Ranging performance models based on negative-binomial (NB) distribution for photon-counting lidars

For photon-counting lidars, the current ranging performance models are based on Poisson statistics that are a special case of a negative-binomial (NB) distribution. In this paper, a new ranging performance model that considers the effect of a target's speckle, the noise, and the dead-time of photon-counting detectors is derived from the NB distribution. The derived ranging performance model is verified by both an experiment based on a Geiger mode avalanche photodiode (GM-APD) lidar and a simulation using the recursive method. The ranging performance model is then used to analyze the effect of target speckle for two typical photon-counting ranging systems aimed at different types of target: the space-borne Ice, Cloud and land Elevation Satellite-2 (ICESat-2) for detecting the Earth's surface, and the ground-based laser ranging system at Shanghai Astronomical Observatory (SHAO) station for detecting space debris. The results indicate that for space-borne or airborne lidar, the ranging performance model can be approximated to the classic models based on Poisson statistics, but for a ground-based laser ranging system, the approximation model introduces differences of ~1 cm in ranging bias and 4.8 cm in ranging precision from the theoretical model of the NB distribution. In addition, the new model is universal because it is compatible with the classic model of a Poisson distribution, i.e., when the speckle diversity is greater than 100, the result calculated from the new model is identical to the classic model.