Counting Statistics of Actively Quenched SPADs Under Continuous Illumination

This work presents stochastic approaches to model the counting behavior of actively quenched single-photon avalanche diodes (SPADs) subjected to continuous-wave constant illumination. We present both analytical expressions and simulation algorithms predicting the distribution of the number of detections in a finite time window. We also present formulas for the mean detection rate. The approaches cover recovery time, afterpulsing, and twilight pulsing. We experimentally compare the theoretical predictions to measured data using commercially available silicon SPADs. Their total variation distances range from $10^{-5}$ to $10^{-2}$.