依据双向反射分布函数理论, 推导出散射光谱的加和性原理。 散射光谱加和性是指对于材质质点之间无相互作用的平面漫反射体系, 在光源与入射面材质不存在干涉、 衍射、 荧光、 光谱上转换和光谱下转换等相互转换作用, 且无光化学现象及非线性效应发生的前提下, 且符合能量守恒定律的同时, 由单光源或多光源照射的材料的散射光谱, 等于该材料中每种材质的散射光谱的线性叠加。 实验上, 以几种材料的散射光谱为例, 通过改变探测条件、 照明条件和材质比例, 进行了散射光谱加和性的实验验证, 并且针对实验结果进行了误差分析。 单光源条件下的最大实验误差为2.64%, 多光源条件下则为2.35%, 加和计算偏差均在实验误差允许范围内。 由此证明了材料的散射光谱具有加和性, 不受组成的材质差异性、 材质的面积比例组合多样性、 以及实验条件多变性影响。 散射光谱加和性的首次提出, 不仅为基于散射光谱的复杂结构体的特征提取及识别研究提供了确切的理论依据和有效的分析方法, 而且对相关的实验分析和应用研究有着重要的借鉴和参考意义。

In this paper, the additivity principle of scattering spectrum is proved with bidirectional reflectance distribution function theory coupled with the reference of Lambert-Beer law. For planar diffuse system with non-interacting between material particle, there is no interference, diffraction, fluorescence, spectral conversion, down conversion and other mutual conversion effects between the light source and incident surface material. Furthermore, in the context of non-photochemical phenomenon, nonlinear effects and in accordance with the law of conservation of energy, the material scattering spectrum irradiated by single or multiple light source equal to the linear superposition of the material scattering spectra of each material, which is called the additivity of scattering spectrum. In the experiment, the additivity principle is tested under different lighting conditions and material proportions. It is found that the maximum relative errors are 2.64% and 2.35% for the single and multiple light sources, respectively, which are less than those of theoretical results. Thus, it is shown that the scattering spectrum of material has the additive property which is independent from different lighting conditions and diverse materials and the different proportion of materials. This theory may give a useful method and theoretical reference for extracting feature and recognizing scattering spectra of complex systems. The first propose of the additivity of scattering spectrum provides not only the exact theoretical basis and effective analysis method for the extraction and recognition of complex structures characteristic scattering spectrum and has an important reference value for the experimental analysis and applied research.