SPAD-based time-of-flight discrete-time statistical model and distortion compensation

Abstract

Time-resolved single-photon detection is a robust technique exploited in many fields, ranging from biology, e.g. in fluorescence lifetime imaging (FLIM), to industrial fields, such as in Light Detection and Ranging (LiDAR). Such technique can take major advantage from Single-Photon Avalanche Diodes (SPADs) and their single-photon sensitivity and picosecond time-resolution. For best system design, environmental conditions and optics should be simulated along with SPAD’s actual parameters. Monte Carlo simulations are usually employed, being able to emulate detector’s non idealities and photons’ statistical behavior. However, those simulations are time-consuming. As an effective alternative, we present a detailed discrete-time statistical model for SPAD detectors. The proposed analytical model provides the expected photon time-distribution, given the actual incoming photon-rate, optical setup, laser power and pulse width, background light, object properties, and takes into account all SPAD’s nonidealities, such as hold-off time, crosstalk, afterpulsing, photon detection efficiency, and dark-counting rate. Moreover, the model can predict and correct one big limitation of SPAD systems, namely the detector dead-time (every time a photon is revealed, the SPAD needs to stay quenched for a not nil time interval), which causes distortion in the measured timing histogram, known as “pile-up”. To this purpose, we present how our reversed model can be applied to the measured histogram in order to compensate and correct such a distortion, so to estimate the actual incoming photon distribution. Eventually, the model can be used for both single photon Time-Correlated Single Photon Counting (TCSPC) and multi-photon detection (free-running) regimes, whether the timing electronics has a dead-time shorter than the detector’s one, resulting in a powerful design tool.