Method and system for analyzing an object by diffractometry using a scattering spectrum and a transmission spectrum

Abstract

A method for analyzing an object includes irradiating the object with incident photon radiation and acquiring an energy spectrum scattered by the material using a spectrometric detector in scatter mode. An energy spectrum transmitted by the material is acquired using a spectrometric detector in transmission mode. A signature (f) is reconstructed representing the object, both from the scatter spectrum measured and from the transmission spectrum measured, and the reconstructed signature thereof is compared with signatures of standard materials.

Claims

1. A method of analyzing an object using a detection system comprising a first spectrometric detector, the method comprising: irradiating the object with incident photon radiation; acquiring a measured scattering energy spectrum scattered by the object at a scattering angle () comprising between 1 and 15 using the first spectrometric detector, placed for scattering; acquiring a measured transmission spectrum of energy transmitted by the object, using a second spectrometric detector placed for transmission; reconstructing a signature function (f) representative of the object, based on both the measured scattering energy spectrum and the measured transmission spectrum and estimating an incident spectrum attenuated by the object using the measured transmission spectrum; and comparing the signature function with signatures 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 reconstructing the signature function of the object comprises an operation of constructing an overall response matrix (A) of the detection system that establishes a relationship between an energy detected by the first spectrometric detector placed for scattering and a momentum transfer.

3. The analyzing method according to claim 2, 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.

4. The analyzing method according to claim 3, wherein the operation of constructing the overall response matrix (A) of the detection system is furthermore made on the basis of a calibrated response matrix (R.sub.Ed) of the first spectrometric detector placed for scattering, and of a calibrated response matrix (R.sub.Et) of the second spectrometric detector placed for transmission.

5. The analyzing method according to claim 1, wherein the first 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 () comprised between 1 and 5.

6. The analyzing method according to claim 1 further comprising: first calibrating a response matrix (R.sub.Ed) of the first spectrometric detector placed for scattering (6); second calibrating a response matrix (R.sub.Et) of the second spectrometric detector placed for transmission; and third calibrating an angular response matrix (R.sub.) of the detection system, wherein the first, second and third calibrating steps are carried out irradiating the object.

7. The analyzing method according to claim 6, wherein the first and second calibrating steps are carried out by simulation using a simulation software application of a Monte-Carlo type.

8. The analyzing method according to claim 7, wherein the response matrix of the first spectrometric detector placed for scattering obtained by simulation is refined using at least one measurement of a spectrum scattered by a calibration material irradiated by a source of gamma rays, in the same way as the response matrix of the first spectrometric detector placed for transmission obtained by simulation is refined using at least one measurement of a spectrum transmitted by a calibration material irradiated by a source of gamma rays.

9. A detection system for analyzing an object comprising: a source of photon radiation; a zone for the reception of an object to analyze; a detector apparatus downstream of the zone that acquires an measured scattering energy spectrum scattered by the object at a scattering angle () comprising between 1 and 15, and that acquires a measured transmission spectrum of energy transmitted by the object; a computer processing means for reconstructing a signature function (f), representative of the object, from the measured scattering spectrum and from the measured transmission spectrum that includes estimating an incident spectrum attenuated by the object using the measured transmission spectrum, and for comparing the reconstructed signature function (f) with signatures of calibration materials stored in a database for the purposes of identifying a material constituting the object.

10. The detection system according to claim 9, wherein the detector apparatus comprises a first spectrometric detector for acquiring the measured scattering energy spectrum, and a second spectrometric detector for acquiring the measured transmission spectrum.

11. The detection system according to claim 9, wherein the computer processing means is further configured to implement a method based on an inverse problem type approach and to construct an overall response matrix (A) of the detection system, which the overall response matrix (A) establishes a relationship between an energy detected by the spectrometric detector placed for scattering and a momentum transfer.

12. The detection system according to claim 11, wherein the overall response matrix (A) of the detection system is constructed from: an attenuated incident spectrum (SincAtt) estimated using the measured transmission spectrum, and a calibrated angular response matrix (R.sub.) of the detection system.

13. The detection system according to claim 12, wherein the overall response matrix (A) of the detection system is further constructed from: a calibrated response matrix (R.sub.Ed) of the spectrometric detector (6) placed for scattering, and a calibrated response matrix (R.sub.Et) of the spectrometric detector (7) placed for transmission.

14. The detection system according to claim 9, wherein the first 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, 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 the response matrix of the spectrometric detector placed for transmission of a detection system according to the invention such as that of FIG. 3.

(6) FIG. 5 is a graph representing the response matrix of the spectrometric detector placed for scattering of the detection system of FIG. 3.

(7) FIG. 6 is a graph representing the angular distribution of the spectrometric detector placed for scattering of the detection system of FIG. 3.

(8) FIG. 7 is a graph representing the angular resolution matrix of the detection system of FIG. 3.

(9) FIG. 8 is a graph representing transmission spectra for cylindrical samples of 40 mm diameter of acetone (C.sub.2H.sub.6CO), water (H.sub.2O) and nitromethane (CH.sub.3NO.sub.2), as measured by the spectrometric detector placed for transmission of the detection system of FIG. 3.

(10) FIG. 9 is a graph representing estimated attenuated incident spectra for cylindrical samples of 40 mm diameter of acetone, water and nitromethane, as estimated according to the invention from measured transmission spectra of FIG. 8.

(11) FIG. 10 is a diagram illustrating an operation of constructing an overall response of a detection system according to the invention such as that of FIG. 3.

(12) FIG. 11 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.

(13) FIG. 12 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.

(14) FIG. 13 is a graph representing the theoretical scattering signature (FIM) of a cylindrical sample of water of 40 mm diameter, and the signature of that sample as reconstructed by a method and by a detection system according to the invention, and also representing the theoretical scattering signature (FIM) of a cylindrical sample of acetone of 40 mm diameter, and the signature of that sample as reconstructed by a method and by a detection system according to the invention.

(15) FIG. 14 is a graph representing the theoretical scattering signature (FIM) of a sample of water and the signature of that sample reconstructed from a measured scattering spectrum for the sample by using a method and a detection system according to the invention.

(16) FIG. 15 is a graph representing the theoretical scattering signature (FIM) of a sample of water and the signature of that sample reconstructed from a measured scattering spectrum for the sample without taking into account the attenuation of the incident spectrum.

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 incident 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 diffracted 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 spectrum (of energy) for scattering, that is to say an energy spectrum of the radiation diffracted by the object in the direction D; preferably, the spectrometric detector 6 placed for scattering is a semiconductor material based 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; preferably, the spectrometric detector 7 placed for transmission is 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 a spectrum of the detected radiation.

(20) The method according to the invention is directed to providing a signature of a material constituting the object to analyze based on a measured scattering spectrum (provided by the spectrometric detector 6), the term signature designating a function representative of the material for scattering: Bragg peaks or Molecular Interference Function according to the naturecrystalline or amorphousof the material.

(21) This method preferably uses the following model, describing the relationship between the 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:

(22) g: the vector of the measured (coherent) scattering spectrum, of size (Nb.sub.Ejd1)

(23) 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.

(24) S.sub.inc: vector of the incident spectrum of the X-ray tube of size (1Nb.sub.Ei);

(25) 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, 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.

(26) 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 a momentum transfer.

(27) f: 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;

(28) 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.

(29) The symbol 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);

(30) The symbol . corresponds to the conventional matrix product;

(31) 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.

(32) 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.

(33) The originality of the method according to the invention is that it uses a measured transmission spectrum (provided by the spectrometric detector 7), of which the direct model is the following:
h=R.sub.Et.Math.(S.sub.incAtt)
With:

(34) h: the vector of the measured transmission spectrum of size (Nb.sub.Ejt1)

(35) 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.

(36) S.sub.inc: the vector of the incident spectrum of the X-ray tube of size (1Nb.sub.Ei)

(37) Att: the attenuation vector of size (1Nb.sub.Ei) which takes into account the effects of attenuation in the object,

(38) The vector (S.sub.incAtt) represents the spectrum of the radiation source attenuated by the object. In the most effective version of the invention providing the most precise signatures, one of the key elements is to take into account this vector in the construction of the response matrix A of the system.

(39) Nb.sub.Ejt, 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.

(40) The symbol 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).

(41) The symbol . corresponds to the conventional matrix product.

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

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

(44) 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.

(45) The Maximum LikelihoodExpectation Maximization algorithm (ML-EM) 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.

(46) 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:

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

(48) Its log-likelihood is then expressed

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

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

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

(52) The iterative solution of this problem is then written, with n designation the iteration:

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

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

(55) Thus, based on an estimation of A and of the measurement of g, it is possible to reconstruct f by iterating the MLEM algorithm.

(56) In other words, based on measurements made for transmission and for scattering on an unknown object, it is possible to reconstruct a function (i.e. a molecular interference function in the case of an amorphous material or Bragg peaks in the case of a crystalline material) relative to the structure of a material constituting the object. The values of this function are represented in the matrix A.

(57) As this material is unknown, the objective is to identify it.

(58) 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 malignant biological tissue type in the case of a medical analysis application) of which the signatures are tabulated and stored in a database, and the analysis 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.

(59) 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.

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

(61) 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.

(62) The response matrix R.sub.Et of the spectrometric detector 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.

(63) FIG. 4 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. 4 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).

(64) 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.

(65) The calibrated response matrix R.sub.Ed obtained is illustrated in FIG. 5. Here too, the x-axis represents the incident energy in keV, and the y-axis corresponds to the detected energy in keV, the probability of the pair (Ei, Ej) being expressed by gray tones.

(66) 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 the geometry of the acquisition system and more specifically on 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 is defined by the solid angle under which the source irradiates the object, whereas the observation cone is defined by the solid angle under which the detector sees the object.

(67) 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 .

(68) FIG. 6 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. 7, 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.

(69) The construction of the overall response 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).

(70) Advantageously and according to the invention, this step of estimating the attenuated incident spectrum uses a transmission spectrum measured by a spectrometric detector placed for transmission. Such a transmission spectrum h may be written:
h=R.sub.Et.Math.(S.sub.incAtt)

(71) In other words, it is considered, according to 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 comprised between 1 and 5.

(72) To estimate (S.sub.incAtt) based on the measured transmission spectrum h and on the calibrated response matrix R.sub.Et of the detector 7, the system according to the invention advantageously again uses a technique of MLEM type.

(73) FIG. 9 shows different spectra (S.sub.incAtt) obtained after MLEM inversion of the experimental data recorded on the spectrometric detector 7 placed for transmission, which data (measured spectra for transmission) are illustrated in FIG. 8, for a cylindrical sample of 40 mm diameter constituted respectively of water (H.sub.2O), acetone (C.sub.2H.sub.6CO), and nitromethane (CH.sub.3NO.sub.2).

(74) 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. 10 in which the numerical reference 10 designates a row by row multiplication and in which the numerical reference 11 designates a matrix multiplication.

(75) The method according to the invention uses a detector placed for transmission which is a spectrometric detector. In the interest of economy and to limit the acquisition times, it could be attempted to use, instead of this spectrometric detector, a simple integration detector making it possible to record the number of photons transmitted through the object (independently of the energy released). The overall response matrix of the detection system could then be written A=k.Math.R.sub.Ed.Math.R.sub. in which k would be given by the signal for integration delivered by the detector placed for transmission.

(76) The inventors have shown that this solution is to be ruled out.

(77) FIG. 14 reproduces the theoretical signature (molecular interference function) for a sample of water and the signature f obtained for this same sample of water according to the invention, that is to say by using a spectrometric detector placed for transmission and using, in this case, the model given by the formula A=(R.sub.EdS.sub.incAtt).Math.R.sub. as well as a MLEM algorithm with 100 iterations for the inversion of g=A.Math.f. It may be noted that the two curves more or less coincide over a large part of the field of momentum transfer represented.

(78) FIG. 15 reproduces the theoretical signature of the sample of water and the signature obtained for that same sample using an integration detector placed for transmission and using the model given by the formula A=k.Math.R.sub.Ed.Math.R.sub..

(79) It may be noted that the two curves are very different over the whole of the field of momentum transfer represented and that the signature so reconstructed shows peaks which do not exist in the theoretical signature, such that it is not possible based on the signature so reconstructed to deduce that the sample is constituted by water.

(80) By contrast, the invention is not limited to the model provided in the preferred example described above for the construction of the overall response matrix A of the detection system.

(81) Thus for example, it may be envisioned to directly use the measured transmission spectrum without inversion of it to construct the overall response matrix A. In this case:
A=(R.sub.Edh).Math.R.sub.=(R.sub.Ed(R.sub.Et.Math.(S.sub.incAtt))).Math.R.sub.

(82) This variant is in accordance with the invention despite providing imperfect results. However, the inversion of the measured transmission spectrum in the preferred example described earlier, to remove the effect of the detector response, enables the results of the reconstruction of the signature to be greatly improved and to get as close as possible to the theoretical scattering signature of the object (cf. FIGS. 13 and 14).