Remote sensing hyperspectral and more generally spectral instruments are common tools to decipher surface features in Earth and Planetary science. While linear mixture is the most common approximation for compounds detection (mineral, water, ice, etc...), the transfer of light in surface and atmospheric medium are highly non-linear. The exact simulation of non-linearities can be estimated at very high numerical cost. Here I propose a very simple non-linear form (that includes the regular linear area mixture) of radiative transfer to approximate surface spectral feature. I demonstrate that this analytical form is able to approximate the grain size and intimate mixture dependence of surface features. In addition, the same analytical form can approximate the effect of Martian mineral aerosols. Unfortunately, Earth aerosols are more complex (water droplet, water ice, soot,...) and are not expected to follow the same trend.

翻译：遥感高光谱及更一般的光谱仪器是解译地球与行星科学中地表特征的常用工具。虽然线性混合是化合物检测（矿物、水、冰等）中最常用的近似方法，但光在表面与大气介质中的传输过程具有高度非线性特性。对非线性的精确模拟需耗费极高的数值计算成本。本文提出一种极为简洁的非线性形式（包含常规线性面积混合），用于近似地表光谱特征的辐射传输。我证明了该解析形式能够近似表征粒径及紧密混合效应对表面特征的依赖关系。此外，该解析形式同样可近似火星矿物气溶胶的影响效应。遗憾的是，地球气溶胶（水珠、水冰、黑碳等）更为复杂，预计不遵循相同的变化规律。