X-ray spectroscopy with photon counting imaging detectors such as Timepix

The energy response spectrum of highly pixelated photon-counting detectors with a semiconductor sensor layer (e.g. silicon) differs significantly from the impinging X-ray spectrum due to charge sharing and Compton scattering. Therefore determining the impinging X-ray spectrum from the measured energy deposition spectrum is a non-trivial task. A detailed model of all relevant physical processes in the sensor layer is necessary to simulate monoenergetic response functions, which can be used to deconvolve the measured spectrum of energy depositions to reconstruct the impinging X-ray spectrum. We have investigated the uncertainties that spectrum reconstruction algorithms, like spectrum stripping or response matrix inversion, impose on reconstruction results. We show that applying Bayesian deconvolution leads to significant stability improvements, which result in a reduced minimum fluency needed for the reconstruction. In this contribution we present our investigations and measurements, focusing on the Bayesian approach and its possibilities for evaluating small ROI.