Dead time models for multi-threshold counting detectors in paralyzable and retrigger-based nonparalyzable modes

This work presents the derivation and validation of a mathematical framework describing the recorded count rate as a function of the incident rate for arbitrary threshold levels k , for both paralyzable and retrigger-based nonparalyzable counting modes. The analytical models, developed for Poissonian arrival processes and ideal rectangular signals, are validated through Monte Carlo simulations. The study is further extended to realistic detector conditions in terms of pulse shaping and energy distribution. Here, analytical models are employed as fitting functions, treating the dead-time parameters as effective, threshold-dependent entities. While the paralyzable model shows increased sensitivity to non-ideal signal shapes, the retrigger-based model remains remarkably robust. Finally, we demonstrate that the maximum detectable count rate scales linearly with the number of available thresholds. This confirms that leveraging multi-threshold logic represents a highly effective strategy for pushing the operational limits of photon-counting detectors into high-flux environments.