Method for the energy calibration of a spectrometry detector

1 . A method for processing a calibration spectrum formed by a spectrometric measurement device, the device comprising:

a detector configured to detect particles and to form, on each detection, a pulse whose amplitude depends on an energy of a particle having interacted in the detector; and

a spectrometric measurement circuit configured to form a spectrum, the spectrum corresponding to a number of particles detected in channels, each channel being assigned a rank, a pulse amplitude corresponding to each rank,

the method comprising:

a) arranging the device facing a calibration object, the calibration object emitting, to the detector, particles of different known emission energies;

b) detecting part of the particles by the detector and forming a calibration spectrum of the detected particles, the calibration spectrum comprising different peaks, each peak corresponding to one of the known emission energies;

c) detecting some of the peaks of the calibration spectrum and assigning a channel rank to each detected peak;

d) from the channel ranks assigned to different peaks in c) and the known emission energies, determining a calibration function, the calibration function determining an energy from the rank of each channel, the calibration function being a bijective function;

wherein d) comprises:

d-i) forming an analytical model of the calibration function, the analytical model being parameterized by a set of parameters;

d-ii) for different values of each parameter of the set of parameters:

applying the calibration function to the rank of each channel assigned to each detected peak, so as to obtain, for each rank, an energy determined by the calibration function, or

applying a reciprocal function that is a reciprocal of the calibration function to each emission energy, so as to obtain, for each emission energy, a channel determined by the reciprocal function; and

d-iii) determining the value of each parameter for which:

the energies determined in d-ii) are closest to the emission energies of the calibration object, or

the channels determined in d-ii) are closest to the channels assigned to each detected peak.

2 . The method of claim 1 , wherein d-iii) comprises:

calculating a likelihood function of the value of each parameter of the set of parameters; and

estimating the value of each parameter maximizing the likelihood function.

3 . The method of claim 2 , wherein

c) comprises determining a width of each peak; and

the likelihood function is defined with the width of each peak.

4 . The method of claim 2 , wherein d-iii) comprises:

forming different pairings, each pairing comprising an emission energy and a channel assigned to a peak, following c);

determining the value of each parameter of the set of parameters for which the calibration function links several pairings, each determined value forming an initial value of each parameter; and

for each initial value, defining a search area extending around the initial value of each parameter, such that the value of each parameter maximizing the likelihood function is estimated in the search areas defined around initial values of the parameter.

5 . The method of claim 2 , wherein d-iii) is implemented using an optimization algorithm.

6 . The method of claim 1 , wherein c) comprises selecting the peaks of the calibration spectrum based on a criterion of selection of the peak.

7 . The method of claim 6 , wherein the selection criterion is a number of photons detected in each peak or a signal-to-noise ratio determined for each peak.

8 . The method of claim 1 , wherein d-iii) comprises using an a priori regarding the value of at least one parameter to determine the value of the at least one parameter.

9 . The method of claim 1 , wherein the particles are chosen from among photons, neutrons, or charged particles.

10 . A device configured to acquire a spectrum of particles emitted by an object, the device comprising:

a detector configured to detect particles and to form, on each detection, a pulse whose amplitude depends on an energy released by the particle having interacted in the detector;

a spectrometric measurement circuit configured to form a spectrum, the spectrum corresponding to a distribution of the amplitudes of the pulses detected by the detector;

a processing unit, programmed to implement d) of the method of claim 1 from the spectrum.

11 . A non-transitory medium, configured to be connected to a computer, comprising instructions when executed by the computer perform d) of the method of claim 1 from a spectrum representative of the energy of detected particles.