Abstract:
A spectrometer system employs a gridless Xenon detector having an anode and a cathode supported in spaced relation from the anode devoid of structure intermediate the anode and cathode. Pulses resulting from charge collection due to radiation ionization of the Xenon gas are detected and parametrized by a computation engine through multiple detected pulses. Simultaneous determination of the position and ionization energy allows selective presentation of the data to compensate for various position dependent phenomena.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application claims priority of the Provisional Application Ser. No. 60/474,792 of the same title filed on Jun. 2, 2003. 
     
    
     REFERENCE TO COMPUTER PROGRAM CD  
       [0002]     This application includes as an appendix a CD providing a source code written in IGOR Pro for a computer program incorporating the source code elements of an exemplary embodiment of the present invention as disclosed herein. The materials contained on the CD are incorporated by reference as though fully set forth herein. The program provided is copyrighted and no express or implied release of rights through its listing herein is contemplated  
       BACKGROUND OF THE INVENTION  
       [0003]     1. Field of the Invention  
         [0004]     This invention relates generally to the field of measuring the energy of ionizing electromagnetic radiation and, more particularly, to a vibration resistant high pressure xenon detector for such measurement.  
         [0005]     2. Description of the Related Art  
         [0006]     There are many fields in which the measurement of the energy of ionizing electromagnetic radiation such as gamma-radiation or X-radiation is desired. For the purposes of this application, the energy of ionizing electromagnetic radiation is equivalent to or a function of the wavelength or frequency of the radiation. Devices to accomplish this measurement are generally referred to as spectrometers. Spectrometry of electromagnetic radiation is a common method of determining the composition of the material from which the radiation emanated. Specifically, gamma-ray spectroscopy will determine the elemental composition of the material from which it emanates. X-Ray spectroscopy will determine the elemental or chemical composition of the material from which it emanates.  
         [0007]     Gamma-ray spectrometry is important is all areas of nuclear measurement where gamma-ray energy must be measured or an isotope must be identified. Nuclear reactions or atomic transitions produce gamma-rays or X-rays whose energy identifies the interaction and the constituents in the reaction. Gamma-ray spectrometers typically consist of scintillators (see e.g. Radiation Detection and Measurement, Glenn Knoll, 3rd Ed., pp 219-264) which emit light whose intensity is proportional to the number of electrons ionized in the scintillating material by the gamma ray, semiconductors diode devices (Knoll at 353-404) in which the charge collected proportional to the number of electrons ionized a gamma-ray, or a gas-filled device whose charge is proportional to the number of electrons ionized (Knoll at 159-200). Geiger counters  5  are gas-filled detectors whose charge collected is not proportional to the number of electrons ionized, hence are not spectrometers in the current art.  
         [0008]     For the purposes of gas-filled spectrometers with which this invention deals, a radiation event occurs within the gas filled chamber when a single gamma ray or single X-ray interacts inside the gas in the chamber within or in proximity to an electro-magnetic field. This event strips off electrons from the gas within the chamber thus creating one or more ions (an ionization event—one radiation event can and usually does create more than one ionization event). The actual physical location of the point where an electron is stripped off is called the “interaction position” which is of importance in determining the spectroscopic information which will be further discussed below. The combination of the influences of all free electrons and ions form a single event which creates the pulse waveform time series influence on the electro-magnetic field.  
         [0009]     Gas-filled spectrometers presently suffer from a shortcoming in that the apparent charge collected on the electrodes is dependent on interaction position. (Technically, this is the mirror-charge induced on the electrodes by the motion of the charged particles in the electric field needed to keep the electrodes at their fixed potential—this will be referred to as “collection” as is common in the art.) This “collection” results in a charge induced on the electrodes as the electric charge moves under the influence of the electro-magnetic field. As the charge is induced over time it produces a time series pulse.  
         [0010]     As stated above, gamma-rays create electron-ion pairs in the gas. These electron-ion pairs are then counted to determine gamma-ray energy. In a gas, ionized by electromagnetic radiation, ions move much more slowly than the electrons. This leads to a position dependence in apparent charge collected, since the ions are not observed to move or be “collected” on the time scale in which the electrons are observed to move. In other words, the influence the ionization of an atom on an electro-magnetic field is dependant upon and in part a function of the distance of the interaction position from the electrodes that create the electro-magnetic field. This results in two unknown quantities: the energy deposited by the ionizing radiation and the location of the interaction position. Simple measurement of the resulting magnitude of change in the charge of the electrodes is inadequate for spectrometry purposes.  
         [0011]     This problem is circumvented in three main ways in the current art. 1) Gas-filled proportional counters are spectrometers by virtue of the fact that they remove the position dependence by electron multiplication near the charge collecting electrode (the anode), so that the observed difference in collection with position is negligible. Any gain element sufficiently near the anode will accomplish this task. 2) Gridded ion chambers solve this problem by limiting the drift distance over which the electrons are observed, by a screening grid, called a Frisch grid. A spectrometer incorporating a Frisch grid is shown in  FIG. 1 . 3) It has been suggested that a “Luke grid” (See U.S. Pat. 5,530,249) could be constructed in which the electron charge is mainly measured by a set of interlocked grids in semiconductor detectors.  
         [0012]     The preferred method of addressing this problem in the current state of the art for gas detectors is through the use of a Frisch grid. A current design detector employing a Frisch grid is shown in  FIG. 1  wherein an anode  100  is supported within a cylindrical cathode  102 . The grid  104  is supported around the anode and a ceramic feed through  106  allows signal transmission from the anode. The Frisch grid is a source of added mechanical complexity and additional electronic noise caused by its capacitance and its microphonic vibration.  
         [0013]     It is therefore desirable that spectrometry is performed in the apparatus and the spectroscopic information is extracted from the apparatus in a way that enhances accuracy and reliability.  
         [0014]     It is also desirable that a gas spectrometer be provided that is more reliable and sensitive while having greatly reduced sensitivity to mechanical vibration.  
       SUMMARY OF THE INVENTION  
       [0015]     A spectrometer system according to the present invention employs a gridless Xenon detector having a pressure vessel containing high pressure Xenon gas, an anode supported within the pressure vessel and a cathode supported in spaced relation from the anode devoid of structure intermediate the anode and cathode. An electric field is created between the anode and cathode and maintained at a fixed potential using a preamplifier electrically connected to the anode and cathode. Pulses from the preamplifier resulting from charge collection due to radiation ionization of the Xenon gas are detected and a computation engine connected to the detecting means stores multiple detected pulses. A curve fitting routine operates on the stored data for fitting a curve to each detected pulse to create a fitted waveform. The fitted waveforms are then stored and categorized to create histogram data. The histogram data is then integrated to provide radiation energy data.  
         [0016]     The present invention simultaneously determines the position and ionization energy rather than eliminating the position dependence as required in the prior art. The detector output waveform is recorded as a time series. The waveform is the result of several variables including interaction position (or alternatively pulse rise time as functionally related) and the ionization energy of the radiation. The anode and cathode radii and the electron velocity are physical parameters of the detector that can be employed in the analysis. By comparing the actual detector waveform to a model of the pulse (i.e. an equation for the time series) the variables defining the pulse can be simultaneously extracted by simultaneous determination of variables using a selected technique such as least squares fit. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0017]     These and other features and advantages of the present invention will be better understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein:  
         [0018]      FIG. 1  demonstrates a prior art spectrometer using a Frisch grid;  
         [0019]      FIG. 2  is an exemplary embodiment of the present invention with a planar format;  
         [0020]      FIG. 3  is an exemplary embodiment of the present invention with a cylindrical format;  
         [0021]      FIG. 4  is an exemplary embodiment of the present invention with a spherical format;  
         [0022]      FIG. 5  is a detailed section view of an exemplary physical embodiment of the invention using the cylindrical format with oscilloscope and computer elements of the combination comprising the invention shown in schematic form;  
         [0023]      FIG. 6  is a section view of an embodiment of the ceramic feed through applicable for the embodiment of  FIG. 5 ;  
         [0024]      FIG. 7  is a graphical representation of the pulses received at the anode in the present invention compared to the prior art Frisch grid implementation;  
         [0025]      FIG. 8 a  flow chart of one embodiment of an algorithm for signal processing of the pulses received to resolve the distance and energy of the electrons resulting from an ionization event;  
         [0026]      FIGS. 9   a - f  are graphs of pulse traces with resulting curve fits;  
         [0027]      FIGS. 10   a - d  are graphical depictions of the histograms from an event;  
         [0028]      FIGS. 11   a - c  are graphs of exemplary digitally reconstructed spectra;  
         [0029]      FIG. 12  is a diagrammatic representation of the cross section of the detector showing the relative depth of various radiation interactions;  
         [0030]      FIG. 13  is a plot of the number of events versus energy for description of the advantages of position information in correcting for particular events; and,  
         [0031]      FIG. 14  is an exemplary reconstructed spectra weighted for position influenced data. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0032]     Referring to the drawings,  FIGS. 2, 3  and  4  represent three geometrical embodiments of the present invention, but are not intended to be exclusive—the number of geometric configurations that would be suitable for use of the invention is virtually unlimited. In each of the embodiments, a negative voltage is applied on the cathode  10  with respect to the anode  12 , and ionized electron—ion pairs are swept by the electric field toward the anode, inducing a charge on the anode. In each case, the apparent charge collected is dependent on the distance from the anode, but not on the lateral position from the anode. In each case, the charge collection time sequence will have a functional dependence on the number of electron-ion pairs and on the distance from the anode. And in each case, the information about both that distance and the number of electron-ion pairs is extracted from the pulse shape by an analyzer  14 .  
         [0033]     The planar embodiment of  FIG. 2  has a planar cathode and planar anode separated by some distance filled with active gas. The cylindrical embodiment of  FIG. 3  employs concentric cylindrical anode and cathode with the space between them filled with active gas. The spherical embodiment of  FIG. 4  employs concentric spheres with the space between them filled with active gas. Although the cathode is shown to be larger than the anode in each figure, this is not a requirement.  
         [0034]      FIG. 5  provides a detailed example of an embodiment of the invention in the cylindrical format for a xenon gas detector. The components of the detector  20  are carried between a head plate  22  and a base plate  24 . A preamplifier  26  is mounted adjacent the base plate and, for the embodiment shown, is carried in an enclosure  28  extending from the base plate. A pressure vessel  30  extends between a pressure vessel base plate  32  and a pressure vessel head plate  34 . Xenon gas is contained within the vessel at 0.3-0.7 g/cm 3 . The anode  10  is supported between a base ceramic  34  and a ceramic feed through  36 , which will be described in greater detail subsequently.  
         [0035]     The cathode  12  is cylindrical and extends from the pressure vessel head plate to the pressure vessel base plate, insulated from the anode by the base ceramic and ceramic feed through. Signal leads  38  and  40  for the anode and cathode, respectively, extend from the ceramic feed through into the preamplifier enclosure for connection to the preamplifier.  
         [0036]     Significant advantages are gained by elimination of any grid from the detector through reduction of capacitance and leakage current which impact the noise and vibration sensitivity of the detector.  
         [0037]     A valve  42  is carried by the pressure vessel base plate and communicates with the interior of the pressure vessel. A reliable ultra-high vacuum closure is required for the xenon detector application and a valve comparable to the COTS valve produced by NUPro has been demonstrated to provide sufficient capability for the system. A high voltage power supply  44  is carried by the base plate for powering the detector.  
         [0038]     The preamplifier provides the signal from the electrodes to an oscilloscope  46  for detecting and recording the pulses from Gamma ray ionization events collected by the electrodes. An output of the oscilloscope is provided to a computer  48  having a storage system  50  including a magnetic disc or comparable storage device and output devices such as a monitor  52  and printer  54  for graphical output of the spectrographic data and interim processing data as will be described subsequently.  
         [0039]     Details of an embodiment of the feed through  36  for the invention are shown in  FIG. 6 . A ceramic cylinder  56  carries the anode conductor  58  which attaches to the anode with a mechanical fitting  60  and extends to the signal lead  38 . A braze ring  62  provides an attachment point for the cathode. A ground ring  64  provides a ground reference for the signal.  
         [0040]     Ionization events are captured by the detector when radiation ionizes the Xenon gas within the pressure vessel causing charge collection by the electrodes. Since no intermediate grid is present for distance correction, the signal pulse from the event may take several forms such as charge clouds from multiple interaction points shown in  FIG. 7  where a grid corrected pulse  700  is shown on the left side of the figure and the multiple pulses  702   a -  d  created by events of differing distance are shown on the right side of the figure.  
         [0041]     In this example simplified using a planar embodiment of the invention, the pulses are linear with the slope of the charge pulse proportional to the energy. In the figure, four ionization events are shown by  702   a - d . They all have the same slope (induced by the same number of electrons ionized) but different durations due to differing interaction positions. With a detector employing a Frisch grid all four pulses are identical and have the same amplitude. Therefore, the physical construct of the Frisch grid has eliminated the interaction position dependence on the pulse. Measurement of the number of electron-ion pairs is merely the measurement of the amplitude of the waveform. Without the Frisch grid the amplitude is not a measure of the number of electron-ion pairs. Digital analysis of the entire pulse waveform can extract the amplitude by simultaneous determination of both interaction position and the number of electrons. The present invention removes the devices to correct for the position dependence (i.e. the Frisch grid) allowing the position dependence to be determined and removed by mathematical (rather than mechanical) means.  
         [0042]     By digitizing the amplitude of the charge pulse versus time on a sufficiently fast time scale (approximately 10-100 times faster that the transit time) the energy information can be extracted (or corrected for) by analysis with an external signal processor operating on the charge collection signal. Possible implementations of the digital processing include a mathematical fit (such as a least squares fit) to the charge pulse to the function derived from the Hecht relation to simultaneously extract position and amplitude.  
         [0043]     Analysis of the entire waveform allows fitting of a mathematical function for the separation of the number of electron-ion pairs (which is proportional to the energy of the radiation) from the interaction position and deriving both pieces of information from each waveform. This technique works in any geometry having a regular calculable electric field, including but not limited to the planar, cylindrical and spherical node to cathode geometries disclosed herein.  
         [0044]     For an exemplary embodiment, the pulses are acquired from the preamplifier with a Tektronix TDS 410 60 MhZ oscilloscope and read into a into a PC type computer.  
         [0045]     The input signal is analyzed employing software performing the steps shown in  FIG. 8 . A communications port connected to the oscilloscope is initialized  810  for pulse acquisition. A wave is then read  812  from the oscilloscope. For the embodiment shown, a file counter is then incremented  814  to allow sequential storage of the acquired waves. The pulse acquisition and storage is repeated for a predefined number of pulses  816 . The stored waveforms are then recalled from memory  818 , a fit function performed  820  on each waveform and the fitted waveform is then added to a histogram file  822   a  or  822   b . Two histogram files are available in the present embodiment for the fitted waveforms, number of electrons versus rise time or the height of the pulse step versus rise time.  
         [0046]     An example of code to accomplish the fit step is shown in Table 1 wherein the variables in the fit are a0, a1, a2, Ne, startpoint and endpoint where: 
    a0, a1, a2 are the quadratic background coefficients     Ne is the number of electrons     startpoint and endpoint are the starting and ending times of the pulse from which rise time is derived.    
 
         [0050]     These variables are determined for the pulse waveform. The known physical parameters of the detector are Ra and V 
    Ra is the fixed radius of the anode    
 
         [0052]     V is the electron velocity. V is determined empirically for each detector. A simple constant for V works to the first order although the actual V may be more complicated as described in Scaling Law for Electron Transport Coefficients in Mixture Xe+H2 with Various Concentrations of Molecular Impurities, V. M. Atrazhev, I. V. Chemysheva. E. V. Davydovskaya. V. V. Dmitrenko, Z. M. Uteshev, Proceedings of the International Seminar: “High Pressure Xenon: Fundamental Research, Detectors and Their Application” 2003 pp 200-201, ISBN 5-7262-0470-0  
               TABLE 1                           variable result       variable transit_time       variable ra=0.4       if (x &lt; startpoint)       result = a0 + a1*x + a2 * x * x + Ne * ln(1+V*(endpointstartpoint)/       ra)       else       if (x &lt; endpoint)       result = a0 + a1 * x + a2 *x*x + Ne * ln(1+V*(endpointx)/       ra)       else       result = a0 + a1 * x + a2 *x*x       endif       endif       transit_time =startpoint − endpoint       f(x) = result                  
 
         [0053]     The triggered waves are fit with a function of constant electron velocity and cylindrically symmetric field. The fit is a function of 6 parameters. Three are a quadratic baseline, which is fit throughout the entire region. Superimposed on this background is the detector ramp function. This is a function of the number of electrons inducing the pulse, the start time of the pulse, and the end time of the pulse. Each pulse fits (typically) in 5-20 iterations which takes 2-3 seconds and each result can be shown on the computer monitor and/or printed.  
         [0054]      FIG. 9  shows a variety of pulse shapes using a  137 Cs source. The raw data designated as “a” in the graphed pair is the digitized pulse and the line designated “b” is the fit that the fit routine previously described with respect to Table 1 produces for each pulse. The first row of curve fits  910   a  and  b ,  912   a  and  b ,  914   a  and  b  contains all fairly normal pulses. The second row  916   a  and  b ,  918   a  and  b  and  920   a  and  b  contains three multiple events. Curves  916   a  and  918   a  are probably multiple Compton events from the same gamma-ray, while curve  920   a  shows multiple events which are separated in time so far that they must be from separate gamma-rays (pile-up). Various pulse shapes have the classic shape corresponding to the logarithmic electric field in the detector ( 910   b ,  912   b  and  914   b ). Many pulses have a rounded edge at the top ( 910   b ). These pulses are presumably electron clouds caused by a single gamma-ray interaction with a large radial distribution of the electron cloud. The extent of this rounding varies with the pulse. The rounding leads to a large deviation in the fit at the end of the pulse created by the fitting algorithm&#39;s need to optimize the deviation through the entire pulse.  
         [0055]     Many pulses are modified by multiple events. Pulses  916   a ,  918   a  and  920   a  are examples of such pulses. While is impossible to tell what interaction caused a particular gamma-ray pulse, it is likely that events d and e are multiple interaction radii of a single gamma-ray at a single time. Event  920   a  is clearly distinct events from two separate gamma-rays. For the embodiment shown, a fit is accomplished for a single interaction radius and energy to the pulse. In fitting the pulse shape to multiple events, gamma-ray energy and interaction radii for each event are solved for in alternative embodiments. Events with non-physical radii combinations can be rejected. Clearly event  920   a  is not multiple interaction locations from a single gamma ray that occurred at one time, because the first electron cloud has stopped (was completely “collected”) before the second cloud is created. Using the interaction positions from the fit, it is possible to sensitively detect “pile-up” events. Using a standard Gaussian shaping amplifier, the pulses must be clearly separated before they can be rejected by a pile-up rejection routine. By fitting each pulse individually, events with very small separation can be rejected and events with significant separation can be saved and analyzed as two pulses. The fitting function gives an estimate for the error of every pulse fit. The error of fitting several typical pulses are shown in Table 2, below. The average error is 1.5%. This is completely consistent with the electronics error (pulser resolution of about 10 keV; 1.5%) for the components of the embodiment described herein.  
                                     TABLE 2                       Error   Amplitude   % error                                .118   8.732   1.35       .132   8.372   1.58       .119   12.315   0.97       .285*   12.298   2.32       .119   8.466   1.40               Average 1.52                 *this pulse is a multiple event/Compton pulse.             
 
         [0056]     Returning to the description with respect to  FIG. 8 , the histogram files created from the fitted pulses as either frequency at a certain type of gamma-ray event versus rise time versus the number of electrons or frequency versus rise time versus pulse step height or amplitude are printable to the monitor or printer.  FIGS. 10   a  through  10   d  graphically depict the histograms created.  
         [0057]      FIG. 10   a  shows a 3D plot demonstrating the two dimensional number of electrons versus rise time while  FIG. 10   b  shows a similar 3D plot for a two dimensional spectrum of pulse amplitude versus rise time.  FIG. 10   c  is the two-dimensional spectrum corresponding to  FIG. 10   a  while  FIG. 10   d  is the two dimensional spectrum corresponding to  FIG. 10   b .  FIGS. 10   c  and  d  are obtained by integrating the risetime dependence out of  FIGS. 10   a  and  b  respectively.  FIGS. 10   c  and  d  are the frequency versus energy plots in a form commonly referred to as spectra in the known art.  
         [0058]     Again returning to  FIG. 8 , the histogram data is then integrated  826  to provide energy data. Sorting of the histogram data  824  for discrimination of results is selectively accomplished to reduce effects of multiple interaction or pile-up events present in the data. Various detector phenomena can be corrected or discriminated as will be described subsequently. Sorting by rise time has been demonstrated to sharpen data results as will be described subsequently.  FIG. 11   a  is a digital reconstruction of the fit parameter Ne with the number of electrons inducing the charge pulse based on a least squares fit of the pulse as the ordinate. The number of electrons is the closest measure of gamma-ray energy available in the detector. For the data in  FIG. 11   a , sorted for only the top 50% of the rise times are summed. The electron velocity parameter was selected at 3.0. The peak to valley is about 8:1 and the resolution is about 10%.  FIG. 11   b  shows the same digitally reconstructed spectra with all rise times included. The resulting peak to valley is about 5:1 and the resolution is similar to  FIG. 11   a  at about 10%.  
         [0059]      FIG. 11   c  shows the pulse height spectra reconstruction. The overall pulse height based on the fit is the ordinate. No full-energy peak is visible. This is evidence that for the lower rise times, corresponding to the events nearest the anode, the pulse height is diminished such that it curves under the lower-energy events so badly that the peak disappears. As shown in  FIG. 11   d , the digital reconstruction for a sorting of the upper 50% of rise times restores the main gamma-ray peak-to valley ratio from 1:1 (no peak) to about 5:1. Furthermore, it restores the peak to valley of the largest 50% of the rise times from 2:1 to 9:1.  
         [0060]     Although prior art spectrometer systems provide gamma-ray energy information by eliminating position dependence, the position information provided in the present invention is also useful in refining the data due to several phenomena which are specifically position dependent within the detector. These phenomena are encompassed within the number of events versus energy data shown in  FIG. 12 .  
         [0061]     The first of these is X-Ray escape. Xenon detectors have an “x-ray escape” feature. This feature is caused when the energy of a xenon x-ray is not captured resulting in a misinterpretation of the energy of the gamma-ray. This is shown diagrammatically in  FIG. 12  as interaction  1202  and represented by region  1302  in  FIG. 12 . These events preferentially occur near the cathode or anode because the x-ray is able to escape from these positions. Hence the position information may be used to discriminate in favor of or against these events.  
         [0062]     Similarly in Compton Escape, Gamma-ray detectors have a feature where the gamma-rays are misinterpreted as a lower energy due to Compton scattering and the escape of the Compton scattered gamma-ray. The energy of the escape gamma-ray plus the detected gamma-ray energy sums to the actual gamma-ray energy. The high-energy Compton-escape events, or those closest to the photo peak shown in region  1308  of  FIG. 13 , result from the escape of a low-energy Compton scattered gamma-ray as represented by interaction  1208  in  FIG. 12 . These events will be preferentially near the surface of the detector. The full energy gamma-rays of this energy will be distributed more uniformly through the detector volume and hence may be discriminated in favor of or against these events.  
         [0063]     Low-energy Compton-escape events shown generally in region  1306  of  FIG. 13  resulting from high-energy gamma-rays result from the escape of a higher-energy gamma-ray. Low-energy gamma-rays interacting in the detector, interact preferentially near the outside surface of the detector. The escape events are more uniformly distributed through the volume of the detector. Hence the position information may be used to discriminate in favor of or against these events.  
         [0064]     It is also probable that other particles, specifically neutrons, may interact in the detector with a different depth profile than gamma-rays. In particular, it has been suggested that doping the detector with He-3 will make it sensitive to neutrons through the charged particle producing reaction of He-3 with a neutron producing a proton and a triton with 768 keV of energy. These interactions will have a different position character than gamma-ray interactions (a much more localized electron ionization cloud) hence may be discriminated in favor of or against these events.  
         [0065]      FIG. 14  shows an exemplary spectra in which the data selected for integration has been discriminated in favor of a low energy gamma-ray in the presence of interference caused by Compton scattering which is determined based on the position information available. The discrimination is achieved by utilizing the depth information to ignore interaction depths with low contributions to the effect for which observation is desired in favor of regions with high contribution to those effects. In  FIG. 13 , region  1306 B is ignored and data from region  1306 A is emphasized to construct the energy histogram in order to enhance a low energy gamma-ray in a background of Compton scattered interference.  
         [0066]     The peaks in the spectrum of  FIG. 14  are associated with the regions of interaction as shown in  FIG. 13  wherein peak  1402  corresponds to the X-ray escape events represented by region  1302  in  FIG. 13  which in turn, corresponds to the interaction diagrammatically represented as  1202  in  FIG. 12 . Similarly, the general interactions represented as interaction  1204  and by region  1304  resolve as peak  1404 . As previously described, the region  1306 A is emphasized in the calculation over regions  1306 B to capture the low-energy Compton escape events represented as  1206 , resulting in the peak  1406  in the spectrum. The Compton background depicted as  1408  is representative of region  1308  resulting from Compton scattering events represented by  1208  in  FIG. 12 . Finally, peak  1410  results from region  1310  which is representative of the high energy events occurring at all depths in the detector.  
         [0067]     Having now described the invention in detail as required by the patent statutes, those skilled in the art will recognize modifications and substitutions to the specific embodiments disclosed herein. Such modifications are within the scope and intent of the present invention as defined in the following claims.