Optimization of a Range Walk Error Correction for Underwater Photon Counting LiDAR Under Low-Photon Conditions

Underwater gated time-correlated single-photon-counting (TCSPC) LiDAR is advantageous when weak target echoes coexist with strong backscatter. However, under the first-photon-triggering and SPAD dead-time mechanism, the estimated time of flight becomes dependent on the return strength, thereby producing a range walk error (RWE). This paper develops a condition-calibrated correction framework for accumulated-histogram underwater ranging in the low-photon regime. A non-homogeneous Poisson first-arrival model that jointly includes gate-limited signal photons and in-gate background triggering yields a computable expression for the total trigger probability and the conditional first-arrival time. A first-order expansion around $N_{pe}\approx 0$ leads to an approximately linear RWE–$N_{pe}$ relation under the present system–water condition. A density-based signal-window localization method and a noise-occlusion-compensated estimator of $N_{pe}$ are combined with reference-plane differential calibration. Experiments in a 10 m clear-freshwater tank at 9.11 m show that the mean absolute error is reduced from 39.205 mm to 2.130 mm, corresponding to a 94.57% improvement. Compared with a quadratic model used under higher-photon conditions, the proposed linear model yields an order-of-magnitude smaller residual error in the low-photon region ($N_{pe}<1.6$).