Statistical Model for SPAD-based Time-of-Flight systems and photons pile-up correction

Many applications rely on time-resolved single-photon detection techniques, for achieving ultimate sensitivity and temporal precision, from molecule level application such as fluorescence lifetime imaging (FLIM), to measurement of objects distances such as in Light Detection and Ranging (LiDAR). Single-Photon Avalanche Diode (SPAD) detectors can be the best candidate for such techniques. Anyway, proper simulations and system-level modelling, taking into account both optical setup and environmental conditions, should be performed to predict system performance and to achieve the best design optimization. Montecarlo simulations are often employed to this purpose [1] , though they are usually time-consuming and give no analytical insight to trade-offs among design choices and parameters selection. Herewith we present a reliable discrete-time statistical model of SPAD detectors [2] , as a valid alternative to Montecarlo simulations, and we exploit it to demanding Time-of-Flight based LiDAR acquisitions under very high background illumination.