Methods for processing X-ray or gamma ray spectra

Abstract

The invention is based on a method for processing X-ray and gamma radiation spectra acquired by a spectroscopic device (1). The processing method takes into account a spectral variance matrix (D), which models the energy response of the device. The method comprises using the spectral variance matrix to establish a transfer matrix (U,U',D'). The transfer matrix is ​​then used to establish a direct model, linking measured variables to form an input vector (m) and linking estimated variables to form an output vector. The invention of the direct model allows to estimate the output vector (a,s,h,ε). The invention can be applied to quantify the radioactivity of an object to be examined or to perform a calibration of the energy or efficiency of a spectroscopic device.

Description

[Technical field]

[0001] The technical field of the invention is spectroscopy applied to the detection of ionizing radiation, which essentially includes X-ray or gamma spectroscopy. [Background technology]

[0002] Devices for detecting ionizing radiation based on gaseous, semiconductor or scintillation detector materials are able to obtain electrical pulses formed by the interaction of radiation with the detector material. The amplitude of each pulse depends on the energy deposited by the radiation in the course of each interaction. These devices are usually connected to a spectrometric measurement circuit. The fields of application are wide and include, in particular, the measurement of nuclear waste, installations or facilities or the performance of radiological environmental monitoring.

[0003] Spectroscopic measurement systems are nowadays widely used in industry. Software allows parameterization of the pulse processing and automatic measurement control and analysis.

[0004] However, some steps are difficult to automate and still leave a lot of room for manual adjustments, including, for example, energy calibration, efficiency calibration, or specific measurement interpretation.

[0005] The invention described below facilitates automation and reproducibility of the major steps involved in a calibration or measurement analysis. Summary of the Invention

[0006] A first subject of the invention is a method for processing an X-ray or gamma-ray radiation spectrum produced by a spectrometric measuring device, said device comprising: a detector configured to detect X-ray or gamma ray photons and to form, upon each detection, a pulse having an amplitude dependent upon the energy emitted by the interacting X-ray or gamma ray photon in the detector; a spectrometry circuit configured to generate a spectrum corresponding to the number of photons detected in the various channels, and an amplitude or energy corresponding to each channel; The method comprises the steps of: a) positioning said device facing an object that may contain one or more radionuclides that emit x-ray or gamma ray photons incident on said detector, each radionuclide emitting photons at at least one emission energy; b) the detector detects a portion of the incident photons and forms a spectrum of the detected photons, the spectrum including peaks extending around each emission energy of each radionuclide, each peak resulting from a pulse detected in a channel and corresponding to one of the emission energies; c) processing the spectrum to obtain a quantity of pulses detected at each peak of the spectrum; The method further comprises the steps of: c1) taking into account the list of radionuclides present or likely to be present in said object; c2) consider an input vector where each term contains the amount of pulses in each peak; c3) considering a spectral dispersion matrix, each term being associated with a channel and an emission energy, the energy of which corresponds to the probability that an incident photon with said emission energy is detected in said channel; c4) forming a transfer matrix based on the spectral dispersion matrix; c5) Considering a direct model, the input vector is obtained by the matrix multiplication of the transfer matrix and the output vector, and each term of the output vector corresponds to: Radioactivity of at least one radionuclide; or the number of photons detected at an energy corresponding to the emission energy of the radionuclide; · or detection efficiency at the emission energy of the radionuclide; c6) inverting the direct model to estimate the output vector. Sub-step c6) may comprise estimating said input vector together with said output vector. According to one embodiment, Step c) comprises considering a matrix of reference spectra, each term of which relates to a radiation energy and a radionuclide, and each term corresponds to the number of photons detected in a peak centered on a channel corresponding to said radiation energy, when said activity of said radionuclide is equal to a predetermined reference activity; In step c), the transfer matrix is ​​the product of the spectral dispersion matrix and the matrix of a reference spectrum or its transpose, each term of the transfer matrix being associated with a radionuclide and a channel, each term of the transfer matrix corresponding to the number of photons emitted by a radionuclide in the reference spectrum and detected in the channel; The output vector includes a term representing the radioactivity of each radionuclide present in the object. The reference radioactivity may be 1 Bq. According to one embodiment, In step c), the transfer matrix is ​​the spectral dispersion matrix; The output vector includes terms each representing a number of photons detected in a channel corresponding to a different emission energy of the radionuclide present in the object.

[0007] Sub-step c6 may comprise estimating a width of each peak of the input vector, each estimated width parameterizing the spectral covariance matrix.

[0008] Sub-step c6 comprises estimating the position among the channels corresponding to the centre of each peak of the input vector, each estimated position parameterising the spectral covariance matrix.

[0009] According to one possibility, the object comprises a calibration radionuclide having a known radiation energy; The method further comprising: selecting a channel whose spectrum includes a number of photons greater than a threshold based on the output vector; comparing said selected channel with the emission energy of said calibration radionuclide; determining an energy function linking each channel to an energy based on said comparison.

[0010] According to one embodiment, The object comprises a calibration radionuclide whose properties and optionally its radioactivity are known; Step c) includes considering an incidence vector, each term of which corresponds to the number of photons incident on said detector at each emission energy; In step c), the transfer matrix is ​​a product of each term of the spectral dispersion matrix associated with an emission energy and a value of the incidence vector at the emission energy, each term of the transfer matrix being associated with an emission energy and a channel, each term of the transfer matrix corresponding to the number of photons emitted by each calibration radionuclide and detected in the channel; The output vector includes terms each representing the detection efficiency of the device at various emission energies.

[0011] Step c) may comprise considering an energy function, said energy function being: The energy function establishes a correspondence between a rank and an energy value of a channel; the energy function is a parametric function parameterized by at least one parameter; The method further comprises a sub-step c6) of estimating at least one parameter of the energy function.

[0012] Step c) may comprise considering a resolution function, said resolution function being: The resolution function determines a width of each peak as a function of channel or energy; the resolution function is a parametric function parameterized by at least one parameter; The method further comprises a sub-step c6) of estimating at least one parameter of the resolution function.

[0013] The method may take into account a shape function, which establishes an analytical relationship that models the shape of each peak in the detected spectrum.

[0014] A second subject of the invention is a device intended to obtain a spectrum of X-ray or gamma-ray photons emitted by an object possibly containing a radioactive nuclide, comprising: a detector configured to detect X-ray or gamma ray photons and to form, upon each detection, a pulse having an amplitude dependent upon the energy emitted by the interacting X-ray or gamma ray photon in the detector; a spectrometry circuit configured to form a spectrum corresponding to a distribution of amplitudes of the pulses detected by the detector; and a processing unit programmed to carry out step c) of the method according to the first subject of the invention.

[0015] A third subject of the invention is a medium connectable to a computer and comprising instructions for carrying out step c) of the method according to the first subject of the invention on the basis of the spectrum obtained from the spectroscopic detector, said medium being integrated in the computer or connected to the computer by a wired or wireless link.

[0016] The invention will be better understood by reading the description of exemplary embodiments presented in the remainder of the specification, with reference to the following drawings, in which: [Brief description of the drawings]

[0017] [Figure 1] 1 shows an example of an apparatus for carrying out the present invention. [Figure 2A] An example of a spectrum is shown. [Figure 2B] Detail of FIG. 2A. [Figure 3A]Here is another example of a spectrum. [Figure 3B] The spectrum in FIG. 3A has had the baseline removed. [Figure 4] 1 illustrates an example of a spectral variance matrix. [Diagram 5] Each term represents a vector corresponding to the detection efficiency at one energy. [Figure 6] 1 shows an example of a matrix of reference spectra. [Figure 7] 1 illustrates the steps of a first embodiment. [Figure 8] 3 shows a transfer matrix used in the first embodiment. [Figure 9] 2 shows a schematic diagram of the steps of the second embodiment; [Figure 10] 13 shows an example of peak region extraction performed by implementing the second embodiment. [Figure 11] 3 illustrates diagrammatically the steps of the third embodiment; [Figure 12] 13 shows a transfer matrix used in the third embodiment. [Figure 13] 13 shows an example of peak region extraction performed by implementing the third embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0018] Figure 1 shows an apparatus 1 for carrying out the invention. The apparatus is a measurement system including a detector 10 capable of interacting with ionizing radiation 5 emitted by an object 2. The object 2 in this case is nuclear waste, which contains various radionuclides 2 j Typically, the radionuclides that may be present in the measured object are known in advance. In particular, a list of the radionuclides that may be present in the analyte can be created. The index j denotes each radionuclides.

[0019] Ionizing radiation is understood to mean, for example, X-ray or gamma-ray photon radiation formed from photons with energies between 1 keV and 2 MeV.

[0020] In the illustrated example, the detector comprises a germanium (Ge) semiconductor material, but may also comprise semiconductor materials commonly used to detect ionizing photons, e.g., Si, CdTe, CdZnTe. The photons forming the incident radiation form interactions in the detector material. A bias voltage V is applied to the detector material. Each interaction generates charge carriers that are collected by an electrode, typically the anode.

[0021] Other types of detectors, such as a scintillator coupled to a photon / charge carrier converter, or a gas detector such as an ionization chamber, may also be used, provided they are capable of collecting a quantity of charge Q under the influence of energy E released by ionizing radiation during interaction within the detector 10. Common scintillator detectors include NaI(Tl) or LaBr3.

[0022] The detector 10 is connected to an electronic circuit 12 configured to generate a pulse whose amplitude is dependent on, and preferably proportional to, the amount of charge collected during the interaction, which corresponds to the energy deposited by the radiation during the course of the interaction.

[0023] The electronic circuit 12 is connected to a spectroscopic unit 13, which is placed downstream of the electronic circuit and allows to collect all the pulses formed during the collection period. Each pulse corresponds to the interaction of the incident radiation in the detection material. The spectroscopic circuit then classifies the pulses as a function of the amplitude A and provides a histogram containing the number of detected pulses as a function of the amplitude. This histogram is the amplitude spectrum. It is usually obtained using a multichannel analyzer. Each amplitude is discretized for a channel and each channel is assigned an amplitude band. The value of each channel of the spectrum corresponds to the number of pulses whose amplitude is within the amplitude band assigned to the channel. Each amplitude band corresponds to an energy band, the correspondence is bijective. Each channel is therefore assigned an energy band or an amplitude band.

[0024] The relationship between amplitude and energy can be established by illuminating the detector with a calibration source that emits radiation of known energy, particularly radiation that has at least one discontinuity or energy peak at a known energy value. This operation is usually referred to as energy calibration. For example, in gamma spectroscopy, the detector produces photons of known radiation energy. 152 Exposed to a Eu calibrated light source, producing mainly photons with energy of 661.6 keV 137 It is also possible to use a Cs source, which produces mainly photons with energies of 1173 keV and 1332 keV. 60 It is also possible to use a Co source. The energy calibration allows to establish an analytical relationship between the amplitude and the energy by the energy function f e It allows us to establish the energy function f e Considering that by changing the variables, the amplitude spectrum y A This allows us to obtain the energy spectrum y from

[0025] The spectrum y corresponds to a histogram of the amplitudes of each detected pulse, discretized by energy or amplitude channel. Each channel is assigned an energy band, e.g., [401, 402] keV. The spectrum y is a vector (y1,…,y i ,…,y n ), where n is the total number of channels. Each channel is assigned a rank i, with 1≦i≦n.

[0026] Each channel of rank i has a lower amplitude A i and upper amplitude A i+1 and the amplitude of the detected pulse is A i and A i+1 If the pulse is between i and y, then it is assigned to the channel of rank i.

[0027] Lower amplitude A of each channel i is the lower energy e i The upper amplitude A of each channel corresponds toi+1 is the upper energy e i+1 The correspondence between amplitude and energy is expressed by the energy function f e It is established by:

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[0028] The variable (i-1) / n corresponds to the relative position of the channel with respect to the maximum number of channels in the spectrum. It is the normalized rank of each channel between 0 (i=1) and 1 (i=n+1). The normalization results in an energy function f that is independent of the number of channels n. e It becomes possible to establish, the latter being parameterized.

[0029] The energy function may be a polynomial. For example, it may be a linear function, where β = (β0, β1,) and

number

number

[0030] The vector β is assumed to be known after an energy calibration operation on the detector or is estimated based on the spectrum of radiation emitted from a calibration object of known composition. Optionally, the device comprises a collimator 16 intended to limit the observation range of the detector. The collimator is usually made of a material that attenuates gamma ray photons, for example a lead or tungsten-containing alloy.

[0031] In the illustrated example, the detector 10 is connected to a cryostat 18 that contains liquid nitrogen to keep the Ge detector at an operating temperature.

[0032] The apparatus comprises a processing unit 14 programmed to carry out the steps of the algorithm described with reference to figures 3A to 3C. The processing unit 14 is connected to the spectroscopic unit 13 and receives therefrom the respective spectra measured.

[0033] We will now explain various variables, described below, that are used in the processing operations performed by processing unit 14.

[0034] Useful components of the spectrum

[0035] The purpose of gamma spectrometry is to detect radionuclides 2 present in the object 2. j The objective of the present invention is to identify and preferably estimate the radioactivity of each of the radionuclides. 152 Figure 2B shows the spectrum obtained from a germanium detector exposed to a Eu-containing source. The x-axis corresponds to the channel and the y-axis corresponds to the number of pulses of amplitude corresponding to each channel. Figure 2B is a detailed view of Figure 2A and corresponds to the rectangular area depicted in Figure 2A.

[0036] The spectrum y shown contains multiple peaks, each of which corresponds to the emission energy E of a radionuclide present in the object 2. k These peaks form useful information of each spectrum, on the basis of which it is possible to identify the radionuclides and to quantify their respective radioactivity. The spectrum also contains a continuum c, which corresponds to the photon scattering within the detector or before the photons reach the detector. The continuum corresponds to the spectral parts below and between each peak. In Figure 2B, the continuum c is represented by a dashed line. The spectrum also contains a background noise component b, which is reflected by the statistical fluctuations of the spectrum y.

[0037] The spectrum y can therefore be decomposed as follows:

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[0038] The information about the peaks is contained in vector m, which forms the useful component of spectrum y. Vector m is a vector that contains all the peaks of spectrum y and represents the mixture of peaks in spectrum y. Vectors m and y have the same dimensions.

[0039] We now describe various embodiments involving the processing of a measured spectrum y. One step common to the various embodiments is the extraction of the useful component m from the spectrum y.

[0040] As described in the publication "Contribution to continuum estimation in gamma spectrum by observation by local minima" by K. et al., the continuum c can be estimated by implementing the baseline suppression algorithm. This thus gives the following equation:

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[0041] FIG. 3A shows the spectrum established on a LaBr3 spectrometer detector with dimensions 1.5 inches by 1.5 inches. FIG. 3B shows the spectrum after extracting the continuum. FIG. 3B contains the useful component m along with background noise b.

[0042] Alternatively, the vector m may be established using dedicated software to extract the spectroscopic peaks individually, by baseline suppression or estimation, or the vector m may be obtained from the concatenation of each peak extracted individually from the measured spectrum.

[0043] In the following, if an object potentially contains q radionuclides, jEach radioactivity forms a radioactivity vector a of dimension (q,1), a1,…a j ,…a q A list of q radionuclides potentially present in the object is created in advance. This includes all gamma-emitting radionuclides that may be present in the object. The radionuclides in the list are of energy E1…E k …E p A photon is emitted with energy E1…E k …E p corresponds to a non-overlapping set of emission energies of radionuclides sorted in ascending order. A subset of this set may be included, e.g., limited to energies where the emission intensity is considered sufficient. Each radionuclide j with activity equal to 1 Bq has an intensity I jk Energy E k The index k is the emission energy E k If it corresponds to intensity I jk will be non-zero.

[0044] The vector m is the contribution u of each radionuclide present in the object. j It is formed by j is a vector of dimension (1,n), and each term u ji corresponds to the amount of photons emitted by radionuclide j and detected in channel i, with 1 ≤ j ≤ n. Therefore,

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[0045] Spectral Variance Matrix

[0046] Under the influence of defects in the detector 10, the circuit 12 or the spectroscopic unit 13, the emitted energy E k The interaction that releases the energy E kThis means that the peaks do not correspond to a Dirac distribution centered on the channel of rank k corresponding to that energy, but rather to a specific region s on either side of the channel of rank s. k FIG. 2B shows three channels of ranks k−1, k, and k+1, corresponding to three consecutive peaks.

[0047] The spectral dispersion is k Full width at half maximum of the peak at w k It is expressed as follows:

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[0048] The resolution function can take various parametric forms, for example:

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[0049] In addition to the full width at half maximum, the spectral dispersion can also be modeled by the shape of the peak. The shape of the peak is determined by a shape function f s The shape function may be pre-determined, for example based on feedback or previous tests. In the following examples, the shape function is considered to be a Gaussian function. For example:

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[0050] Full width at half maximum w k and the shape function f s Considering this, the detector detects the energy E k The probability that a photon emitting d is detected in a channel of rank i is ik can be determined by the following formula:

number

number

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[0051] Probability d ik is the p-number of emitted energies E k (1≦k≦p) and for all n spectral channels (1≦i≦n). ikBased on this, we can form a spectral variance matrix D of dimension (n,p), whose terms D(i,k) are D(i,k)=d ik It becomes.

[0052] The spectral variance matrix D is a function of the resolution function f r , shape function f s , and the energy function f e The spectral variance matrix corresponds to the spectral response of the detector, which is understood to mean a function that models the shape of the peak as a function of energy.

[0053] Figure 4 shows an example of a spectral variance matrix, where the axis X corresponds to each channel i, the axis Y corresponds to each emitted energy peak k, and the axis Z corresponds to the values ​​d ik Corresponds to.

[0054] Alternatively, the spectral dispersion matrix is ​​set based on modeling of the detector and, whenever possible, retuned based on experimental measurements, or may be determined experimentally, especially if the detector is intended to be used repeatedly with the same radionuclide.

[0055] Matrix of reference spectra

[0056] In the course of certain steps described below, a pre-established matrix of reference spectra S of dimension (q,p) is considered, each term S(j,k) of which represents the energy E when a radionuclide j with a given activity is present in the source. k The given radioactivity is, for example, unit activity of 1 Bq for each radionuclide. Thus, each term S(j,k) is the emitted energy E for unit activity of radionuclide 2j. k corresponds to the amount of photons detected at the peak centered at . The reference matrix S has dimensions (q,p).

number

[0057] ε k is the energy E k is the observation efficiency of the instrument at ε k is its energy E k The observation efficiency ε is the number of photons detected at the peak centered at ε divided by the number of photons emitted from the object at that energy. k is obtained by calibration, for example by placing standard sources of known radionuclide and activity on a calibration target that is representative of the target to be measured. Determining the observation efficiency also involves modelling, especially using computer codes based on Monte Carlo methods (e.g. MCNP).

[0058] Each term ε k (1≦k≦p) is the energy E k We can form an observation efficiency vector ε of dimension (p,1) which is the observation efficiency at p, p, p, 1. The observation efficiency ε can be thought of as the product of two vectors:

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[0059] The matrix of the reference spectrum S corresponds to the efficiency response of the detector, which is understood to mean a function that models the ratio between the pulses detected at a peak related to the energy and the number of photons emitted by the source of said energy.

[0060] FIG. 6 shows an example of a matrix of reference spectra. The X-axis corresponds to each radionuclide j, the Y-axis corresponds to each emission energy peak k, and the Z-axis corresponds to the value s jk Corresponds to.

[0061] First embodiment: Quantification of radioactivity

[0062] The purpose of this first embodiment is to process the measured spectrum y to identify each radionuclide 2 possibly present in the test object. j Radioactivity of a j The aim is to estimate the The main steps of this embodiment are shown diagrammatically in FIG.

[0063] Step 100: Measure the spectrum y using a measurement device.

[0064] Step 110: Extract the vector m+b.

[0065] The vector m+b is estimated, for example, by performing a subtraction.

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[0066] Step 120: Consider a preset spectral variance matrix D. In this embodiment, the coefficient kD It is assumed that the spectrum variance matrix is ​​known, except for . If spectrum y contains a peak at 511 keV, coefficient k D Estimate.

[0067] Step 130: Consider a matrix of predefined reference spectra S.

[0068] Step 140: The following transfer matrix U is calculated.

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[0069] U is a matrix of dimensions (n,q), and each term u ij is the contribution of radionuclide j of activity 1 Bq to the photon detected in channel i.

[0070] The transfer matrix U corresponds to the response function of the detector for the radionuclide j under consideration. It may also be taken into account that a screen is present between the detector and the radionuclide. The spectral response function corresponds to the matrix D and the efficiency response function corresponds to the matrix S.

[0071] By considering the transfer matrix U corresponding to a particular given radionuclide, it is possible to create a matrix with one reduced dimension. An example of a transfer matrix U of dimension (8192 × 7) is shown in Figure 8. Each row of the matrix represents an image of the emission peak in each channel for unit activity of the radionuclide.

[0072] Step 150: Estimate the activity of each radionuclide m.

[0073] In this step, each term is the radioactivity a of radionuclide j in the measured object. j We want to estimate a vector a such that m and a are linked by a direct model.

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[0074] The optimization algorithm that minimizes the cost function J is given by vectors a, b, and optionally a scalar k D This is implemented to estimate a is a vector of dimension (q,1). The cost function J is as follows:

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[0075] The estimates of m and a are linked by the relationship m=Ua.

[0076] Another possibility is to assume that J(θ) follows a normal law in θ, so the cost function becomes

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[0077] W is a diagonal matrix of dimensions (n,n) where each term is the inverse of the variance of the observation noise assigned to each channel of the vector y. For example, for each channel i:

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[0078] Regardless of the cost function used, minimize θ=arg by imposing m=Ua. θConstraining min(J(θ)) predetermines the matrix U, facilitating the implementation of the inversion algorithm. Thus, a direct model formulation in the analytical form m = Ua allows the constraints m, a, and optionally k D This allows joint estimation of

[0079] Second embodiment

[0080] The objective of the second embodiment is to process the spectrum y measured during calibration to extract peaks and estimate at least one parameter of the position, area, and full width at half maximum of the peaks present in the vector m. In this embodiment, the object is arbitrary. Unlike the first embodiment, the energy function f e and the resolution function f r is not assumed to be known. The same is true for the observation efficiency ε. Therefore, the following steps are performed to calibrate the detector.

[0081] The main steps of this embodiment are illustrated diagrammatically in FIG.

[0082] Step 200: The measurement device 1 is used to measure the spectrum y.

[0083] Step 210: Extract the vector m+b.

[0084] The vector m+b is estimated, for example, by performing a subtraction.

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[0085] The spectral dispersion matrix D' can be considered as the initial spectral dispersion matrix used before determining the energy function of the detector. The initial spectral dispersion matrix D' is set similarly to the above matrix, taking into account the simplification of an arbitrary energy function where each channel corresponds to 1 keV.

[0086] Unlike the first embodiment, -value w c,k are unknown but constitute the parameters of the spectral variance matrix D'; -Channel E c,k are unknown and constitute the parameters of the spectral variance matrix D'. - the matrix D' is not determined. Its parametric form is known and corresponds to equation (21).

[0087] Step 230: Extract the peak areas.

[0088] In this step, the direct model is considered.

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[0089] TIFF2025501255000027.tif15162

[0090] The optimization algorithm minimizes the cost function J and the vectors s and m, and the parameters w c and E c This allows one to determine the vector of

[0091] As in the first embodiment, the optimization algorithm for minimizing the cost function J is c、 and E c The method is implemented to determine The cost function may be:

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[0092] Regardless of the cost function used, the minimization of θ=arg imposed by m=D's of the conditioned matrix D' θ Bounding min(J(θ)) makes the inversion algorithm easier to implement.

[0093] Vector W c is the energy function f e Using the resolution function f r This allows one to define and establish channel / energy relationships.

[0094] Vector E c During energy calibration, the above-mentioned energy function f e can be used to determine and establish the channel / energy relationship. k For each channel corresponding to , a threshold value above which it is considered to contain a significant amount of detected photons can be considered. k The ranks of channels where f is greater than a threshold are extracted. The selected channels are likely to encounter the emission energy of radionuclides present in the calibration object. This allows the energy function f e Various channel-energy pairs are obtained that can be used to determine

[0095] For example, the ranks of the selected channels can be sorted in ascending order, similar to the emission energies, to associate an emission energy with each channel. The channel with the lowest rank is associated with the lowest emission energy, and the channel with the highest rank is associated with the highest emission energy. The energy function f e has a predefined parametric form, for example a polynomial form. The parameters of the energy function (the coefficients of the polynomial) are adjusted based on the different channel-energy pairs.

[0096] It should be noted that this embodiment makes it possible to carry out the calibration in a highly automated manner, without having to carry out manual or computer-assisted delimitation of the peaks that form the spectrum y.

[0097] One embodiment of the peak area extraction implementing the second embodiment is shown in Figure 10. Figure 10 shows the measured spectrum y (dark curve) together with the estimate of the component c+b (light curve) of the element on different energy channels (x-axis). The vector m corresponds to the difference between the two curves.

[0098] Third embodiment

[0099] The objective of the third embodiment is to process the spectrum y measured during calibration to perform the following operations: -Estimate the transfer function h or observation efficiency ε mentioned above. -Energy function f e We estimate the parameter β of -resolution function f r We estimate the parameter α of - When at least one radionuclide emits a photon at 511 keV, the scalar k stated in (8) D Estimate.

[0100] In this embodiment, the target may be a calibration object having a source containing a known radionuclide and associated radioactivity. a If is known, the method allows for the estimation of h, otherwise it allows for the estimation of ε.

[0101] When the activity of the radionuclide is unknown, this method makes it possible to extract the areas of the peaks that form the vector m.

[0102] The main steps of this embodiment are shown diagrammatically in FIG.

[0103] Step 300: Measure the spectrum y using a measurement device.

[0104] Step 310: Extract the vector m+b.

[0105] The vector m+b can be estimated by performing the following subtraction:

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[0106] Step 320: Consider a predefined spectral variance matrix D. Each term of the spectral variance matrix D is as follows:

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[0107] The spectral variance matrix D is β, α, k D It is parameterized by

[0108] Step 330: Consider a vector s', called the incident vector, taking into account the radioactivity of the various radionuclides placed in the calibration object and a detection efficiency equal to 1 for each energy. The reference vector has dimensions (1,k). s' k is the energy E k corresponds to the number of photons detected in the peak centered at , taking into account the radioactivity of the calibration radionuclide and considering a detection efficiency equal to 1 at each energy. According to such an assumption, each incident photon is detected. k is the energy E incident on the detector k This also corresponds to the number of photons.

[0109] Step 340: Obtain a transfer matrix U′ in which each term is expressed as follows:

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[0110] U' is a matrix of dimensions (n,p), and each term u' ik is an estimate of the number of photons detected in each channel of rank i, taking into account the radioactivity of the calibration radionuclide and the detection efficiency at each energy equal to 1. U' is the Dis conditioned by

[0111] If the activity of the radionuclide is unknown, s' k =1 is imposed.

[0112] FIG. 12 shows an example of a matrix U′, where the X-axis corresponds to each channel i, the Y-axis corresponds to each emitted energy peak k, and the Z-axis corresponds to the value u′. ik Corresponds to.

[0113] Step 350: For each energy E k Estimate the detection efficiency at

[0114] The direct model is established as follows:

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[0115] TIFF2025501255000036.tif16161

[0116] TIFF2025501255000037.tif24162

[0117] Vectors m, β, α, h, and an arbitrary scalar k D is determined by executing an optimization algorithm as described in the first and second embodiments.

[0118] Absorption efficiency ε a If is unknown, it is assigned a unit value at each energy. Equation (14) becomes:

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[0119] This method then computes the β, α, ε, and any scalar k D This allows the determination of

[0120] This method allows for simultaneous energy calibration, resolution calibration and efficiency calibration.

[0121] According to one possibility, the method may comprise the following: - implementing the third embodiment to perform efficiency, resolution and energy calibration of the detector; - carrying out the first embodiment to determine the radioactivity of an analyte.

[0122] One implementation of peak area extraction implementing the second embodiment is shown in Figure 13. Figure 13 shows the measured spectrum y (dark curve) along with the estimate of the component c+b (light curve) on different energy channels (x-axis). The estimated vector m corresponds to the difference between the two curves.

[0123] Although the invention has been described in relation to nuclear waste, the invention may be applied to the inspection of any other object, such as equipment or structures of a nuclear facility, unused or irradiated fuel, or samples taken from the environment.

Claims

1. A method for processing an X-ray or gamma-ray radiation spectrum (y) produced by a spectrometric measurement device (1), said device comprising: a detector (10) configured to detect X-ray or gamma ray photons and to form, upon each detection, a pulse having an amplitude dependent on the energy emitted by the interacting X-ray or gamma ray photon in the detector; a spectroscopic measurement circuit (12) configured to generate a spectrum corresponding to the number of photons detected in the various channels, and an amplitude or energy corresponding to each channel; The method comprises the steps of: a) one or more radionuclides (2) that emit X-ray or gamma ray photons that are incident on the detector; ｊ The device is placed facing an object (2) that may contain radionuclides, each of which has at least one emitted energy (E ｋ ) emits a photon; b) the detector detects a portion of the incident photons and forms a spectrum (y) of the detected photons, the spectrum comprising each emission energy (E ｋ ), each peak resulting from a pulse detected in channel (i) and corresponding to said emitted energy; c) processing the spectrum (y) to obtain a quantity of pulses (m(i)) detected at each peak of the spectrum; The method further comprises the steps of: c1) considering a list of radionuclides present or likely to be present in said object; c2) considering an input vector (m) whose terms contain the amount of pulses within each peak extracted from said spectrum obtained from step b); c3) Considering the spectral dispersion matrix (D), each term (D(i,k), D'(i,k)) corresponds to the channel (i) and the emission energy (E ｋ ) corresponding to the probability that an incident photon whose energy is the emission energy is detected in the channel; c4) forming a transfer matrix (U, U', D') based on the spectral covariance matrix; c5) Considering the direct model, the input vector (m) is obtained by the matrix multiplication of the transfer matrix and the output vector (a,s,h,ε), where each term of the output vector corresponds to: The radioactivity of at least one radionuclide (a ｊ ). or the number of photons detected at an energy corresponding to the emission energy of the radioactive nuclide (s ｋ ). - or detection efficiency at the emission energy of a radioactive nuclide (h ｋ , ε ｋ ). c6) inverting the Direct Model to estimate the output vector (a, s, h, ε).

2. 2. The method of claim 1, wherein sub-step c6) comprises estimating the input vector (m) together with the output vector (a, s, h, ε).

3. 2. A method according to any one of the preceding claims, comprising: Step c) is a step of calculating the amount of radiation energy (E ｋ ) and radionuclides (2 ｊ ), each term corresponding to the number of photons detected in a peak centered on a channel (k) corresponding to said radiant energy; In step c), the transfer matrix (U) is the product of the spectral variance matrix (D(i,k), D'(i,k)) and the matrix of the reference spectrum or its transpose, and each term of the transfer matrix (U(i,j)) corresponds to a radionuclide (2 ｊ ) and a channel (i), each term of the transfer matrix corresponding to the number of photons emitted by a radionuclide at the reference activity and detected in the channel (i); The output vector (a) includes terms (a ｊ ).

4. 4. The method of claim 3, wherein the reference activity is 1 Bq.

5. 3. The method according to claim 1 or 2, In step c), the transfer matrix is ​​the spectral covariance matrix (D'); A method according to claim 1, wherein the output vector (s) includes terms each representing a number of photons detected in a channel (k) corresponding to a different emission energy of the radionuclide present in the object.

6. 6. The method according to claim 5, wherein the sub-step c6 determines the width (w ｃ ), each estimation span parameterizing said spectral covariance matrix (D').

7. 7. The method according to claim 5, wherein sub-step c6 comprises: selecting the channel (E ｃ，ｋ ), each estimated position parameterizing said spectral covariance matrix (D').

8. The method according to any one of claims 5 to 7, the object includes a calibration radionuclide having a known emission energy; The method further comprising: Based on the output vector, a channel (E ｃ，ｋ ) and select The selected channel is calculated based on the emission energy (E ｋ ) vs. Based on the comparison, an energy function (f ｅ ) determining the

9. 3. The method according to claim 1 or 2, The object comprises a calibration radionuclide whose nature and optionally its radioactivity are known; Step c) includes considering an incidence vector (s') whose terms correspond to the number of photons incident on said detector at each emission energy; In step c), the transfer matrix (U′) is calculated based on the emitted energy (E ｋ ), each term (D(i,k)) of the spectral dispersion matrix (D) associated with an emission energy and a channel is a product of the value of the incident vector at the emission energy, and each term (U′(i,k)) of the transfer matrix is ​​associated with an emission energy and a channel, each term of the transfer matrix corresponding to the number of photons emitted by each calibration radionuclide and detected in the channel; The output vector (h, ε, s) contains the detection efficiency (h ｋ , ε ｋ , s ｋ ) respectively.

10. 10. The method of claim 9, wherein step c) comprises considering an energy function, the energy function being: The energy function (f ｅ ) establishes the correspondence between the rank and the energy value of the channel; the energy function is a parametric function parameterized by at least one parameter (β); A method wherein sub-step c6) comprises estimating at least one parameter of said energy function.

11. 11. The method of claim 10, wherein step c) includes taking into account a resolution function, said resolution function (f ｒ ) is as follows: The resolution function determines the width of each peak as a function of channel or energy; the resolution function is a parametric function parameterized by at least one parameter (α); A method wherein sub-step c6) comprises estimating at least one parameter of said resolution function.

12. The method according to any one of the preceding claims, characterized in that the shape function (f ｓ ), wherein the shape function establishes an analytical relationship that models the shape of each peak in the detected spectrum.

13. A device (1) intended to obtain a spectrum of X-ray or gamma-ray photons emitted by an object possibly containing a radioactive nuclide, comprising: a detector (10) configured to detect X-ray or gamma ray photons and to form, upon each detection, a pulse having an amplitude dependent on the energy emitted by the interacting X-ray or gamma ray photon in the detector; a spectrometry circuit (12) configured to form a spectrum (y) corresponding to the distribution of the amplitudes of the pulses detected by the detector; A processing unit (14) programmed to carry out step c) of the method according to any one of the preceding claims.

14. A medium connectable to a computer and comprising instructions for carrying out step c) of the method according to any one of claims 1 to 12 based on a spectrum obtained from a spectroscopic detector.

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