U.S. patent application number 12/130671 was filed with the patent office on 2009-02-19 for method and apparatus for resolving individual signals in detector output data.
This patent application is currently assigned to Southern Innovation International Pty, Ltd.. Invention is credited to Robin John Evans, Paul Andrew Basil Scoullar.
Application Number | 20090048795 12/130671 |
Document ID | / |
Family ID | 36059646 |
Filed Date | 2009-02-19 |
United States Patent
Application |
20090048795 |
Kind Code |
A1 |
Scoullar; Paul Andrew Basil ;
et al. |
February 19, 2009 |
METHOD AND APPARATUS FOR RESOLVING INDIVIDUAL SIGNALS IN DETECTOR
OUTPUT DATA
Abstract
A method and apparatus for resolving individual signals in a
radiation detector output data. The method comprising: obtaining a
signal form characterizing the detector; obtaining digitized
detector output data in a form of a digital time series; making
parameter estimates of one or more parameters of at least one
signal present in the detector output data, wherein the one or more
parameters comprise at least a signal temporal position of the at
least one signal; forming a mathematical model based on the digital
time series and as a function of at least the signal form, the
temporal position of the at least one signal, and an amplitude of
the at least one signal; and determining the amplitude of the at
least one signal based on the mathematical model, the amplitude
being indicative of a radiation event.
Inventors: |
Scoullar; Paul Andrew Basil;
(Fitzroy North, AU) ; Evans; Robin John;
(Aspendale, AU) |
Correspondence
Address: |
KNOBBE MARTENS OLSON & BEAR LLP
2040 MAIN STREET, FOURTEENTH FLOOR
IRVINE
CA
92614
US
|
Assignee: |
Southern Innovation International
Pty, Ltd.
Melbourne
AU
|
Family ID: |
36059646 |
Appl. No.: |
12/130671 |
Filed: |
May 30, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11685719 |
Mar 13, 2007 |
7383142 |
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12130671 |
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PCT/AU2005/001423 |
Sep 16, 2005 |
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11685719 |
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Current U.S.
Class: |
702/66 |
Current CPC
Class: |
G01T 1/171 20130101;
G01T 1/202 20130101 |
Class at
Publication: |
702/66 |
International
Class: |
G06F 19/00 20060101
G06F019/00 |
Foreign Application Data
Date |
Code |
Application Number |
Sep 16, 2004 |
AU |
2004905364 |
Claims
1. A method of resolving individual signals in a radiation detector
output data, the method comprising: obtaining a signal form
characterizing the detector; obtaining digitized detector output
data in a form of a digital time series; making parameter estimates
of one or more parameters of at least one signal present in the
detector output data, wherein the one or more parameters comprise
at least a signal temporal position of the at least one signal;
forming a mathematical model based on the digital time series and
as a function of at least the signal form, the temporal position of
the at least one signal, and an amplitude of the at least one
signal; and determining the amplitude of the at least one signal
based on said mathematical model, the amplitude being indicative of
a radiation event.
2. The method as recited in claim 1, wherein obtaining the signal
form comprises receiving data about the signal form from a
memory.
3. The method as recited in claim 1, wherein obtaining the signal
form comprises deriving the signal form based on at least one
signal present in the detector output data.
4. The method as claimed in claim 1, further comprising determining
energy of the at least one signal based on at least the signal form
and the parameter estimates.
5. The method as recited in claim 1, further comprising determining
accuracy of the parameter estimates based on a comparison between
the detector output data and the mathematical model.
6. The method as recited in claim 1, wherein obtaining the signal
form comprises determining the signal form by measuring a response
of the detector to one or more detections.
7. The method as recited in claim 6, further comprising
interpolating the detector output data with a function to generate
an expected signal form, wherein the function comprises a
polynomial, exponential or spline function.
8. An apparatus for resolving individual signals in a radiation
detector output data, the apparatus comprising a processor
configured to: obtain a signal form characterizing the detector;
obtain digitized detector output data in a form of a digital time
series; make parameter estimates of one or more parameters of at
least one signal present in the detector output data, wherein the
one or more parameters comprise at least a signal temporal position
of the at least one signal; form a mathematical model based on the
digital time series and as a function of at least the signal form,
the temporal position of the at least one signal, and an amplitude
of the at least one signal; and determine the amplitude of the at
least one signal based on the mathematical model, the amplitude
being indicative of a radiation event.
9. The apparatus as recited in claim 8, wherein the processor is
configured to obtain the signal form from a memory.
10. The apparatus as recited in claim 8, wherein the processor is
configured to obtain the signal form by deriving the signal form
based on at least one signal present in the detector output
data.
11. The apparatus as recited in claim 8, wherein the processor is
further configured to determine energy of the at least one signal
based on at least the signal form and the parameter estimates.
12. The apparatus as recited in claim 8, wherein the processor is
further configured to determine accuracy of the parameter estimates
based on a comparison between the detector output data and the
mathematical model.
13. The apparatus as recited in claim 8, wherein the processor is
further configured to determine the signal form by measuring a
response of the detector to one or more detections.
14. The apparatus as recited in claim 13, wherein the processor is
further configured to interpolate the detector output data with a
function to generate an expected signal form, wherein the function
comprises a polynomial, exponential or spline function.
15. A data storage medium storing instructions, when executed by a
processor, causing the processor to perform a method of resolving
individual signals in a radiation detector output data, the method
comprising: obtaining a signal form characterizing the detector;
obtaining digitized detector output data in a form of a digital
time series; making parameter estimates of one or more parameters
of at least one signal present in the detector output data, wherein
the one or more parameters comprise at least a signal temporal
position of the at least one signal; forming a mathematical model
based on the digital time series and as a function of at least the
signal form, the temporal position of the at least one signal, and
an amplitude of the at least one signal; and determining the
amplitude of the at least one signal based on said mathematical
model, the amplitude being indicative of a radiation event.
16. The data storage medium as recited in claim 15, wherein
obtaining the signal form comprises receiving data about the signal
form from a memory.
17. The data storage medium as recited in claim 15, wherein
obtaining the signal form comprises deriving the signal form based
on at least one signal present in the detector output data.
18. The data storage medium as recited in claim 15, further
comprising instructions that cause the processor to determine
energy of the at least one signal based on at least the signal form
and the parameter estimates.
19. The data storage medium as recited in claim 15, further
comprising instructions that cause the processor to determine
accuracy of the parameter estimates based on a comparison between
the detector output data and the mathematical model.
20. The data storage medium as recited in claim 15, further
comprising instructions that cause the processor to determine the
signal form by measuring a response of the detector to one or more
detections.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of U.S. patent
application Ser. No. 11/685,719, filed Mar. 13, 2007, titled
"METHOD AND APPARATUS FOR RESOLVING INDIVIDUAL SIGNALS IN DETECTOR
OUTPUT DATA," which is a continuation of International Application
No. PCT/AU2005/001423, filed Sep. 16, 2005, which claims the
benefit of Australian Patent Application No. 2004905364, filed Sep.
16, 2004. Each of the foregoing applications is incorporated by
reference in its entirety.
BACKGROUND
[0002] 1. Field
[0003] The present invention relates generally to the field of the
detection and measurement of radiation and in particular, though
not exclusively, to a method and apparatus for the recovery, from a
radiation detector, of data affected by pulse pile-up.
[0004] 2. Description of the Related Technology
[0005] The accurate detection and measurement of radiation is
employed in many industries including homeland security, scientific
instrumentation, medical imaging and the minerals processing
industry. These and other industries use the detection and
measurement of radiation for the non-invasive analysis of materials
or other specimens. Transmission based imaging, spectroscopic
analysis or other modalities can be used to perform such
analysis.
[0006] Spectroscopy, for example, is commonly used to analyze
materials. Knowledge about the material is obtained by analysis of
radiation emission from elements within the specimen. This emission
of radiation can be stimulated emission due to some form of
incident radiation or the result of natural emission from the
constituent elements.
[0007] Gamma-ray spectroscopy, for example, is a form of
spectroscopy in which the emitted electromagnetic radiation is in
the form of gamma-rays. In gamma-ray spectroscopy the detection of
the resulting radiation is commonly performed with a scintillation
crystal (such as thallium-activated sodium iodide, NaI(Tl)), though
there are a number of other detector types that can also be used.
NaI(Tl) crystals generate ultra-violet photons pursuant to incident
gamma-ray radiation. These photons may then be directed to a
photomultiplier tube (PMT) which generates a corresponding
electrical signal or pulse. As a result, the interaction between
the photons and the detector gives rise to pulse-like signals, the
shape of which is determined by the incident gamma-ray radiation,
the detecting crystal and the PMT. The fundamental form of these
pulse-like signals is referred to as the impulse response of the
detector.
[0008] The output from the photomultiplier is an electrical signal
representing the summation of input signals, of determined form,
generated in response to discrete gamma rays arriving at the
scintillation crystal. By examining the detector output over time,
and in particular the amplitude of the component signals, it is
possible to deduce information regarding the chemical composition
of the material.
[0009] Analysis by gamma-ray spectroscopy requires the
characterization of the individual signals generated in response to
incident gamma-rays. Signal parameters of particular interest
include signal amplitude, number and time of occurrence or temporal
position (whether measured as time of arrival, time of maximum or
otherwise). If the arrival times of two gamma-rays differ by more
than the response time of the detector, analysis of the detector
output is relatively straightforward. However, in many applications
a high flux of gamma-rays cannot be avoided, or may be desirable so
that spectroscopic analysis can be performed in a reasonable time
period. As the time between the arrivals of gamma-rays decreases,
characterization of all resultant signals becomes difficult.
[0010] In particular, the analysis is affected by a phenomenon
known as pulse pile-up [G. F. Knoll, Radiation Detection and
Measurement, 3rd edition, Chapter 17, pp. 632-634, 658 and 659,
John Wiley and Sons, New York 2000], whereby multiple gamma-rays
arriving more or less simultaneously produce signals which sum
together and may be counted as a single signal. The magnitude of
this combined signal is greater than the individual components,
leading to errors in later analysis.
[0011] The energy of an incident gamma-ray may be reflected in the
amplitude of the pulse-like signal produced by the detector. The
presence of specific gamma-ray energies within the detector signal
is indicative of particular elements in the material from which
gamma-rays originate. Thus, a failure to differentiate a large
amplitude signal caused by a single scintillation event from the
superposition of multiple events can have a serious effect on the
accuracy of subsequent spectroscopic analysis.
[0012] Some existing techniques aim to prevent corruption of the
spectroscopic analysis due to pulse pile-up. Certain pulse shaping
electronics have been shown to reduce the response time of the
detector resulting in a diminished prevalence of pile-up in the
final spectrum [A. Pullia, A. Geraci and G. Ripamonti, Quasioptimum
.gamma. and X-Ray Spectroscopy Based on Real-Time Digital
Techniques, Nucl. Inst. and Meth. A 439 (2000) 378-384]. This
technique is limited, however, by detector response time. Another
approach is `pulse pile-up rejection` whereby signals suspected to
contain pulse pipe-up are discarded. Only signals free from pulse
pile-up are used in spectroscopic analysis. However, as the rate of
radiation incident on the detector increases, so too does the
likelihood that pulse pile-up will occur and the more it is
necessary to discard data. Accordingly, existing pulse pile-up
rejection is of limited usefulness since a state is quickly reached
beyond which a higher incident radiation flux ceases to reduce the
time needed for analysis, as an increasing percentage of data must
be rejected.
[0013] A more sophisticated approach is to make use of prior
knowledge about the profile of a single pulse from the detector or
to model mathematically the parameters of a signal. It is then
possible in principle to distinguish signals or pulses that
originate from a single event from those caused by pulse pile-up.
In one such method of analysis [R. J. Komar and H.-B. Mak, Digital
signal processing for BGO detectors, Nucl. Inst. and Meth. A 336
(1993) 246-252], signals that depart from the simple profile are
selected for subsequent analysis. This analysis involves fitting,
via an iterative process, two pulses of varying separation and
amplitude. Once the fit has been determined, the characteristics of
the individual pulses are known from the fitting parameters and
hence a pulse arising from two closely occurring signals can be
decomposed into the corresponding discrete signals. However, this
approach fails to accommodate circumstances where pulse pile-up is
caused by the superposition of more than two signals. The iterative
optimization is computationally expensive and the time taken to
carry out this procedure renders it impractical in most
situations.
SUMMARY
[0014] According to a first aspect of the invention, therefore,
there is provided a method for resolving individual signals in
detector output data, comprising determining a signal form of
signals present in the data (or the impulse response), making
parameter estimates of one or more parameters of the signals,
wherein the one or more parameters comprise at least signal
temporal position, and determining the energy of the signals from
at least the signal form and the parameter estimates.
[0015] Thus, this method endeavors to characterize as much data as
possible, but it will be appreciated that it may not be possible to
adequately characterize some data (which hence is termed `corrupt
data`), as is described below. It will be understood that the term
`signal` is interchangeable in this context with `pulse`, as it
refers to the output corresponding to individual detection events
rather than the overall output signal comprising the sum of
individual signals. It will also be appreciated that the temporal
position (or timing) of a signal can be measured or expressed in
various ways, such as according to the time (or position in the
time axis) of the maximum of the signal or the leading edge of the
signal. Typically this is described as the arrival time (`time of
arrival`) or detection time.
[0016] It will also be understood that the term `detector data`
refers to data that has originated from a detector, whether
processed subsequently by associated or other electronics within or
outside the detector.
[0017] The method may include constructing a model of the data from
the parameter estimates, and determining the accuracy of the
parameter estimates based on a comparison between the detector
output data and the model.
[0018] The signal form (or impulse response) may be determined by a
calibration process that involves measuring the detector's time
domain response to one or more single event detections to derive
from that data the signal form or impulse response. A functional
form of this signal form may then be obtained by interpolating the
data with (or fitting to the data) a suitable function such as a
polynomial, exponential or spline. A filter (such as an inverse
filter) may then be constructed from this detector signal form. An
initial estimate of signal parameters may be made by convolution of
the output data from the detector with the filter. Signal
parameters of particular interest include the number of signals and
the temporal position (or time of arrival) of each of the
signals.
[0019] The particular signal parameters of interest can then be
further refined. Firstly, the estimate of the number and arrival
times of signals is refined with the application of peak detection
and a threshold. Secondly, knowledge of the number of signals and
their arrival time, coupled with the detector impulse response (and
hence signal form) makes it possible to solve for the energy
parameters of the signals.
[0020] The accuracy of the parameter estimation can be determined
or `validated` by comparing a model (in effect, an estimate) of the
detector data stream (constructed from the signal parameters and
knowledge of the detector impulse response) and the actual detector
output. Should this validation process determine that some
parameters are insufficiently accurate, these parameters are
discarded. In spectroscopic analysis using this method, the energy
parameters deemed sufficiently accurate may be represented as a
histogram.
[0021] The method may include making the estimates of signal
parameters in accordance with the signal form (i.e. the impulse
response of the detector used for generating the signal). The
method may include determining the signal form by a calibration
process including measuring the response of the detector to one or
more single detections to derive a data based model of the signal
form. In particular, the method may include obtaining a functional
form of the model by interpolating the data with a function to
generate the expected signal form. The function may be a
polynomial, exponential or spline function.
[0022] The method may include designing a filter on the basis of
the predetermined form of the individual signals produced by the
radiation detector. The filter may be, for example, of matched
filter or inverse filter form.
[0023] In one embodiment, the method includes using convolution of
the detector output and filter to make an initial estimate of the
signal parameters. The method may include refining the estimate of
the signal parameters. The method may include refining the estimate
of signal number with a peak detection process. The method may
include making or refining the estimate of signal temporal position
by application of a peak detection process. The method may include
refining the estimate of signal energy by solving a system of
linear equations, by matrix inversion or by iterative
techniques.
[0024] In an embodiment of the invention, the method includes
creating a model of the detector output using the signal parameters
in combination with the detector impulse response. The method may
include performing error detection by, for example, comparing the
actual detector output data with the model of the detector output,
such as by using least-squares or some other measure of the
difference between the data and the model.
[0025] The method may include discarding parameters deemed not
sufficiently accurately estimated.
[0026] In one embodiment, the method includes presenting all
sufficiently accurate energy parameters in a histogram.
[0027] The data may include signals of different forms. In this
case, the method may include determining where possible the signal
form of each of the signals.
[0028] For example, in some detectors the signal form depends on
the depth within the detector at which the radiation/detector
interaction occurs. In other detectors, the signal form may depend
on how much time has elapsed since the previous radiation/detector
interaction occurred in the same region of the detector.
[0029] In one embodiment, the method includes progressively
subtracting from the data those signals that acceptably conform to
successive signal forms of a plurality of signal forms, and
rejecting those signals that do not acceptably conform to any of
the plurality of signal forms.
[0030] In another aspect, the invention provides an apparatus for
pulse pile-up recovery from data comprising a plurality of signals
output from a radiation detector. The term `recovery` is used
because data that would otherwise be unusable owing to pile-up is
`recovered` and rendered useable. The apparatus of this aspect
comprises a processor for receiving the data in digitized form, and
is programmed to determine the signal form of each of said signals
present in the data, to make parameter estimates of one or more
parameters of the signals, and to determine the energy of the
signals from at least the signal form and the parameter estimates,
wherein the one or more parameters comprise at least signal
temporal position.
[0031] The apparatus may include an analog to digital converter
adapted to receive the data, to convert the data into digitized
form, and forward the data in digitized form to the processor. This
would be of particular use where the detector outputs analog
data.
[0032] The processor may comprise a field programmable gate array
(or an array thereof). Alternatively, the processor may comprise a
digital signal processor (or an array thereof). In a further
alternative, the processor comprises a field programmable gate
array (or an array thereof) and a digital signal processor (or an
array thereof). The apparatus may include an analog front end that
includes the analog to digital converter.
[0033] The apparatus may include an electronic computing device in
data communication with the processor, for controlling the
processor and for displaying an output of the processor. The
apparatus may include the radiation detector.
[0034] The apparatus may be, for example, a metal detector, a
landmine detector, a medical imaging apparatus, a mineral detection
apparatus, an oil well logging apparatus, an unexploded ordnance
detector, a cargo screening apparatus, an X-ray fluorescence
apparatus or an X-ray diffraction apparatus.
[0035] According to still another aspect of the invention, there is
provided a method for resolving individual signals in detector
output data, comprising determining the form of signals present in
the data, and making parameter estimates of one or more parameters
of the signals from at least the form, wherein the one or more
parameters comprise at least signal temporal position.
[0036] According to another aspect of the invention, there is
provided a method for pulse pile-up recovery from detector output
data, comprising determining the form of signals present in the
data, making parameter estimates of one or more parameters of the
signals, wherein the one or more parameters comprise at least
signal temporal position, and determining the energy of the signals
from at least the form and the parameter estimates.
BRIEF DESCRIPTION OF THE DRAWINGS
[0037] In order that the invention may be more clearly ascertained,
preferred embodiments will now be described, by way of example
only, with reference to the accompanying drawing, in which:
[0038] FIG. 1 is a view of a gamma-ray spectroscopy apparatus
according to an embodiment of the present invention;
[0039] FIG. 2 is a view of a Sodium Iodide NaI(Tl) gamma-ray
detector of the apparatus of FIG. 1;
[0040] FIGS. 3a, 3b and 3c are graphs illustrating pulse
pile-up.;
[0041] FIG. 4 is a diagram illustrating the mathematical modeling
of radiation detection used by the signal processing method
embodied in the apparatus of FIG. 1;
[0042] FIG. 5 is a diagram detailing the mathematical model of
radiation detection used by the signal processing method embodied
in the apparatus of FIG. 1;
[0043] FIG. 6 is a schematic diagram of the apparatus of FIG.
1;
[0044] FIGS. 7a, 7b and 7c are plots of unprocessed digitized data
collected directly from the output of the detector of FIG. 2 over
time ranges of 1000 microseconds, 100 microseconds and 10
microseconds respectively;
[0045] FIG. 8 is a schematic representation of the signal
processing method for pulse pile-up recovery employed by the
apparatus of FIG. 1 for analyzing spectroscopic data according to
this embodiment of the invention;
[0046] FIG. 9 is a schematic flowchart of the signal processing
method for pulse pile-up recovery employed by the apparatus of FIG.
1 for analyzing spectroscopic data according to this embodiment of
the invention;
[0047] FIGS. 10a, 10b and 10c are plots of the results at different
stages of the signal processing method of FIG. 9;
[0048] FIG. 11 are plots of gamma-ray spectra for a 137Cs source at
various input count rates, processed with the method of FIG. 9;
[0049] FIG. 12 is a plot of the results of a computer simulation of
the signal processing method of FIG. 9 prepared using a simulated
data set produced by a digital nuclear pulse generator;
[0050] FIG. 13 is plot of the performance of the simulation of FIG.
12 for a gamma-ray source over a range of count rates;
[0051] FIGS. 14a, 14b, 14c and 14d depict the results of applying
the signal processing method of FIG. 9 to the output of a 76
mm.times.76 mm NaI(Tl) gamma-ray detector;
[0052] FIGS. 15a, 15b, 15c and 15d depict the results of applying
the signal processing method of FIG. 9 to data collected with a
HPGe detector; and
[0053] FIGS. 16a, 16b, 16c and 16d depict the results of applying
the signal processing method of FIG. 9 to the output of a Xenon gas
proportional detector.
DETAILED DESCRIPTION OF EMBODIMENTS
[0054] FIG. 1 is a schematic view of a gamma-ray spectroscopy
apparatus adapted to perform pulse pile-up recovery according to an
embodiment of the present invention, with an item to be analyzed.
The apparatus of FIG. 1 includes a neutron generator (10) for
generating neutrons for interacting with an item under analysis or
specimen (12), and a detector unit (14), in the form of a
scintillation based gamma-ray radiation detector, for detecting
gamma-ray radiation resulting from the interaction of neutrons and
the specimen (12). The detector unit includes sensors or detector
elements (16) that each has a scintillation crystal (in this
example, sodium iodide) coupled to a photomultiplier tube (not
shown). It will be appreciated that the apparatus could readily be
modified, particularly by substituting a different form of detector
unit, to detect other forms of radiation.
[0055] The apparatus also includes a signal processing unit (18)
that comprises two parts: 1) an analog to digital converter which
produces a digital output corresponding to the analog output of the
detector unit, and 2) a processing unit which implements digital
signal processing (DSP) routines in accordance with the invention.
The electrical output signals of the photomultiplier tubes are
connected to the signal processing unit. The apparatus also
includes cables (20) and a computer (22) for display, the former
for coupling the output from the signal processing unit to the
computer (22).
[0056] FIG. 2 is a view of one of the detector elements (16). The
illustrated detector element is in the form of a NaI(Tl)
scintillation based gamma-ray detector, and comprises a cylindrical
housing in the form of aluminium body (24) with a NaI(Tl) crystal
(26) located therein at one (forward) end positioned between an
aluminium outer end cap (28) (forward of the NaI(Tl) crystal (26))
and an inner optical window (30) (rearward of the NaI(Tl) crystal
(26)). The detector includes a photomultiplier tube (32) rearward
of the optical window (30). Optical coupling fluid (34) may be used
between the NaI(Tl) crystal (26) and the optical window (30), and
between the optical window (30) and the photomultiplier tube
(32).
[0057] When a gamma-ray interacts with the detector by passing into
the detector through the end cap (28), energy is transferred from
the gamma-ray to electrons within the NaI(Tl) crystal (26). Upon
the emission of ultra-violet photons the electrons lose said
energy) promoting electrons within the crystal to excited states.
Upon the emission of ultra-violet photons the electrons decay to
lower energy states. The aforementioned ultra-violet photons pass
through the optical window to the photocathode (36) of the
photomultiplier tube (32) where they are converted into
photoelectrons and subsequently multiplied by an electron
multiplier (38) before arriving at the anode (40) of the
photomultiplier tube (32). A further multiplication stage can be
provided by a preamplifier (42). In this manner an electrical
signal, whose amplitude is proportional to the energy of the
incident gamma-rays, is present at the detector output terminals
(44) of the detector. It will also be appreciated that the detector
may additionally include a mu metal magnetic shield (46) located
about the sides (48) of the photomultiplier tube (32) and extending
forwardly of the photomultiplier tube (32) sufficiently far to
surround a portion of the NaI(Tl) crystal (26).
[0058] Scintillation detectors of the kind last described have high
efficiencies, that is, exhibit a high probability of detecting an
incident gamma-ray. However, they also exhibit a relatively long
detector response time. The detector response time is the time
required by the detector to detect an incident gamma-ray and return
to a state where the next incident gamma-ray can be accurately
detected. Radiation detectors with long detector response times are
thus prone to pulse pile-up. That is, the output, which ideally
consists of completely discrete pulses each corresponding to the
incidence of a single gamma-ray, instead exhibits a waveform in
which individual pulses can overlap making them difficult to
characterize.
[0059] FIGS. 3a, 3b and 3c illustrate the effect of pulse pile-up,
and show illustrative signals or pulses plotted as energy E versus
time t (both in arbitrary units). FIG. 3a illustrates so-called
`tail-end pile-up` where, depending on the type of pulse
conditioning employed, the tail (50) of one pulse (51) can provide
a significant positive or negative bias (positive in the
illustrated example) to the amplitude of a subsequent pulse (52).
Although the time displacement between the two pulses, .DELTA.t, is
relatively large (when compared with the overall time interval for
which the pulses prevail), the signal envelope or resultant
waveform (54) is significantly above zero at the arrival of the
second pulse (52).
[0060] The absence of a true zero signal state between the two
pulses corrupts the pulse characterization, as the amplitude of the
second pulse is falsely inflated by the tail of the first. FIG. 3b
illustrates another form of pulse pile-up, `peak pile-up`. Here two
pulses (56) and (58) arrive closely spaced in time (i.e. the time
displacement .DELTA.t between the pulses is small compared with the
overall time interval over which the pulses prevail). The resultant
output waveform (60) appears more or less as a single pulse of
somewhat greater amplitude than either of the component pulses. In
situations where the flux of gamma-rays through the detector is
extreme, it is not uncommon to have multiple events arriving within
the response time of the detector leading to multiple pile-up
events. Such a case is illustrated by FIG. 3c. Multiple signals or
pulses (such as those shown at 62) arrive with random time
separation .DELTA.t and sum to produce a resultant waveform (64)
from which the parameters of the component signals are difficult to
extract.
[0061] One component of the method of addressing pulse pile-up
according to this embodiment is the estimation of certain
parameters of the signals or pulses; these parameters are the
number, time-of-arrival and energy of all gamma-rays in the
detector data stream. These parameters are estimated, according to
this embodiment, by modeling the signals in the data stream
mathematically. The model employed in this embodiment includes
certain assumptions about the data and the apparatus, as are
discussed below.
[0062] FIG. 4 is a diagram that illustrates the modeling of the
radiation detection process. The radiation g(t) (70) is incident on
the detector (72) represented by the measurement process m(t),
resulting in output data from the detector y(t) (74). The addition
of a sampling process (76) produces the digital detector data or
`time-series` x[n] (78).
[0063] It is possible to add to the above-described model some
knowledge about the physical processes of radiation detection. FIG.
5 illustrates a more detailed mathematical model of the detection
process shown in FIG. 4. The input g(t) to the detector is
characterized by Equation 1, in which the input g(t) is assumed to
be an unknown number (N) of delta-function-like impulses of random
amplitude (.alpha.) and time of arrival (i). An illustrative
example of such input is shown at (80).
g ( t ) = i = 1 N .alpha. i .delta. ( t - .tau. i ) i = 1 , 2 , 3 ,
, N . ( 1 ) ##EQU00001##
[0064] The radiation detector is assumed to have a specific
response to the incoming radiation, referred to as the detector
impulse response d(t) (or, equivalently, the signal form of the
signals in the data), which is illustrated at (82). The digitized
version of the detector impulse response (i.e. signal form) is
denoted d[n].
[0065] The output from the detector is shown at (86) and
characterized by Equation 2, in which the detector output y(t) is
the sum of an unknown number of signals of predetermined signal
form d(t), with unknown energy (.alpha.) and unknown time of
arrival (.tau.). Sources of random noise .omega.(t) (84) are also
considered. The digital detector data x[n] (88) is produced by the
analog to digital converter (76).
y ( t ) = i = 1 N .alpha. i d ( t - .tau. i ) + .omega. ( t ) i = 1
, 2 , 3 , , N . ( 2 ) ##EQU00002##
[0066] The digitized signal x[n] (which constitutes a time series
of data) at the output of the analog to digital converter (76), as
illustrated at (88), is therefore given by
x [ n ] = i = 1 N .alpha. i d [ n - .DELTA. i ] + .omega. [ n ] , (
3 ) ##EQU00003##
where d[n] is the discrete time form of the signal form d(t),
.DELTA..sub.i is the delay in samples to the ith signal, and
.omega.[n] is the discrete time form of the noise. The digitized
signal x[n] may also be written in matrix form as
x=A.alpha.+.omega., (4)
where A is an M.times.N matrix, the entries of which are given
by
A ( n , i ) = { d [ n - .DELTA. i ] .DELTA. i .ltoreq. n < min (
M , .DELTA. i + T - 1 ) 0 otherwise . ( 5 ) ##EQU00004##
[0067] Also, T is the length of d[n] in samples, M is the total
number of samples in the digitized signal x[n], .alpha. is the
vector of N signal energies, and .omega. is the noise vector of
length M. Matrix A may also be depicted as follows:
A = [ 0 0 0 0 d [ 1 ] d [ 2 ] 0 d [ 1 ] d [ T ] 0 d [ 1 ] d [ T ] d
[ 2 ] 0 0 d [ r < T ] ] .rarw. row .DELTA. 1 .rarw. row .DELTA.
2 .rarw. row .DELTA. N ##EQU00005##
[0068] Thus, the columns of matrix A contain multiple versions of
the signal form. For each of the individual columns the starting
point of the signal form is defined by the signal temporal
position. For example, if the signals in the data arrive at
positions 2, 40, 78 and 125, column 1 of matrix A will have `0` in
the first row, the 1st datum point of the signal form in the second
row, the 2nd datum point of the signal form in the 3rd row, etc.
The second column will have `0` up to row 39 followed by the signal
form. The third column will have `0` up to row 77; the fourth
column will have `0` up to row 124 and then the signal form. Hence
the size of matrix A is determined by the number of identified
signals (which becomes the number of columns), while the number of
rows depends on the number of samples in the time series.
[0069] The signal processing method of this embodiment thus
endeavors to provide an accurate estimate of some unknown
parameters of the detector data, including not only the number of
component signals (N) in the detector output but also the energy
(.alpha.) and time-of-arrival (.tau.) of each of the component
signals.
Signal Processing Method
[0070] FIG. 6 is a schematic diagram of the functional elements of
the gamma-ray spectroscopy apparatus of FIG. 1, and is provided to
explain in more detail the signal processing method for pulse
pile-up recovery employed by the apparatus of FIG. 1. Referring to
FIG. 6, the radiation detector unit (14) is connected to a pulse
processing board (92) via an analog front end (AFE 94). The purpose
of the AFE (94) is to digitize the signal produced by the radiation
detector unit (14) by performing analog to digital conversion at,
in this embodiment, 125 MHz with 12-bit conversion accuracy.
[0071] FIGS. 7a, 7b and 7c illustrate the waveform resulting from
such digitization, over time ranges of 1000 microseconds, 100
microseconds and 10 microseconds respectively. The various peaks in
these figures correspond to the detection of respective gamma-rays.
Some peaks appear as discreet signals or pulses (110, 112) which
may indicate the presence of only a single gamma-ray. Other peaks
are due to the pile-up either of two peaks (116) or of three or
more peaks (114).
[0072] After the output of the radiation detector unit (14) has
been digitized by the AFE (94), the signal processing method for
pulse pile-up recovery is implemented. Referring again to FIG. 6,
the digital signal produced by the AFE (94) is passed into the
pulse processing Field Programmable Gate Array (FPGA) (96). The
pulse processing FPGA (96) then implements the pulse processing
method of this embodiment; a digital signal processing coprocessor
(98) may optionally be used to assist the pulse processing FPGA
(96) to implement the pulse processing method. Variables required
by the pulse processing FPGA (96) and data produced at interim
steps of the pulse processing method are optionally stored in
memory (100). The signal processing is controlled via a
Data/Control Interface (102) which, in conjunction with a Control
Processor (104), can be used to modify the implementation of the
signal processing. The output data from the signal processing
method can be displayed on a display (106) via the Data/Control
Interface (102). Display (106) is provided in a computer that may,
if desired, be used to perform post-processing and system
control.
[0073] FIG. 8 is a schematic diagram of the signal processing
method for pulse pile-up recovery of radiation signals in the
detector time series of this embodiment. The digitized detector
signal (from AFE (94)) forms the input (120) for this signal
processing method. Offline System Characterization (122) is used to
determine the detector impulse response unique to the particular
digitized detector signal. Characterization data generated in
System Characterization phase (122) is use in a Pulse Localization
phase (124). The Pulse Localization phase (124) estimates, in
real-time, the number and temporal position (or time-of-arrival) of
radiation pulses within the digitized detector signal. In a Pulse
Identification phase (126), the digitized detector signal, the
detector impulse response and the output from the Pulse
Localization phase (124) are used to determine the energy of the
signals or pulses. Validation (128) involves comparing the output
of the Pulse Identification phase (126) with the digitized detector
signal (120). If this comparison indicates that any of the pulse
parameters have been estimated inaccurately, those parameters are
rejected so that only valid data is output (130). The error signal
generated in the Validation phase (128) is also employed in System
Characterization (122). In circumstances where the detector impulse
response may change over time, such as owing to the aging of
components, temperature variations or increased radiation fluxes,
System Characterization (122) updates the detector impulse response
online and adaptively by employing the error signal. Such updating
of the detector impulse response may be performed with any suitable
adaptive method, such as least mean squares adaptation, normalized
least mean squares adaptation or recursive least squares adaptation
as described, for example, by S. Haykin [Adaptive Filter Theory,
4th Ed, Prentice Hall, 2002].
[0074] FIG. 9 is a flow diagram of the signal processing method of
this embodiment. At step (140), calibration is performed. This
involves Data Regularization or Conditioning (142), Data Selection
and Fitting (144) and Optimal Filter Construction (146). In Data
Regularization (142), calibration data (signals recorded at a low
incident radiation flux) are loaded from data files, the integrity
of these calibration data is checked and any bias in the baseline
of the data removed. Data Selection and Fitting (144) involves
selecting only that data corresponding to the detection of single
radiation events and constructing a data based model of the
detector impulse response. A functional form of this model is then
obtained by fitting a suitable function to the data, such as a
polynomial, exponential or spline function. This results in the
expected impulse response of the detector d[n]. Optimal Filter
Construction (146) employs this detector impulse response to
construct a suitable filter for the detector, such as an inverse
filter or a matched filter.
[0075] At step (150) data is acquired, but may be affected by
significant pulse pile-up. The data may be input (152) either from
a file or directly from the detector elements (16).
[0076] At step (160) signal processing routines are applied to
determine the amplitude and timing parameters of the signals in the
time series. Firstly the data is conditioned (162) to remove any
bias in the baseline of the data. Next, the detector data is
convoluted (164) with the filter derived in step (146) to provide
an initial estimate of the time-of-arrival parameters (.tau.) and
number of pulses (N). The timing parameters and estimate of the
number of pulses are then further refined (166) using a suitable
peak detection process, and the energy parameter (.alpha.) is
determined from .tau., N and the detector impulse response d[n]
(such as by linear programming, matrix inversion or convolution
techniques). Finally, from the number (N), energy (.alpha.), timing
(.DELTA.i) and detector impulse response (d[n]), an estimate of the
detector data stream ({circumflex over (x)}[n]) is made (168).
[0077] The parameter vector (.alpha.) may be determined by linear
programming or by solving the system of linear equations defined in
Equation 4 using a suitable method for solving such systems of
equations, such as one of those described, for example, by G. H.
Golub and C. F. Van Loan [Matrix Computations, 2nd Ed, Johns
Hopkins University Press, 1989].
[0078] At step (170) the validation phase (128) referred to above
is performed, which may be referred to as error checking as, in
this embodiment, validation involves determining an error signal
e[n], computed successively for the set of samples corresponding to
each signal i where 1.ltoreq.i.ltoreq.N (N being the total number
of signals in the data stream). This error signal is calculated by
determining (172) the squares of the differences between the time
series data x[n] and the model based data-stream ({circumflex over
(x)}[n] from step (168)); e[n] is thus the square of the difference
between x[n] and {circumflex over (x)}[n], as given in Equation
6.
e[n]=(x[n]-{circumflex over (x)}[n]).sup.2 (6)
[0079] If e[n] exceeds a predetermined threshold, these parameters
are rejected (174) as this condition indicates that the signal
parameters do not produce a model of the respective signal that
acceptably conforms to that signal (that is, is sufficiently
accurate); the relevant signal is deemed to constitute corrupted
data and excluded from further spectroscopic analysis. The
threshold may be varied according to the data and how closely it is
desired that the data be modeled; generally, therefore, in any
particular specific application, the method of validation and
definition of the threshold are chosen to reflect the requirements
of that application.
[0080] One example of such a threshold is the signal energy
.alpha.i multiplied by a suitable factor, such as 0.05. Validation
will, in this example, deem that the model acceptably conforms to
the data constituting signal i when:
e[n]>0.05.alpha..sub.i (7)
[0081] Validation may be performed by defining the error signal and
threshold in any other suitable way. For example, the error signal
may be set to the absolute value of the error. The threshold may be
defined to be a multiple other than 0.05 of the signal amplitude.
Another threshold comprises a number of noise standard
deviations.
[0082] Decreasing the threshold (such as by decreasing the
coefficient of .alpha.i in Equation 7) enables improved energy
resolution at lower throughput, while increasing the threshold
enables improved throughput at reduced energy resolution.
[0083] At step (180) a decision is made as to whether there is
sufficient data. If not, processing continues at step (150).
Otherwise, the method proceeds to step (190). At step (190) a
gamma-ray energy spectrum is created. The gamma-ray energy
parameters determined at step (166), which were deemed to be of
sufficient accuracy at step (174), are represented (192) in the
form of a histogram. This is the gamma-ray energy spectrum on which
spectroscopic analysis may be performed.
Results of Signal Processing Method
[0084] FIGS. 10a, 10b and 10c are plots of the results at various
stages of processing of the digital signal processing method
described above by reference to FIGS. 8 and 9, for digitized data
collected with a scintillation gamma-ray detector. The detector
data stream was digitized by an analog to digital converter at 125
MHz and 12 bit accuracy; the gamma-ray source used was a 137Cs
source with a primary gamma-ray emission of 661.7 keV.
[0085] Scintillation detectors employ light generated by the
detector/radiation interaction to detect and measure that incident
radiation. A scintillation detector may comprise organic
scintillators or inorganic scintillators. Organic scintillators
include both organic crystalline scintillators and liquid organic
solutions (where the scintillating material has been dissolved to
form a liquid scintillator, which can then be plasticized to form a
plastic scintillator. Inorganic scintillators include crystalline
scintillators such as NaI(Tl), BGO, CsI(Tl) and many others, and
photo switch detectors (in which a combination of two or more
dissimilar scintillators are optically coupled to a common PMT to
exploit the differing decay times of the scintillators to determine
where a radiation/detection interaction has occurred).
[0086] In this example the detector comprised a 76 mm.times.76 mm
NaI(Tl) gamma-ray scintillation detector. FIG. 10a is a plot of a
portion of the digitized detector data (200) prior to processing by
the signal processing method plotted as energy E(keV) versus time
t(.mu.s), together with the results (for example, at 210) of the
signal processing method plotted in terms of the temporal position
and energy of the component signals. For example, what may appear
to be a single peak (220) in the original digitized detector data
(200) at approximately 75.8 .mu.s has been resolved into two
distinct signals (222, 224) at respectively 75.3 and 75.7
.mu.s.
[0087] From the determined temporal positions, energies and forms
of the signals it is possible to generate a model of the detector
data. FIG. 10b is a plot of the resulting data model (230), shown
as energy E(keV) versus time t(.mu.s), of that portion of the
digitized detector data stream (200) shown in FIG. 10a. An inverted
error plot (240), comprising a plot of the squares of the
differences between the detector data (200) and the data model
(230), is also shown, and indicates the error in the model (230).
The error signal is small where the model (230) has tracked the
output of the detector accurately, but the error becomes large when
there are inconsistencies between the model (230) of the detector
data and the detector data (200) itself. Based on this error signal
(240), a decision can be made as to whether to accept or reject the
signal parameters estimated by the signal processing method.
[0088] FIG. 10c is a gamma-ray energy spectrum (250), shown as a
log-linear plot, produced by the signal processing method. The
energy parameters that have been accepted are plotted as a
histogram, where the horizontal axis represents the energy E(keV)
of each signal in a respective bin, and the vertical axis
represents the number of counts N of that energy determined to have
been detected in the collection period (in this example, 1 s).
[0089] FIG. 11 is a plot of exemplary gamma-ray energy spectra,
collected using a sodium iodide NaI(Tl) gamma-ray detector. The
gamma-ray energy spectra shown in FIG. 11 demonstrate the
performance of the signal processing method for pulse pile-up
recovery at a range of count rates. The experimental data were
collected using a 76 mm.times.76 mm Canberra brand NaI(Tl)
gamma-ray detector (model number 802) coupled to a detector base
(model number 2007); no preamplifier was used. The signal
processing hardware was connected to the dynode output of the
detector base via a 65 MHz 14-bit analog to digital converter.
[0090] The NaI(Tl) crystal was irradiated with a collimated
gamma-ray beam, which ensured that the central portion of the
detector was illuminated with an essentially parallel beam of
gamma-rays; the beam diameter was 50 mm.
[0091] Two 137Cs gamma-ray sources of 0.37 GBq and 3.7 GBq, in
combination with three calibrated aluminium transmission filters,
were used to obtain a range of gamma-ray fluxes at the detector
face. The detector to source distance remained constant during data
collection.
[0092] Referring to FIG. 11, the spectra (260), (262), (264),
(266), (268) and (270) were collected at count rates of
respectively 529 kHz, 230 kHz, 167 kHz, 124 kHz, 67 kHz and 9 kHz.
As would be expected, the energy resolution of the data collected
with the apparatus and processed with the method of this embodiment
deteriorated as the count rate increased. Expressed as a percentage
of the peak energy (i.e. 661.7 keV), the full width at half maximum
(FWHM) of the peak was found to be, respectively, 9.6% 7.3%, 7.1%,
6.9%, 6.7% and 6.7%. For count rates of 9 kHz to 230 kHz, the
energy resolution of the 137Cs gamma-ray energy peak at 661.7 keV
remained less than 7.5%; that is, despite more than a 25 fold
increase in the count rate from the NaI(Tl) detector, the energy
resolution at 661.7 keV decreased by less than 0.5%.
[0093] The performance of the signal processing method of this
embodiment is also illustrated in FIG. 12 and FIG. 13. These two
figures were generated from the results of a computer simulation,
in which the input count rate could be accurately controlled hence
enabling a very wide range of input count rates to be considered.
FIG. 12 is a log-log plot of the throughput of the signal
processing method (i.e. that portion of the input count rate
accurately detected) against input count rate from 0.1-2.5 MHz. The
theoretical limit (i.e. where the throughput equals the input) is
shown with a dashed line. This figure demonstrates that, over a
very wide range of input count rates, the throughput of the signal
processing method remains greater than or equal to 90%.
[0094] FIG. 13 is a linear-log plot comparable to FIG. 12 but with
percentage throughput plotted against input count rate from
0.005-10 MHz. In addition, FIG. 13 includes plots of the energy
resolution and peak position performance of the signal processing
method of this embodiment. The energy resolution of the 137Cs peak
degrades by less than 10% over 0-2.5 MHZ, and the peak position
shows very little change over that range.
[0095] FIGS. 14a, 14b, 14c and 14d also depict the results of
applying the signal processing method for pulse pile-up recovery of
this embodiment to the output of a 76 mm.times.76 mm NaI(Tl)
gamma-ray detector. Approximately 14 .mu.s of data was used to
generate the data plotted in these figures. The figures are plots
of energy E in arbitrary units against time t(.mu.s).
[0096] FIG. 14a is a plot of the output of the AFE (94): an analog
to digital conversion rate of 65 MHz and 14 bit resolution was used
to covert the time varying voltage output of the detector to
digital data. FIG. 14b is a plot of the results of applying the
method. The temporal positions of the signals (depicted as vertical
lines) have been resolved, as have the energies of the component
signal (depicted as crosses). The temporal position and the energy
of the component signal were used as described above, in
conjunction with the signal form, to determine a model of the
gamma-ray detector output: the resulting model is plotted in FIG.
14c.
[0097] The digitized output of the gamma-ray detector was compared
with the model of the gamma-ray detector output to derive an
estimate of the error made in characterizing the gamma-ray detector
output. This error signal is plotted in FIG. 14d. It is then
possible, on the basis of this error signal, to determine
thresholds for the exclusion of signal parameter estimates, such as
the decision to accept or reject an estimate of signal energy may
be determined by the magnitude or the error near the position of a
signal peak.
[0098] FIGS. 15a, 15b, 15c and 15d depict the results of applying
the signal processing method for pulse pile-up recovery of this
embodiment to data collected with a semiconductor (or solid state)
detector. Such detectors employ the interaction of incident
radiation with the electrons in the crystalline lattice of the
semiconductor, forming electron hole pairs. Examples of these
detectors include High-Purity Germanium (HPGe) detectors, Silicon
Diode detectors, semiconductor drift detectors (such as Silicon
Drift detectors), Cadmium Telluride (CdTe) detectors and CZT
detectors.
[0099] Hence, the apparatus of FIG. 1 was employed, though with a
detector unit in the form of a Canberra Industries brand High
Purity Germanium (HPGe) detector substituted for detector unit
(14), and with a 57Co gamma-ray source (whose two principal
gamma-rays have energies of 122.1 and 136.5 keV) rather than a
neutron source and specimen. The output of the HPGe detector was
fed through a pre-amplifier and then into an Ortec brand pulse
shaping amplifier. Approximately 92 .mu.s of data was collected,
from which was generated the data plotted in FIGS. 15a, 15b, 15c
and 15d as energy E in arbitrary units against time t(.mu.s). FIG.
15a is a plot of the output of the AFE (94). The time varying
voltage output of the detector was converted to digital data at an
analog to digital conversion rate of 65 MHz with 14 bit resolution.
FIG. 15b is a plot of the results of applying the method. The
temporal positions of the signals (depicted as vertical lines) have
been resolved, as have the energies of the component signal
(depicted as crosses). The temporal position, the energy of the
component signal and the signal form were used to determine a model
of the processed HPGe detector output, which is plotted in FIG.
15c.
[0100] FIG. 15d is a plot of the error signal, derived from a
comparison of the digitized processed output of the HPGe detector
and the model of that output. This error signal can again be used
to determine thresholds for the exclusion of signal parameter
estimates.
[0101] FIGS. 16a, 16b, 16c and 16d depict the results of applying
the signal processing method for pulse pileup recovery of this
embodiment to the output of a gas proportional detector used for
detecting X-rays. Gas proportional detectors are a class of
detector whose behavior is similar to that of solid state
detectors. Gas proportional detectors rely on the interaction of
the radiation with a gas in a chamber. An electric field is created
in the chamber between an axial wire and the walls of the chamber.
Radiation passing through the gas ionizes the gas, which produces
electrons that then collect on the wire owing to the electric
field, and are output as the detector data.
[0102] Thus, the apparatus of FIG. 1 was employed, though with a
detector unit in the form of a Xenon gas proportional detector
substituted for the detector unit (14), and with an X-ray generator
from an X-ray diffraction apparatus rather than a neutron source
and specimen. Approximately 300 .mu.s of data was used to generate
the data plotted in FIGS. 16a, 16b, 16c and 16d, which plot energy
E in arbitrary units against time t(.mu.s). A significantly longer
data collection period was used compared with that of the previous
examples, owing to the relatively long decay time of the xenon gas
proportional detector (of the order of 50 .mu.s or more). For this
reason also the sampling rate of the AFE (94) was reduced.
[0103] FIG. 16a is a plot of the output of the AFE (94); in this
example an analog to digital conversion rate of 15 MHz and 14 bit
resolution was used to covert the time varying voltage output of
the detector to digital data. FIG. 16b is a plot of the results of
applying the method. The temporal positions of the X-ray signals
(depicted as vertical lines) have been resolved, as have the
energies of the component signal (depicted as crosses). The
temporal position and the energy of the component signal were used
as described above, in conjunction with the signal form, to
determine a model of the Xenon gas proportional detector output:
the resulting model is plotted in FIG. 16c.
[0104] The digitized output of the Xenon gas proportional detector
was compared with the model of the Xenon gas proportional detector
output to derive an estimate of the error made in characterizing
the Xenon gas proportional detector output. This error signal is
plotted in FIG. 16d. This error signal can then be used to
determine thresholds for the exclusion of signal parameter
estimates, such as the decision to accept or reject an estimate of
signal energy may be determined by the magnitude or the error near
the position of a signal peak.
Plural Signal Forms
[0105] For some detector types, such as large volume solid state
detectors, the form of a given signal may be one of a plurality of
possible signal forms. This may be intrinsic to the detector type,
or be due to temperature or other measurement-specific factors.
[0106] For example, a CsI(Tl) detector is a scintillation detector
that, depending on whether a neutron or gamma-ray is being
detected, exhibits two distinct signal forms. Solid state radiation
detectors can exhibit a time-varying signal form, even when
detecting only one form of radiation; large volume High Purity
Germanium (HPGe) detectors, for example, can produce an output
signal whose form depends on the specific site of interaction
between the radiation and the detector. The interaction of
radiation with the Germanium crystal of a HPGe detector produces a
multitude of electron-hole pairs; radiation induced charge is
carried by both the electrons and the holes. However, the electrons
and holes travel through the HPGe detector at different velocities,
so the charge pulse produced by the electrons generally has a
different form from that produced by the holes. Thus, the pulse
produced by the detector (being the sum of the charges carried by
both the electrons and holes) has a form dependent on the location
of interaction.
[0107] Hence, the plurality of signal forms are the result of these
varied physical mechanisms. The respective signal forms may be
denoted d1[n], d2[n], . . . , dQ[n], where Q is the total number of
different signal forms that may be generated by a particular
detector type. Each of the possible signal forms is characterized
in the same way that the signal form of data having a single signal
form is characterized. With plural signal forms, however, the
calibration process must be extended for an appropriate length of
time to ensure that all of the possible signal forms have been
identified and characterized; the estimation of signal parameters,
including temporal position and signal energy, can be performed
once the form of each signal in the data stream has been
identified. In order to estimate these signal parameters correctly,
a number of possible extensions of the method described above (for
data with a single signal form) may be employed.
[0108] 1. The signal parameters, including signal temporal position
and signal energy, may be estimated for each signal in the data
stream by treating all signals in the data stream as having the
same form, such as of the first signal, viz. d1[n]. The parameters
for those signals that do not acceptably conform to signal form
d1[n] are rejected at the validation phase; signals for which the
parameters have been estimated successfully and thus acceptably
conform to signal form d1[n] are subtracted from the data stream.
This process is repeated successively for d2[n] up to dQ[n], where
at each stage signal parameters are estimated for signals that are
of the signal form used at that stage. At each stage matrix
Equation 4 is solved with matrix A constructed repeatedly using, in
iteration p, the signal form dp[n]. At the conclusion of the
process, those signals that have not passed the validation phase
for any of the plurality of signal forms are rejected as not
acceptably conforming to any of the plurality of signal forms.
[0109] 2. In a variation of the first approach, the signal
parameters are estimated for each of the signal forms in turn, but
the signal estimates are not subtracted at each stage. Instead, the
estimated signals are used in a final signal validation stage to
determine the signal form and signal parameters that provide the
best overall estimate of the data stream. This allows for the
possibility that a signal is incorrectly estimated to be of one
form, when it is actually of a form that has not yet been used to
estimate the signal parameters.
[0110] 3. In a further variation of the first approach, it may be
possible to model each of the signal forms dp[n] as a linear
combination of two signal forms, termed d1[n] and d2[n] for
convenience. Hence, the pth signal form dp[n] is modeled as:
d.sub.p[n]=(a.d.sub.1[n]+b.d.sub.2[n]) (8)
where a and b are unknown constants that can be determined directly
from this equation if necessary. In order to solve the matrix
equation in this case, the matrix equation is extended to be:
x = [ A 1 A 2 ] [ .gamma. .beta. ] + .omega. , ( 9 )
##EQU00006##
where the sub-matrices A.sub.1 and A.sub.2 are formed from the
signal forms d.sub.1[n] and d.sub.2[n] respectively using Equation
5. The vector of unknown signal energies a has been redefined as
being made up of vectors .gamma. and .beta., so that the energy of
the actual signal form of signal i can be estimated as
.alpha..sub.i=.gamma..sub.i+.beta..sub.i. The new system of linear
equations is solved using the same methods as those used to solve
the earlier matrix equation, Equation 4. It should be noted that
this approach eliminates the need for explicitly estimating the
unknown constants .alpha. and b, and also allows for the
possibility that the signal form may be from a continuum of
possible signal forms that can be represented as a linear
combination of the two signal forms d.sub.1[n] and d.sub.2[n].
[0111] Thus, this approach permits a practically unlimited number
of signal forms to be represented.
[0112] 4. In a further variation of approach 3, the procedure of
decomposition of each of the plurality of signal forms into a
linear combination of just two signal forms may be extended to the
general case where the plurality of signal forms may be decomposed
as a linear combination of an arbitrary number of signal forms. The
matrix A and the signal energy vector a is augmented
accordingly.
[0113] Modifications within the scope of the invention may be
readily effected by those skilled in the art. It is to be
understood, therefore, that this invention is not limited to the
particular embodiments described by way of example hereinabove.
[0114] In the claims that follow and in the preceding description
of the invention, except where the context requires otherwise owing
to express language or necessary implication, the word "comprise"
or variations such as "comprises" or "comprising" is used in an
inclusive sense, i.e. to specify the presence of the stated
features but not to preclude the presence or addition of further
features in various embodiments of the invention.
[0115] Further, any reference herein to prior art is not intended
to imply that such prior art forms or formed a part of the common
general knowledge.
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