Correcting for accidental correlations in saturated avalanche photodiodes

In this paper we present a general method for estimating rates of accidental coincidence between a pair of single photon detectors operated within their saturation regimes. By folding the effects of recovery time of both detectors and the detection circuit into an "effective duty cycle" we are able to accomodate complex recovery behaviour at high event rates. As an example, we provide a detailed high-level model for the behaviour of passively quenched avalanche photodiodes, and demonstrate effective background subtraction at rates commonly associated with detector saturation. We show that by post-processing using the updated model, we observe an improvement in polarization correlation visibility from 88.7% to 96.9% in our experimental dataset. This technique will be useful in improving the signal-to-noise ratio in applications which depend on coincidence measurements, especially in situations where rapid changes in flux may cause detector saturation.