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.

中文翻译：

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小足迹高光谱 LiDAR 距离和入射角效应独立性的理论演示：基本物理概念


距离和入射角效应在确定光探测和测距 （LiDAR） 系统捕获的原始强度方面起着至关重要的作用。对于这两种效应，高光谱 LiDAR 的出现需要对潜在的耦合关系和波长依赖性进行深入的理论探索。从理论角度来看，本研究在理论推导的基础上，重点关注距离和入射角效应的独立性及其波长依赖性，同时考虑自然目标的异质性，提供了系统的论证。主要发现如下：（1） 距离效应与波长无关，由距离和 LiDAR 系统决定，其特征是“距离效应函数”的概念。（2） 入射角效应是波长依赖性的，由目标的背向散射特性引起，其特征是被测目标的双圆锥反射。这种效果的准确表述应该是“高光谱 LiDAR 条件下目标的入射角效应”，而不是“高光谱 LiDAR 系统的入射角效应”。（3） 强度数据同时受距离和入射角的影响，但这些影响是独立的，可以单独校正。（4） 一旦为某个 LiDAR 系统获得了距离效应函数，就可以在扫描任务中随时直接用于校正距离效应。但是，入射角效应不能直接校正;它需要额外的测量来获取目标在不同入射角下的表面反射特性。 此外，本研究回顾了光学遥感界普遍采用的几个基本物理概念，用于模拟 LiDAR 信号和自然目标之间的反向散射和反射过程。用于小足迹高光谱 LiDAR 的简化激光雷达方程证实了 Kavaya 的经典发现，为推理和理解辐射效应提供了理论基础。虽然为高光谱 LiDAR 量身定制，但所提出的基本物理概念和结论也适用于传统的小尺寸单波长和多光谱 LiDAR 系统。