Solution for atmospheric optical transfer function using spherical harmonics method

Abstract

This paper presents a numerical algorithm for computation of atmospheric optical transfer function (OTF) for the problem with Lambertian reflectance. OTF is a Fourier transform of the atmospheric point spread function, and it describes photon transport over a spatially non-uniform surface. The boundary-value problem for OTF is obtained from the 3D radiative transfer problem linearized in the spatial albedo variation. This problem is then solved with an efficient SVD modification of the spherical harmonics method with the smoothing procedure of the source function integration. This combination allowed us to develop a fast stable algorithm allowing calculations in arbitrary directions for vertically inhomogeneous atmosphere with arbitrary optical thickness and scattering function.