Microfacet-based physics-driven framework for single-photon LiDAR rough-surface scattering and detection.

The scattering characteristics of rough surfaces play a fundamental role in single-photon LiDAR, remote sensing, and optical target characterization. Conventional electromagnetic models describe the underlying optical scattering process, whereas photon-counting statistics and detector response must be modeled separately to describe measurements in the single-photon regime. In this study, a unified simulation model for rough-surface scattering and single-photon detection is developed based on the microfacet model. The model incorporates laser emission, photon propagation, surface scattering, and detector response within a single framework. Surface scattering is determined from the complex relative permittivity, root-mean-square height, and correlation length of the target, while photon absorption, specular reflection, diffuse reflection, and detector response are modeled using the Fresnel equations and photon-counting statistics. Simulations and experiments are performed for different photon transmittance levels, incident angles, material types, and surface roughness. The simulated and experimental scattered-photon distributions exhibit consistent trends and show good overall agreement for both metallic and dielectric targets. The proposed model provides an effective approach for analyzing rough-surface scattering and single-photon detection, offering theoretical support for single-photon LiDAR system design, optical target characterization, and rough-surface analysis.