Patent application title: System and Method For Measuring and Analyzing Target Emissions
Inventors:
George Vourvopoulos (Melbourne Beach, FL, US)
Daniel T. Holslin (San Deigo, CA, US)
Juan J. Martinez (San Diego, CA, US)
IPC8 Class: AG01T100FI
USPC Class:
250393
Class name: Radiant energy invisible radiant energy responsive electric signalling with radiant energy source
Publication date: 2012-07-05
Patent application number: 20120168635
Abstract:
An interrogation component is controllable between three detection/timing
modes: neutron generator OFF for predetermined amount of time (Mode 1),
neutron generator pulsing at 5-10 kHz/2-10 microseconds (Mode 2), and
neutron generator pulsing at 200-400 Hz/25-200 microseconds (Mode 3).
Utilizing the interrogation component in the three detection/timing modes
to inspect a target facilitates data collection in both passive and
active modes for both passive and stimulated emissions of gamma and
neutron radiation.Claims:
1. A method of interrogating the contents of a target comprising:
directing neutron pulses having a first frequency at the target;
detecting a first type of radiation emitted from the target in response
to the neutron pulses at the first frequency; directing neutron pulses
having a second frequency at the target; and detecting a second type of
radiation emitted from the target in response to the neutron pulse at the
second frequency.
2. The method according to claim 1, further comprising directing gamma radiation at the target and detecting at least a portion of the gamma radiation that passes through the target.
3. The method according to claim 1, further comprising detecting a third type of radiation emitted from the target that is not response to interrogation by the neutron pulses.
Description:
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] The current application is a divisional application of and incorporates by reference in its entirety U.S. application Ser. No. 11/033,552 entitled SYSTEM AND METHOD FOR MEASURING AND ANALYZING TARGET EMISSIONS filed Jan. 12, 2005, which claims the benefit of priority to U.S. Provisional Patent Application No. 60/602,041 entitled METHODS FOR ANALYZING TARGET EMISSIONS filed Aug. 17, 2004, also incorporated by reference.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The invention related generally to the field of target inspection to determine the contents thereof through radiation detection. The invention relates more specifically to the use of inspection systems and method.
[0004] 2. Description of the Related Art
[0005] The installation of cargo inspection systems has been instrumental in reducing the flow of illicit contraband into the United States. Although such systems were primarily installed for the detection of drugs, such systems have also contributed to stemming the occurrence of human trafficking and the flow of stolen vehicles. The role of current inspection systems is now being amplified as they are asked to not only look for illicit drugs but also for explosives and weapons of mass destruction. These cargo inspection systems are "anomaly" detectors. Currently, when an anomaly is detected, it can only be identified through an intrusive manual inspection which is inherently limited by the ability, condition and initiative of inspection personnel. This is a costly and time consuming operation which exposes inspection personnel to serious risks and has resulted in increasing delays at border crossings. Often it lacks the specificity to clearly identify the nature of the anomaly necessitating additional resources and/or the destruction of unverifiable suspect items. There is a need for companion devices that can provide identification of anomalies in a reliable, rapid and non-intrusive manner.
SUMMARY OF THE INVENTION
Summary of the Problem
[0006] There is a current need for the ability to inspect targets, e.g., vehicles, cargo and the like, arriving at ports of entry and other similar locations to secure the movement of freight to and from various countries. More particularly, explosives and weapons of mass destruction and the fundamental building blocks thereof, i.e., fissionable materials, are increasingly being trafficked between countries. While the gamma signature of unshielded fissile and fissionable materials can be easily observed by commonly available passive detector systems, this signature can be shielded with modest amounts of lead. For example, both HEU and weapons grade Plutonium (WGPu) have relatively low gamma ray emission rates that have an average low energy spectrum that is easily shielded. In contrast, neutron emissions from fissile materials, primarily from the 240Pu content in WGPu is virtually unaffected by equivalent amounts of lead shielding. Therefore, passive gamma-ray and neutron measurements are necessary and important but not sufficient tools for counter-terrorism and nuclear security applications.
[0007] While all nuclear material is applicable to detection with active interrogation, HEU has been demonstrated to be much more difficult to detect than plutonium due to its very low spontaneous neutron emissions and low-energy gamma-ray emissions. Passive gamma measurements of shielded HEU are very difficult to detect.
Summary of the Solution
[0008] The solution system and method described herein are based on a neutron interrogation with multiple-detector configuration that may be used to inspect targets, e.g., cargo and vehicles, for prohibited materials including, inter alia, explosives, chemical warfare agents, illicit drugs and special nuclear materials (SNM).
[0009] In a first embodiment of the present invention, an interrogation component for inspecting the contents of a target is described. The interrogation component includes a neutron generator capable of generating neutron pulses at a first frequency and at a second frequency and directing the first and second frequency neutron pulses at the target; a first detector configured to detect a first type of radiation emitted from the target in response to the first frequency neutron pulses; and a second detector configured to detect a second type of radiation emitted from the target in response to the second frequency neutron pulses.
[0010] In a second embodiment of the present invention, an interrogation system for inspecting a target is described. The interrogation system includes a first interrogation component including (i) a first neutron generator capable of generating neutron pulses at a first frequency and at a second frequency and directing the first and second frequency neutron pulses at the target; (ii) a first detector configured to detect a first type of radiation emitted from the target in response to the first frequency neutron pulses; and (iii) a second detector configured to detect a second type of radiation emitted from the target in response to the second frequency neutron pulses. The system further includes a second interrogation component including: (i) a second neutron generator capable of generating neutron pulses at a first frequency and at a second frequency and directing the first and second frequency neutron pulses at the target; (ii) a third detector configured to detect a first type of radiation emitted from the target in response to the first frequency neutron pulses; and (iii) a fourth detector configured to detect a second type of radiation emitted from the target in response to the second frequency neutron pulses. The first and second interrogation components are located on opposite sides of the target.
[0011] In a third embodiment of the present invention, a method of interrogating the contents of a target is described. The method includes directing neutron pulses having a first frequency at the target; detecting a first type of radiation emitted from the target in response to the neutron pulses at the first frequency; directing neutron pulses having a second frequency at the target; and detecting a second type of radiation emitted from the target in response to the neutron pulse at the second frequency.
BRIEF DESCRIPTION OF THE FIGURES
[0012] In the Figures:
[0013] FIGS. 1a and 1b show an interrogation component according to an embodiment of the present invention;
[0014] FIG. 2 shows a prior art neutron die away curve for depleted uranium;
[0015] FIG. 3 shows a neutron generator firing sequence according to an embodiment of the present invention;
[0016] FIGS. 4a and 4b show target inspection systems according to embodiments of the present invention;
[0017] FIG. 5 shows a neutron capture vs. time analysis for elemental identification according to an embodiment of the present invention;
[0018] FIG. 6 shows a neutron generator firing sequence according to an embodiment of the present invention; and
[0019] FIG. 7 shows process steps for data analysis according to an embodiment of the present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE PRESENT INVENTION
[0020] Referring to FIGS. 1a and 1b, a preferred target inspection system includes at least one detector/source interrogation component (hereafter "interrogation component") 10 that includes gamma radiation detectors 12 and neutron detectors 14 and at least one neutron source 16 on a height adjustable pillar 18. In a particular embodiment of the interrogation component 10, four gamma radiation detectors 12 are placed at the corners of a square, e.g., approximately 3 feet from each other. Each detector 12 includes by a cylindrical radiation shield 13b made of, e.g., lead or tungsten, to minimize the gamma rays coming from the background. Detection material 13a is recessed approximately 2 to 3 inches inside the radiation shield 13b to limit the area seen by the detector, thus increasing the signal to background ratio. Further, because the neutrons produced from the neutron generator are emitted isotropically in all directions, radiation shielding (trapezoid-shaped) 15 made of a combination of materials such as iron, lead, polyethylene, and borated polyethylene is placed between each detector and the neutron generator.
[0021] In a specific embodiment, the neutron generator 16, e.g., operating at 14 MeV, is configured to pulse neutrons approximately 2-10 microseconds wide in a first frequency range of approximately 5,000-10,000 Hz, in order to excite and detect gamma radiation from a first class of prohibited materials, e.g., explosives, chemical warfare agents, and illicit drugs. The emitted gamma radiation is detected with a first set of detectors 12 and subjected to chemical elemental analysis. A detailed description of an exemplary chemical elemental analysis method is described below and in U.S. Pat. Nos. 5,982,838 and 6,563,898 which are incorporated herein by reference in their entirety. The same neutron generator 16 also uses pulsed neutrons that are approximately 25-200 microseconds wide in a second frequency range, i.e., 200-400 Hz, in order to excite and detect neutron radiation from a second class of prohibited materials, e.g., special nuclear materials such as 235U or 240Pu, with a second set of detectors 14 using a differential die-away technique (DDAT). These stimulated neutrons emanating from the target have detectable characteristic decay curves which are detectable by the neutron detectors 14, e.g., Li-6 doped glass fibers, He-3 counters or the like, even when the fissionable materials are being intentionally shielded within the target. By way of example, the preferred target inspection system and method is capable of differentiating between 3 g and 6 g of 235U (1 kg and 2 kg of depleted uranium, respectively) as shown in FIG. 2 from the prior art.
[0022] Additionally, the interrogation component may also be utilized in a passive mode in order to detect gamma and/or neutron radiation with gamma detectors 12 and neutron detectors 14 that are being emitted from the target without the need for active interrogation. More particularly, referring to FIG. 3, in a preferred embodiment, the interrogation component is controllable between three detection/timing modes: neutron generator OFF for predetermined amount of time (Mode 1) 22, neutron generator pulsing at 10 kHz/10 microseconds (Mode 2) 20, and neutron generator pulsing at 200-400 Hz/25-200 microseconds (Mode 3) 24. Utilizing the interrogation component in the three detection/timing modes to inspect a target facilitates data collection in both passive and active modes for both passive and stimulated emissions of gamma and neutron radiation.
[0023] Given the fact that the chemical elements and several elemental ratios are quite different for innocuous substances, drugs, explosives, chemical weapon agents, etc., the system and method described herein are applicable in a variety of situations, e.g., identification of filler of shells, differentiating chemical agents from innocuous or high explosive fillers, confirming buried landmines etc. With respect to Mode 2, the neutron generator, e.g., pulsed deuterium-tritium (d-T), generates neutrons upon application thereto of a DC high voltage (of the order of 100 kV) between the cathode and a tritiated target. Deuterium atoms are emitted from the cathode when it is heated. These atoms are then ionized and accelerated in a high voltage field of up to 100 kV, to impinge on tritium atoms in the target. The fusion of the deuterium and tritium nuclei creates neutrons with energy of 14 MeV. The deuteron beam is pulsed by applying a gated, e.g., 2-3 kV, voltage between the cathode and an intermediate electrode. This type of neutron generator allows for the production of neutrons "on demand." Since the neutrons are only produced when the high voltage is applied on the generator, when there is no high voltage, there is no external radioactivity.
[0024] The neutrons generated by neutron generator 16 can initiate several types of nuclear reactions ((n,n'γ), (n,pγ), (n, γ) etc.) on the target under interrogation. The gamma (y) rays from these reactions are detected by the gamma ray detectors 12 which may be, for example, bismuth germanate (BGO) or NaI scintillators. During the Mode 2 neutron pulse, the gamma-ray spectrum is primarily composed of gamma rays from the (n,n'γ) and (n,pγ) reactions of fast neutrons with elements such as C and O. This spectral data is stored at a particular memory location within a data acquisition system (not shown). Between pulses, some of the fast neutrons that are still within the target lose energy by collisions with light element composing the target. When the neutrons have energy less than 1 eV, they are captured by such elements as H, N, Cl and Fe through (n, γ) reactions. The gamma rays from this set of reactions are detected by the same set of detectors 12 but stored at a different memory address within the data acquisition system (not shown). This procedure is repeated with a frequency of approximately 10 kHz. After a predetermined number of pulses, there is a longer period that allows the detection of gamma rays emitted from elements such as Si and P that have been activated. Therefore, by utilizing fast neutron reactions, neutron capture reactions, and activation, a large number of elements contained in a target can be identified through the target inspection system operating in Mode 2. FIG. 5 shows the time sequence of the nuclear reactions taking place.
[0025] Further to Mode 2, during the neutron pulse, the gamma ray spectrum is primarily composed of gamma rays from inelastic scattering and neutron capture reactions and is stored at a particular memory location within the data acquisition system. These reactions happen immediately and are eliminated as soon as the neutron generator is turned off. Between pulses, some of the fast neutrons are slowed down and thermalized, and may eventually be captured by nuclei in the target, producing gammas with different characteristic energies. The gamma detectors 12 are gated so that two spectra, a fast and a thermal spectrum, are acquired independently. As referenced above, in Mode 2, the neutron pulse duration is 10 microseconds with a frequency of 10 KHz. The spectra are acquired by counting for 2 to 5 minutes.
[0026] High explosives, e.g., TNT, RDX, C-4, etc., are composed primarily of the chemical elements hydrogen, carbon, nitrogen, and oxygen. Similarly, illicit drugs are typically composed of high amounts of hydrogen and carbon and, in many instances, show a strong chlorine signature. Many innocuous materials are also primarily composed of these same elements, but the elemental ratios and concentrations are unique to each material. Table 1 set forth below shows the atomic density of elements for various materials along with the atomic ratios. The problem of identifying explosives and illicit drugs is thus reduced to the problem of elemental identification. Nuclear techniques show a number of advantages for nondestructive elemental characterization. These include the ability to examine bulk quantities with speed, high elemental specificity, and no memory effects from the previously measured target.
TABLE-US-00001 TABLE 1 Density Or Ratio H C N O Cl C/O C/N Cl/O Narcotics High High Low Low Medium High > 3 High Very High Explosives Low- Med High Very Medium Low < 1 Low > 1 Low to Medium High to None Medium Plastics Medium- High High Medium Medium Medium Very -- High to Low to None High
[0027] Neutrons have high penetrability and can traverse with ease the part of the target volume behind which a suspected anomaly is to be interrogated. The incident neutrons interact with the nuclei of the various chemical elements in the anomaly, emitting characteristic gamma rays which act as the fingerprints of the various chemical elements. The gamma rays are collected by gamma ray detector(s) 12, capable of differentiating them according to their energy and their quantity at each energy level. The incident neutrons interact with the chemical elements in the anomaly and also with surrounding target material. These interactions result in gamma rays that constitute the background of the measurement.
[0028] The chemical elements of interest for the detection of illicit drugs, explosives, etc., require different neutron energies in order to be observed. Elements such as H, Cl, and Fe are best observed through nuclear reactions initiated from very low energy neutrons. Other elements such as C and O need neutron energies of several MeV to be observed at all. To satisfy this, a neutron source is required that can produce the high-energy neutrons for measurement of elements such as C and O, and low energy neutrons (energy <0.025 eV) for elements such as H and Cl. Such a task can be accomplished with the use of a pulsed (d,T) neutron generator.
[0029] With respect to Mode 3, the neutron generator produces neutrons, i.e., frequency of 200-400 Hz for between 25-200 μs, that interact with fissionable materials within a target, e.g., 235U and 24° Pu. At the end of the of the neutron pulse neutrons emitted by any fissionable materials will be detectable by neutron detectors and identifiable due to their characteristic decay curves.
[0030] Depending on the size of the target, it may be necessary to utilize more than one interrogation component in a preferred target inspection system. For example, referring to FIG. 4a, because of the 4 foot effective range of the interrogation, there may be two interrogation components 10a and 10b utilized to inspect a vehicle, i.e., one on each side of the interrogated vehicle 30. With respect to this embodiment, although the detectors 12a and 14a (not explicitly shown) within interrogation component 10a will be recessed and shielded as described above from the neutron generator 16a (not explicitly shown), each of the detectors 12a and 14a within interrogation component 10a will inadvertently be exposed to the neutron flux coming from the neutron generator 16b (not explicitly shown) within interrogation component 10b on the other side of the vehicle. And vice versa for detectors 12b and 14b (not explicitly shown). This will result in an unwanted increase of the gamma-ray background. To avoid this, the firing sequence of the two neutron generators will be controlled so that each side's detectors will not be accumulating while the other side's neutron generator is on. An exemplary timing sequence is shown in FIG. 6 wherein during a first time T1, e.g., 10 μs along the "TIME" continuum, the first neutron generator in Mode 2 16a is ON and fast data acquisition for first neutron generator 16a is ON 40, while the second neutron generator 16b, is OFF and no data is being acquired therefore 50. During a time T2, e.g., 40 μs, the first and second neutron generators are OFF and thermal data acquisition for both is ON 45. During a time T3, e.g., 25 μs, the first neutron generator in Mode 3 is ON 48, while the second neutron generator remains OFF 50. During a time T4, the first and second neutron generators are OFF while neutron emission data is being acquired 45. During time T5, the first neutron generator is OFF 50, while the second neutron generator in Mode 2 is ON 40. Time T6 follows Time T2. During time T7, the first neutron generator is OFF 50, while the second neutron generator in Mode 3 is ON 48. Time T8 follows time 4.
[0031] Further, in addition to the vertical movement Y of the interrogation component by virtue of the adjustable pillar 18 (FIG. 1) the interrogation component(s) may be set on translatable platform(s) 19 so as to control horizontal movement X of the interrogation component 10 towards and away from the target 30. Further still, in an alternative embodiment, additional detectors, i.e., gamma and neutron, may be utilized in conjunction with the interrogation component(s) 10 in order to accommodate different target sizes while maximizing the signal to noise ratio.
[0032] In a further embodiment of the present invention, the target inspection system further includes a threshold anomaly detection system and method, wherein gamma source/gamma detector and/or x-ray source/x-ray detector configurations (hereafter "gamma/x-ray interrogator") are first utilized in order to identify the mere presence of an anomaly in a target during an initial scan. Referring to FIG. 4b, a two phase target inspection system includes an initial scan of the target 30 using a gamma/x-ray interrogator 35 and a secondary scan using the interrogation components 10 described herein to identify the particulars of an anomaly once the presence of an anomaly has been detected during the initial scan. Various embodiments of appropriate gamma/x-ray interrogator configurations are described in U.S. Pat. No. 6,507,025, entitled, "DENSITY DETECTION USING REAL TIME DISCRETE PHOTON COUNTING FOR FAST MOVING TARGETS," U.S. patent application Ser. No. 10/767,723, entitled "METHOD AND SYSTEM FOR AUTOMATICALLY SCANNING AND IMAGING THE CONTENTS OF A MOVING TARGET," filed Jan. 30, 2004 by Richardson et al., U.S. patent application Ser. No. 10/717,632, entitled, "SYSTEM AND METHOD FOR TARGET INSPECTION USING DISCRETE PHOTON COUNTING AND NEUTRON DETECTION," filed Nov. 21, 2003, by Verbinski et al.; U.S. patent application Ser. No. 10/833,131 entitled, "DENSITY DETECTION USING REAL TIME DISCRETE PHOTON COUNTING FOR FAST MOVING TARGETS," filed Apr. 28, 2004, by Verbinski et al., which is a continuation of U.S. patent application Ser. No. 09/925,009, entitled, "DENSITY DETECTION USING REAL TIME DISCRETE PHOTON COUNTING FOR FAST MOVING TARGETS," filed Aug. 9 2001, by Verbinski et al.; all of the aforementioned patent applications are also incorporated herein by reference in their entireties.
[0033] Referring to FIG. 7, in a first exemplary processing embodiment, once the gamma and neutron emission data is collected by the detectors of the interrogation component S10, the spectra data 60 is processed by the target inspection system to identify contraband hidden among innocuous objects within the target. The spectra data are analyzed using a primary analysis application by performing a least squares analysis which uses a library of gamma (and neutron) spectra for several chemical elements that are expected to be either on the background (e.g. other parts of the target) or in the target to be interrogated S20. The least squares analysis ("LSA") method does not rely on any specific chemical element. Instead, it utilizes all chemical elements that are present or, in certain cases, absent from a spectrum. Utilizing spectra data 60, based on the assumed linear model, a generic spectrum |S can be written as follows:
|S=c1|R1+c2|R2+ . . . +cn|Rn
where the ci are coefficients and |R1 . . . |Rn are generalized responses (in particular |R1 is the background). The equation above can be written as a matrix vector product, as follows:
|S=R|c
where R is a known matrix. If R were a square matrix the solution would be
|cR-1|S.
Since R is not a square matrix (R may have four or five columns and hundreds of lines, corresponding to the channels in the spectrum), the system of equations is over determined. The matrix RTR (where T indicates the transpose) is a square matrix, and the system can be solved in the least squares sense, as follows:
|c=(RTR)-1RT|S
[0034] The vector |c contains the indicators based on the LSA method. The LSA primary analysis application provides the results in counts/second for each chemical element of importance 62. These results are then used in a secondary analysis application to identify the target S30, 64.
[0035] In order to maximize the reliability of the results 64 from the target inspection system, the system must utilize a secondary analysis application that maximizes probability of detection and minimizes probability of false alarm. Applying The Generalized Likelihood Ratio Test (GLRT) process (S30) to the detected data 62 in conjunction with training data sets for known materials, the target inspection system optimizes the probability of detection and minimizes the probability of false alarms. More particularly, the training data sets are based on an elemental concentrations data bank established by interrogating a large number of innocuous objects as well as drugs, explosives, WMD, etc., i.e., known targets. Based on elemental concentrations, as well as several elemental ratios, the target inspection system is "trained" to distinguish contraband from innocuous objects. Drugs, for example, are primarily distinguished through the elements H, C, and Cl; Chemical Warfare Agents through C, H, O, Cl, S, P, etc. The GLRT approach is a statistical analysis tool that allows one to do hypothesis testing based on a ratio of two likelihoods: the likelihood that the data point of the target being evaluated is inert and the likelihood that the target is a real threat or contraband item, i.e., explosive. To apply the tool one needs a set of representative data to train on, after which one selects a threshold and applies the tool to the stream of data points that follow. By moving the threshold one can develop a ROC (Receiver Operating Characteristic) curve, which is a good indicator of the detection capability of the system.
[0036] In operation, for each sample the indicators are known and it is known whether the sample is explosive or inert. By way of example, using the data 60 from the LSA method, a sample may consist of a vector W with 4 components (C, H, N, and O intensities, obtained from the primary analysis application S20). The samples could include all the measurements, or a subset, for example all the measurements made on a particular kind of environment, such as on a concrete surface. We compute the mean and the covariance matrix for the explosives (μ1, Cov1) and for the inert items (μ0, Cov0), respectively. For a generic vector W compute
λ=(W-μ1)T(Cov1)-1(W-μ1)-(W-μ.sub- .0)T(Cov0)-1(W-μ0)
where T indicates the transpose. The quantity λ can be used to make a declaration, by comparing its value to a threshold level. The procedure for the declaration is as follows: [0037] If λ<Threshold the declaration is explosive. [0038] If λ>Threshold the declaration is inert. By comparing the result of the declarations to the known state (explosive or inert) of the sample we can calculate the detection probability (DP) and the probability of false alarms (FA) for that particular threshold. If we let the threshold vary over the entire range of λ we obtain a ROC (receiver operating characteristic) curve, which is a plot of detection probability versus probability of false alarms. The ROC curve is a global way of assessing the performance of both primary and secondary analysis applications. The GLRT method can then be used for making decisions on new data. A threshold value that corresponds to an acceptable level on the ROC curve (for example 10% FA, 80% DP) is selected, and the same procedure described above is used for making the decision. The result of the decision may be explosive or inert. The GLRT parameter may also be used to calculate a confidence value to associate with the declaration. If enough information is available for a range of different substances, the GLRT parameter can also be used for substance identification. The substance is identified as belonging to the class (either explosive or inert) corresponding to the highest confidence.
[0039] Still referring to FIG. 7, in a second exemplary embodiment, the primary analysis application may utilize principal component analysis ("PCA") which is based on a particular expansion in terms of orthonormal functions. The PCA method relies on general features of the accumulated spectrum and not on the particular chemical elemental content of the "anomaly" under interrogation. This approach is completely heuristic and as such it does not require any auxiliary measurements or underlying models. Every spectrum (or the difference between signal and background) can be represented as a weighted sum of basis vectors. If an adequate representation of a spectrum can be attained with only a small number of basis vectors, the coefficients of the expansion form a feature vector that can also be used to characterize the sample. One advantage of the PCA method is that it is self-consistent within one data set and does not require auxiliary measurements outside that data set. This means that, where the system is well trained, it is possible to analyze a target without relying on spectral de-convolution.
[0040] More particularly, any vector, including a spectrum |S, can be decomposed into a sum of vectors as follows:
|S=c1|P1+c2|P2+ . . . +cn|Pn
where the c1 . . . cn coefficients are numbers, and the vectors |P1 . . . |Pn form an orthonormal basis. The above equation is true for any orthonormal set. The question is, is there a preferred way to choose the |Pi? When we have many vectors|S we can arrange them to form a matrix X. This matrix is not square, however the matrix XTX that is proportional to the covariance of the matrix X (provided that the data has been mean centered) is square. The eigenvectors of this square covariance matrix by definition form an orthonormal set. They can be ordered in descending order according to the magnitude of the corresponding eigenvalues. The advantage of this procedure is that often one does not need all of the eigenvectors to expand the spectra. Instead, a relatively small number of components may be sufficient for the spectral expansion, and most of the variance in the data is captured by the first few principal components. Once the principal components have been determined, a particular spectrum is represented by a small number of indicators, also known as scores, which are obtained by projecting the vector onto the principal components, as follows:
ci=Pi|S
[0041] Accordingly, applying the PCA method described above to the spectra data 60, a matrix of all the spectra data 60 is formed, including taking into account the background. The covariance of this matrix is calculated. The set of eigenvectors of the covariance matrix is computed and they are ordered in descending order by eigenvalue. A smaller subset of eigenvectors from the top of the ordered list is selected and these are the principal components to be used. Finally, the data vector (spectrum) is projected on the above components, thus extracting a group of indicators, i.e., scores, for each data vector 62. The GLRT secondary analysis method is then performed on the data vector scores 62 as described above with respect to the elemental intensities from the LSA method.
[0042] The embodiments described above are intended to exemplary. One skilled in the art recognizes the numerous alternative components and embodiments which may be substituted for the particular examples described herein and still fall within the scope of the invention.
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