Theoretical model considering optimal ranging performance and energy efficiency for photon-counting lidars with multiple detectors

Abstract

With an orbital speed of several kilometers per second, space-borne photon-counting lidars can only perform several to a few tens of measurements on the same target. The ranging uncertainty can exceed tens of centimeters with a pulse width of several nanoseconds and has a great impact on the total ranging error. When multiple photons are recorded (using multiple detectors) in a single laser shot, the ranging uncertainty can be effectively suppressed by the average method. Higher signal levels (receiving more photons) introduce a better ranging uncertainty, but a worse ranging bias is caused by the dead time effect of photon-counting detectors. In this study, a theoretical ranging performance model is proposed to address that question: What signal levels and how many detectors are the optimum selection to achieve a better ranging performance? A photon-counting lidar system with four photomultiplier tubes is used to verify the proposed ranging performance model. Experiments are conducted under nine sets of different signal levels, and the ranging performance of experiment results agree well with the theoretical predictions. The average residual error is 0.31 cm and all error ratios are less than 10%. The energy efficiency and ranging uncertainty are further quantitatively analyzed. When multiple detectors are employed, the total ranging error (i.e., the root sum square of the ranging bias and ranging uncertainty) has the minimum value. For a space-borne photon-counting lidar, the expected signal photon number in each detector is recommended as 0.5∼1 (wasting a small part of the received energy). With a 4×4 detector array and a received pulse width of 1.5 ns, the total ranging error can reach approximately 5 cm when the expected signal photon number is close to 10. This theoretical model is essential in estimating the ranging performance for a give photon-counting lidar and in optimizing the design of lidar system parameters.