  Dead time effects have been considered a major limitation for fast data
acquisition in various time-correlated single photon counting applications,
since a commonly adopted approach for dead time mitigation is to operate in the
low-flux regime where dead time effects can be ignored. Through the application
of lidar ranging, this work explores the empirical distribution of detection
times in the presence of dead time and demonstrates that an accurate
statistical model can result in reduced ranging error with shorter data
acquisition time when operating in the high-flux regime. Specifically, we show
that the empirical distribution of detection times converges to the stationary
distribution of a Markov chain. Depth estimation can then be performed by
passing the empirical distribution through a filter matched to the stationary
distribution. Moreover, based on the Markov chain model, we formulate the
recovery of arrival distribution from detection distribution as a nonlinear
inverse problem and solve it via provably convergent mathematical optimization.
By comparing per-detection Fisher information for depth estimation from high-
and low-flux detection time distributions, we provide an analytical basis for
possible improvement of ranging performance resulting from the presence of dead
time. Finally, we demonstrate the effectiveness of our formulation and
algorithm via simulations of lidar ranging.
