Abstract
We develop a modified method to simplify the analytical solutions to the simplified spherical harmonics equations (SP(N)). The scheme decouples the SP(N) partial differential equations into independent equations using eigen decompositions and calculates the Green's function of the photon migrations based on the eigenvectors and eigenvalues. In contrast to the established solutions that are based on the original coupled equations, the proposed derivation is theoretically concise and universally extendable to other regular geometries. We validate the proposed method in comparison with Monte-Carlo simulations for an infinite scattering medium and a circular geometry as an example of the boundary value problems.
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