We developed an analytical model to evaluate the effect of signal pileup on the recorded energy spectrum in X-ray photon-counting detectors affected by dead time and equipped with retrigger capability. The retrigger function allows the system to work in a specific non-paralyzable counting mode by counting the time-over-threshold of piled-up signals in multiples of a predefined and selectable retrigger time. The model, designed for rectangle-like-shaped signals, allows for arbitrary input energy spectra and can significantly help understand and optimize the behavior of counting detectors with spectral capabilities and retrigger mechanisms in applications involving polychromatic beams, e.g., spectral X-ray imaging and computed tomography (CT), in a time-efficient way. Dedicated numerical simulations were used to validate the model under several conditions of incoming flux and threshold energy, with excellent results.
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