A response matrix determined with a coincidence-based acquisition for correction of charge sharing spectral distortions in energy-resolved photon counting detectors

A model-independent method is proposed to characterize and correct charge sharing spectral distortions in energy-resolved X-ray acquisitions with pixellated photon-counting detectors. The technique is based on the determination of a coincidence-based response matrix (CBRM) through a preliminary calibration with a uniform irradiation and an arbitrary polychromatic spectrum. The calibration requires the collection of the number of coincidences between a reference pixel and its neighbours for different combinations of energy bins, in order to calculate a set of charge sharing probabilities which are independent of the input spectrum. A detector response matrix is determined, which can afterwards be applied to correct other spectra acquired with the same detector and a conventional multi-comparator electronics, without introducing penalties in terms of processing time. The technique was validated with Geant4 simulations of a 1 mm thick CdTe detector and with data collected with a pixel hybrid detector made of a 300 um thick silicon sensor coupled to a Timepix4 ASIC chip. The differences between the reconstructed spectra and reference distributions of an ideal detector or a 3x3 offline clustering algorithm were evaluated in terms of mean absolute percentage errors. It is demonstrated that the response matrix can restore the spectral information with a performance close to standard clustering algorithms and is less affected by noise artifacts than analog charge summing techniques.