Robust framework for modelling long range dToF SPAD Lidar performance

Time-of-flight Lidars based on single-photon avalanche diode (SPAD) detector arrays are emerging as a strong candidate technology for long range three-dimensional imaging in challenging environmental conditions. However, reaching this bound requires the existence of an unbiased estimator, which does not necessarily exist for data acquired by realistic SPAD-based Lidar systems. Here, we extend our existing SPAD Lidar modelling framework to include a novel metric, which we term the 'Binomial Separation Criterion', as a means of quantifying whether a depth estimation algorithm will reach the Cramér-Rao bound (CRB). This enables us to evaluate the performance of SPAD Lidar systems over a significantly larger state space range than previously, i.e., evaluation in scenarios where the total number of measured photons and peak signal-to-noise ratio change by an order of magnitude. We validate this new approach against data acquired from two separate depth imaging systems, one operating at 532 nm and one at 1550 nm wavelengths, measuring targets at a range of 1.4 km. We present strong agreements between the outputs of our framework and the experimental results across different operating wavelengths, spatial resolutions, target types, and sensor architectures. We expect this framework to serve as a highly versatile tool with wide-ranging applicability to the SPAD Lidar community.