A Radon-based criterion for the energy resolution of photon counting x-ray detectors

Thanks to recent developments in photon counting detectors, X-Ray spectral imaging has received increasing attention. This technique permits the quantication of the chemical components in an object. The energy selectivity of the detector is known to have a strong impact in the material decomposition capabilities of an imaging device. Although spectral imaging devices are widely used in conjunction to polychromatic illuminations, detectors are typically characterized for one or few incident energies. To the best of our knowledge, no criterion for the overall energy resolution of a photon counting detector is available yet. In this paper, we propose a criterion for energy selectivity over a range of incident energies. Our criterion is based on the analysis of the response of the detector to multiple monochromatic illuminations. In particular, it can be easily computed from the Radon transform of the energy response function of the detector. After a simulation study, we show how this criterion is related to the quality of material decompositions obtained from photon counting measurements