Consideration of non-Poisson distributions for lidar applications

Poisson statistics are traditionally used to estimate the mean and standard deviation of the mean in time—range realizations of received photon counts from stationary processes in incoherent-detection lidar systems. However, this approach must be modified if the process under study is measurably nonstationary to account for any additional (and potentially unanticipated) variability. We demonstrate that the modified approach produces a different form for the estimated standard deviation of the mean for lidar return counts, which can also be applied to binning of higher-order data products. This modified technique also serves to determine optimum time–range integrations, diagnose system stability, and constrain operational modes.