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    • 专利摘要:
    The invention relates to a method for estimating the effective atomic number of a material from a transmission spectrum of said material. A likelihood function of the effective atomic number and the thickness of the material from the transmission spectrum as well as the calibration spectra obtained in a pre-calibration phase for a plurality of variables are first calculated (230). samples of calibration materials of known effective atomic numbers and known thicknesses. The effective atomic number (Z) of the material is then estimated (240) from values of the likelihood function.
    公开号:FR3015681A1
    申请号:FR1363174
    申请日:2013-12-20
    公开日:2015-06-26
    发明作者:Alexia Gorecki；Jean Rinkel
    申请人:Commissariat a lEnergie Atomique CEA；Commissariat a lEnergie Atomique et aux Energies Alternatives CEA；
    IPC主号:
    专利说明:

    [0001] TECHNICAL FIELD The present invention relates to the field of the physical characterization of a material and more particularly to the measurement of its effective atomic number by X or gamma spectroscopy. SUMMARY OF THE INVENTION It is particularly applicable in the field of medical imaging and non-destructive testing. STATE OF THE PRIOR ART The effective atomic number is one of the parameters that can characterize a material. Remember that the atomic number of a simple body is defined as the number of protons present in the nucleus of an atom of this body. On the other hand, when one considers a chemical compound, one must appeal to the notion of effective atomic number. This is defined as the atomic number of a single body that would lead to the same transmission spectrum in a given energy band. In general, the effective atomic number of a chemical compound is obtained by means of a combination of the atomic numbers of the atomic numbers of the constituent single bodies of the compound, each atomic number being assigned a weighting coefficient dependent on the mass fraction. or atomic single body in the compound. Thus, in practice, the effective atomic number Zeff of a compound of N simple NP field, satisfies Zeff ~~~ (Zeff) P where Zelif is the atomic number of the simple body ii -1, ..., N and p is a constant related to the photoelectric effect (p = 4.62). The measurement of the effective atomic number of a material is conventionally carried out using X-ray or gamma-ray spectrometry. This is generally done using direct conversion spectrometric sensors, ie sensors in which the X or gamma photons interacting with the material to be analyzed are absorbed by a semiconductor element (CdTe for example). More precisely, a photon incident on this element creates a cloud of electronic charges (typically 10,000 electrons for a 60 keV X-ray photon). These charges are then collected by collection electrodes arranged on this element. The charges generated by an incident photon and thus collected form a transient electrical signal of impulse form. If the collection of charges is complete, the integral of the measured pulse is proportional to the energy of the incident photon. The histogram of the energies thus measured gives a spectrum of the radiation having interacted with the material. This spectrum provides information on the density as well as the nature of the material, and makes it possible to estimate the effective atomic number. A method of measuring the effective atomic number of a material is described in US-A-6069936. It consists of irradiating the material with a first radiation having a first energy spectrum to obtain a first attenuation profile, then with a second radiation having a second energy spectrum to obtain a second attenuation profile, and to determine the effective atomic number of the material from a ratio between the first and second profiles thus obtained. The first energy spectrum may correspond to a high energy range and the second energy spectrum may correspond to a lower energy range. The effective atomic number is determined from a table in which profile reports have been stored during a calibration phase for known atomic number materials. This method does not, however, make it possible to determine the atomic number of a material with a satisfactory degree of precision and reliability. The object of the present invention is therefore to provide a method for measuring the effective atomic number of a material which is both reliable and accurate. DISCLOSURE OF THE INVENTION The invention relates to a method for measuring the effective atomic number of a material for a predetermined X or gamma spectral band, in which: a transmission spectrum (Sa + la) of a sample of said material is measured; in a plurality (N) of energy channels of said spectral band; a likelihood function of the effective atomic number and the thickness of the sample of said material is calculated from the thus measured transmission spectrum and a plurality of transmission spectra (Sc (Zpc, e, c)), said calibration spectra, obtained for a plurality of samples of calibration materials having known effective atomic numbers and known thicknesses, said likelihood function being calculated for at least said known effective atomic numbers (Zpc) and known thicknesses (and) to provide a plurality of values of said likelihood function, the effective atomic number (Z) of said material is estimated from the values of the likelihood function thus obtained. Advantageously, the calibration spectra are interpolated to obtain an interpolated calibration spectrum for each effective atomic number belonging to a first interval ([Z, Z.]), And one calculates for each effective atomic number belonging to this interval and each given thickness, a value of said likelihood function. In the same way, the calibration spectra can be advantageously interpolated to obtain an interpolated calibration spectrum for each effective atomic number belonging to a second interval ([e., Emax]) and to calculate for each thickness belonging to this interval and each number. given effective atomic atom, a value of said likelihood function. According to a first embodiment, for each calibration material (p) of known effective atomic number (Zpc), the maximum value (Vp) of the likelihood function is determined among the values of the likelihood function (V (Z , q = 1, ..., Q) obtained for the known thicknesses of the samples of this material, said maximum value then being associated with the material.
    [0002] According to a second embodiment, for each calibration material (p) of known effective atomic number (Zpc), an interpolation is made between the calibration spectra relating to known thicknesses in order to determine an interpolated calibration spectrum for each thickness. of a given thickness interval ([e., e.]), the likelihood function being evaluated on this thickness interval from the interpolated calibration spectrum, and the maximum value of the function determined likelihood on said thickness range, said maximum value being associated with the material. According to the first embodiment, the effective atomic number (Z) of the material can be estimated as the average of the known effective atomic numbers of the calibration materials, weighted by the maximum values of the likelihood function which are respectively associated with them. According to the second embodiment, the effective atomic number () of the material can be estimated as the average of effective atomic numbers belonging to a first interval ([Z., Z.]), Weighted by the maximum values of the likelihood function which are respectively associated with them. According to the second embodiment, it is possible alternatively to perform, for each calibration material (p) of known effective atomic number (Zpc), an interpolation between the calibration spectra relating to known thicknesses in order to determine an interpolated calibration spectrum for each thickness of a given thickness interval ([e, e.]), the likelihood function being evaluated over this thickness interval from the interpolated calibration spectrum, and then integrated over this thickness interval to give a marginal likelihood function value associated with this calibration material.
    [0003] In this case, the effective atomic number (Z) of the material can be estimated as the average of the known effective atomic numbers of the calibration materials, weighted by the values of the marginal likelihood function respectively associated with these calibration materials.
    [0004] In all cases, the values of the likelihood function can be determined for each pair (Zpc, e, c) of effective atomic number and thickness by: V (Z'P N1 ec) = exp ni i = 1 i = 1 where the i = 1, ..., N are the values of the transmission spectrum of the material in the different channels, nic, i = 1, ..., N are the values of the transmission spectrum of the calibration material in these same channels and is the ratio between the number of photons received in the channel i in the absence of material during the calibration (no i) and the number of photons received in the absence of material during the measurement (na) in the same channel . Advantageously, according to the second embodiment, for each pair (Z, e) of effective atomic number belonging to a first interval and of thickness belonging to a second interval, the likelihood function V (Z, e) is calculated from of: ln (V (Z, e)) = -, w7c + ln (, an ".) where the, i = 1, ..., N are the values of the transmission spectrum of the material in the different channels, nic , i = 1, ..., N are the values of the interpolated transmission spectrum in these same channels, y is the ratio between the total number of photons received in the set of channels and in the absence of material during the measurement and the total number of photons received in the same set of channels and in the absence of material during the calibration, and F, is the total number of photons received in the same set of channels in the presence of the calibration material, during calibration.
    [0005] The atomic number of the material can then be estimated as that (ZML) which maximizes the likelihood function V (Z, e) on the block formed by the Cartesian product between the first interval and the second interval. Alternatively, one can determine the marginal density (p (Z)) of the likelihood function on said first interval, integrating the density of the likelihood function on the second interval. The actual atomic number of the material can then be estimated as that (2maig) maximizing the marginal density on said first interval. Alternatively, the actual atomic number of the material can be estimated as the average of the effective number (Zmoy) weighted by the marginal density of the likelihood function on said first interval. Advantageously, according to the second embodiment, for a thickness e between a first known thickness eqc and a second known thickness egc + 1 where eqc <e <eqc, i, an interpolated calibration spectrum Sc (Z ', e ) for the effective atomic number Z 'and the thickness e from the calibration spectra Sc (Zc, e, c) and Sc (Zc, e, c + i) respectively obtained for the same effective atomic number and the respective thicknesses eqc and egc, i, by means of: ln Ln ". (Z ', e) 1 = (ec - ln Ln". (, eqc) 1+ (ln Ln "., eqc + i) 1 q + 1 e e-eq ccccee q + 1 - eq) q + 1 - eq) where, e),, e, c) and r ((zc, e, c + i) are the respective values of the spectra (Z ', e) , (Z ', eqc) and Sc (Z', eqc +1) in channel i of the spectral band, Similarly, for an effective atomic number Z between a first known effective atomic number Zpc and a second atomic number known effective Zp + 1 where Z '<Z <Zp + 1 is advantageously obtained a calibration spectrum in terpole Sc (Z, ec) for the effective atomic number Z and the thickness ec from the calibration spectra Sc (Z, ec) and Sc (Z +1, ec) respectively obtained for the same thickness ec and the atomic numbers Zpc and Zpc + i by means of: 1-7; P Pp Pp + 1) ((2 / 1P ln [nic c, ec)] + -2 / 9 ln [r (ec) 1 "" ) fr "p +1) P where n". (Z, ec), (Z, ep +1 'ec) are the respective values of the spectra Sc (Z, ec), Sc (Zpc, ec) and Sc (Zpc + pec) in the channel i of the spectral band, nos is the (Zr.-Zr Zr - (Zpc full flux spectrum in channel i, ÿ = p + 1 ^ r2p, r is P (zep + i) r - (Z p) (ze p + i ) r (zep) 10 a predetermined real constant, pp, pp + 1 are respectively the densities of the materials p and p + 1, and where p is the density of the atomic number material Z obtained by interpolation between the densities pp and pp ± BRIEF DESCRIPTION OF THE DRAWINGS Other features and advantages of the invention will be apparent from the reading of preferred embodiments of the invention, with reference to the appended figures, in which: Fig. 1 schematically represents a flowchart of a Measuring method according to a first embodiment of the invention Fig. 2 schematically shows a flowchart of a measuring method according to a second embodiment of the invention. Figure 3A shows the likelihood function of the effective atomic number and the thickness for a sample, FIG. 3B represents the likelihood function ln [no ', 1 + marginal corresponding according to the effective atomic number, and FIG. 3C represents the marginal likelihood function as a function of thickness. DETAILED PRESENTATION OF PARTICULAR EMBODIMENTS We will consider in the following a material whose effective atomic number is to be measured using X or gamma transmission spectrometry measurements. For this purpose, a direct conversion spectrometer as mentioned in the introduction may be used. It will be assumed that the measurement of atomic number is carried out in a homogeneous zone of the material, whether the material is itself homogeneous, or that the X or gamma beam is sufficiently fine so that the irradiated zone can be considered homogeneous. It will be understood in particular that it will be possible to scan an object with a beam so as to make a measurement at each point and thus achieve an effective atomic number map.
    [0006] The transmission spectrometry measurement, hereinafter more simply transmission spectrum, is represented by a vector sa = (nia, n2a where N is the number of energy channels (also called detection channels), each value nia being representative of the number of pulses observed in the channel i during a measurement time, T, given The value nia is also called the score of the channel i during the measurement time T. The effective atomic number of the material is denoted Zeff or, more simply Z, and its estimate from the spectrometry measurement, is denoted by I. It will be assumed that a calibration of the Z measurement has previously been carried out using a plurality PQ of samples of different materials. p = 1, ..., P and different thicknesses called calibration samples (or standards) We will assume, without loss of generality, that for each material p calibration is performed for the same plurality of thicknesses Q, It is said that, for each calibration material p, there are Q standards of different thicknesses. The effective atomic number of a sample of material p and thickness e, is denoted Z.pc, q. The idea underlying the invention is to adopt a probabilistic approach by performing, from the transmission spectrum of a sample, an estimate of the effective atomic number of the constituent material of the sample, and if necessary of the thickness of this sample, according to a MAP criterion (Maximum A Posteriori) or according to a maximum likelihood criterion, also called ML criterion (Maximum Likelihood). More precisely, the probability that the analyzed sample has an effective atomic number Z and a thickness e, given the measured transmission spectrum Sa, is given by the Bayes theorem: Pr (0Sa) "Pr (Sa 10) Pr ( 0) (1) where "is the sign of proportionality (the term Pr (Sa) in the denominator in the Bayes formula can be omitted because independent of 0), Pr (xly) represents the conditional probability of x knowing that y is realized and where 0 = (Z, e) is the pair consisting of the effective atomic number and the thickness of the material. The MAP estimation criterion is an optimal criterion to search for the maximum posterior probability, ie: ttAir, - argmax (Pr (91Sa)) (2) 0 Assuming that the probability distribution of 0 is uniform that is, if all material and material thicknesses to be analyzed are equiprobable, Pr (9) is a constant and then an estimate can be made in the sense of the maximum likelihood criterion, ie: = argmax (Pr ( Sa 19)) (3) For a given transmission spectrum Sa (observation), the function V (0) = Pr (Sa e) is called the likelihood function of 9. The transmission spectrum Sa can be considered as a random vector of dimension N parameterized by 9, in other words the distribution law of probability of Sa is parametrized by 9. V (9) then represents the likelihood (or in an abusive way the probability) that the parameter of the law of distribution is 9, account given the realization sa.
    [0007] Assuming that the components of the random vector Sa are independent, in other words that the scores in the different channels of the spectrum are independent random variables, the likelihood function can still be written: V (0) = n Pr ( Fi ': 19) (4) Assuming furthermore that the material analyzed is one of the calibration materials, the likelihood function is simply given by: V (Z',) = n Pr (il ': (Z ', ec)) i = 1 N (5) where nic (Zc, ec) denotes the score of channel i in the calibration phase for the sample of effective atomic number Zc and thickness ec.
    [0008] According to a first embodiment, a statistical modeling of the transmission rate of the material in each energy channel is used: when the number N of channels is sufficiently large (finely discretized spectrum) and the measurement time T sufficiently long, the rate The transmission coefficient in each channel follows a distribution law (Gaussian.) We then denote ai = nal the coefficient of transmission of the material in the no, i energy channel i during the measurement, where no`li is the score of the channel. under conditions of full flow, ie in the absence of the material and for the same irradiation time Similarly, we denote a ". = + n the transmission coefficient in the energy channel no , ii of the sample during the calibration phase The probability Pr (a) of the transmission coefficient follows the Gaussian law: (ai) 2 (6) Pr (ai) oc exp with o-2 = 2o-2 and therefore the probability of the nia score is given by: - (ne: - ni 2 2 (n ".) 2 with du, = no, i = 0.1 Pr (n /) = exp (7) The ratio of, expresses the drift of the source and detector set between the calibration instant and the moment of the measurement. In the absence of drift, we have du = 1. We deduce from expressions (4) and (7) that: V (Z ', ec) = N1 exp i = 1 a -c) 2 ini n, (8) ni. 2 (c) 2 i = 1 Equivalently, the likelihood function can still be written from the transmission coefficients in the following form: V (Z ', ec) = N 1 ai no i = 1 x-1N 1 (2 (8 ') L i = 1 exp, where it is recalled that the nic score depends on the effective atomic number and the thickness of the standard, for which reason it will also be denoted n ". (Zpc, e, c) Similarly, the transmission coefficient aic will also be denoted aic (Z, e, c) According to the first embodiment of the invention, for each calibration material, the maximum of the likelihood function on the various thicknesses, ie the value of the likelihood function: V = max (V (Z '(9) P' q The effective atomic number of the material to be analyzed is then estimated by averaging the numbers effective atomic values of the calibration materials weighted by the respective values of the likelihood function for these materials, ie: IVpZpc 2 = P-1 P (10) Vp p = 1 According to a variant of this first embodiment, a first interpolation is carried out for each material p, depending on the thickness, between the calibration spectra (or, if appropriate, an extrapolation from them) to determine an interpolated calibration spectrum for each thickness ee [einin, en.] (where [emiii, emax] is a range of thickness assumed common to all calibration samples). The likelihood function V (Zpc, e) can then be evaluated over a thickness range. This evaluation is obtained by replacing in expression (8) the scores nt (Zpc, e, c) of the calibration spectra by their interpolated values defined by: (q + 1 - e - e q + 1 q) ln [ ni (Z, eqc +1) 1 (11) ln [ni '(Z, e) 1 + ln Ln "(Z, e) 1 = (e - e, e - e q + 1 q) where eq and egc +1 are the thicknesses such that eq <e <eqc + 1 (it is assumed here that the thicknesses are indexed by increasing values).
    [0009] In the case of an extrapolation to a thickness greater than the highest known thickness, eQ, the expression (11) is used where, preferably, eq + 1 corresponds to the highest thickness of the standard. In the case of an extrapolation to a thickness less than the lowest known thickness, e1, the expression (11) is used, where eq is preferably the lowest thickness of the standard.
    [0010] Expression (11) assumes, however, that the source and detector assembly has not drifted between the calibration instant and the instant of measurement (i.e., = 1, i = 1, .. .,NOT ). In the presence of drift, the scores of the different channels should be normalized by the full flux scores, ie: (, e - q + 1 e - eq i (Z p'eqc) i, i (Zpc, eqc (e - e, e - eq i, eqc +1) i (Z, eqc +1) ln ln (12) where no i (Z, eq) and no i (Z, eqc, i) are respectively the full flow scores in the channel i during the calibration with the calibration material p for the sample thicknesses eq and egc, i, respectively, and where no i (Z, e) is the interpolated full flow score: 25 Z e - 'c ) c e + (Z ee (13) p, q + 1 0.1 P e 'c) c - Z eee =' c) c P '/) c- eq p' q q + 1 0.1 p, q +1 q eq + 1 qe - ecc q + 1 q In any case, once the interpolation / extrapolation of the likelihood function is performed as a function of the thickness, we can deduce the value of the function marginal probability: ena (14) Vp = (V '(ZeP e)) of gear If the materials (Z' e) are not equiprobable, then the marginal likelihood function is written: ena Vp = (V '' (Z'P e)) Pr (Z'P e) key Pr (Z'P 'e) designating the prior probability of the material p to the thickness e.
    [0011] The effective atomic number of the analyzed material is then estimated as an average of the effective atomic numbers of the calibration materials, weighted by the respective values of the marginal likelihood function for these materials, namely: IV; Z pc Z P IV; p = 1 FIG. 1 shows in the form of a flow chart the method for estimating the effective atomic number of a material from its transmission spectrum, according to the first embodiment of the invention. (15) (16) Prior to the estimate itself, it is assumed that in a step 110 a calibration was performed from a plurality PQ of samples of P different calibration materials, each material being represented by Q samples of different thicknesses. The effective atomic numbers Z, P, p = 1, ..., P, of these calibration materials are assumed to be known. They can be for example simple bodies for which the effective atomic number corresponds to the atomic number of this body. The transmission spectra obtained for the PQ samples, called calibration spectra, are denoted Sc (Zpc, e, c) or more simply Scp,, p = 1, ..., P, q = 1, ..., Q . Each spectrum Sc (Zpc, e, c) can correspond in practice to the average of a large number (several hundred or even thousands) of calibration acquisitions. The calibration step 110 may have been performed once and for all or be repeated regularly or even be systematically performed before any new measurement. It is thus clear that this step is optional in the estimation method. She was represented for this reason in broken lines.
    [0012] In step 120, a measurement is made of the transmission spectrum of the material to be analyzed. We obtain the transmission spectrum sa = (nia, n2a, ..., nNa) r In step 130, we calculate from the transmission spectrum Sa and the PQ calibration spectra, the PQ values V (Zpc, e , c) the likelihood function using expression (8). These values indicate the respective proximity of the spectrum measured with each of the PQ spectra of the calibration samples. In step 140, the maximum likelihood values V or the marginal likelihood values V are calculated; for the different calibration materials, depending on the variant considered.
    [0013] In step 150, the effective atomic number of the material is estimated as an average of the atomic numbers of the calibration materials weighted by the maximum or marginal likelihood values calculated in the previous step. (nie, n2a, ..., nNa T) = According to a second embodiment of the invention, a statistical modeling of the transmission spectrum of the material to be analyzed is used. To do this, the number of photons transmitted by the analyzed material is determined by assuming that the arrival of the photons in each energy channel follows a Poisson's law. More precisely, for each energy channel i, the probability of having exactly one nia photon score transmitted by the material during the irradiation time T, knowing that the material has an effective atomic number Z and thickness e, is given by: na (17) Pr (na, e) = v tic /! where y. is the average number of photons transmitted by the material (Z, e) in the channel i during the irradiation time T (chosen identical for the measurement and the calibration). As in the first embodiment, we have PQ transmission spectra Sap corresponding to PQ calibration samples (P materials, Q thicknesses for each material). In the second embodiment, the spectra Sap are interpolated and, where appropriate, extrapolated to obtain a calibration spectrum (Z, e) = (nic, n2c for each effective atomic number Z included in an interval [Zmin and each thickness e included in an interval [emin, emax] The laws of interpolation of the spectra Sap, as a function of the effective atomic number and the thickness are specified below. has an effective atomic number Z and a thickness e, the average number of photons transmitted by the material, via, during the irradiation time can be connected to the score ri.> of the calibration spectrum Sc (Z, e) (non-noisy ) in the same channel, by: -na with, u = `) no where Foc = i In0c. and 120a = no a are respectively the total number of photons in the full flux spectrum (i.e. in the absence of material), during calibration and during measurement. The report reflects the drift of the spectrometer between the calibration phase and the measurement phase. This drift may be due to the source and / or detector. In the absence of drift, = 1. The natural logarithm of the likelihood function given by (5) is expressed as follows: ln (V (Z, e)) = ln [Pr (n`, '(Z, e)) 1 (19) and, in taking into account (17) and (18): ln (V (Z, e)) = + In 'lnv, -! (20) = / te + il "'ln (Jin".) -! with Fia = In "the number of total photons transmitted on all the channels during the calibration phase.
    [0014] We look for the effective atomic number and, if necessary, the thickness that maximizes V (Z, e), or equivalently ln (V (Z, e)). In other words, we generally search for the pair (Z, e) leading to the probability distribution of Sc (Z, e) closest to Sa. The last term of (16), In "', depending only on the 17 (18) transmission spectrum of the analyzed sample, it can be overcome in the expression of ln (V (Z, e)) which then reduces to: ln (V (Z , e)) = -, a + In ': In (, uni) (21) Finally, the effective atomic number and, if applicable, the thickness of the analyzed material can be estimated by: (2mL, = arg max - "DT. (Z, e) + In`: ln (" in ". (Z, e)) (22) Ze [Z min, Z maxi ee [e min, max e 10 the search for the maximum being carried out on all the pairs (Z, e) of the [Zimn, Zmax] x [emin, emax] block In practice, those skilled in the art will be able to implement known search algorithms, in particular The thickness not being necessarily a parameter of interest for the analysis of the material, we can restrict the search to the only parameter Z by using the the marginal function of the likelihood function: ema '(23) V (Z, e) of p (Z) = zn_en "" Sz' '' in 'en'-v (z, e) dz.de 20 where likelihood function V (Z, e) is given by (21). According to a first variant of the second embodiment, the effective atomic number of the analyzed material is estimated by the value corresponding to the maximum of the marginal density: 2.arg = argmax (p (Z)) (24) Alternatively, according to a second Alternatively, the effective atomic number of the analyzed material can be estimated using the expectation of Z, that is, the average of Z weighted by the marginal density: rzma (25) = j ', , Zp (Z) dZ oy z Other estimates using the likelihood function V (Z, e) or its p (Z) marginal density may be envisaged by those skilled in the art without departing from the scope of the present invention. . As mentioned above, the second embodiment requires an interpolation (or, if necessary, an extrapolation) of the likelihood function (or its logarithm) both as regards effective atomic numbers and thicknesses. At the end of the calibration, we have PQ calibration spectra Scp, and therefore, for each calibration sample p, q scores c (Zpc, enc), i = 1, ..., N. The interpolation of the calibration spectra over a thickness range [e., Emax] is obtained by means of the expression (11) in the absence of drift of the spectrometer (source and detector) and by means of the expression (13). ) if the spectrometer is affected by a drift. Similarly, if the spectra are to be extrapolated below the value and / or beyond the eQc value, the expressions (12) and (14) will be used respectively in the absence and in the presence of drift.
    [0015] In all cases, for a given material p, and for any thickness ee [eimii, emax], an interpolated calibration spectrum defined by Zp, e), i = 1 N is obtained thus using the scores interpolated in this way. Equation (21) can be used to calculate the likelihood function irrespective of the thickness ee [emin, emaj, ie ln (V (Zpr, e)) = - / + In 'ln (, unic (Z; e)). Similarly, the interpolation (or, if necessary, an extrapolation) of the calibration spectra is carried out over a range of effective atomic number Ze [Z, Z]. To do this, we start from the calibration spectra already interpolated in thickness, and thus from the scores nic (Zpr, e), i = 1,, N; p = 1, ..., P. The dependence of ni '(Z, e) as a function of the effective atomic number Z is modeled by the following law: nc (Z, e) = ni :, exp (-p (aZr + PI)) (26) no is the full-channel spectrum score in channel i when measuring the transmission spectrum for the sample of effective atomic number Z and thickness e, or again in logarithmic form: ln [nic (Z, e) 1 = ln Ln, - p (aZr + fi) (26 ') where cy, fl, r are constants and p is the density of the material. This modeling is based on the fact that the interaction cross section of the photons with the atoms of the material is decomposed into a Zr-dependent photoelectric cross section (where the exponent r ".62, this value can be optimized experimentally) and a Compton cross section that does not depend on it (constant, 6) The interpolated value n ". (Z, e) between two consecutive effective atomic numbers of calibration materials, i.e. for Z; <Z <Zr '. +1, is then given by: Pp Pp + 1 ((71 P)) pj ± ln [r ((Zp pc, e) 1 + 11 Zpc + i, e) 1 - Pp P p + 1 (27) Zc Zr Zr - (Z where yl = (P +1) r and where ppp p_pi are the (z +1) r - Zp) r r2p (Z pc + if (Z pc densities of materials p and p +1. similar expression can be used in the case of extrapolation, but the relation (27) assumes that the source and detector set has not drifted between the calibration instant and the moment of the measurement (ie ie = 1, i = 1, ..., N) In the presence of drift, the scores of the different channels should be normalized by the full flux scores, ie: ((Z 'p nos (Zp, e ) (ni (Z +1, e) (Zc e) = ± 2 19 0 p yl - P 1 +1, - P19 ln p + 1 P ln niC (Z, e) _ 0. (Z, e) ln (28) where no (Z, e) and no (Z +1, e) are the full flux scores in channel i, relative to the interpolated calibration spectra at thickness e, for the respective calibration materials of number effective atoms Z pc and Zcp + i, and where n o (Z, e) is the full flux score for this same channel, interpolated to the effective atomic number Z, defined by: (Z +1, e) - no (Z, e) n0c (Z'-F e) Z 'p - 0 (Z' ', i p1,, i pe) Zp + 1 Ze Ze Ze Ze p + 1 p p + 1 p (29) The density of the material varies slightly with the effective atomic number Z. This law of variation can for example be approximated by a linear law, in other words: Pp + 1 Pp Pp + 1Zp PpZp + 1 (30) P = Ze -Ze Ze -Ze p + 1 p p + 1 p The interpolation of the calibration spectra on the [Z., Zmajx [eimn, emaj] keypad was performed above by interpolation on the thicknesses followed by a second interpolation on the effective atomic numbers. Other interpolation formulas other than those skilled in the art will also include that the calibration spectra could alternatively have been interpolated on the effective atomic numbers followed by interpolation on the thicknesses. Fig. 2 shows in the form of a flow chart the method for estimating the effective atomic number of a material from its transmission spectrum, according to the second embodiment of the invention. As in the first embodiment, a calibration is made in 210 from a plurality PQ of samples of P different materials, each material being represented by Q samples of different thicknesses. The effective atomic numbers Z, P, p = 1, ..., P, of these calibration materials are assumed to be known. At the end of this step, a plurality PQ of transmission spectra Scp, respectively obtained for the PQ standards, are available. This step is optional in that it is not necessarily repeated at each measurement and may have been done once and for all before a measurement campaign. In step 215, the transmission spectra Scp are interpolated to obtain calibration spectra Sc (Z, e) for each value of ZE [Z, 7.] And each value of ee [emin, emax]. In practice, these interpolations are carried out for a large number of discrete values (much greater than PQ) corresponding to a fine sampling of the intervals [Z, Z.1 and [e., Emax] - This step, like the previous one, can be carried out once and for all, prior to measurements.
    [0016] In step 220, a measurement is made of the transmission spectrum of the material to be analyzed in a plurality N of energy channels, ie its = (nia, n2a). At step 230, the transmission spectrum Sa is calculated. = (nia, n2) T and calibration spectra Sc (Z, e) for ZE [Z, m ,,, Zmax] and ee [emm, emaj, the likelihood function, or its logarithm given by the expression ( 21).
    [0017] Optionally, in step 240, the marginal density of the likelihood function is calculated using expression (23). In step 240, the effective atomic number of the material to be analyzed is estimated as that which maximizes the likelihood function (see expression (22)) or its marginal density with respect to Z (see expression (23)), or even as the average of the effective atomic number on [Zmiii, Z,] weighted by said marginal density (see expression (25)). The estimation method according to the invention was evaluated using a simulation. The simulated spectrometer is a CdTe-based detector composed of 800 x 800, um2 and 3mm thick pixels. The induction effect related to the propagation of charges in the detector as well as the charge sharing effect with the neighboring pixels was taken into account, as was the degradation of the resolution of the detector response with the intensity of the flow. A spectrum of 20000 incident photons between 15 keV and 120 keV was simulated. The number of energy channels considered was N = 105 (not 1 keV).
    [0018] The calibration materials were Polyethylene (PE), Polyoxymethylene (POM) or DelrinTM, Polyvinylidene Fluoride (PVDF) or KynarTM. The samples of these materials were of thickness ranging from 0.5cm to 20cm in steps of 0.5cm. In other words, in this case P = 3 and Q = 40. The effective atomic numbers of the calibration materials were taken respectively at Z (PE) = 5.80; Z (PO) = 7.26; Z (PVDF) = 8.20. The sample to be analyzed was Polytetrafluoroethylene (PTFE) or TeflonTM (effective atomic number Z (PTFE) = 8.56) and a thickness of 4.5 cm.
    [0019] Fig. 3A represents the likelihood function V (Z, e) of a noisy realization of a transmission spectrum of 5.5cm of PTFE. The step of discretization in effective atomic number Z was 0.025 and that in thickness e of 0.025 cm. Fig. 3B represents the marginal likelihood function density (or marginal likelihood function) as a function of the atomic number as defined in the expression (23). Note that this function has a peak for 2marg = 8.42 (estimator defined by expression (24)). The maximum likelihood estimate (estimator defined by (22)) gives 2ML = 8.52 and the marginal density weighted average (estimator defined by (25)) gives 211,0y = 8.46 . We see that in this case, the 2ML estimator is the closest of real value (Z (PTFE) = 8.56). Fig. 3C represents the marginal density of the likelihood function as a function of the thickness. We see that it has a peak at 5.2 cm, with here a prediction error of 0.7 cm.
    [0020] These estimates can be further improved by taking into consideration a larger number of calibration materials and using finer discretization in effective atomic number and thickness.
    权利要求:
    Claims (17)
    [0001]
    REVENDICATIONS1. A method for measuring the effective atomic number of a material for a predetermined X or gamma spectral band, characterized in that a transmission spectrum (Sa = (nia) of a sample of said material is measured (120, 220) in a plurality (N) of energy channels of said spectral band, and calculating (130,230) a likelihood function of the effective atomic number and the sample thickness of said material from the thus measured transmission spectrum and a plurality of transmission spectra (Sc (Zpc, e, c)), said calibration spectra, obtained for a plurality of calibration material samples having known effective atomic numbers and known thicknesses, said likelihood function being calculated for at least said known effective atomic numbers (Z;) and the thicknesses (eqc) known to provide a plurality of values of said likelihood function, it is estimated (140, 240) the atomic number e ffective () of said material from the values of the likelihood function thus obtained.
    [0002]
    2. Method for measuring the effective atomic number of a material according to claim 1, characterized in that the calibration spectra are interpolated to obtain an interpolated calibration spectrum for each effective atomic number belonging to a first interval ([Z ., Z.1), and for each effective atomic number belonging to this interval and each given thickness, a value of said likelihood function is calculated.
    [0003]
    Method for measuring the effective atomic number of a material according to claim 1 or 2, characterized in that the calibration spectra are interpolated to obtain an interpolated calibration spectrum for each effective atomic number belonging to a second interval ([ eimii, emax]) and that for each thickness belonging to this interval and each given effective atomic number, a value of said likelihood function is calculated.
    [0004]
    4. Method for measuring the effective atomic number of a material according to claim 1, characterized in that, for each calibration material (p) of known effective atomic number (Zcp), the maximum value (V "of the likelihood function among the values of the likelihood function (V (Z, q = 1, ..., Q) obtained for the known thicknesses of the samples of this material, said maximum value then being associated with the material.
    [0005]
    5. Method for measuring the effective atomic number of a material according to claim 3, characterized in that for each calibration material (p) of known effective atomic number (Zpc), an interpolation is made between the calibration spectra relative to known thicknesses for determining an interpolated calibration spectrum for each thickness of a given thickness interval ([and., emax]), the likelihood function being evaluated on this thickness range from the interpolated calibration spectrum , and that the maximum value of the likelihood function is determined over said thickness interval, said maximum value being associated with the material.
    [0006]
    6. Method for measuring the effective atomic number of a material according to claim 4, characterized in that the effective atomic number (Z) of the material is estimated as the average of the known effective atomic numbers of the calibration materials, weighted by the values maxima of the likelihood function associated with them respectively.
    [0007]
    7. A method of measuring the effective atomic number of a material according to claim 5, characterized in that the effective atomic number (Z) of the material is estimated as the average of effective atomic numbers belonging to a first interval ([Zmin, Z. ]), weighted by the maximum values of the likelihood function associated with them respectively.
    [0008]
    8. A method for measuring the effective atomic number of a material according to claim 3, characterized in that for each calibration material (p) of known effective atomic number (Zpc), an interpolation is carried out between the calibration spectra relative to known thicknesses for determining an interpolated calibration spectrum for each thickness of a given thickness interval ([e .., emaj), the likelihood function being evaluated over this thickness range from the interpolated calibration spectrum , then integrated over this thickness range to give a marginal likelihood function value associated with this calibration material.
    [0009]
    9. A method for measuring the effective atomic number of a material according to claim 8, characterized in that the effective atomic number (Z) of the material is estimated as the average of the known effective atomic numbers of the calibration materials, weighted by the values of the marginal likelihood function respectively associated with these calibration materials.
    [0010]
    10. A method for measuring the effective atomic number of a material according to one of the preceding claims, characterized in that the values of the likelihood function are determined for each pair (Zpc, e, c) of effective atomic number and thickness by: V (Z'P N1 ec) = exp a "i = 1 where the na, i = 1, ..., N are the values of the transmission spectrum of the material in the different channels, nic, i = 1, ..., N are the values of the transmission spectrum of the calibration material in these same channels and the, is the ratio between the number of photons received in the channel i in the absence of material during the calibration (i) and the number of photons received in the absence of material when measuring (na) in the same channel.
    [0011]
    11. Method for measuring the effective atomic number of a material according to claim 3, characterized in that, for each pair (Z, e) of effective atomic number belonging to a first interval and of thickness belonging to a second interval, the likelihood function V (Z, e) is calculated from: ln (V (Z, e)) = + ln Gun "where the na, i = are the values of the transmission spectrum of the material in the different channels , n>>, i = 1, ..., N are the values of the interpolated transmission spectrum in these same channels, y is the ratio between the total number of photons received in the set of channels and in the absence of material when of the measurement and the total number of photons received in the same set of channels and in the absence of material during the calibration, and TT, is the total number of photons received in the same set of 20 channels in the presence of the calibration material , during calibration.
    [0012]
    12. A method for measuring the effective atomic number of a material according to claim 11, characterized in that the atomic number of the material is estimated as that () which maximizes the likelihood function V (Z, e) on the block 25 by the Cartesian product between the first interval and the second interval.
    [0013]
    13. A method for measuring the effective atomic number of a material according to claim 11, characterized in that the marginal density (p (Z)) of the likelihood function on said first interval is determined by integrating the density of the likelihood function on the second interval.
    [0014]
    14. A method for measuring the effective atomic number of a material according to claim 12, characterized in that the effective atomic number of the material is estimated as that (2maig) maximizing the marginal density on said first interval.
    [0015]
    15. A method for measuring the effective atomic number of a material according to claim 12, characterized in that the effective atomic number of the material is estimated as the average of the effective number (Zmoy) weighted by the marginal density of the likelihood function on said first interval.
    [0016]
    16. A method for measuring the effective atomic number of a material according to one of claims 3, 11-15, characterized in that for a thickness e between a first known thickness eqc and a second known thickness egc + 1 where eqc <e <eqc, i, we obtain an interpolated calibration spectrum Sc (Z`, e) for the effective atomic number Z 'and the thickness e from the calibration spectra Sc (Zc, e, c) and Sc ( Zc, e, c + i) respectively obtained for the same effective atomic number and the respective thicknesses eqc and egc, i, by means of: (e, - e q + 1 e - e - q + 1 q) ln Ln " ln Ln ". , ecq + i) 1 ln [r ((Z ', e) 1 =, eqc) 1+ (e - e, e - e - q +1 q) where nic, e), (Z', eqc) and r ((Zc, eqc + i) are the respective values of the spectra Sc (Z ', e), (Z', eqc) and Sc (Z ', eqc +1) in the channel i of the spectral band.
    [0017]
    17. A method for measuring the effective atomic number of a material according to one of claims 2, 11-16, characterized in that for an effective atomic number Zcompris between a first known effective atomic number Zpc and a second known effective atomic number Zpc + i where Zpc <Z <Zpc + 1, we obtain an interpolated calibration spectrum Sc (Z, ec) for the effective atomic number Z and the thickness ec from the calibration spectra Sc (Z, ec) and Sc (Z +1, ec) respectively obtained for the same thickness ec and the respective atomic numbers Zpc and Zpc + i, by means of: (c) 1 = 1-2,11, 212p 1) ln [1+ Pp Pp + 1 ((ln [nc (ec) 1 + 1,2 p ln [n, C cp ec) 1 P p) t 19, Pp + 1) where n ". (Z, ec), (Z, ec (Zp +1, ec) are the respective values of the spectra Sc (Z, ec), Sc (Z'19 'ec) and Sc (Zcp + 1, ec) in channel i of the spectral band, nos is the score of Ze - Zr, r is p + 1 Zr - (Ze full flux spectrum in channel i, yl = = (Zep + i) (z;) P (Z pc + i) r (Z pc a real constant the predetermined, pp, pp + 1 are respectively the densities of the materials p and p + 1, and where p is the density of the atomic number material Z obtained by interpolation between the densities pp and pp ± i.
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    优先权:
    申请号 | 申请日 | 专利标题
    FR1363174A|FR3015681B1|2013-12-20|2013-12-20|METHOD OF MEASURING THE EFFECTIVE ATOMIC NUMBER OF A MATERIAL|FR1363174A| FR3015681B1|2013-12-20|2013-12-20|METHOD OF MEASURING THE EFFECTIVE ATOMIC NUMBER OF A MATERIAL|
    EP14821527.0A| EP3084406B1|2013-12-20|2014-12-09|Method for measuring the effective atomic number of a material|
    JP2016540535A| JP6427195B2|2013-12-20|2014-12-09|How to measure the effective atomic number of a substance|
    PCT/EP2014/076960| WO2015091083A1|2013-12-20|2014-12-09|Method for measuring the effective atomic number of a material|
    US15/106,569| US20160363545A1|2013-12-20|2014-12-09|Method for measuring the effective atomic number of a material|
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