A robust framework for modelling long range dToF SPAD Lidar performance

Single-Photon Avalanche Diode (SPAD) array Lidars with their picosecond timing precision and single-photon sensitivity are a crucial technology for imaging in challenging environments. Given a particular environment, optical system, a finite acquisition time, and a data processing algorithm, what quality of depth resolution can be achieved? Prior works have demonstrated Cramér-Rao Bound (CRB) analyses to answer questions of this type however, these analyses are not valid in all SPAD imaging regimes. Here, we present a robust framework for modelling the performance of direct Time-of-Flight (dToF) SPAD Lidars in all regimes, including at ranges of 1.4 km. We perform an in-depth examination of the applicability of CRB approaches for various SPAD Lidar configurations and propose the ‘Binomial Separation Criterion’ (BSC) as a means of quantifying the operational regime of a system. Our approach combines a physical model of photon arrivals with a 3D virtual environment, creating a physically significant digital twin. We experimentally verify our predictions achieving depth resolutions of <1 mm. We present strong agreements between the predictions of our framework and the experimental results across different operating wavelengths, resolutions, target types, and sensor architectures, including the generation of simulated depth images and point clouds for complex multi-surface scenes. We expect this framework to serve as a highly versatile tool with wide ranging applicability to the SPAD Lidar community.