Decoupling path-scattering of light in a homogeneous layer and multiple bouncing at its non-Lambertian bottom

Radiative transfer theories are usually used to calculate light transmitted and reflected on a layer of homogeneous medium.But if the layer has limited optical thickness and a non-Lamhertian lower bound,the multiple bouncing between the layer and the lower bound will be coupled with the multiple scattering within the layer,thus making the solution very complicated.Through atmospheric correction for FOS MODIS MISR BRDF product and modeling shortwave absorption of snow under forest canopies,it is found that two complicated and apparently different cases can he handled similarly by decoupling the problem into two simpler and more basic formulations.i.e anahtical approximations ot path scattering i.e assuming a perfect absorbing lower bound: and the multiple bouncing between the layer and ils non-Lamhertian lower bound.