Direct Time-of-Flight TCSPC Analytical Modeling Including Dead-Time Effects

The optimization of a TCSPC system requires modeling which considers the design specifications and parameters of the target application under different operating scenarios. Since single-photon detection is fundamentally a stochastic process, extensive behavioral Monte Carlo simulations are normally used. Their accuracy depends upon computation time. However, the trend towards larger SPAD arrays and emerging complex TDC sharing architectures requires much faster simulation methods. In this paper, a simple, fast and accurate analytical model is presented to address this need. It accounts for dead time effects which result in missed photon counts through the analysis of inhomogeneous continuous time Markov chain. The effective received power and photon detection rate are determined and the corresponding analytical histogram is created. This histogram is the basis for calculating time of flight and can be used to explore architectural alternatives and accelerate design verification. Outputs of the presented analytical model match those of Monte Carlo simulations, and are produced considerably faster. The computation time improvement grows with array sizes and this enables parametric analysis of TCSPC system.