A theoretical demonstration on the independence of distance and incidence angle effects for small-footprint hyperspectral LiDAR: Basic physical concepts

Distance and incidence angle effects play crucial roles in determining the raw intensity captured by light detection and ranging (LiDAR) systems. For these two effects, the emergence of hyperspectral LiDAR necessitates a deep theoretical exploration of potential coupling relationships and wavelength dependence. From a theoretical standpoint, this study provides a systematic demonstration, based on theoretical derivation, focusing on the independence of distance and incidence angle effects and their wavelength dependence, while considering the heterogeneity of natural targets. The key findings are as follows: (1) the distance effect, which is wavelength-independent, is determined by the distance and LiDAR system, characterized by the concept of a “distance effect function”. (2) The incidence angle effect is wavelength-dependent and arises from backscattering characteristic of the target, characterized by the biconical reflectance of the measured target. An accurate expression for this effect should be “incidence angle effect of the target under hyperspectral LiDAR conditions”, rather than the “incidence angle effect of hyperspectral LiDAR system”. (3) Intensity data are simultaneously affected by distance and incidence angle, but these effects are independent and can be individually corrected. (4) Once the distance effect function is obtained for a certain LiDAR system, it can be directly used to correct the distance effect at any time during scanning tasks. However, the incidence angle effect cannot be directly corrected; it requires additional measurements to acquire surface reflection characteristics of the target at various incidence angles. Additionally, this study reviews several basic physical concepts commonly adopted by the optical remote sensing community for modeling the backscattering and reflection processes between LiDAR signals and natural targets. A simplified laser radar equation for small-footprint hyperspectral LiDAR corroborated the classic finding by Kavaya, serving as a theoretical basis for reasoning and understanding the radiative effects. While tailored for hyperspectral LiDAR, the presented fundamental physical concepts and conclusions are also applicable to traditional small-footprint single-wavelength and multispectral LiDAR systems.