FR3090128A1 - METHOD FOR CHARACTERIZING A SPECTROMETER, COMPUTER PROGRAM PRODUCT AND RELATED COMPUTER - Google Patents

Abstract

The invention relates to a method for calibrating a spectrometer, comprising: - for each one of nx detection channels of the spectrometer and nz experimental configurations, determination of an experimental measurement yield of the spectrometer; - implementation of a calculation step (26) comprising: • a phase (30) of developing nm models; • for each of the nm models developed, a phase (32) of determining a simulated measurement yield of each detection channel; • for each of the nm models developed, a phase (34) of calculating a corresponding merit criterion; • for each of np predetermined parameters, a phase (36) of adaptation of the corresponding characteristic quantities, from the value of the merit criterion; - when a predetermined condition is met, step (28) of choosing a calibrated value of each predetermined parameter; nx, nz, np and nm being predetermined integers. Figure for the abstract: Figure 2

Description

Description

Title of the invention: PROCESS FOR CHARACTERIZING A SPECTROMETER, COMPUTER PROGRAM PRODUCT AND RELATED COMPUTER

Technical area

The present invention relates to a method for calibrating a spectrometer comprising a detector, the spectrometer being associated with a range of detection energy comprising n _x detection channels.

The invention also relates to a computer program product and a calculator.

The invention applies to the field of nuclear physics, in particular to the characterization of spectrometers dedicated to nuclear instruction, more particularly to the performance calibration of said spectrometers.

Prior art

Conventionally, an X and / or γ spectrometer is a nuclear measurement device comprising, on the one hand, a detection chain comprising a detector and an acquisition device, and, on the other hand, an analyzer configured to analyze a detection signal generated by the detection chain, the analyzer being associated with a predetermined detection energy range, subdivided into a predetermined integer n _x of detection channels. The correspondence between each detection channel of the analyzer and the corresponding interval of the detection energy range is established during an energy calibration.

The spectrometer is configured to provide, following exposure of the detector to ionizing radiation, a spectrum of the radiation, that is to say a histogram of the population of photons detected as a function of the energy deposited in the detector by said photons, in accordance with the subdivision into n _x of detection channels of the predetermined detection energy range.

[0006] Such a spectrometer, in order to be able to fulfill a function of quantifying the radiological activity, requires, in addition to its energy calibration, a calibration known as "measurement efficiency in total absorption", also called "yield calibration".

Such a yield calibration consists in associating, with each of the n _x detection channels, and for a given experimental configuration (defined, in particular, by a position of the source relative to the detector, a geometry of the source, and an influence of the environment), a corresponding output of the whole spectrometer. In other words, once the calibration has been carried out, if the experimental configuration remains unchanged, determining the number of pulses detected in each detection channel gives access to the activity of any source.

However, it is difficult to establish a performance calibration of a given spectrometer which describes exhaustively, for a given radioisotope, all of the experimental configurations. This is the reason why a digital model of the spectrometer is generally used.

To establish such a digital model, it is known to use software which, by providing the input of measured values, when implementing predetermined experimental configurations, predetermined parameters, analyze the response of the spectrometer in each of said predetermined experimental configurations in order to determine the impact of each parameter and generate the digital model sought from prerecorded solutions.

However, such an approach is not entirely satisfactory.

Indeed, such an approach does not offer a user with adequate expertise and calculation tools the possibility of modeling the environment and exposure himself. However, it is sometimes difficult to match an experimental configuration to an expected predetermined experimental configuration. Furthermore, such an approach assumes that the supplied values of the predetermined parameters are fair and precise. However, the results of the calibration procedure can prove to be extremely sensitive to any variation in said parameters, and the internal parameters of the spectrometer (for example, dimensions of the detector) can, in most cases, be determined only with large relative uncertainties.

An object of the invention is therefore to propose a calibration method which is more flexible for the user, and which can be implemented even if the parameter values of a model cannot be obtained with great precision. Statement of the invention

To this end, the invention relates to a calibration method of the aforementioned type, comprising the following steps:

- for each of n _z experimental configurations in which the detector is exposed to at least one source of ionizing radiation, and for each of the n _x detection channels, determination, as a function of a detection signal obtained by means of the spectrometer, d '' a corresponding experimental measurement yield;

- implementation, successively over time, of a calculation step comprising:

• a phase of developing n _m models of the spectrometer, the development of each of the n _m models comprising the drawing, for each predetermined parameter from among n _p predetermined parameters, of a respective value according to a current probability law corresponding to the parameter predetermined;

• for each of the n _m models developed, a phase of determining, for each of the n _z experimental configurations, a simulated measurement yield for each of the n _x detection channels;

• for each of the n _m models developed, a calculation phase, based on the simulated measurement yield and the experimental measurement yield associated with each of the n _z experimental configurations and each of the n _x detection channels, of a criterion of corresponding merit;

• for each of the n _p predetermined parameters, a phase of adaptation of the quantities characteristic of the corresponding current probability law, from the evolution of the value of the merit criterion as a function of the n _m values taken by the predetermined parameter;

- when a predetermined condition is fulfilled, step of choosing, for each of the n _p predetermined parameters, a respective calibrated value from the last corresponding current probability law;

n _x , n _z , n _p and n _m being predetermined integers.

Indeed, with such a calibration process, the user is able to use any experimental configuration that the circumstances or that his experience pushes him to set up, so that he is no longer constrained by predetermined experimental configurations potentially difficult to implement.

In addition, such a calibration process allows greater tolerance in the entered values of the parameters of the model, insofar as the value of each parameter is updated (by means of the update of the corresponding probability law) during the execution of the process which is the subject of the invention, said updating being guided by an optimization of the merit criterion obtained from the results provided by the model and from the simulated results (in this case, simulated measurement yield and experimental measurement yield).

The method of the invention is therefore more flexible for the user, and is capable of being implemented even if the parameter values of a model cannot be obtained with great precision, while leading to a reliable result.

According to other advantageous aspects of the invention, the method comprises one or more of the following characteristics, taken in isolation or in any technically possible combination:

- The adaptation phase includes, for each of the n _p predetermined parameters:

• for each of the n _m models developed, an association of the corresponding value of the predetermined parameter and the corresponding merit criterion;

• modeling, from the n _m values taken by the predetermined parameter and the corresponding n _m merit criteria, of the evolution of the merit criterion as a function of the value of the predetermined parameter;

• from the result of the modeling, a modification of the quantities characteristic of the corresponding current probability law;

- For each of the n _p predetermined parameters, if the value of a form factor depending on a result of the corresponding modeling is greater than a first predetermined value, the modification of the quantities characteristic of the corresponding current probability law is a reduction in the standard deviation of the probability law and / or a modification of the expectation of the probability law;

- For each of the n _p predetermined parameters, if the value of a form factor depending on a result of the corresponding modeling is less than a second predetermined value, the modification of the corresponding current probability law is an increase the standard deviation of the probability law;

- The predetermined condition is fulfilled if the calculation step is implemented a predetermined number of times, and / or if, for each of the n _p predetermined parameters, the relative variation of all or part of the characteristic quantities of the corresponding probability law between two successive implementations of the calculation step is less than or equal to a predetermined threshold;

- For each of the n _p predetermined parameters, the respective calibrated value chosen is the expectation of the last corresponding current probability law.

The invention also relates to a computer program product comprising program code instructions which, when executed by a computer, implement the method as defined above.

In addition, the invention relates to a computer for calibrating a spectrometer comprising a detector, the spectrometer being associated with a range of detection energy comprising n _x detection channels, the computer being configured for :

- for each of n _z experimental configurations in which the detector is exposed to at least one source of ionizing radiation, and for each of the n _x detection channels, determine, as a function of a detection signal obtained by means of the spectrometer, a corresponding experimental measurement yield;

- implement, successively over time, a calculation step comprising:

• a phase of developing n _m models of the spectrometer, the development of each of the n _m models comprising the drawing, for each predetermined parameter from among n _p predetermined parameters, of a respective value according to a current probability law corresponding to the parameter predetermined;

• for each of the n _m models developed, a phase of determining, for each of the n _z experimental configurations, a simulated measurement yield for each of the n _x detection channels;

• for each of the n _m models developed, a calculation phase, based on the simulated measurement yield and the experimental measurement yield associated with each of the n _z experimental configurations and each of the n _x detection channels, of a criterion of corresponding merit;

• for each of the n _p predetermined parameters, a phase of adaptation of the quantities characteristic of the corresponding current probability law, from the evolution of the value of the merit criterion as a function of the n _m values taken by the predetermined parameter;

- when a predetermined condition is met, choose, for each of the n _p predetermined parameters, a respective calibrated value from the last corresponding current probability law;

n _x , n _z , n _p and n _m being predetermined integers.

Brief description of the drawings

The invention will be better understood using the description which follows, given solely by way of nonlimiting example and made with reference to the appended drawings in which:

[Fig.l] is a schematic representation of a spectrometer associated with a calibration system according to the invention;

[Fig.2] is a flow diagram schematically illustrating the calibration process according to the invention; and

[Fig. 3] is a graph representing the evolution of the average bias of models of a spectrometer as a function of the iteration index of a calculation step of the calibration method according to the invention.

DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

A spectrometer 2 is shown in Figure 1. The spectrometer 2 is associated with a calibration system 4 according to the invention.

The spectrometer 2 is configured to provide, following its exposure to radiation, in particular ionizing radiation, originating from a source 5, a spectrum of said radiation. In addition, the calibration system 4 is configured to perform a performance calibration of the spectrometer 2. The calibration system 4 is similar to a computer.

By “computer”, it is understood for example, within the meaning of the present invention, a computer, or even an ASIC type circuit (from the English “application-specific in te grated circuit”, meaning its own integrated circuit to an application) or a programmable logic circuit (in English, "programmable logic device"), such as an FPGA circuit (from the English "field-programmable gate array", meaning network of programmable doors in situ).

The spectrometer 2 is, for example, an X and / or γ spectrometer.

Conventionally, the spectrometer 2 comprises a detection chain 6 and an analyzer 8 connected at the output of the detection chain 6.

The detection chain 6 is configured to generate a detection signal representative of the detection of particles radiated by the source 5. In addition, the analyzer 8 is configured to analyze the detection signal generated by the detection chain 6 .

The detection chain 6 comprises a detector 10 and an acquisition member 12 connected at the output of the detector 10.

The detector 10 is configured to detect particles of radiation from the source 5, and to deliver an electrical signal representative of said detection. In the case where the source 5 emits γ photons, the detector 10 is, for example, an HPGe diode (from the English “high-purity germanium”, meaning “germanium of high purity”).

The acquisition device 12 is configured to generate the detection signal from the electrical signal delivered by the detector 10. For example, the acquisition device 12 is configured to amplify and / or filter and / or digitizing the electrical signal delivered by the detector 10 in order to generate the detection signal.

The detector 10 and the acquisition device 12 are known and will not be described further.

The analyzer 8 is configured to analyze the detection signal delivered by the detection chain 6, to establish a spectrum of the radiation emitted by the source 5, or even to measure the radiological activity of the source 5.

The analyzer 8 is associated with a predetermined detection energy range, subdivided into a predetermined integer n _x of detection channels.

Each detection channel is identified by a rank noted x. Thereafter, the expression "channel x" will denote a given channel of rank x.

In addition, each detection channel x of the analyzer 8 is associated with a corresponding energy interval of the detection energy range, denoted E _x . Thereafter, the expression “energy interval E _x ” will designate the energy interval associated with the channel x.

Within the meaning of the present invention, the spectrum is defined as a histogram of the population of particles detected, as a function of the energy deposited in the detector 10 by said particles. More precisely, each channel x is associated with the number of particles which have deposited, in the detector 10, an energy comprised in the energy interval E _x .

Such an analyzer 8 is conventionally known and will not be described further.

Da conventionally, the operation of the spectrometer 2 is capable of being described by a physical model, such a physical model of the spectrometer having n _p predetermined parameters. The physical model of the spectrometer is, in particular, intended to be used to determine the radiological activity of any source as a function of a response of the spectrometer 2 during the exposure of the detector 10 of the spectrometer 10 to said source.

Such a physical model is, as will be described later, stored in the calibration system 4.

The calibration system 4 is configured to determine, during a calibration of the spectrometer 2, a value, called "calibrated value", of each of the n _p predetermined parameters of the predetermined physical model of the spectrometer 2.

Each parameter is identified by a rank noted p. Thereafter, the expression "parameter p" will designate a predetermined parameter of rank p given.

The calibration system 4 comprises a memory 14, a processor 16 connected to the memory 14 and, for example, a man / machine interface 18.

The memory 14 includes a configuration memory location 20, a processing memory location 22 and a calibration software 24.

The configuration memory location 20 is configured to store data relating to the spectrometer 2.

In particular, the configuration memory location 20 is configured to store the physical model of the spectrometer 2. As stated above, the physical model of the spectrometer 2 includes n _p parameters. Such parameters are, for example, the dimensions of the detector 10, the densities of the materials constituting the spectrometer 2 (in particular, constituting the detector 10), or else the concentrations of the various isotopes present in said materials.

The configuration memory location 20 is also configured to store the energy interval E _x associated with each of the n _x detection channels.

The configuration memory location 20 is further configured to store information relating to experimental configurations implemented for the calibration of the spectrometer 2, and for each of which the detector 10 is exposed to at least one source. of ionizing radiation. The experimental configurations are two by two distinct.

Such information includes, for example, a number n _z of experimental configurations implemented for the calibration of the spectrometer 2.

Each experimental configuration is identified by a rank noted z. Thereafter, the expression "experimental configuration z" will designate an experimental configuration of given rank z.

In addition, such information relating to the experimental configurations implemented for the calibration of the spectrometer 2 and stored in the configuration memory location 20 include, for example, the nature of the source (s) used ( s) during each experimental configuration z, as well as the position of the source (s) relative to the spectrometer 2.

In addition, the configuration memory location 20 is configured to store, in relation to each of the n _z experimental configurations, the corresponding detection signal obtained by means of the spectrometer 2.

The configuration memory location 20 is, in addition, configured to store a first predetermined value strictly positive, called "first significance threshold".

The configuration memory location 20 is also configured to store a second predetermined strictly negative value, called "second significance threshold", for example equal to the opposite of the first significance threshold.

In addition, the configuration memory location 20 is configured to store, for each of the n _p parameters of the physical model of the spectrometer 2, a corresponding probability law. Such a probability law is, for example, a normal law.

The configuration memory location 20 is also configured to store a first real coefficient strictly greater than 1, and a second real coefficient strictly greater than 1.

The processing memory location 22 is configured to store, for each of the n _p parameters of the physical model of the spectrometer 2, the values of quantities characteristic of the corresponding probability law. By way of example, in the case where said probability law is a normal law, such characteristic quantities are its expectation and its standard deviation.

Thereafter, the expression "current probability law" will denote the data of a probability law and the current value of its characteristic quantities.

As will be described later, the value of the characteristic quantities of each probability law is updated over time, during the implementation of the calibration method of the invention.

The calibration software 24 is configured to calculate the calibrated value of each of the n _p parameters of the physical model of the spectrometer 2. To do this, the calibration software 24 is configured to implement a step 25 of determining experimental measurement yield, a calculation step 26, a verification step 27 and a choice step 28.

The calibration software 24 is configured so as to determine, during the determination step 25, for each experimental configuration z, an experimental measurement yield corresponding to each channel x, and this from the signal of detection provided by spectrometer 2 in said experimental configuration z.

More precisely, the calibration software 24 is configured to determine the experimental measurement yield, denoted f ^ex P, by the implementation of the following relation (1):

[Math.l] exp S ₇ T _r

Cz a ir

Where _f exp ^A x, z is the experimental measurement yield associated with the experimental configuration z, for the channel x;

S _XjZ is the number of pulses (obtained after deduction of the background noise) corresponding to the deposition, in the detector 10, of an energy belonging to the energy interval E _x , for the experimental configuration z;

A _z is the activity, known, of the source (s) in the experimental configuration z;

I _x is the number of photons of energy E _x emitted by disintegration of the radioisotope (s), accessible in the nuclear databases;

R _a is an active measurement time, defined as the difference between a total measurement time and a measurement dead time; and

Τ _Γ is a real time of the measurement, defined as the total time of the measurement.

The standard deviation corresponding to the experimental measurement yield f ^ex P, denoted σ, is given by the following relation (2):

[Math.2]

The calibration software 24 is also configured to implement, after the determination step 25, the calculation step 26. More specifically, the calibration software 24 is configured to implement the step computation 26 iteratively, that is to say several times, successively over time, until a predetermined condition is fulfilled.

The calculation step 26 comprises a phase 30 of developing models, a phase 32 of determining simulated measurement yield, a phase 34 of calculating merit criteria and an adaptation phase 36.

The description of phases 30, 32, 34 and 36 will be made with reference to any given iteration, denoted k, of calculation step 26.

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The calibration software 24 is configured to generate, during the development phase 30, n _m models of the spectrometer 2.

Each model of the spectrometer is identified by a rank noted m. Thereafter, the expression "model m" will denote a model of row m given from spectrometer 2.

More specifically, the software 24 is configured to, during the development phase 30, generate any model m from the physical model of the spectrometer 2 stored in the configuration memory location 20, choosing, for each of the n _p predetermined parameters of the model m, a respective value depending on the corresponding current probability law.

In other words, for a given experimental configuration z, and for a given model m, the value of a parameter p is obtained by a draw implementing the associated current probability law.

In addition, the calibration software 24 is configured to determine, after the development phase 30, and during the phase 32 of determining the simulated measurement yield, for each experimental configuration z, and for each model m developed ( that is to say generated), a simulated measurement efficiency of each of the n _x detection channels. The simulated measurement yield is denoted f ^sim .

More precisely, for each experimental configuration z and for each model m, the simulated measurement yield f ^sim is obtained by means of said model m, for said configuration z.

The calibration software 24 is also configured to calculate, after the phase 32 of determining the simulated measurement yield, and during the calculation phase 34, a merit criterion associated with each model m generated during the development phase. 30.

More precisely, for any model m of the iteration k, the calibration software 24 is configured to calculate the corresponding merit criterion, denoted B _{m> k} , from the simulated measurement yield f ^sim associated with each of the nz experimental configurations and to each of the nx detection channels, and of the experimental measurement yield f ^exp associated with each of the nz experimental configurations, to each of the n _x detection channels, and to the current iteration k.

For example, the merit criterion B _{m> k} associated with any model m of the iteration k is defined as a bias, for example obtained by means of the following formula (3):

[Math.3] i _ n * _x n ₇ ^Β ηΔ- = ηχηζΣχ = 1 ^Σ ζ = 1 'psim „exp f —tx, z, m, kx, z _f exp

(3) where ¹ x, z, m, k is the simulated measurement efficiency associated with channel x, in the experimental configuration z and for the model m, at Γ iteration k current; and ^[0093] CrffXnk) is the standard deviation of performance measurement simulated -SIM ¹ x, z, m, k

In addition, the calibration software 24 is configured to, after the calculation phase 34, and during the adaptation phase 36, update the current value of the quantities characteristic of the probability law associated with each of the n _p predetermined parameters. In other words, the calibration software 24 is configured to, during the adaptation phase 36 of the iteration k, write to the processing memory location 22, for the probability law associated with each of the n _p predetermined parameters, the values of the corresponding characteristic quantities which will be implemented during the following iteration k + 1.

More specifically, the calibration software 24 is configured to, during the adaptation phase 36, update the value of the quantities characteristic of the probability law associated with each parameter p from the analysis the evolution of the value of the merit criterion as a function of the n _m values drawn for the parameter p during the development phase 30.

To do this, the calibration software 24 is preferably configured to, during the adaptation phase 36, associate the value of the parameter p and the value of the merit criterion B _{m> k} obtained for each model m. In other words, for each parameter p, the calibration software 24 is configured so as to associate the value of the parameter p drawn for each model m and the value of the merit criterion corresponding to said model m. As a result, for each parameter p, n _m couples associating the value of the parameter p drawn for each model m generated and the value of the merit criterion corresponding to said model m.

In this case, the calibration software 24 is also configured to calculate, for each parameter p, and from the n _m values taken by said parameter p and from the corresponding n _m merit criteria, an approximation of the evolution of the merit criterion B _mk as a function of the value of the parameter p.

Such an approximation is, for example, based on a quadratic approximation function, denoted y _p , of the form y _p = a _p .p ² + b _p .p + c _p , where a _p , b _p and c _p are reals associated, for the iteration k, with the parameter p and which are determined by the calibration software 24 during the modeling described above, for example by means of the method of least squares.

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In addition, in this case, the calibration software 24 is configured to modify the current value of the quantities characteristic of the probability law corresponding to each parameter p from the result of the modeling.

To do this, the calibration software 24 is, for example, configured to calculate, for each parameter p, a form factor, denoted V _p , representative of the convexity of the approximation function y _p .

For example, for any given parameter p, the calibration software 24 is configured to calculate the corresponding form factor V _p by implementing the following relation (4):

[Math.4]

a _n var Pf <m <n _m yp, m

I ^a p I var l <m <n _m (®m, k) (4) where var is the operator "variance"; and y _{p> m} is the value taken by the approximation function y _p for the value of the parameter p corresponding to the model m.

The variable var (y _{p> m} ) is the variance, for the parameter p, of the n _m values taken by the approximation function y _p for each of the n _m values taken from the parameter p.

Furthermore, the magnitude var (B _{m> k} ) is the variance of the n _m values taken by the merit criterion B _{m> k} for the set of n _m models generated.

The calibration software 24 is also configured to compare, for each parameter p, the form factor V _p corresponding to the first and second significance threshold stored in the configuration memory location 20.

The value of the first and second significance threshold is, for example, fixed on the basis of a Monte-Carlo calibration.

If, for a given parameter p, the corresponding form factor V _p is strictly greater than the first significance threshold, the approximation function y _p is said to be “significantly convex”, the approximation function y _p highlighting a minimum local evolution of the merit criterion B _{m> k} over the set of m values taken by the parameter p.

In this case, the calibration software 24 is configured to modify the current values of the quantities characteristic of the probability law associated with the parameter p considered. In particular, the calibration software 24 is advantageously configured to reduce the standard deviation of the probability law and / or modify the expectation of the probability law.

For example, the new current value assigned to the standard deviation of the probability law associated with the parameter p is equal to the result of the division of the previous value of the standard deviation by the first coefficient stored in the configuration memory 20.

[0112] For example again, the new current value assigned to the expectation of the probability law associated with the parameter p is equal to -b _p /(2.a _p ).

Furthermore, if, for a given parameter p, the corresponding form factor V _p is strictly less than the second significance threshold, the approximation function y _p is said to be “significantly concave”, so that the drawing of the parameter p during the development phase 30 does not make it possible to highlight a minimum of the merit criterion B _{m> k} over all of the m values taken by the parameter p.

In this case, the calibration software 24 is configured to modify the current values of the quantities characteristic of the probability law associated with the parameter p considered. In particular, the calibration software 24 is configured to increase the standard deviation of the probability law, that is to say write, in the processing memory location 22, a new current value of the deviation -type strictly greater than the previous value of the standard deviation.

For example, the new current value assigned to the standard deviation of the probability law associated with the parameter p is equal to the result of the multiplication of the previous value of the standard deviation by the second coefficient stored in the configuration memory 20.

If, for a given parameter p, the corresponding form factor V _p is between the second significance threshold and the first significance threshold, the trend of the approximation function y _p is undetermined, and nothing can be deducted regarding the parameter.

In this case, the calibration software 24 is configured to keep unchanged the values of the quantities characteristic of the probability law associated with the parameter p considered.

The calibration software 24 is also configured to implement the verification step 27 after each execution of the calculation step 26.

The calibration software 24 is configured to, during the verification step 27, check whether the predetermined condition, mentioned above, is fulfilled.

For example, the predetermined condition is fulfilled if the calculation step 26 is implemented a predetermined number of times, and / or if, for each of the n _p predetermined parameters, the relative variation of all or part of the quantities characteristics of the corresponding probability law between two successive implementations of the calculation step 26 is less than or equal to a predetermined threshold.

If the predetermined condition is not fulfilled, the calibration software 24 is configured to implement the calculation step 26 again. Furthermore, if the predetermined condition is fulfilled, the calibration software is configured to then implement the choice step 28.

During the selection step 28, the calibration software 24 is configured to choose, for each of the n _p predetermined parameters, a respective value from the last corresponding current probability law. For each parameter p, the value chosen by the calibration software 24 during the selection step 28 constitutes the calibrated value of said parameter p.

Preferably, for each of the n _p predetermined parameters, the respective calibrated value chosen is the expectation of the last corresponding current probability law.

The processor 16 is configured to execute the calibration software 24 stored in the memory 14.

The man / machine interface 18 is configured to allow an operator to enter, in memory 14, the data necessary for the operation of the calibration system 4.

In particular, such data include, for each parameter p, initial values of the quantities characteristic of the corresponding probability law. For example, in the case of the dimensions of the detector 10, such initial values are, for the expectation of the probability law, the dimensions measured, and for the standard deviation of the probability law, the uncertainty over each measured dimension.

As a variant, all or part of the data necessary for the operation of the calibration system 4 being prerecorded in memory 14. For example, the probability law corresponding to each parameter p may be previously stored in memory 14 .

The operation of the calibration system 4 will now be described.

[0129] During an initialization step, an operator writes, in the configuration memory location 20, the information described above.

[0130] Preferably, the operator also writes, in the processing memory location 22, initial values of the quantities characteristic of the probability law corresponding to each parameter p.

Then, during the determination step 25, the calibration software 24 determines, for each experimental configuration z, the experimental measurement yield corresponding to each channel x.

Then, the calibration software 24 implements, successively over time, the calculation step 26.

During each execution of the calculation step 26, the calibration software 24, the calibration software 24 implements the phase 30 of developing models, the phase 32 of determining the simulated measurement yield, phase 34 of calculation of merit criteria and adaptation phase 36.

During the development phase 30, the calibration software 24 generates n _m models of the spectrometer 2 from the physical model of the spectrometer 2 stored in the configuration memory location 20, choosing, for each of the n _p predetermined parameters of the model m, a respective value depending on the corresponding current probability law.

Then, during phase 32 of determining the simulated measurement yield, the calibration software 24 determines, for each experimental configuration z, and for each model m generated, the simulated measurement yield f ^sim of each of the n _x detection channels.

Then, during the calculation phase 34, the calibration software 24 calculates the merit criterion associated with each model m generated during the development phase 30.

Then, during the adaptation phase 36, the calibration software 24 calculates, for each parameter p, and from the n _m values taken by said parameter p and from the corresponding n _m merit criteria, l approximation of the evolution of the merit criterion B _{m> k} as a function of the value of the parameter p.

Then, depending on the result of the approximation, the calibration software 24 updates or not the current value of the quantities characteristic of the probability law associated with each of the n _p predetermined parameters.

Then, during the verification step 27, the calibration software 24 verifies whether the predetermined condition is fulfilled.

If the predetermined condition is not fulfilled, the calibration software 24 again implements the calculation step 26. Otherwise, the calibration software 24 then implements the choice step 28.

Finally, during the selection step 28, the calibration software 24 chooses, for each of the n _p predetermined parameters, the corresponding calibrated value.

FIG. 3 illustrates the evolution, in a particular example, of an average of the merit criterion over all of the models generated during the development phase 30 with the number of iterations of l 'calculation step 26 (curve in solid line).

In this example, a standard source of europium 152 was used. The characteristics of such a standard source (in particular, the energy of each absorption peak and its intensity), which are perfectly known, are involved in the calculation of the experimental measurement yields f ^ex P.

In addition, eight experimental configurations were chosen (n _z = 8). The positions of the standard source were chosen so as to construct a quasi-isotropic model of the response of the detector 10.

The detector 10 is an HPGe diode, marketed under the reference REGel020 by the company MIRION Canberra, the spectrometer 2 having a range of detection energy between 100 keV (kiloelectronvolt) and 1.5 MeV (megaelectronvolt).

In particular, the physical model of the spectrometer 2 was produced using a known particle transport code MCNP6.1. In this example, the physical model includes twenty predetermined parameters (n _p = 20), whether physical or geometric parameters.

As shown in FIG. 3, the average merit criterion, which is an average bias, is less than 8% at the end of the second iteration of the calculation step 26 only (the first iteration, corresponding to an evaluation from manufacturer's data, presents the abscissa 0 in this figure). However, originally, the bias obtained with the manufacturer's ratings, refined by X-ray, reached an average value of 28%.

The implementation of the calibration method according to the invention therefore provides much more reliable results than with the conventional method.

Claims (1)

[Claim 1] [Claim 2] Claims Method for calibrating a spectrometer (2) comprising a detector (10), the spectrometer (2) being associated with a range of detection energy comprising n _x detection channels, the calibration method comprising the following steps: - for each of n _z experimental configurations in which the detector (10) is exposed to at least one source of ionizing radiation, and for each of the n _x detection channels, determination, as a function of a detection signal obtained by means of the spectrometer (2), of a corresponding experimental measurement yield; - implementation, successively over time, of a calculation step (26) comprising: • a phase (30) of developing n _m models of the spectrometer, the development of each of the n _m models comprising the drawing, for each predetermined parameter from among n _p predetermined parameters, of a respective value according to a current probability law corresponding to the predetermined parameter; • for each of the n _m models developed, a phase (32) of determining, for each of the n _z experimental configurations, a simulated measurement yield for each of the n _x detection channels; • for each of the n _m models developed, a calculation phase (34), from the simulated measurement yield and the experimental measurement yield associated with each of the n _z experimental configurations and with each of the n _x detection channels, a corresponding merit criterion; • for each of the n _p predetermined parameters, a phase (36) of adaptation of the quantities characteristic of the corresponding current probability law, from the evolution of the value of the merit criterion as a function of the n _m values taken by the predetermined parameter; - when a predetermined condition is fulfilled, step (28) of choosing, for each of the n _p predetermined parameters, a respective calibrated value from the last corresponding current probability law; n _x , n _z , n _p and n _m being predetermined integers. Method according to claim 1, in which the adaptation phase (36) comprises, for each of the n _p predetermined parameters: - for each of the n _m models developed, an association of the corresponding value of the predetermined parameter and the corresponding merit criterion; a modeling, from the n _m values taken by the predetermined parameter and from the corresponding n _m merit criteria, of the evolution of the merit criterion as a function of the value of the predetermined parameter; - from the result of the modeling, a modification of the characteristic quantities of the corresponding current probability law. [Claim 3] Calibration method according to claim 2, in which, for each of the n _p predetermined parameters, if the value of a form factor depending on a result of the corresponding modeling is greater than a first predetermined value, the modification of the quantities characteristics of the corresponding current probability law is a reduction in the standard deviation of the probability law and / or a change in the expectation of the probability law. [Claim 4] Calibration method according to claim 2 or 3, in which, for each of the n _p predetermined parameters, if the value of a form factor depending on a result of the corresponding modeling is less than a second predetermined value, the modification of the corresponding current probability law is an increase in the standard deviation of the probability law. [Claim 5] Calibration method according to any one of Claims 1 to 4, in which the predetermined condition is fulfilled if the calculation step is carried out a predetermined number of times, and / or if, for each of the n _p predetermined parameters , the relative variation of all or part of the quantities characteristic of the corresponding probability law between two successive implementations of the calculation step (26) is less than or equal to a predetermined threshold. [Claim 6] Method according to any one of Claims 1 to 5, in which, for each of the n _p predetermined parameters, the respective calibrated value chosen is the expectation of the last corresponding current probability law. [Claim 7] Computer program product comprising program code instructions which, when executed by a computer, implement the method according to any of claims 1 to 6. [Claim 8] Computer (4) for the calibration of a spectrometer (2) comprising a detector (10), the spectrometer (2) being associated with a range of detection energy comprising n _x detection channels, the computer (4) being configured for: - for each of n _z experimental configurations in which the detector (10) is exposed to at least one source (5) of ionizing radiation, and for each of the n _x detection channels, determine, as a function of a detection signal obtained by means of the spectrometer (2), a corresponding experimental measurement yield; - implement, successively over time, a calculation step comprising: • a phase of developing n _m models of the spectrometer, the development of each of the n _m models comprising the drawing, for each predetermined parameter from among n _p predetermined parameters, of a respective value according to a current probability law corresponding to the parameter predetermined; • for each of the n _m models developed, a phase of determining, for each of the n _z experimental configurations, a simulated measurement yield for each of the n _x detection channels; • for each of the n _m models developed, a calculation phase, based on the simulated measurement yield and the experimental measurement yield associated with each of the n _z experimental configurations and each of the n _x detection channels, of a criterion of corresponding merit; • for each of the n _p predetermined parameters, a phase of adaptation of the quantities characteristic of the corresponding current probability law, from the evolution of the value of the merit criterion as a function of the n _m values taken by the predetermined parameter; - when a predetermined condition is met, choose, for each of the n _p predetermined parameters, a respective calibrated value from the last corresponding current probability law; n _x , n _z , n _p and n _m being predetermined integers.