Modeling and Correction of Underwater Photon-Counting LiDAR Returns Based on a Modified Biexponential Distribution

Laser pulses experience significant temporal broadening in underwater environments due to strong turbulence and scattering effects. As water turbidity increases, the likelihood of multiple scattering events rises, further intensifying pulse broadening and thereby degrading the ranging accuracy of underwater single-photon LiDAR systems. Accurate characterization of the return pulse shape is crucial for precise distance extraction, typically achieved via cross-correlation with the system’s Instrument Response Function (IRF). Conventional models often fail to accurately characterize the distinctive asymmetric shape of underwater LiDAR returns, which feature a rapid rise and a slow decay. To address this limitation, this paper proposes a Modified Biexponential Distribution (MBD) model, specifically designed to capture both the sharp leading edge and the gradual trailing decay of the pulses. This model enables a more accurate representation of the broadened pulse, effectively mitigating the ranging error induced by scattering. Experimental validation demonstrates that, at an attenuation length of 6.9, the Depth Absolute Error (DAE) is reduced from 3.82 cm to 3.15 cm (a 17.54% improvement), while the probability of achieving a DAE below 3.82 cm increases from 49.70% to 74.83%. These results confirm the effectiveness and robustness of the proposed model in enhancing the ranging accuracy of underwater photon-counting LiDAR systems. Furthermore, this study provides a model-driven analytical basis for improving underwater photon detection and bathymetric performance in turbid conditions.