High-order coupling effects in underwater laser transmission and their constraints on single-photon lidar design

To address the characterization biases of traditional radiative transfer equations and their approximate models in short-range underwater single-photon detection scenarios, this paper proposes a multi-dimensional modeling improvement for single-photon lidar observation systems, considering time, space, and phase. In the time dimension, cumulative absorption modeling based on higher-order scattering path lengths is introduced to correct the survival probability and energy proportion of scattered photons at each order. In the spatial dimension, a particle radial distribution function and a structure factor are introduced to correct the angular distribution of the scattering phase function. In the phase dimension, a mechanism for regulating absorption on optical coherence and weak localization effects is established, enabling the separate expression of coherent and incoherent transmission channels. Based on these, a parameterized model for single-photon detection is constructed, and calculable constraints for time-gated width, adaptive sampling step size, and travel error compensation are derived, achieving a mapping from optical transmission physical quantities to system parameters. An underwater single-photon lidar system is built based on this model, and experimental verification is conducted. The results show that the established model provides a data foundation for system timing control, scanning design, and point cloud reconstruction and exhibits stable performance improvements in actual underwater imaging.