, &amp; C are at essentially the same potential. 
     The signal  107  in the timing diagram of FIG.  9  and FIG. 10 illustrates the voltage at node B with respect to node C at the time the switch  52  is closed. The impulse closely represents an impulse function. The resonant piezo-transducer  12  connected to the pulser  24  will resonate at its fundamental frequency. FIGS. 10 and 11 represent the pulser output function in time and frequency domain, respectively. 
     If the transducer  12  is properly coupled to a coating, such as with the use of a gel, a vibration at the frequency of resonance will propagate into the coating. Although the above pulser  24  is disclosed, it is recognized that any suitable means of generating an impulse function will suffice. 
     The variable gain RF amplifier  26  preferably comprises a wide band RF amplifier that provides a gain of up to 70 dB, which has been shown to be suitable for the coating/substrate combinations of interest for most industrial applications. 
     In order to vary the gain and/or the delay to compensate for different coatings and substrates, the RF amplifier  26  provides a variable gain control input. The gain of the amplifier  26  can be adjusted from 0 dB to over 70 dB. 
     The high speed sampler  28  is used to track the amplified echo waveform until a control signal instructs the sampler to hold the present state of the amplified echo waveform. 
     The sampler  28  of FIG. 13 includes a front end sampler that differs from traditional track and hold amplifier configurations, such as the unit  72 ,  74 ,  76 ,  78  of FIG.  14 . The sampler  28  includes a hold switch that is incorporated into a first stage closed loop buffer  66 . Conventional track and hold architectures place the hold switch  74  after the closed loop buffer  72 . The sampler  28  provides error correction for both the switch and buffer while still achieving slew rates representative of an open loop design. The acquisition slew current for the hold capacitor  68  is higher than conventional diode bridge switch configurations  74 ,  76 . The acquisition current is the main contributor to the limits of maximum sampling rate, input frequency, and distortion. The closed loop output buffer  70  provides isolation of the hold capacitor from the output of the sampler. 
     To further improve the temporal resolution of the sampler, a low voltage input is applied to the sampler. The output of the sampler is subsequently amplified and scaled for the A/D converter. By taking special care to ensure a low noise (electrical) environment for the RF amplifier/sampler, it is possible to obtain very small acquisition times on the order of 4 nsec while maintaining a settling tolerance of 1% full scale. Since algorithms used in the present invention are not generally concerned with the absolute tolerance of the settled state of the track and hold amplifier, it is possible to further increase the temporal resolution of the sampler at the expense of amplitude tolerance. An acceptable sampler is sampler number AD9101, manufactured by ANALOG DEVICES. 
     The A/D converter  30  in the present invention is used to digitize the settled output of the sampler  28 . The A/D converter  30  is triggered by the timing generator  32  at approximately 500 nsec after the hold signal is used to hold the present state of the input to the sampler. The timing generator  32  is used to provide a very precise time base for the timing of each pulse/echo/sample/digitize cycle. 
     Turning attention to FIG. 15, the timing generator  32  includes a precision ramp generator  80  that is started by a signal ( 100 ) from the microprocessor  22 . See FIG.  9 . The ramp waveform is illustrated in the timing diagram as ( 112 ). A fast comparator  82  compares a reference voltage ( 103 ) with the ramp signal ( 112 ). When the ramp signal ( 112 ) equals the reference voltage ( 103 ), usually at about several hundred nanoseconds after the ramp ( 112 ) has begun, the output of the comparator  82  closes the discharge switch  52  (FIG. 8) and triggers a pulse ( 107 ) from the pulser  24 . 
     Alternatively, the pulser  24  can be triggered by the microprocessor  22  prior to triggering by the ramp. This allows the echo window to be moved in time with respect to the pulse generated from the pulser. 
     The comparator  84  compares the ramp signal ( 112 ) to a second reference voltage ( 102 ). The second reference voltage ( 102 ) is the output of a D/A converter  86 . When the ramp signal ( 112 ) equals the reference voltage ( 102 ), the signal ( 110 ) becomes high. The signal or delayed trigger ( 110 ) acts as the hold switch on the sampler. 
     By adjusting the reference voltage ( 102 ), the hold trigger can be shifted in time. Thus, in order to create a complete equivalent time sample, for each pulse of the pulser  24 , the second reference voltage ( 102 ) is incremented an amount corresponding to the effective period of time between samples. 
     The output ( 105 ) of the sampler  28  tracks the echo waveform ( 108 ) until the delayed trigger holds the output ( 109 ) of the sampler  28 . The delay generator  88  provides a hold settling delay ( 111 ) that triggers the A/D converter. The delay ( 111 ) is required to allow the signal ( 109 ) to settle prior to conversion. Since the hold circuit is not ideal, there is a droop in the held signal ( 109 ) over time. Since this droop is constant and the A/D converter  30  is triggered at the same time each cycle ( 111 ), the effect is observed on the output of the A/D converter  30  as a loss of gain. 
     Thus, the sampling system incorporates an equivalent time sampling method that progressively samples a small portion of the echo waveform. The pulse/echo/sample/digitize cycle is repeated while changing the input to the D/A converter. The hold switch in the sampler is thus delayed by a programmed amount each cycle. The sample period is defined as follows: 
     Sample period=D/A output (volts/bit)/ramp slope (volts/second) 
     By adjusting the slope of the ramp ( 112 ) it is possible to adjust the echo window. However, in the present invention, the ramp slope is preferably fixed, and the echo window is adjusted by changing the reference voltages ( 103 ) and ( 102 ). To measure very thick coatings an adjustable ramp or delayed ramp configuration could be used. The delayed ramp configuration triggers the pulser  24  prior to starting the ramp. Thus, the temporal resolution (sample period) of the instrument remains constant. The instrument adjusts the delay period for the start of the ramp such that the echo window overlaps the echo of interest. The output of the acquisition subsystem is a one dimensional array of numbers that represents the magnitude of ultrasonic vibrations in time as detected by the transducer  12 . 
     The Preanalysis Subsystem 
     The preanalysis subsystem  16  is used to enhance the raw digitized result from the sampler  28  for use by the analysis subsystem  18 . The preanalysis subsystem  16  will provide as output a one dimensional array of numbers that represents the intensity of any echoes located within the echo waveform as digitized in the acquisition subsystem  14 . The preanalysis subsystem  16  is composed of three software components: a digital filter, a temporal resolution increasing algorithm and a deconvolution algorithm. 
     The digital filter is preferably composed of a FIR filter. The filter provides a technique tc improve the signal to noise ratio of the digitized echo (compare FIGS.  6  and  7 ). 
     The temporal resolution increasing algorithm is used to improve the temporal resolution of sampled data. 
     The deconvolution algorithm provides a technique to reduce the signal bandwidth required by the acquisition subsystem  14  while maintaining the temporal resolution required for investigating thin coatings. 
     The preanalysis involves filtering (if required) and temporal enhancement (if needed). The more acoustically similar the coating is to the substrate, the more difficult it is to obtain a meaningful echo from the interface of the coating and substrate. Prefiltering will improve the signal to noise ratio and thus increase the success of the analyzer. In addition, coarse materials used as coatings result in echo waveforms that have many echo paths. 
     The strengths of a digitized echo waveform become apparent when the echo waveforms are not well defined, as illustrated in FIG. 6 (unfiltered) and FIG. 7 (filtered). Digital filtering techniques enable the construction of very well defined/behaved filters. 
     In some inspection configurations no filtering is required to analyze the echo waveform. The preanalyzer determines the necessity of filtering and the type of filter to use based on the configuration of the gauge and the type of transducer being used. The filter type can be easily adjusted by simple selection of a different program branch. 
     If the coating is thin, situations may occur wherein the echo obtained from a coating/substrate interface interferes with the echo obtained from the transducer/coating interface. In such situations, deconvolution can be used to assist in obtaining time domain reflection characteristics of the coating. 
     The following analysis illustrates how deconvolution can be used in a coating thickness gauge. Assume that the propagation of ultrasonic vibrations and the reflection of those vibrations from acoustic boundaries is a linear process. If given the incident wavelet i j  (FIG. 16) and the time domain reflection characteristics h j  (FIG. 17) of the delay line/coating and coating/substrate system, it would be possible to derive the reflection wavelet o j  (FIG. 18) by using convolution. The time domain reflection characteristics (h j ) can be thought of as an xy plot where the x axis represents propagation time, with respect to the incident wavelet, of the ultrasonic vibration and the y axis represents the intensity of reflections from boundary layers as described earlier. Peak  171  on FIG. 17 represents the delay line/coating echo. Note that this echo is located at time 0. Peak  172  represents the coating/substrate echo. Note that this echo is located at time 1.5 μsec. This indicates that the round trip time for the portion of ultrasonic vibration that reflects from coating/substrate boundary is 1.5 μsec. 
     An echo obtained from the delay line of the transducer can be used to represent the incident wavelet i j . It is possible to digitize the reflection wavelet o j . Given the digitized representations for both the incident and reflection wavelets (i j  and o j ), it is possible, by using deconvolution, to obtain the time domain reflection characteristics h j  of the coating/substrate. From the time domain reflection characteristics h j , the round trip time for the ultrasonic vibration can be determined, which can be used to determine the thickness of the coating. In the present invention, frequency domain deconvolution is practiced using inverse fast Fourier transforms (ifft) and fast Fourier transforms (fft): 
     h j =ifft(fft(o j )/fft(i j )) 
     where the deconvolution can be calculated as a point by point division in the frequency domain of the reflection wavelet and the incident wavelet. 
     In operation the gauge  10  is calibrated by sampling an ultrasonic reflection from the delay line of the transducer (i j ). The reflection wavelet (o j ) is the sampled echo waveform as described. h j  is calculated, as set forth above. 
     Conventionally, different transducer frequencies are preferred for different combinations of coating and substrate materials and thickness ranges. Using a broad band transducer and deconvolution the present invention can be used to measure a wide variety of coating and substrate combinations and thickness ranges with a single transducer. One advantage of the present invention is that the system may be adjusted to avoid having to change the frequency of the transducer to measure thin coatings. 
     The following example will demonstrate the use of deconvolution to limit the frequency bandwidth requirements of the acquisition subsystem. The coating to be measured is 1 mil epoxy on a plastic substrate. The longitudinal velocity in the epoxy coating is 105 mils/microsecond. An ultrasonic vibration reflected from the epoxy/plastic interface will arrive at the transducer within about 20 nsec. after being produced by the transducer. 
     (2*1 mil)/(105 mils/microsecond)=19.05 nsec. 
     The wavelength of the vibration within the delay line for a 10 MHz resonant transducer is calculated as follows: 
     
       
         {fraction (1/10)}*10 6  Hz=100 nsec. 
       
     
     Thus the echo from the delay line/coating interface will overlap with the echo from the epoxy/plastic interface. The result of such an overlap is illustrated in FIG.  23 . Using conventional ultrasonic inspection techniques, the reflection wavelet of FIG. 23 would not provide an indication of coating/substrate interface directly. However, using deconvolution, the result of FIG. 24 is obtained. FIG. 24 illustrates an echo at time 0 (the delay line and coating interface) and an echo at 0.019 microseconds (19 nsec). 
     Without using the principles of the present invention, the above sample could be analyzed directly using a high frequency (low wave length), highly damped (low ring) transducer. Such a transducer would have to have a resonant frequency of at least 75 MHz to ensure that the delay line/coating echo passed before the coating/substrate echo arrived. 
     It should be recognized that other algorithms could be used in-place of deconvolution. Cepstral domain processing, split spectrum deconvolution, and weiner deconvolution are just a few. The present invention preferably uses a temporal resolution increasing algorithm to reduce the bandwidth requirements of the acquisition system. 
     The output of the preanalysis subsystem  16  will preferably be a time domain representation of the reflection character of the investigation denoted h j . 
     To enhance the temporal resolution of the echo waveform obtained from the acquisition subsystem, a fitting algorithm can be employed to fit the digitized waveform. The fitted waveform is then sampled in software at the desired resolution. The new waveform represents with error the original sampled echo. 
     For example, turning attention to FIG. 20, the dashed line  90  represents the waveform as sampled. However, the actual waveform  92  may include a peak  94  at a point in time t 1  beyond the measured peak that is between two samples 5 and 6. Using a fitting algorithm, a fitted waveform  96  may be created that more closely approximates the actual waveform  92  than the measured waveform  90 . If the new waveform  96  is then sampled at  1 ,  1 ′,  2 ,  2 ′,  3 ,  3 ′, etc., a digitized representation of the waveform  96  can be constructed with twice the temporal resolution of the original signal  90 . The temporal resolution enhancement algorithm is preferably used by the present invention when high resolution thickness measurements are required. 
     The Analysis Subsystem: 
     The analysis subsystem  18  is composed of a peak detector, and a thickness converter. The analysis subsystem  18  is used to locate the boundary echo within the time domain reflection character as calculated by the preanalyzer. FIG. 19 illustrates an example plot of the output from the preanalysis subsystem  16 . This plot has, as the x axis, time with respect to the signal  113  in FIG. 9 minus the round trip time of the delay line/coating echo. The result obtained from the analysis subsystem  18  is a measure of the coating thickness. 
     Since the result of the preanalysis subsystem  16  is a time domain representation of the intensity of echoes within the echo window, and the intensity of the echo obtained from a coating/substrate boundary will in all likelihood be the largest within the reflection character (assuming the gain control is configured properly) the peak detector has been designed to find the maximum peak within a defined region of the reflection character. 
     The defined region is determined given prior knowledge of the coating/substrate combination. The prior knowledge is obtained by configuration and calibration. Some coating/substrate combinations will provide surface echoes due to rough surface conditions, as well as subsurface echoes due to coating scatter and substrate surface roughness. Accordingly, the peak detector uses gates  193  and  192  to control where to look for peaks in the reflection character. The position of the gates within the reflection character define the region where the peak detector is to operate. The low gate  193  and high gate  192  are set by converting low range and high range settings that are input by an operator. 
     The low gate  193  is defined such that the peak detector will only analyze points beyond the low gate  193 . The high gate  192  is defined such that the peak detector will only analyze points prior to the high gate  192 . 
     The result of the deconvolution is a time domain reflection character as illustrated in FIG.  19 . The x axis of the reflection character is time measured with respect to the incident wavelet. The incident wavelet represents the echo from the delay line/coating interface. Thus, the time on the x axis of the reflection character is the time of propagation beyond the delay line. The propagation time of the ultrasonic vibration from the delay line to the coating/substrate boundary and back to the delay line can be measured from the largest peak  191  within the gated reflection character. This time is denoted as T o  (FIG.  19 ). 
     Thickness of the coating can then be derived if the acoustic velocity is known for the mode of propagation by means described earlier. If multiple echoes are obtained, it is possible to instruct the instrument to detect the location of the multiple echoes. Such multiple echoes may be present in the analysis of laminated structures. 
     The Configuration Subsystem: 
     The configuration subsystem  20  is used to configure the instrument given a selection for coating and substrate as supplied by the operator. These material selections are converted by the configuration subsystem  20  into configuration parameters for the other subsystems illustrated in FIG.  2 . The configuration subsystem  20  is composed of five software components: gain configuration, echo window configuration, impulse response storage (incident wavelet), material tables configuration, and calibration control. 
     FIG. 21 illustrates an operator interface  98  for the gauge  10  of FIG.  1 . The unique design of the instrument allows the operation of the gauge  10  to be controlled by a combination of two keys  200 ,  202  labelled “−” and “+”, and an LCD panel  204  capable of displaying alphanumerics. 
     All gauge field operations are controlled by the activation of the − and + keys  200 ,  202 . Sophisticated gauging operations can be accessed via an integrated serial interface  221  (FIG. 22) to a host computer. 
     In the power off state, the gauge  10  is activated by depressing the button  42  on the transducer, or either of keys  200 ,  202 . Once powered, the gauge  10  resumes the operation that it was last performing when it was powered down. Typically, the gauge  10  will be configured for a particular inspection. 
     When the transducer  12  is engaged on a coating, the gauge  10  will acquire echo waveforms and perform the required processing/analysis to derive a measurement. If no measurement can be obtained, appropriate error indications are presented to the operator on the LCD panel  204 . 
     To change the operational characteristics of the gauge  10 , the operator selects a menu operation by simply activating both keys  200 ,  202  simultaneously. Menu option  1  will be displayed on the LCD panel  204 . To activate this option depress the + key  202 , which functions as the “YES” key. To move on to the next available menu option, depress the − key  200 , the “NO” key. If no more options are available the gauge falls out of the menu mode and continues as if the menu were not invoked. The use of two keys allows the operator to select any option and instruct the gauge. 
     Example: One option of the menu mode enables the operator to set the coating material. When entering that option the display may read “COATING?” If the operator responds with the yes key  202 , the screen displays the first of several materials likely to be found as a coating. The operator scrolls through the different materials by depressing the no key  200  if the displayed material is not the coating material. When the coating material to be investigated is displayed, the operator presses the yes key  202 , signalling the microprocessor  22  to adjust the system parameters for the selected coating material. 
     Another menu option allows the operator to select the substrate material in the same manner in which the coating material is selected. 
     When the appropriate coating and substrate materials have been selected, the microprocessor  22  selects or calculates an appropriate gain for the amplifier  26 , and selects an appropriate gate for the detection of an echo from an interface between the selected coating/substrate materials. The selection or calculation of the appropriate gain and gate are made through a suitable memory or programmed function. 
     The menu may also request the operator to identify an expected range, or at least an expected minimum value for the thickness of the coating. That range data can also be used for purposes of calculating appropriate gates. See FIG.  19 . 
     The microprocessor  22  can be programmed so that when a category in the menu is brought up, the selectable items for each menu option are displayed in the order of most frequent use. For example, if the coating most frequently selected is PAINT, then when the COATING? option is activated, the first option to be displayed will be PAINT. If PAINT is not selected, the second most frequently selected option will be displayed next, etc. 
     Alternatively, the system can be set up so that the items can be displayed in any other order, such as in alphabetical order. 
     Accordingly, using the various criteria selected by the user, the system calibrates itself so that the measurements are as quick and accurate as possible. The primary calibrations made are the adjustment of the gain of the amplifier  26  and the setting of the gate. 
     The following analysis illustrates how the intensity of an echo can be calculated given certain properties of the coating and substrate: 
     Given: 
     σ density in          Kg         m     3                            
     μ Poissons ratio 
     E Modulus of elasticity in          N       m     2       ,                          
     then          C   1     =         E        (     1   -   μ     )           σ        (     1   +   μ     )            (     1   -     2      μ       )                                  
     (Longitudinal velocity), and 
     Z=σ·C 1  (acoustic impedance). 
     If the properties of the coating and substrate are provided, the acoustic impedance of the coating and substrate can be calculated: 
     
       
         Z coating =σ coating ·C 1     coating     
       
     
     
       
         Z substrate =σ substrate ·C 1     substrate     
       
     
     The intensity of a reflection from the boundary layer of the coating and substrate is defined as: 
     
       
         J R =J·R 
       
     
     Where        J   =       1   2     ·     Z   coating     ·     ω   2     ·     Ϛ   2                              
     (intensity of the incident vibration)        R   =       (         Z   substrate     -     Z   coating           Z   substrate     +     Z   coating         )     2                            
     ω=angular frequency of vibration in 
     and            rad       sec       ,                          
     ζ=vibrational displacement in meters. 
     Using the attenuation law for intensity and the properties for plane wave reflection/transmission, the following derivation illustrates how the gage can calculate the gain vs delay function for a given coating/substrate combination as selected from the menu. 
     The resistance a material exhibits to the propagation of an ultrasonic vibration is referred to as the attenuation constant. Different coatings will exhibit different attenuation constants. 
     
       
         I=I o e −ad   
       
     
     where 
     I=intensity at distance d. 
     I o =intensity at distance 0. 
     a=attenuation constant nepers/distance. 
     therefore 
     
       
         ad=10 log 10 (I o /I)dB 
       
     
     where 
     a=attenuation in dB/distance. 
     Given I o , a, and d, then I can be calculated to be: 
     
       
         I=10 −(ad/10) . 
       
     
     D is defined as D=(4Z 1  Z 2 )/(Z 1 +Z 2 ) 2 , which is the intensity of the transmitted portion of the incident vibration from a boundary between material 1 and 2. 
     Defining: 
     R 0 =intensity of the reflection from delay line/coating (R as defined earlier) 
     D 0 =intensity of the transmitted portion from the delay line/coating 
     R 1 =intensity of the reflection from the coating/substrate, we can thus derive the intensity of an echo for an arbitrary coating thickness d by: 
     I o =R o , and 
     I d =D 0   2 10 −(ad/10) . 
     Using this relation, it is possible to calculate the gain vs delay to effect an ultrasonic inspection given the attenuation constant of the coating, the delay line material, the coating material and substrate matter. 
     The gain required is: G d =G delay line +10log(1/Id), 
     where G delay line =gain required to obtain an acceptable delay line only (I j ) echo. By selecting an appropriate small step size for d, it is possible to construct a gain vs distance plot. The present invention performs just such an analysis when configuration is being performed. 
     As explained above, the gain is initially set by determining a gain vs delay function, which is a factor of the acoustic impedance of the coating and base materials. Thus, by using the menu options, the acoustic impedance of the coating and substrate can be used to calculate the appropriate gain. 
     In a similar manner, the reading of the system can be further calibrated using the + and − keys  202 ,  200 . To calibrate the system, a reading is made on a coating of a known material and thickness. If the displayed reading is not exactly the thickness of the coating, the displayed reading can be changed using the + and − keys  202 ,  200  until the displayed value equals the known thickness of the coating. Changing the displayed value using the + and − keys adjusts the value used to represent velocity of the ultrasound in the coating. Thus, the gain vs delay function can be recalculated. The changes to the gain vs delay function are “locked” until the system is reset again, either by the + and − keys, or by some function on the menu. 
     Overall Ergonomic Design 
     The location of the keys are placed such that one handed operation of keys is possible. The pressure required to activate the keys is chosen such that accidental operation is minimized but operation remains simple. No bias is presented to the operator in terms of left/right handed operation. 
     As can be seen in FIG. 22, the gauge  10  has a replaceable battery pack  204  to allow for convenient replacement of the power source while on an inspection. The gauge  10  also includes a left hand strap  206  and a right hand strap  208  so that the gauge  10  can be conveniently used by both left and right handed operators. The gauge  10  also includes a cover flap  210  that can be held in place with releasable snaps to protect elements on the gauge  10 . 
     At the back side of the gauge  10 , the lead wire from the transducer is attachable by means of a jack ( 212 ). The plug on the coax cable  58  that connects the transducer to the gauge is designed such that the wire runs parallel to the back side of the case. It does not project perpendicularly from the case. 
     In addition, the case also includes an RS232 port ( 221 ) so that the gauge can be connected to a computer. Using the RS232 port, measurements can be taken while the system is connected to a computer so that the measurements can be analyzed or displayed in real time. Alternatively, measurements can be stored in a memory in the gauge  10  so that after returning from taking measurements, an operator can download the stored data from the memory into a computer for more detailed analysis by the computer. Both the actual waveforms, as well as the thickness reading can be stored in accordance with techniques well known to those of ordinary skill in the art. 
     The pouch design for the gauge  10  incorporates a strap  214  that functions as a shoulder strap. The pouch further includes straps  208  and  206  that can be used by either a left hand or a right hand for convenient carrying of the gauge  10 . 
     The pouch is illustrated in FIGS. 1 and 22. In field operations it is necessary to provide a simple means of replacing batteries. The pouch design of the present invention incorporates a battery compartment  204  that forms an integral aspect of the design. Battery replacement is accomplished by removing the integral battery pack from the pouch (not each individual battery) and replacing the battery pack with a fresh pack. Incorporated into the pouch is an envelope to store gauge operational instructions. The pouch also includes a flap  210  that can be used to cover the front face of the gauge  10  that includes the visual display and the + and − keys. 
     Attached to the strap  212  is a vinyl pouch  216  that having a slit type opening. The vinyl pouch  216  is provided to hold the transducer  12  when not in use. The vinyl pouch  216  is particularly useful because it is not harmed by the gel necessary to use at the end of the transducer. The pouch  216  also prevents the gel from getting on the operator&#39;s clothing or hands. 
     FIGS. 25 and 26 illustrate additional views of the gauge. 
     Although only preferred embodiments are specifically illustrated and described herein, it will be appreciated that many modifications and variations of the present invention are possible in light of the above teachings and within the purview of the appended claims without departing from the spirit and intended scope of the invention.
A gauge for determining a thickness of a coating on a substrate includes a transducer for emitting ultrasonic signals into the coating and for generating electrical signals proportional to the ultrasonic signals received by said transducer, said received signals include first signals reflected from a transducer/coating interface and second signals reflected from a coating/substrate interface; a pulser for sending pulses to the transducer to trigger the emission of said ultrasonic signals; a sampler for sampling the electrical transducer signals and generating sampled data; a timer for controlling the pulser and the sampler so as to perform an equivalent time sampling of the signals received by the sampler; and a controller for calculating a thickness of the coating based on said sampled data, said controller includes the ability to subject said sampled data to a deconvolution analysis so as to distinguish sampled data corresponding to said first signals from sampled data corresponding to said second signals when the coating is thinner than a wavelength of the ultrasonic signal emitted by the transducer.