We derive the anisotropic diffusion equation for optical random media from the radiative transfer equation by correcting errors or eliminate simplifications in previous studies. The derived equation makes explicit the relation between microscopic (extinction cross-section and phase function) and macroscopic (transport mean free path tensor) parameters. We discover that transmittance and reflectance for a film made of an anisotropic material are determined from a dimensionless factor, which we define as anisotropy tensor, in addition to scattering/transport mean free paths and extrapolation length ratio. According to our derived equations, a direction component of the diagonalized transport mean free path tensor can be smaller than that of the diagonalized scattering mean free path tensor for forward scattering, which is physically impossible. We demonstrate that a direction component of the diagonalized inner product of transport mean free path tensor and the anisotropy tensor preserves the physical meaning of transport mean free path.

中文翻译：

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光学介质各向异性扩散方程中的输运平均自由程张量和各向异性张量

我们通过校正错误或消除先前研究中的简化，从辐射传递方程推导出光学随机介质的各向异性扩散方程。导出的方程明确了微观（消光截面和相位函数）和宏观（传输平均自由程张量）参数之间的关系。我们发现由各向异性材料制成的薄膜的透射率和反射率除了散射/传输平均自由程和外推长度比之外，还由无量纲因子确定，我们将其定义为各向异性张量。根据我们推导出的方程，对角化传输平均自由程张量的方向分量可以小于前向散射的对角化散射平均自由程张量的方向分量，这在物理上是不可能的。