Probabilistic characterization of Solid State Photomultipliers based on transit time histograms

Precision measurement of weak light pulse arrival time is very important in various time-of-flight applications in high energy physics and medical imaging. Key characteristics of photodetectors responsible for time resolution in these applications are Photon Detection Efficiency (PDE) and single photon Transit Time Spread (TTS). Measurements of PDE and TTS are mostly carried out independently using rather different techniques and setups. We consider probability to detect single photon as defective cumulative distribution function (CDF) of single photon transit time and found analytical expressions how it may be reconstructed from multi-photon TTS histogram affected by dark counts. It allows us to propose a robust quantitative method of characterization of single photon detection process in form of instrumental response function (IRF), which provides both single photon TTS and PDE. The method seems to be especially relevant and useful for Solid State Photomultipliers (SSPM) with high dark count rate.