Abstract:
Disclosed are circuits for automatic calibration of the gain of electronic amplification and digitization systems for use with X-ray detectors. The calibration is based on injecting predetermined pulses into the electronic system and deriving a calibration ratio based the digital value of their amplitude with the digital value of the same pulses, unamplified and digitized with a high accuracy reference ADC. All ADCs, as well as the DACs used to control the pulser amplitude are referenced to a single common reference voltage. Calibration for non-linearity of the gain is disclosed with an alternative embodiment for the same circuits.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to X-ray analyzers for detecting X-rays and generating corresponding response electronic signals, and more particularly to improved signal processing circuits which enhance stability and accuracy of the energy scale of the X-ray spectra by using a pulser. 
       BACKGROUND OF THE INVENTION 
       [0002]    An X-ray analyzer, such as an X-ray fluorescence (XRF) or X-ray diffraction (XRD) instrument generally comprises an X-ray source, an X-ray detector and associated electronics. The X-ray detector is usually energy dispersive, with each incident X-ray producing an electronic signal whose charge is proportional to the energy of the X-ray. The detector electronics is designed to amplify each signal so that it becomes large enough to accurately measure the charge corresponding to the X-ray energy. The amplified signals are subsequently digitized and the digital values are used to construct an X-ray spectrum. Provided the gain of the entire electronic amplification and digitization system remains constant, the digital value of the amplified pulse is proportional to the energy of the associated X-ray, and with suitable calibration the X-ray energy can be determined. Knowing the energy of each X-ray, the signals from multiple X-rays striking the detector can be converted into a spectrum, which is a plot of X-ray energies vs the number of X-rays received with that energy. Such a spectrum exhibits peaks at energies which correspond to the characteristic X-ray energies of elements within the sample being measured. The position, magnitude and width of the peaks are critical parameters enabling identification of the elements in the sample and determination of their concentration. 
         [0003]    In order to ensure that test results are accurate and repeatable, it is important to avoid electronic drift of signals from the detector. Signal drift results in X-rays of the same energy being assigned a different energy in the spectrum at different measurement times. The signal drift may cause misidentification of elements and/or errors in measurement of their concentration. 
         [0004]    Drift of the gain of the electronic amplification and digitization system is a major source of signal drift. The drift may be due to instability of any of the components of the electronic system. For example, it is well known that the properties of electronic components are sensitive to temperature, and this temperature sensitivity can be particularly important for a compact, hand-held XRF instrument whose temperature may rise significantly from a cold start during the course of a long measurement or series of measurements. The temperature change results in variable electronic gain which causes drift in the energy scale of measured X-ray spectra. Energy scale drift includes drift during a single measurement, drift of the energy scale between different measurements on the same instrument, and inconsistent measurements of the same or similar sample made on different instruments. 
         [0005]    One solution to the problem of energy scale drift in existing practice is to perform frequent manual calibrations. Energy scale calibration may be achieved by exposing the X-ray detector to X-rays of known energy, either using X-rays emitted from a radioactive source, or using secondary X-rays emitted from a known target material. In one example from existing practice, the energy scale is re-calibrated every few hours using Fe and Mo characteristic X-rays from a stainless steel sample containing both elements. However, irrespective of the calibration method used in existing practice, useful operation of the X-ray instrument must be interrupted, which is inconvenient and is therefore often neglected by operators. In the case of a handheld instrument, the instrument must usually be manually inserted into a docking station containing a known target material. The known energy of X-ray peaks from the target is compared with the measured energy in order to calibrate the gain. Since frequent manual calibration is inconvenient, the time between successive calibrations can be many hours, during which time significant temperature change and consequent energy drift may occur, causing degradation of the XRF measurement accuracy. 
         [0006]    There is therefore a need in existing practice for a calibration method which is automatic and fast, causing minimal or no interruption to normal operation of the measuring device. The calibration method should be programmable to occur either after each measurement or continuously during the course of all measurements. In addition, the calibration method should encompass the entire electronic amplification and digitization system. 
         [0007]    Another problem in existing practice is that the determination of X-ray energy in the amplified and digitized signal is subject to non-linearity in the amplification and digitization components. The primary effect of non-linearity is that the system gain varies with the amplitude of the signal. This problem is especially severe when, as is usually the case, a charge-sensitive pre-amplifier is used as part of the amplification of detector signals. A charge-sensitive amplifier has the property that its output voltage rises approximately as a step-function in response to input of the charge from an incident X-ray. The output voltage continues to rise to higher and higher voltage levels in response to subsequent X-ray signals, with the height of each voltage step being proportional to the energy of the corresponding X-ray. The output voltage continues to rise until an upper voltage threshold is reached and an external reset signal is applied to return the output voltage to zero or a lower voltage threshold. The problem with non-linearity arises because an X-ray of given energy may arrive when the pre-amplifier output voltage is at any level between the lower and upper thresholds, and non-linearity of the subsequent amplification and digitization system causes different energy to be assigned to the X-ray depending on where the pre-amplifier voltage happened to be at its time of arrival. 
         [0008]    The effects of non-linearity in detector amplification and digitization have not been addressed in existing practice even though commercially available X-ray detectors may often incorporate a charge-sensitive preamplifier within the detector enclosure to minimize signal noise. The non-linearity effects generally have weak dependence on temperature, so that there is no significant drift of the non-linear response. A one-time calibration of a particular instrument may be sufficient to compensate for the non-linear effects. However, an efficient method of conducting a calibration to compensate for the non-linear effects is lacking in the existing market. 
       SUMMARY OF THE INVENTION 
       [0009]    The purpose of the invention is to alleviate problems with existing practice, particularly with respect to the inaccuracy and drift in the detector energy scale calibration. This purpose is achieved by frequent calibration of the energy scale with a novelly applied calibration pulse signal which is injected into the same electronic amplification and digitization system as the detector signals. In order to enhance the stability of the calibration, a single common reference voltage is used for all the digitization elements and for setting the amplitude of the calibration pulse signals. Calibration of non-linearity of the electronic amplification and digitization system is achieved with a one-time calibration of each instrument. 
         [0010]    One embodiment of the invention is a circuit for sequential injection of signal pulses and calibration pulses into the electronic amplification and digitization system. The circuit comprises a detector, one or more amplifiers, a pulser, a switch for sequentially injecting detector signal pulses and calibration pulses into the amplifiers, a reference analog-to-digital converter (ADC), a processing ADC, and a common reference voltage for the reference ADC, the processing ADC and the pulser. 
         [0011]    A second embodiment of the invention is a circuit for simultaneous injection of signal pulses and calibration pulses into the electronic amplification and digitization system. The circuit comprises a detector, one or more amplifiers, a pulser, a reference ADC, a processing ADC, a pulse discriminator, and a common reference voltage for the reference ADC, the processing ADC and the pulser. 
         [0012]    A third embodiment of the invention is a circuit and method for using calibration pulses with varying base voltage to perform a one-time calibration of the non-linear behavior of the electronic amplification and digitization system. The circuit comprises one or more amplifiers, a pulser comprising two digital-to-analog converters (DACs) and a pulser switch, a reference ADC, a processing ADC, and a common reference voltage for the reference ADC, the processing ADC and both pulser DACs. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]      FIG. 1  is a schematic of a detector signal processing circuit with sequential calibration pulse injection according to the present disclosure. 
           [0014]      FIG. 2  is a schematic of a detector signal processing circuit with simultaneous calibration pulse injection according to the present disclosure. 
           [0015]      FIG. 3A  is an exemplary graph of amplified voltage value with simultaneous calibration pulse injection according to the present disclosure. 
           [0016]      FIG. 3B  is an exemplary graph of discriminated signal value with simultaneous calibration pulse injection according to the present disclosure. 
           [0017]      FIG. 3C  is an exemplary graph of discriminated calibration value with simultaneous calibration pulse injection according to the present disclosure. 
           [0018]      FIG. 4  is a schematic flow diagram of sequential calibration according to the present disclosure. 
           [0019]      FIG. 5  is a schematic flow diagram of simultaneous calibration according to the present disclosure. 
           [0020]      FIG. 6  shows graphs illustrating the effect of non-linearity on gain and amplified voltage value. 
           [0021]      FIG. 7  shows graphs illustrating the use of calibration pulse signals for calibration of non-linearity effects according to the present disclosure. 
           [0022]      FIG. 8  is a schematic diagram of a circuit for calibration of non-linearity according to the present disclosure. 
           [0023]      FIG. 9  is a graph showing exemplary pulse sequences for non-linearity calibration. 
           [0024]      FIG. 10  is a graph showing alternative exemplary pulse sequences for non-linearity calibration. 
       
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       [0025]    Note that in the description below, the term “voltage” is used to designate analog signals, and the term “value” is used to designate digital quantities. Note also that in the description and the drawings a symbol without angle brackets is used to denote an analog quantity, and a symbol with angle brackets is used to denote a digital quantity. For example, the analog voltage of a calibration pulse is P, and its digitized equivalent is &lt;P&gt;. 
         [0026]      FIG. 1  is a schematic illustration of a detector signal processing circuit  1   a  with sequential calibration pulse injection. Circuit  1   a  includes a detector  10  which produces a detector response signal S- 10  representative of an energy E of an incident X-ray. In an embodiment herein presented, detector  10  includes a charge-sensitive pre-amplifier (not shown) which may be incorporated within the enclosure of detector  10 , and response signal S- 10  consists of a step in output voltage whose height is indicative of energy E. Circuit  1   a  also includes a pulser  12  which produces a calibration pulse signal S- 12  with a pulse amplitude P, and a switch  20 . Optionally, the position of switch  20  is controlled by a calibration mode controller  21  receiving timing information from a clock  19 . Calibration mode controller  21  may set switch  20  either to an operating mode in which detector response signal S- 10  is input into an amplifier  18 , or to a calibration mode in which calibration pulse signal S- 12  is input into amplifier  18 . It is to be understood that amplifier  18  may represent one or more signal amplification elements, including one or more pre-amplifiers, amplifiers or other amplification devices. Amplifier  18 , having a gain g 1 , produces an amplified voltage S- 18 , which is equal to an amplified response signal voltage g 1 E when switch  20  selects detector response signal S- 10 , and is equal to an amplified pulse voltage g 1 P when switch  20  selects calibration pulse signal S- 12 . In practice, gain g 1  is not constant, but is a variable which may drift depending on the temperature of internal amplifier components, such as resistors. 
         [0027]    Amplified voltage S- 18  is input into a processing analog-to-digital converter (ADC)  22 , which is a fast ADC capable of digitizing at high data rates. Ideally the gain of processing ADC  22  should be unity, meaning that its output should be the exact digital equivalent of its analog input. In practice, however, the gain of any ADC is a variable which may change depending on various factors including the value of the reference voltage and the temperature of the ADC components. In particular, a fast ADC such as processing ADC  22  is typically available only with relatively low resolution, such as 16 bits in an exemplary embodiment. The specification for gain drift for such an ADC may be as large as 30-50 ppm. Therefore, to ensure accuracy and reproducibility of the energy scale derived by circuit  1   a , it is essential that the calibration procedure should take account of any drift in the gain of processing ADC  22 . If a gain of processing ADC  22  is g 2 , then the digitized output from processing ADC  22  is an amplified voltage value S- 22 , whose value depends on the product of the gain g 1  of amplifier  18  and the gain g 2  of processing ADC  22 . 
         [0028]    The value of amplified voltage value S- 22  also depends on the position of switch  20 . When switch  20  selects detector response signal S- 10 , amplified voltage value S- 22  is equal to a response signal voltage value &lt;g 1 g 2 E&gt;. When switch  20  selects calibration pulse signal S- 12 , amplified voltage value S- 22  is equal to a pulse voltage value &lt;g 1 g 2 P&gt;. The quantity g 1 g 2  is hereinafter referred to as an overall gain G, where G=g 1 g 2  is the overall gain of the electronic system including both the amplification and the digitization components. 
         [0029]    Circuit  1   a  further includes a router  23  which is in communication with switch  20  via a signal S- 23 . Router  23  is thereby able to route amplified voltage value S- 22  to an amplified calibration voltage value S- 22   a  when switch  20  selects calibration pulse signal S- 12 , and to route amplified voltage value S- 22  to an amplified operating voltage value S- 22   b  when switch  20  selects detector response signal S- 10 . Amplified calibration voltage value S- 22   a  is equal to &lt;GP&gt;, and amplified operating voltage value S- 22   b  is equal to &lt;GE&gt;. 
         [0030]    Calibration pulse signal S- 12  is also input into a reference ADC  16  which outputs a digital reference pulse value S- 16 . Digital reference pulse value S- 16  is equal to &lt;P&gt;, which is a digitized value of pulse amplitude P. Reference ADC  16  does not need to be a fast ADC because it needs only to digitize reference pulses at relatively low rate. Therefore reference ADC  16  is chosen to be a high resolution ADC with superior drift specifications. In an embodiment, reference ADC  16  has 24 bit resolution and drift specification of less than 2 ppm. 
         [0031]    It should be noted that the amplitude of the pulses from pulser  12  is preferably chosen so that the pulse amplitude is approximately the same as an average detector response signal S- 10 . The frequency of pulses from pulser  12  is preferably chosen so that the pulse arrival time in calibration mode is approximately the same as the average arrival time of detector response signals S- 10  in operating mode. These conditions of pulse amplitude and frequency are chosen so that the calibration pulses most accurately mimic the gain and linearity performance of the overall electronic system including both the amplification and the digitization components. 
         [0032]    Circuit  1   a  also includes a single common reference voltage element  14 , which serves as the voltage reference for pulser  12  via a signal S- 14   a , as well as the reference for processing ADC  22  via a signal S- 14   b  and for reference ADC  16  via a signal S- 14   c.    
         [0033]    It should be noted that one of the novel aspects of the design of circuit  1   a  is that connections S- 14   a , S- 14   b  and S- 14   c  all share the same signal, which is reference voltage  14 . 
         [0034]    Circuit  1   a  further includes a calibration ratio calculator  24  providing a value of a calibration ratio. Digital reference pulse value S- 16  and amplified calibration voltage value S- 22   a  are used to calculate the calibration ratio, which is equal to amplified calibration voltage value S- 22   a  (equal to &lt;GP&gt;) divided by digital reference pulse value S- 16  (equal to &lt;P&gt;). The calibration ratio may be calculated for many pulses during a calibration time, and an average value obtained. The result from calibration ratio calculator  24  is a gain value S- 24 , which is equal to a digital representation &lt;G&gt; of overall gain G. 
         [0000]    
       
         
           
             
               
                 
                   &lt; 
                   G 
                   &gt;= 
                   
                     
                       &lt; 
                       GP 
                       &gt; 
                     
                     
                       &lt; 
                       P 
                       &gt; 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where &lt;GP&gt; and &lt;P&gt; are averaged over the calibration time. 
         [0035]    It should be noted that an important novel aspect of the present invention is the use of calibration ratio calculator  24  to calculate overall gain G of the entire electronic system including both amplification and digitization components. The calculation is based on comparison of digitized calibration pulses from pulser  12  obtained by two different electronic routes. The first route is by digitization of calibration pulse signal S- 12  using reference ADC  16  without any amplification. The second route is when switch  20  selects calibration pulse signal S- 12 , and the calibration pulses are amplified by amplifier  18  and then digitized by processing ADC  22 . Importantly, processing ADC  22  and reference ADC  16  use the same reference voltage  14 , so that any drift in the reference voltage causes the same gain drift in both processing ADC  22  and reference ADC  16 , and the drift cancels out by division done by calibration ratio calculator  24 . Moreover, reference ADC  16  has much greater accuracy and much lower drift than processing ADC  22 , so that its output may be used as a calibration reference for the gain of the overall electronic system. 
         [0036]    It should also be noted that the calculation done by calibration ratio calculator  24  may be made any time switch  20  is set to select calibration pulse signal S- 12 . Calibration time may be any chosen value, which may be as short as 100 msec, and therefore calibration may be performed frequently with minimal interruption of useful operation of the X-ray instrument. 
         [0037]    During instrument measurement operation, when switch  20  is set to select detector response signal S- 10 , both gain value S- 24  and amplified operating voltage value S- 22   b  are used by an energy scale corrector  26  to calculate a corrected energy value S- 26 . Corrected energy value S- 26  is equal to amplified operating voltage value S- 22   b  (equal to &lt;GE&gt;) divided by gain value S- 24  (equal to &lt;G&gt;). The result of this calculation is corrected energy value S- 26 , which is a corrected digital representation &lt;E&gt; of detector response signal S- 10 . 
         [0000]    
       
         
           
             
               
                 
                   &lt; 
                   E 
                   &gt;= 
                   
                     
                       &lt; 
                       GE 
                       &gt; 
                     
                     
                       &lt; 
                       G 
                       &gt; 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0038]    Corrected energy value S- 26  is calculated for each detector signal, corresponding to each incident X-ray, and is used to construct an energy spectrum, which is a plot of X-ray energy vs number of X-rays incident on the detector with that energy. Corrected energy value S- 26  is a calibrated energy value which takes account of substantially all drift in the amplification and digitization electronics, and the calibration may be performed as frequently as desired by programming the operation of switch  20  using calibration mode controller  21 . Operation of switch  20  can also be initiated manually by an operator actuating a button or virtual button, (not shown in  FIG. 1 ), whenever a need for calibration is deemed fit. 
         [0039]      FIG. 2  is a schematic illustration of an alternative detector signal processing circuit  1   b  with simultaneous calibration pulse injection. Circuit  1   b  includes components equivalent to those in circuit  1   a  shown in  FIG. 1 , with two notable exceptions. The first difference between circuits  1   a  and  1   b  is that switch  20  is absent in circuit  1   b . The second difference is that router  23  in circuit  1   a  is replaced with a pulse discriminator  28  in circuit  1   b.    
         [0040]    In circuit  1   b , detector response signal S- 10  and calibration pulse signal S- 12  are both injected simultaneously and continuously into amplifier  18 . Amplified voltage S- 18  therefore comprises a mixture of both amplified response signal voltage g 1 E and amplified pulse voltage g 1 P. Similarly, amplified voltage value S- 22  comprises a mixture of response signal voltage value &lt;g 1 g 2 E&gt; and pulse voltage value &lt;g 1 g 2 P&gt;. Amplified voltage value S- 22  is input into a pulse discriminator  28  whose function is to separate the response signal and pulse voltage values contained within amplified voltage value S- 22 . Pulse voltage values are separated to a discriminated calibration value S- 28   a , and detector response signal values are separated to a discriminated response value S- 28   b . The method of operation of pulse discriminator  28  is described below in connection with  FIG. 3 . Subsequent operation of circuit  1   b  is the same as operation of circuit  1   a , namely calibration ratio calculator  24  provides calibration ratio S- 24  used for the calculation of corrected energy value S- 26 . However it should be noted that, in the case of circuit  1   b , calibration occurs continuously throughout every measurement operation, with no interruption or slowdown of the measurement operation. 
         [0041]      FIGS. 3A, 3B and 3C  illustrate the operation of pulse discriminator  28 .  FIG. 3A  shows a graph of amplified voltage value S- 22 , which includes a mixture of detector response and calibration values. In general, a detector response causes a rise in the value of amplified voltage value S- 22 , because detector  10  incorporates a charge sensitive pre-amplifier (not shown) in which charge from successive responses accumulates to cause rising voltage. On the other hand, calibration pulses originate from pulser  12  in which there is no charge sensitive amplifier, so that each calibration pulse causes an initial rise followed by a fall in the value of amplified voltage value S- 22 .  FIG. 3A  illustrates two calibration pulses,  36  and  38 , with initial rising values  36   a  and  38   a  respectively, flat regions  36   b  and  38   b  respectively, and falling values  36   c  and  38   c  respectively. Pulse discriminator  28  may distinguish the calibration pulses by their falling values  36   c  and  38   c  which are not present in detector response values. Alternatively, pulse discriminator  28  may distinguish the calibration pulses using timing signals obtained from pulser  12  (not shown). Using either discrimination method, pulse discriminator  28  identifies calibration pulses  36  and  38 , and removes them to produce discriminated response value S- 28   b  as shown in  FIG. 3B . Information from the removed calibration pulses is used to produce discriminated calibration value S- 28   a  as shown in  FIG. 3C . 
         [0042]      FIG. 3B  illustrates how the discriminated response value S- 28   b  is used to derive an amplified energy signal for each X-ray incident on detector  10 . The response to three incident X-rays can be identified in  FIG. 3B  by rising values  31 ,  32 , and  33 . The magnitude of rising values  31 ,  32 , and  33  corresponds to the quantities &lt;GE&gt; 1 , &lt;GE&gt; 2  and &lt;GE&gt; 3  respectively. These quantities are used by energy scale corrector  26 , together with knowledge of gain value S- 24  obtained from calibration ratio calculator  24 , in order to assign corrected energy value S- 26  to each of the three X-rays. The energy values of all incident X-rays are obtained in this way during the measurement, and counts are accumulated to obtain an energy spectrum. 
         [0043]      FIG. 3C  illustrates discriminated calibration value S- 28   a , showing calibration pulses  36  and  38 . The amplitudes of pulses  36  and  38  correspond to the quantities &lt;GP&gt; 1  and &lt;GP&gt; 2  respectively. These quantities are used by calibration ratio calculator  24  together with reference pulse value S- 16  to calculate gain value S- 24 . Different values of &lt;GP&gt; 1  and &lt;GP&gt; 2  may indicate that the overall gain &lt;G&gt; of the electronic system has changed, and correction may automatically occur at energy scale corrector  26 . Alternatively, rather than applying correction to gain &lt;G&gt; at every successive calibration pulse, values of gain &lt;G&gt; may be averaged over an averaging time which includes many pulses before applying a correction at energy scale corrector  26 . Such averaging may be advantageous to reduce noise in the measurement of gain &lt;G&gt; and is within the scope of the present disclosure. 
         [0044]      FIG. 4  shows a schematic flow diagram of a sequential calibration process  40  according to the present disclosure. Process  40  is described below with reference to  FIG. 4  and  FIG. 1 . Process  40  starts at step  402 , and at step  404  an operator selection is made via calibration mode controller  21  as to whether calibration is to be performed after one or more measurements, or after a specified interval of operating time. If calibration after one or more measurements is selected, process  40  moves to step  410 . At step  412 , calibration mode controller  21  sets switch  20  to calibration mode and in step  414  calibration is performed. Calibration of step  414  comprises calculation by calibration ratio calculator  24  of the calibration ratio, which may be averaged over many pulses. In a typical embodiment herein presented, the calibration pulse frequency may be 500 kHz, and the averaging time in step  414  may be 100 msec. In this embodiment gain value S- 24  at the end of the calibration is an average value of about 50,000 pulses. Gain value S- 24  is represented by the symbol &lt;G&gt;. 
         [0045]    At step  415 , calibration mode controller  21  sets switch  20  to operating mode and in step  416  the energy scale is corrected using the value of &lt;G&gt; derived in step  414 . In step  417  one or more measurements are performed with corrected energy scale, and upon completion of the specified number of measurements the system is ready for a new calibration at step  418 , and the process returns to step  404 . 
         [0046]    If at step  404  calibration after a specified interval of operating time is selected, process  40  moves to step  420 . At step  421  the operator, via calibration mode controller  21 , selects a time interval T between successive calibrations. At step  422 , calibration mode controller  21  sets switch  20  to calibration mode and in step  423  calibration is performed in the same manner as described above for step  414 . At step  424 , calibration mode controller  21  sets switch  20  to operating mode and in step  425  the energy scale is corrected using the value of &lt;G&gt; derived in step  423 . In step  426  the measurement is carried out until either clock  19  indicates that time T has expired or the measurement is complete, whichever occurs first. Step  427  tests whether the measurement is complete, and if not the process returns to step  422  for a new calibration. If measurement is complete, the process returns to step  404 . 
         [0047]    It can be seen that selection of calibration after a specified interval of operating time, as described in steps  420 ˜ 428  allows one or more new calibrations to occur during the course of a single measurement. This may be useful for particularly long measurements. Setting of time interval T depends on the degree to which there is a stable environmental temperature—the less stable the environment the shorter time interval T should be set. In a typical embodiment, time interval T might be set to 10˜100 seconds, and if calibration time is about 100 msec, there is no discernible interruption of instrument operation, even though calibration is occurring with sufficient frequency to avoid any risk of drift of the electronic gain. 
         [0048]    It can be appreciated that, for both embodiments of calibration by time interval or by measurement operations, calibration switching can be initiated either by an automatic trigger or by manual triggering by the operator. All of such variations of implementation are within the scope of the present disclosure. 
         [0049]      FIG. 5  shows a schematic flow diagram of a simultaneous calibration process  50  according to the present disclosure. Process  50  is described below with reference to  FIG. 5  and  FIG. 2 . Process  50  starts at step  502 , and at step  504  pulser  12  is started in order to perform an initial calibration prior to beginning actual operation of the instrument. The initial calibration is performed for an initial calibration time which is sufficiently large to allow calibration ratio calculator  24  to calculate gain value S- 24  by averaging over a large number of pulses. In an embodiment, the initial calibration time may be 100 msec to 1 second. 
         [0050]    In step  506 , the measurement is started by activating the X-ray source and directing X-rays at a sample. In step  508  the measurement is continuing, so that both detector response signal S- 10  and calibration pulse signal S- 12  are input into amplifier  18  and subsequently to processing ADC  22  and pulse discriminator  28 . In step  510 , pulse discriminator  28  separates calibration pulses and detector response into discriminated calibration value S- 28   a  and discriminated response value S- 28   b  respectively. In step  512  calibration ratio  24  is calculated and, after the averaging time, an updated gain value S- 24 , denoted by the symbol &lt;G&gt;, is provided to energy scale corrector  26 . Energy scale corrector  26  updates the energy scale to its most recent updated value in step  514 , using the value of &lt;G&gt; derived in step  512 . In step  516  there is a check of whether the measurement is complete. If not, process  50  loops back to step  508  and the measurement continues uninterrupted. 
         [0051]    It should be noted that the time taken from step  508  to step  516  is almost entirely due to the averaging time which, in an embodiment, is about 100 msec As a result, the energy calibration is updated every 100 msec throughout the measurement. In an embodiment, the pulse frequency of pulser  12  may be 50 kHz, which is 10 times lower than the pulse frequency used in process  40  as described in connection with  FIG. 4 . The reason for using a lower calibration pulse frequency in process  50  is that, since both calibration pulses and detector signals are processed simultaneously, there is a risk that a calibration pulse and detector signal are so closely coincident in time that neither may be distinguished. The probability of such close coincidence can be reduced by lowering the calibration pulse frequency. Nevertheless, at a frequency of 50 kHz, 5,000 pulses are averaged in 100 msec, which is sufficient to obtain reliable updated gain value S- 24  for use during the next 100 msec measurement interval. 
         [0052]    If the measurement is complete at step  516 , the instrument is ready for the next measurement at step  518  and the process loops back to the start at step  502 . 
         [0053]    It should be noted that the simultaneous calibration method of process  50  is particularly useful for measurements with low X-ray count rates. Such measurements are lengthy and frequent calibration is essential to ensure that gain drift during the course of the measurement is taken into account. 
         [0054]    Circuits  1   a  and  1   b  in  FIGS. 1 and 2  and processes  40  and  50  in  FIGS. 4 and 5 , as described above, all relate to calibration of the overall gain of the amplification and digitization electronics. However, no account is taken of non-linear effects. Referring now to  FIG. 6 , and with continued reference to  FIG. 1 , there are shown in  FIG. 6  graphs illustrating the effect of non-linearity on an exemplary detector response signal  63 , in which an X-ray arrives at detector  10  at a time when the charge-sensitive pre-amplifier voltage is V 1 . The step-function increase in detector response signal S- 10  is representative of the energy E of the X-ray. 
         [0055]    On a graph of amplified voltage value S- 22  vs detector response signal S- 10 , the voltages of detector response signal S- 10  before and after arrival of the X-ray, V 1  and V 1 +E respectively, are shown by lines  64  and  65  respectively. A line  61  shows the behavior of a perfectly linear amplification and digitization electronic system, wherein the gain G is equal to the slope of the line as shown. However, if the gain is not linear, then the actual gain is represented by the slope of a line  62 , and although the slope of line  61  is the average of the slope of line  62 , the slope at any particular point on line  62  may be different from the slope of line  61 , and therefore the gain may be different. 
         [0056]    In a graph of gain vs detector response signal S- 10  shown at the top of  FIG. 6 , a line  66  is the slope of line  61  and represents the constant gain of a perfectly linear system, and a line  68  is the slope of line  62  and represents the varying gain of a non-linear system. Line  66  is the average value of line  68 . The quantity &lt;ΔG&gt; represents the difference between the linear and non-linear gain, and it is to be understood that &lt;ΔG&gt; is a varying function of detector response signal S- 10 . 
         [0057]    It should be noted that, in order to clearly illustrate the effect of the non-linearity, the deviation of line  62  from linear gain line  61  and of line  68  from line  66  has been greatly exaggerated relative to actual non-linearity of available electronic systems. Similarly, the size of step function E has been greatly exaggerated relative to the overall range of detector response signal S- 10  and amplified voltage value S- 22 . 
         [0058]    Lines  64  and  65 , representing the change in detector response signal S- 10  due to detector response signal  63 , intersect line  61  at lines  64   b  and  65   b  respectively. Lines  64  and  65  intersect line  62  at lines  64   a  and  65   a  respectively. If the electronic system gain is linear, corresponding to line  61 , then the change in amplified voltage value S- 22  is given by the difference between the values of lines  65   b  and  64   b , represented by the symbol &lt;GE&gt; L . On the other hand, if the electronic system gain is non-linear, corresponding to line  62 , then the change in amplified voltage value S- 22  is given by the difference between the values of lines  65   a  and  64   a , represented by the symbol &lt;GE&gt; NL . It can be seen that &lt;GE&gt; NL  is less than &lt;GE&gt; L  and this is because the slope of line  62  is less than the slope of line  61  in the relevant part of the graph. However, if output voltage V 1  is different, the slopes of lines  61  and  62  may be different, and in some circumstances &lt;GE&gt; NL  may be greater than &lt;GE&gt; L . 
         [0059]      FIG. 7  is a diagram illustrating a solution by use of calibration pulse signals for calibration of non-linearity effects. In order to calibrate for non-linearity effects, pulses are injected into the amplification and digitization system using a circuit  1   c  which is described below in connection with  FIG. 8 . In a graph of calibration pulse signal S- 12  vs amplified voltage value S- 22  shown in  FIG. 7 , non-linear response line  62  is the same as in the graph of detector response signal S- 10  vs amplified voltage value S- 22  as shown in  FIG. 6 . This is because calibration pulses and detector response signals are injected into the same amplification and digitization system, and therefore non-linear gain effects are unchanged. 
         [0060]      FIG. 7  shows two exemplary calibration pulses,  73  and  73 ′, which are injected into the amplification and digitization system at different times, t and t′ respectively. Pulses  73  and  73 ′ have, respectively, lower pulse voltages V 1 , V 1 ′ and upper pulse voltages V 2 , V 2 ′. Pulses  73  and  73 ′ have the same pulse height P, meaning that V 2 −V 1 =V 2 ′−V 1 ′=P. Lower voltages V 1 , V 1 ′ and upper voltages V 2 , V 2 ′ are represented, respectively, by lines  74 ,  74 ′ and  75 ,  75 ′ on the graph of calibration pulse signal S- 12  vs amplified voltage value S- 22 . Lines  74  and  75  intersect line  62  at lines  74   a  and  75   a  respectively, and the change in amplified voltage value S- 22  due to pulse  73  is the difference between the values at lines  74   a  and  75   a , represented by the symbol &lt;GP&gt;. Lines  74 ′ and  75 ′ intersect line  62  at lines  74   a ′ and  75   a ′ respectively, and the change in amplified voltage value S- 22  due to pulse  73 ′ is the difference between the values at lines  74   a ′ and  74   b ′, represented by the symbol &lt;G′P&gt;. It should be noted that G is the gain of the amplification and digitization system at the voltages V 1  and V 2  of pulse  73 , and G′ is the gain of the amplification and digitization system at the voltages V 1 ′ and V 2 ′ of pulse  73 ′, and that G and G′ are different due to non-linearity of the system. Note also that, in practice, pulse height P is very small relative to the overall range of detector response signal S- 10  and amplified voltage value S- 22 . It can therefore be assumed that line  62  is linear over such a small range, and therefore there is no change of gain between voltages V 1  and V 2  or between voltages V 1 ′ and V 2 ′. 
         [0061]      FIG. 8  is a schematic illustration of a circuit  1   c , which is an alternative embodiment of circuit  1   a  shown in  FIG. 1 , and which is used to perform a one-time calibration of non-linearity during a manufacturing calibration phase. This calibration of non-linearity deals with the intrinsic non-linearity exhibited by both amplifier  18  and ADC  22 , and is done only once at the manufacturing level. 
         [0062]    It should be also noted that the description in  FIGS. 6-10  of calibration for non-linearity is an improved calibration process which is independent of the on-board instrument gain calibration described in relation to  FIGS. 1-5 . The result of the non-linearity calibration is preferably a look-up table (described below) which is specific to each instrument, and that can be used by each specific instrument throughout its life. 
         [0063]      FIG. 8  shows that pulser  12 , which is the same pulser as that shown in  FIGS. 1 and 2 , comprises a low-level digital-to-analog converter (DAC)  82 , a high-level DAC  84 , and a pulser switch  86 . A pulse voltage controller  87  produces a lower pulse voltage value &lt;V 1 &gt; and a higher pulse voltage value &lt;V 2 &gt;. Lower pulse voltage value &lt;V 1 &gt; is input to low-level DAC  82 , and, using reference voltage  14  as its reference via signal S- 14   a , DAC  82  produces a lower pulse voltage V 1  at signal S- 82 . Higher pulse voltage value &lt;V 2 &gt; is input to high-level DAC  84 , and, using reference voltage  14  as its reference via signal S- 14   a , DAC  84  produces a higher pulse voltage V 2  at signal S- 84 . Signals S- 82  and S- 84  are input to pulser switch  86  which operates at an operator defined frequency to switch its output between signals S- 82  and S- 84  thereby producing pulses with lower pulse voltage V 1  and higher pulse voltage V 2  at signal S- 12 . 
         [0064]    Signal S- 12  is the same as calibration pulse signal S- 12  which was discussed in relation to circuit  1   a  in  FIG. 1  and circuit  1   b  in  FIG. 2 . The remainder of circuit  1   c  is operates in the same way as circuits  1   a  and  1   b , namely calibration pulse signal S- 12  is input into amplifier  18  and processing ADC  22 , and calibration pulse signal S- 12  is also input into reference ADC  16 . A calibration ratio is calculated by calibration ratio calculator  24  and after an averaging time, gain value S- 24  is output, represented by symbol &lt;G&gt;, which is the gain corresponding to lower pulse voltage V 1  and higher pulse voltage V 2 . Gain value S- 24  and the value of V 1  are input to a look-up table generator  88 . As explained below in connection with  FIG. 9 , pulse voltage controller  87  then changes the value of lower pulse voltage V 1 , and calibration ratio calculator  24  computes a new gain value S- 24  which may be different from the previous value due to non-linearity of the electronic gain. The new values of V 1  and gain value S- 24  are input to look-up table generator  88 . In this way, by changing values of V 1  and computing corresponding values of gain value S- 24 , look-up table generator  88  may build up a table of gain value S- 24  and corresponding values of V 1  which covers the complete range of amplified voltage value S- 22  and which contains as many calibration points as desired. When data acquisition for the desired calibration points has been completed, look-up table generator  88  computes an average gain value for all the calibration points, and converts the table to be a table of the difference, &lt;ΔG&gt;, between the gain value for each calibration point and the average gain value. Therefore, the final product of look-up table generator  88  is a table comprising multiple values of &lt;ΔG&gt; and corresponding values of V 1 . 
         [0065]    It should be noted that circuit  1   c  is equivalent to circuit  1   a  with switch  20  set to calibration mode and with addition of pulse voltage controller  87  and look-up table generator  88 . Circuit  1   c  is also equivalent to circuit  1   b  with omission of detector response signal S- 10  and addition of pulse voltage controller  87  and look-up table generator  88 . Therefore, by adding pulse voltage controller  87  and look-up table generator  88 , circuit  1   c  is available to perform calibration of non-linearity irrespective of whether an X-ray instrument is configured with circuit  1   a  or with circuit  1   b . Note that detector  10  is present in  FIG. 8 , but is not operative during the calibration of non-linearity. 
         [0066]      FIG. 9  shows an embodiment of calibration pulse signal S- 12 , which is a series of pulse sequences produced by pulse voltage controller  87  and pulser  12  for use in calibration of non-linearity. A pulse sequence  92  comprises pulses continuing for a calibration time t 0 , with lower pulse voltage V 1 , higher pulse voltage V 2  and pulse height P. When pulse sequence  92  is used in circuit  1   c , calibration ratio calculator  24  averages the calibration ratio for time t 0  to produce a gain value S- 24 , representative of &lt;G&gt; at lower pulse voltage V 1 . In an embodiment, calibration time to is 100 msec and the pulse frequency is 50 kHz, so that pulse sequence  92  comprises 5,000 pulses. Pulse sequence  92  is followed by a pulse sequence  92 ′ which comprises pulses continuing for a calibration time t 0 , with lower pulse voltage V 1 ′, higher pulse voltage V 2 ′ and pulse height P. When pulse sequence  92 ′ is used in circuit  1   c , calibration ratio calculator  24  averages the calibration ratio for time t 0  to produce a gain value S- 24 , representative of &lt;G′&gt; at lower pulse voltage V 1 ′. Pulse sequence  92 ′ is followed by a pulse sequence  92 ″ which comprises pulses continuing for a calibration time t 0 , with lower pulse voltage V 1 ″, higher pulse voltage V 2 ″ and pulse height P. When pulse sequence  92 ″ is used in circuit  1   c , calibration ratio calculator  24  averages the calibration ratio for time t 0  to produce a gain value S- 24 , representative of &lt;G″&gt; at lower pulse voltage V 1 ″. Gain values &lt;G&gt;, &lt;G′&gt; and &lt;G″&gt; are measurements of gain at different lower pulse voltage V 1 , V 1 ′ and V 1 ″ respectively, and these gain measurements therefore take into account the non-linearity of gain with respect to input voltage. 
         [0067]    Gain values &lt;G&gt;, &lt;G′&gt; and &lt;G″&gt; and corresponding lower pulse voltage values &lt;V 1 &gt;, &lt;V 1 ′&gt; and &lt;V 1 ″&gt; are input to look-up table generator  88  as shown in  FIG. 8 . Only three different lower voltages and corresponding gain values are shown in  FIG. 9 , but the number of corresponding lower voltages and gain values which can be obtained according to the invention is unlimited. By continuing to vary the lower pulse voltage in small increments over the full range of expected variation of detector response signal S- 10 , a calibration map is made of the non-linear gain characteristics of the amplification and digitization system. In effect, the calibration reproduces lines  62  and  68  as shown in  FIGS. 6 and 7  over the full range of the instrument. 
         [0000]    In subsequent operation of the instrument with input from detector response signal S- 10 , the non-linearity due to differing output levels of the charge-sensitive pre-amplifier is taken into account by energy scale corrector  26  using the table from table generator  88 . Referring to  FIGS. 1 and 2 , it can be seen that gain value S- 24 , represented by symbol &lt;G&gt;, is not subject to non-linear variation because the lower pulse voltage of pulses from pulser  12  does not vary. However, the amplified voltage value S- 22 , represented by symbol &lt;GE&gt; is subject to non-linear variation depending on the output voltage of the charge sensitive pre-amplifier associated with detector  10 . Energy scale corrector therefore corrects the energy &lt;E&gt; of an X-ray using the following modification of equation (2): 
         [0000]    
       
         
           
             
               
                 
                   &lt; 
                   E 
                   &gt;= 
                   
                     
                       &lt; 
                       
                         
                           ( 
                           
                             G 
                             + 
                             
                               Δ 
                                
                               
                                   
                               
                                
                               G 
                             
                           
                           ) 
                         
                          
                         E 
                       
                       &gt; 
                     
                     
                       &lt; 
                       G 
                       &gt; 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where ΔG is derived from the table in table generator  88  according to the voltage V 1  of the charge sensitive preamplifier at the time the X-ray was received. 
         [0068]    Pulse height P is kept constant in pulse sequences  92 ,  92 ′ and  92 ″ shown in  FIG. 9 . However, as well as depending on the lower pulse voltage, the non-linear gain of the amplification and digitization system may also depend on the pulse height.  FIG. 10  shows an alternative embodiment of calibration pulse signal S- 12 , which comprises pulse sequences  96 ,  97  and  98 , all with the same lower pulse voltage V 1 , but with differing pulse heights P 1 , P 2  and P 3  respectively. In an embodiment, P 1  may represent a pulse height near the bottom of the voltage range of expected detector response signal S- 10 , P 3  may represent a pulse height near the top of the voltage range of expected detector response signal S- 10 , and P 2  may represent a pulse height at approximately mid-range. Pulse sequences  96 ,  97  and  98  are followed by pulse sequences  96 ′,  97 ′ and  98 ′, all with the same lower pulse voltage V 1 ′, and with pulse heights P 1 , P 2  and P 3  respectively. In the same way as described in connection with  FIG. 9 , by continuing to vary the lower pulse voltage in small increments over the full range of expected variation of detector response signal S- 10 , a calibration map is made of the non-linear gain characteristics of the amplification and digitization system. However, for the pulse sequences of  FIG. 10 , for each value of lower pulse voltage there are three values of gain, one for each of low pulse height, mid pulse height and high pulse height. In effect, the calibration produces three version of lines  62  and  68  as shown in  FIGS. 6 and 7  over the full range of the instrument, and the correct calibration for any pulse height may be determined by extrapolation between the measured calibration data for low-, mid- and high pulse height. In subsequent operation of the instrument with input from detector response signal S- 10 , non-linearity both due to differing output levels of the charge-sensitive pre-amplifier and due to differing X-ray energy are taken into account. 
         [0069]    It should be noted that because the non-linearity has weak dependence on temperature, only a one-time calibration of the instrument non-linearity is required. This calibration may be conveniently performed in the factory before shipment of the instrument to a customer. On the other hand, the actual gain of the instrument is subject to drift, and it is necessary to apply the gain calibration methods described herein in connection with  FIGS. 1 ˜ 5 . Referring to  FIG. 6 , the gain calibration methods of  FIGS. 1 ˜ 5  are designed to correct the slope of line  61  or the level of line  66 , whereas the non-linearity calibration described in connection with  FIGS. 6 ˜ 10  is a determination of the deviation of line  62  from line  61  or, equivalently, the deviation &lt;ΔG&gt; of line  68  from line  66 . It can be assumed with good accuracy that the deviation of line  62  from line  61  remains constant even as the slope of line  61  changes. When gain drift occurs during operation, line  62  pivots about the origin of the graph as the gain changes, but its shape does not change. Similarly, it can be assumed with good accuracy that the deviation of line  68  from line  66  remains constant even as the level of line  66  changes. When gain drift occurs during operation, line  66  moves up and down the graph as the gain changes, but its shape does not change. 
         [0070]    The ability to calibrate the non-linearity of an amplification and digitization circuit as described in connection with  FIGS. 6 ˜ 10  is an important novel aspect of the present invention. 
         [0071]    A further novel aspect is the combination of non-linearity calibration with automatic calibration of the system gain as described in connection with  FIGS. 4 and 5 . 
         [0072]    Yet a further novel aspect is use of single common reference voltage  14  as voltage reference for processing ADC  22 , for reference ADC  16  and for both low-level DAC  82  and high-level DAC  84 . 
         [0073]    Although the present invention has been described in relation to particular embodiments thereof, it can be appreciated that various designs can be conceived based on the teachings of the present disclosure, and all are within the scope of the present disclosure.