Method of analyzing an object in two stages using a transmission spectrum then a scattering spectrum

Abstract

A method for analyzing an object, includes irradiating the object with incident photon radiation, acquiring a spectrum transmitted by the object using a spectrometric transmission detector, determining at least one first property of the object from the transmission spectrum, verifying that at least one doubt criterion relating to the first property of the object is met, and translating the fact that the object contains a material that is potentially dubious for the application under consideration. A second part, carried out only when the doubt criterion is met, includes acquiring an energy spectrum scattered by the object using a spectrometric scattering detector at an angle of 1 to 15, and determining a second property of the object from at least the scatter spectrum and comparing at least the second property of the object with properties of standard materials stored in a database to identify the objects composition material.

Claims

1. A method for analyzing an object in the context of a given application, comprising two parts, a first part comprising: irradiating the object with incident photon radiation; acquiring a measured transmission spectrum of energy transmitted by the object using a spectrometric detector placed for transmission; determining at least a first characteristic of the object based on the measured transmission spectrum; verifying the meeting of at least one suspicion criterion, the suspicion criterion comprising at least one predefined range of values of the first characteristic corresponding to materials searched for having regard to the given application, the verification of the suspicion criterion comprising a step of comparing the first characteristic as determined previously for the object with the predefined range of values, and a second part executed only when the suspicion criterion is met, the second part comprising: acquiring a measured scattering energy spectrum scattered by the object at a scattering angle () comprising between 1 and 15 using a spectrometric detector placed for scattering; determining a second characteristic of the object from either the measured scattering spectrum, or both the measured scattering spectrum and the measured transmission spectrum, and comparing either the second characteristic of the object, or both the first and second characteristics of the object, with characteristics of calibration materials stored in a database, for the purposes of identifying a material constituting the object.

2. The analyzing method according to claim 1, wherein the first characteristic is selected from a form, a dimension, a coefficient of attenuation for one or more predetermined energies or for a predetermined range of energies, an indication as to the nature of a material constituting the object, or an effective atomic number.

3. The analyzing method according to claim 1, wherein the second characteristic is selected from a momentum transfer or a scattering signature representative of the object and showing scattering peaks, reconstructed from both the measured scattering spectrum and the measured transmission spectrum.

4. The analyzing method according to claim 3, wherein the reconstruction of the scattering signature of the object comprises an operation of constructing an overall response matrix (A) of the detection system, which overall response matrix (A) establishes a relationship between an energy detected by the detector placed for scattering and a momentum transfer in the object.

5. The analyzing method according to claim 4, wherein the operation of constructing the overall response matrix (A) of the detection system is made on the basis of an estimated attenuated incident spectrum (SincAtt) and of a calibrated angular response matrix (R.sub.) of the detection system.

6. The analyzing method according to claim 5, wherein the operation of constructing the overall response matrix (A) of the detection system is further made on the basis of a response matrix (R.sub.Ed) of the spectrometric detector placed for scattering and of a response matrix (R.sub.Et) of the spectrometric detector placed for transmission.

7. A detection system for analyzing an object in the context of a given application, the system comprising: a source of photon radiation; a zone for the reception of an object to analyze; a spectrometric detector, downstream of the object receiving zone, for acquiring an measured transmission energy spectrum transmitted by the object and for acquiring a measured scattering spectrum scattered by the object at a scattering angle comprising between 1 and 15; a computer processing means configured to analyze the measured transmission energy spectrum and the measured scattering spectrum and comprising: a means for determining at least a first characteristic of the object based on the measured transmission spectrum; a means for verifying the meeting of at least one suspicion criterion concerning the first characteristic of the object, the verifying means being configured to perform a comparison of the first characteristic as previously determined for the object with a predefined range of values of the first characteristic corresponding to materials searched for having regard to the given application; a means for determining a second characteristic of the object based either on the measured scattering spectrum, or both on the measured scattering spectrum and on the measured transmission spectrum; and a means for comparing with characteristics of calibration materials stored in a database, either for the second characteristic the object, or for the first and second characteristics of the object, for the purposes of identifying a material constituting the object.

8. The detection system according to claim 7, wherein the spectrometric detector is placed for scattering and the detection means further comprises a second spectrometric detector, placed for transmission.

9. The detection system according to claim 7, wherein the spectrometric detector further comprises positioning means for the successive positioning of the spectrometric detector in a position for transmission, for acquiring the measured transmission spectrum, and in a position for scattering for acquiring the measured scattering spectrum.

10. The detection system according to claim 7, wherein the first characteristic is selected from a form, a dimension, a coefficient of attenuation for one or more energies or for a predetermined range of energies, an indication as to the nature of a material constituting the object, or an effective atomic number, and the second characteristic is selected from a momentum transfer or a scattering signature representative of the object and showing scattering peaks, reconstructed from both the measured scattering spectrum and the measured transmission spectrum.

11. The detection system according to claim 7, wherein the computer processing means are configured to to construct an overall response matrix (A) of the detection system that establishes a relationship between an energy detected by the detector placed for scattering and a momentum transfer in the object, the overall response matrix (A) being constructed from an attenuated incident spectrum (SincAtt) estimated using the measured transmission spectrum, and from a calibrated angular response matrix (R.sub.) of the detection system.

12. The detection system according to claim 7, wherein the spectrometric detector placed for scattering is configured so as to present a detection axis (D) forming, with a central axis (Z) of the incident radiation, a scattering angle comprising between 1 and 5.

Description

BRIEF DESCRIPTION OF THE DRAWING

(1) Other details and advantages of the present invention will appear from the reading of the following description, which refers to the diagrammatic appended drawings and which relates to preferred embodiments, provided by way of non-limiting examples. In the drawings:

(2) FIG. 1 is a graph representing the Bragg peaks of TNT (trinitrotoluene) and of salt (NaCl), which peaks illustrate the normalized intensity (y-axis), that is to say the relative number of photons detected during an acquisition operation, according to the momentum transfer x (x-axis) in nm.sup.1 of the detected photons.

(3) FIG. 2 is a graph representing the normalized molecular interference function of water (H.sub.2O), the normalized molecular interference function of oxygenated water (H.sub.2O.sub.2), the normalized molecular interference function of acetone (C.sub.2H.sub.6CO), and the normalized molecular interference function of Plexiglas ((C.sub.5O.sub.2H.sub.8)n), with, along the y-axis the number of photons detected and, along the x-axis, the momentum transfer x in nm.sup.1.

(4) FIG. 3 is a diagrammatic view of a detection system according to the invention.

(5) FIG. 4 is a graph representing transmission spectra for cylindrical samples of 40 mm diameter of water (H.sub.2O) and acetone (C.sub.2H.sub.6CO), as measured by the spectrometric detector placed for transmission of the detection system of FIG. 3.

(6) FIG. 5 is a graph representing scattering spectra for cylindrical samples of 40 mm diameter of water (H.sub.2O) and acetone (C.sub.2H.sub.6CO), as measured by the spectrometric detector placed for scattering of the detection system of FIG. 3.

(7) FIG. 6 is a graph representing the scattering signature (estimated MIF) of a cylindrical sample of water of 40 mm diameter and that of a cylindrical sample of acetone of 40 mm diameter, as reconstructed on the basis of a method and a detection system according to the invention,

(8) FIG. 7 is a graph representing the scattering signature (reconstructed MIF) of a cylindrical sample of water of 40 mm diameter and that of a cylindrical sample of acetone of 40 mm diameter, as reconstructed on the basis of a method and a detection system according to the invention, and also representing the theoretical scattering signatures (theoretical MIF) of these samples,

(9) FIG. 8 is a graph representing a response matrix of the spectrometric detector placed for transmission of the detection system of FIG. 3.

(10) FIG. 9 is a graph representing a response matrix of the spectrometric detector placed for scattering of the detection system of FIG. 3.

(11) FIG. 10 is a graph representing the angular distribution of the spectrometric detector placed for scattering of the detection system of FIG. 3.

(12) FIG. 11 is a graph representing an angular response matrix of the detection system of FIG. 3.

(13) FIG. 12 is a graph representing estimated attenuated incident spectra for cylindrical samples of 40 mm diameter of acetone and water, as estimated according to the invention from measured transmission spectra of FIG. 4.

(14) FIG. 13 is a diagram illustrating an operation of reconstruction of an overall response matrix of the detection system of FIG. 3.

(15) FIG. 14 is a graph representing the overall response matrix A of the detection system of FIG. 3 for a cylindrical sample of water of 40 mm diameter.

(16) FIG. 15 is a graph representing the overall response matrix A of the detection system of FIG. 3 for a cylindrical sample of acetone of 40 mm diameter.

DETAILED DESCRIPTION

(17) The detection system according to the invention illustrated in FIG. 3 comprises: a polychromatic source 1 of ionizing radiation, such as an X-ray tube, a source collimator 2, which makes it possible to channel the radiation from source 1 into an incident beam of central axis Z, a receiving zone 4 for an object to analyze; a scattering collimator 5 having a collimation axis D, a spectrometric detector 6 placed for scattering, which is associated with the scattering collimator 5 such that the detector 6 detects a radiation scattered at a scattering angle (angle between the incident axis Z and the axis of collimation and detection D) for example equal to 2.5 (the representation in FIG. 3 not being to scale); the spectrometric detector 6 placed for scattering is configured to establish a measured scattering spectrum (of energy), that is to say an energy spectrum of the radiation scattered by the object in the direction D; the spectrometric detector 6 is, in the example, a semiconductor material detector, such as a detector with CdTe or CdZnTe; a spectrometric detector 7 placed for transmission, configured to establish a measured transmission spectrum (of energy), that is to say an energy spectrum of the radiation transmitted by the object in the direction Z; the spectrometric detector 7 placed for transmission is, in the example, a semiconductor material detector, such as a detector with CdTe or CdZnTe; computer processing means 8 for processing measured spectra supplied by the spectrometric detectors 6 and 7.

(18) The terms transmitted radiation designate the radiation constituted by photons which have undergone no interaction in the examined object. By transmission spectrum is meant the radiation spectrum transmitted along the axis of the incident beam to the object, constituted by the photons which have undergone no interaction in the object. The expression placed for transmission designates a detector configured to detect the radiation transmitted by the material. Thus, a detector placed for transmission is situated on the axis of the radiation that is incident to the object, the object being placed between the detector and the radiation source.

(19) By spectrometric detector is meant a detector configured to generate an energy spectrum of the detected radiation.

(20) The method according to the invention is directed to determining whether or not an object to analyze is dangerous (explosive, tumor, etc.). For this, the method takes place in two parts. The objective of the first part of the method is not the precise identification of the material constituting the object; this first part is only directed to determining whether the object is suspicious or not, that is to say to determine whether the object merits a more thorough analysis being carried out. This first part thus enables the analysis to be shortened for a high number of objects which clearly prove to be inoffensive.

(21) The method described here has been implemented by the inventors to study two cylindrical samples of 40 mm diameter constituted respectively by acetone (C.sub.2H.sub.6CO) and water (H.sub.2O).

(22) For each inspected sample, the first part of the method exploits a measured transmission spectrum as supplied by the spectrometric detector 7, and of which the direct model is the following:
h=R.sub.Et.Math.(S.sub.incAtt)
With: h: the vector of the measured transmission spectrum of size (Nb.sub.Ejt1) R.sub.Et: the response matrix of the spectrometric detector placed for transmission, of size (Nb.sub.EjtNb.sub.Ei). In the case of a perfect detector, this matrix is a diagonal matrix. Each term R.sub.Et (j,i) of the matrix represents the probability of detecting an energy value equal to j when the photon which is incident on the detector has an energy i. S.sub.inc: the vector of the incident spectrum of the X-ray tube 1 of size (1Nb.sub.Ei) Att: the attenuation vector of size (1Nb.sub.Ei) which takes into account the effects of attenuation in the object. The vector (S.sub.incAtt) represents the spectrum of the radiation source attenuated by the object. In the example described here, and which supplies very precise signatures, this vector is taken into account in the construction of an overall response matrix A of the system, as will be understood later. Nb.sub.Ejt and Nb.sub.Ei respectively correspond to the number of channels of the measured transmission spectrum (that is to say to the number of channels of the energy spectrum detected by the detector placed for transmission) and to the number of channels of the incident energy spectrum. The symbol x corresponds to a term by term product (S.sub.inc and Att are multiplied term by term and a vector is then obtained which has the same size). The symbol . corresponds to the conventional matrix product.

(23) The transmission spectra measured with the spectrometric detector 7 for the aforementioned samples of acetone (C.sub.2H.sub.6CO) and water (H.sub.2O) may be observed in FIG. 4.

(24) Several characteristics may be extracted from such a transmission spectrum: attenuation coefficient, effective atomic number Z.sub.eff of a material constituting the object, an estimation of the nature, or even of the nature and of the thickness, of a material constituting the object.

(25) The effective atomic number Z.sub.eff of the material may for example be obtained by a statistical method which compares the transmission spectrum measured for the object with spectra of calibration samples (calibration materials) measured under the same experimental conditions, and which use a physical model of the spectrum change according to the effective atomic number and the thickness of the material. This technique is described in French patent application No. 1363174 of Alexia Gorecki in the name of CEA, incorporated herein by reference.

(26) The transmission spectrum may also be employed to estimate the nature of the material examined. The estimation of the nature of a material, as well as possibly its thickness, based on a transmission spectrum is described in the applications WO2012000993 or WO2011069748, in the name of the CEA, incorporated herein by reference. Once this characteristic or these characteristics of the object have been estimated, a decision is taken.

(27) If the object inspected appears suspicious, that is to say if one or more suspicion criteria are met (doubtful form, or atomic number belonging to a critical range of values of potentially dangerous materials defined in advance according to the application concerned), then a scattering spectrum of the material will be acquired and studied to enable better discrimination of the material. This second part is not always carried out on all materials since, although highly discriminating, it requires a relatively long time of exposure to the X-rays.

(28) If there is no doubt as to the innocuousness of the object, the first part of the method is conducted on a new object.

(29) The effective atomic number of the two inspected samples (water and acetone) has been evaluated on the basis of the spectra of FIG. 4. The following results were obtained: for the sample of water: estimated Z.sub.eff=7.21. In theory, such a sample possesses an effective atomic number: theoretical Z.sub.eff=7.22. It is thus found that the result obtained is very close to the theoretical value for the sample. For the sample of acetone: estimated Z.sub.eff=6.05, for a theoretical atomic number: Z.sub.eff theoretical=6.03.

(30) A critical zone has been defined for this application (detection of explosives); it corresponds to materials of which the Z.sub.eff is between 6 and 8.5. In other words, the step of verifying the meeting of the suspicion criterion consists of comparing the determined effective atomic number, estimated on the basis of the measured transmission spectrum, with the range of values [6;8.5]. It is to be noted that several discontinuous critical zones (several ranges of values) may be defined for the same first characteristic (for example atomic number).

(31) It is also possible to define several suspicion criteria relating to distinct characteristics; in this case, it may be considered either that the object is suspicious (and thus eligible for the second part of the method) when at least one of these suspicion criteria is met, or that the object is only suspicious if all the suspicion criteria are met.

(32) The two samples inspected here (water and acetone) have Z.sub.eff that are in the critical zone; they are thus considered as suspicious and the second part of the method according to the invention, i.e. the study of these two samples for small angle scattering, must therefore be executed.

(33) The second part of the method is directed to precisely identifying the material constituting the object when it has been considered as suspicious further to the first part. This second part consists for example of providing a scattering signature of said material on the basis of a measured scattering spectrum (provided by the spectrometric detector 6), the terms scattering signature designating a function representative of the material and showing scattering peaks (Bragg peaks or Molecular Interference Function according to the naturecrystalline or amorphousof the material).

(34) The scattering spectra measured by the detector 6 for the two samples may be observed in FIG. 5. In the example described here, it has been chosen to exploit, in an original way, the measured scattering spectra in combination with the measured transmission spectra in the course of the first part of the method. As a variant, it is possible to exploit the measured scattering spectra of FIG. 5 according to another technique such as a known technique used in EDXRD.

(35) In the example chosen here, the second part of the method uses the following model, describing the relationship between the scattering signature f of the material and the measured scattering spectrum g:
g=(R.sub.EdS.sub.incAtt).Math.R.sub..Math.f=A.Math.f
With: g: the vector of the measured (coherent) scattering spectrum, of size (Nb.sub.Ejd1) R.sub.Ed: the response matrix of the spectrometric detector placed for scattering, of size (Nb.sub.EjdNb.sub.Ei). In the case of a perfect detector, this matrix is a diagonal matrix. Each term R.sub.Ed (j,i) of the matrix represents the probability of detecting an energy value equal to j knowing that the radiation which is incident on the detector has an energy equal to i. In general, the response matrix of a spectrometric detector establishes a probabilistic relationship between an energy detected by the detector and the energy of the radiation that is incident on that detector. Each column i of R.sub.Ed (j,i), with j varying from 1 to Nb.sub.Ejd, corresponds to the probability density of energy detected by the detector when the latter is subjected to incident radiation of energy i. S.sub.inc: vector of the incident spectrum of the X-ray tube of size (1Nb.sub.Ei) Att: attenuation vector of size (1Nb.sub.Ei) which takes into account the effects of attenuation in the object. On account of the low value of the age , less than 15 and preferably less than 10 or even 5, the approximation will be made that the attenuation by the object along the path to the two detectors (for scattering and for transmission) is the same. R.sub.: angular response matrix of the detection system, of size (Nb.sub.EiNb.sub.x). Each term R.sub.(j,k) of the matrix R.sub. corresponds to a probability that the energy of a photon detected at the energy j corresponds to a momentum transfer equal to k. In other words, R.sub.(j, k) corresponds to the probability that a momentum transfer k gives rise to the detection of a photon of energy j. Each column k R.sub.(j,k), with j varying from 1 to Nb.sub.Ejd, corresponds to the probability density of energy detected by the detector when there is a momentum transfer equal to k. More generally, the angular response matrix R.sub. enables a probabilistic relationship to be established between the energy detected by the detector placed for scattering and an elastic scattering parameter of a material constituting the object, in particular the momentum transfer. f: scattering signature, of size (1Nb.sub.x), specific to the material constituting the object, which makes it possible to describe either the theoretical Bragg peaks of the material in the case of a crystalline material, or the molecular interference function in the case of an amorphous material, A: overall response matrix of the system for scattering, of size (Nb.sub.EjdNb.sub.x). Each term A(j,k) of A corresponds to a probability that the energy of a photon detected, by the detector for scattering, at the energy j corresponds to a momentum transfer equal to k. In other words, A(j,k) corresponds to the probability that a momentum transfer k gives rise to the detection of a photon at the energy j. The symbol x corresponds to the term by term product (S.sub.inc and Att are multiplied term by term and a vector is then obtained which has the same size). The symbol . corresponds to the conventional matrix product. Nb.sub.Ejd, Nb.sub.Ei and Nb.sub.x respectively correspond to the number of channels of the measured scattering spectrum (that is to say to the number of channels of the energy spectrum detected by the detector placed for scattering), to the number of channels of the spectrum of the incident energy and to the number of channels of the vector describing the momentum transfer.

(36) It is to be noted that the number of photons detected in each channel of the vector g follows a Poisson distribution having as parameter the average number of photons in that channel.

(37) The method according to the invention then comprises an operation of constructing an overall response matrix A of the detection system, using the above model. For this, the terms R.sub. and (SincAtt), and possibly R.sub.Ed. should be determined in advance.

(38) Each of these steps is individually described later.

(39) The prior step of calibrating the response matrix R.sub.Ed of the spectrometric detector placed for scattering is not necessary but advantageous, since it takes into account the degradation of the spectra due to the response of the detector. However, this step is optional or even unnecessary, in particular for detectors that are sufficiently energy resolving and when the response of a detector is judged to be satisfactory. The same applies for the response matrix R.sub.Et of the spectrometric detector placed for transmission, use later.

(40) Once the overall response matrix A has been constructed using the aforementioned model, the method according to the invention reconstructs the signature f (molecular interface function for amorphous materials, distribution of the d.sub.hkl for the polycrystalline materials) based on the model g=A.Math.f (where A and g are then known) by implementing a method based on an inverse problem type approach.

(41) The Maximum LikelihoodExpectation Maximization algorithm (denoted MLEM) is available to estimate the spectrum to be calculated by iterative maximization of the function of log-likelihood. This type of calculation is very frequent when it is required to estimate a maximum likelihood, and relies on a more general algorithm, called ExpectationMaximization (EM). This method has the advantage of taking into account the Poisson-like nature of the measured data.

(42) The coefficients of the overall response matrix A of the system are denoted a.sub.i,j. It is wished to maximize the probability that the estimated f of dimension Nb.sub.x generates measurements g. It is furthermore known that the measured data follow a Poisson distribution, on account of their physical nature. The likelihood function of the estimated f can thus be written:

(43) $\mathrm{Pr}\left(g/f\right)=\underset{j=1}{\overset{{\mathrm{Nb}}_{\mathrm{Ejd}}}{.Math.}}\frac{e^{-\underset{k^{}=1}{\overset{\mathrm{Nbx}}{.Math.}}{a}_{j,k}{f_k\left(\underset{k=1}{\overset{\mathrm{Nbx}}{.Math.}}{a}_{j,k}{f}_k\right)}^{g_j}}}{g_j}$

(44) Its log-likelihood is then expressed

(45) $\left(f\right)=\log \mathrm{Pr}\left(g/f\right)=\underset{j=1}{\overset{{\mathrm{Nb}}_{\mathrm{Ejd}}}{.Math.}}\left(-\underset{k=1}{\overset{\mathrm{Nbx}}{.Math.}}{a}_{j,k}{f}_k+g_j\log \left(\underset{k=1}{\overset{\mathrm{Nbx}}{.Math.}}{a}_{j,k}{f}_k\right)\right)$

(46) Next it is sought to maximize this function, by cancelling its derivative:

(47) $f_k\frac{\left(f\right)}{f_k}=0$

(48) The iterative solution of this problem is then written:

(49) $f_k^{n+1}=f_k^n\frac{1}{\underset{j=1}{\overset{{\mathrm{Nb}}_{\mathrm{Ejd}}}{.Math.}}{a}_{j,k}}\underset{j=1}{\overset{{\mathrm{Nb}}_{\mathrm{Ejd}}}{.Math.}}\left(\frac{g_j{a}_{j,k}}{\underset{k^{}=1}{\overset{\mathrm{Nbx}}{.Math.}}{a}_{j,k^{}}{f}_{k^{}}^n}\right)$

(50) By initializing the vector f.sup.(0).sub.k with positive values, it is ensured to have non-negative results.

(51) Thus, based on an estimation of A and of the measurement of g, it is possible to reconstruct f by iterating the MLEM algorithm. The results of this reconstruction (denoted reconstructed FIM in FIG. 6) for the samples of water and acetone inspected, by employing a MLEM algorithm with 100 iterations, are illustrated in FIG. 6.

(52) In other words, based on measurements carried out for transmission and for scattering on an unknown object, a function can be reconstructed relative to the structure of a material constituting that object. The values of this function are represented in the matrix A.

(53) As this material is unknown, the objective is to identify it. For this, a set of calibration materials is used (of explosive and non-explosive type in the case of an application for analyzing baggage for example; of healthy and tumorous biological tissue type in the case of a medical analysis application) of which the effective atomic numbers or other first characteristic and of which the signatures for scattering (molecular interference function or Bragg peaks) or other second characteristic are tabulated and stored in a database, and the analyzing method according to the invention next consists of comparing the values obtained for the object and of analyzing with those of the database, to identify the unknown object.

(54) As a variant, some parameters making it possible to obtain structural parameters of the material are extracted from the signature reconstructed for the object; for example, in the case of a crystalline material, the extraction of the position of the peaks present in the signature obtained makes it possible to obtain the interplanar spacings of the crystal.

(55) By comparing the values of estimated Z.sub.eff with a base of values of theoretical Z.sub.eff for a set of materials and furthermore comparing the form of the reconstructed molecular interference functions with a form base of molecular interference functions for a set of materials, it is possible to identify the nature of the two samples analyzed (water and acetone). FIG. 7 makes it possible to compare the reconstructed molecular interference functions of the two samples analyzed (water and acetone) and their theoretical molecular interference functions.

(56) There are now described the various steps of the operation of constructing the overall response matrix A of the system.

(57) Prior to any analysis of an object, that is to say off-line, calibration operations are carried out to determine certain specifications of the detection system, which depend in particular on the detectors used and on the geometry of the system, and which, contrary to the attenuation vectors, do not depend on the object to analyze. These specifications are R.sub.Et, R.sub.Ed, R.sub.. They are next stored in the computer processing means 8.

(58) The response matrix R.sub.Et of the spectrometric detector 7 placed for transmission may be obtained from the Monte-Carlo Tasmania simulation software application, which makes it possible to simulate the whole detection chain of a semiconductor detector (photon interactions, transit of charge carriers, etc.). Preferably, this simulation is furthermore compared together with experimental data acquired for example with gamma sources. This makes it possible to adjust the energy resolution obtained on simulation.

(59) FIG. 8 shows the response matrix R.sub.Et calibrated for the spectrometric detector 7 placed for transmission. This matrix defines the probability of detecting a photon at the energy Ej when the incident energy of the photon is Ei. This probability is indicated in FIG. 8 by gray tones (of which the scale has been transferred to the right of the graph), the x-axis of the graph representing the incident energy Ei expressed in keV, the y-axis corresponding to the detected energy Ej expressed in keV. In the case of a perfect detector, the matrix is diagonal (if it is square).

(60) In similar manner, a prior operation of calibrating a response matrix R.sub.Ed of the spectrometric detector 6 placed for scattering is executed off-line, by simulation using the Monte-Carlo simulation software application and/or by experiment.

(61) The calibrated response matrix R.sub.Ed obtained is illustrated in FIG. 9. Here too, the x-axis represents the incident energy Ei in keV, and the y-axis corresponds to the detected energy Ej in keV, the probability of the pair (Ei, Ej) being expressed by gray tones.

(62) A prior operation of calibrating an angular response matrix R.sub. of the detection system is also executed off-line. This angular response depends on two factors. The first corresponds to the geometry of the acquisition system and more specifically to the opening of the source collimator 2 and to the opening of the scattering collimator 5, knowing that it is assumed that the object fills the intersection of two cones, i.e. an irradiation cone and an observation cone. The irradiation cone delimits the solid angle under which the object sees the source, whereas the observation cone corresponds to the solid angle under which the detector sees the object. First of all an angular distribution 1D of the system is evaluated, either based on simulations, or based on calibrations. Using the relationship linking x (momentum transfer), E (energy that is incident on the detector placed for scattering) and (scattering angle), there is deduced the matrix of angular response function of Ei (incident Energy) and of x based on the angular distribution 1D function of .

(63) FIG. 10 shows an example of angular distribution 1D of the scattering system when the collimation axis D of the scattering collimator defines a scattering angle equal to 2.5, the angular distribution expressing the relative quantity of photons that are incident on the detector placed for scattering (y-axis) according to the detection angle in degree (x-axis). This is an example since the use of collimators having different configurations (in particular width and length of the opening of the collimators) would lead to another graph being obtained. An angular response matrix R.sub. of the detection system may be observed in FIG. 11, of which the x-axis represents the momentum transfer x in nm.sup.1, while the y-axis represents the energy E that is incident on the detector placed for scattering in keV, the gray tones expressing the relative quantity of incident photons. As referred to previously, this matrix defines a probabilistic relationship between the number of photons incident on the detector placed for scattering, at a given energy, and the momentum transfer.

(64) The construction of the overall response matrix A of the detection system using the model A=(R.sub.EdS.sub.incAtt).Math.R.sub. still requires a step of estimating an incident spectrum attenuated by the object (S.sub.incAtt).

(65) Advantageously, this step of estimating the attenuated incident spectrum again uses the transmission spectrum measured in the first part of the method by the spectrometric detector 7 placed for transmission. This transmission spectrum h may be written:
h=R.sub.Et.Math.(S.sub.incAtt)

(66) In other words, it is considered in this version of the invention that the term (S.sub.incAtt) in the expression of the matrix A is equal to the term (S.sub.incAtt) in the expression of the transmission spectrum h. The inventors have shown that this approximation is entirely acceptable for scattering at small angles (less than 15) and that it enables signatures f to be obtained of an excellent resolution and accuracy for scattering angles less than 5.

(67) To estimate (S.sub.incAtt) based on the measured transmission spectrum h and on the calibrated response matrix R.sub.Et of the detector, the system according to the invention advantageously again uses a technique of MLEM type.

(68) FIG. 12 shows the different spectra (S.sub.incAtt) obtained after MLEM inversion of the experimental data recorded on the spectrometric detector 7 placed for transmission for the two inspected samples (water and acetone), which data (measured transmission spectra) are illustrated in FIG. 4.

(69) All the terms of the overall response matrix A of the system have been calibrated, the method according to the invention taken as example next consists of combining them according to the formula A=(R.sub.EdS.sub.incAtt).Math.R.sub.. This combination is summarized in FIG. 13 in which the numerical reference 10 designates a row by row multiplication and in which the numerical reference 11 designates a matrix multiplication. The overall response matrices A obtained may be observed in FIG. 14 for the sample of water and in FIG. 15 for the sample of acetone.

(70) The invention may be the subject of numerous variants in relation to the preferred embodiment described above. Thus for example, the second part of method may consist of a conventional analysis by diffractometry using the EDXRD technique for example. Furthermore, the detector placed for transmission may be a simple integration detector, in which case the first characteristic of the object evaluated for the purposes of verifying a suspicion criterion is not the effective atomic number of the material.