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Theoretical ranging performance model that considers laser pointing errors for laser ranging systems in detecting diffusely reflecting targets.

A photon-counting lidar ranging system equipped with a single-photon detector and high-power laser sources for tracking low earth orbit (LEO) diffusely reflecting targets has attracted a large amount of attention, and the ranging performance is the key indicator of a laser ranging system. The fluctuation of the pointing error has a considerable effect on the ranging performance, and a theoretical model can be used to optimize the systematic parameters when the ranging system is designed. In this paper, the joint probability distribution function of the laser pointing error is first derived, from which an improved lidar equation that considers the pointing error is derived. The energy expectation value of laser illuminating LEO uncooperative targets is calculated and analyzed by this analytical expression. A Monte Carlo method is used to verify the energy expectation value, and the simulation results match the theoretical results well. The average signal photon number (calculated by the improved lidar equation) also matches well with the experiment conducted by the Shanghai Astronomical Observatory station. Next, the range performance model consists of the range walk error, and the ranging precision is further developed; the results indicate that the range walk error and ranging precision caused by the pointing error are increased to 31.75 cm and 2.5 cm, respectively, when the laser source is powerful (∼2  J) and the pointing error is approximately 1''. The value of the pointing error should be constrained to be less than 20% of the laser divergence angle to avoid a significant influence on the ranging performance.