Characterizing a sample by material basis decomposition

A method for improving accuracy of a characterization of a sample by material basis decomposition, the method comprising:

• acquiring, by circuitry comprising a memory and a detector connected to a processor, a spectrum transmitted through the sample, said spectrum being an energy spectrum defined by a number of photons transmitted through the sample in each channel of a plurality of energy channels located in an X spectral band and/or a gamma spectral band;
• acquiring, by said memory, calibration spectra, wherein each of the calibration spectra corresponds to a calibration spectrum transmitted through a stack including plural gauge blocks, each gauge block of said stack consisting of a different calibration material, and said stack consisting of a different set of thicknesses for each of the gauge blocks consisting of a different calibration material;
• calculating, by said circuitry, values of a likelihood function from said acquired calibration spectra and from the spectrum transmitted through the sample;
• determining, by said circuitry, a maximum likelihood value from among the calculated values of the likelihood function, the determined maximum likelihood value corresponding to an acquired calibration spectrum corresponding to a stack of gauge blocks, each gauge block of the stack consisting of a different calibration material, the acquired calibration spectrum being most similar to the acquired spectrum transmitted through the sample;
• and
• outputting, from the circuitry, a plurality of estimated characteristic thicknesses, each of the outputted estimated characteristic thicknesses being associated with a different calibration material, from the stack of gauge blocks of the acquired calibration spectrum corresponding to said determined maximum likelihood value.