X-ray spectra reconstruction from analysis of attenuation data: A Back Scattering Thomson source application

It is known that useful information about the spectral distribution of an X-ray beam can be extracted by measuring and analyzing its transmission curve. This kind of approach to the characterization of the distribution in energy of photons is justified when the direct measurements of the energy of a single photon becomes too expensive or cannot just be performed. Thomson Scattering sources can produce up to 108108 photons within a pulse 10 ps long. Hence the rate of incidence of photons is too high to apply traditional X-ray spectroscopy methods while methods based on the transmission curve can still be used.In order to propose an application of these techniques in the characterization of a Thomson Scattering source we studied an iterative statistical algorithm (Expectation-Maximization) used as a regularization method on simulated measurement computed starting from a calculated energy distribution with peak energy of 20 keV. Results show that this method can give good approximations in the low energy range (approximately 20 keV) and that it is at least sensible to a small amount of radiation in the higher part of the energy range (approximately 70 keV). The robustness of the method against non-ideal experimental conditions is also considered.