Computation of Scattering Kernels in Radiative Transfer

TL;DR

This paper introduces efficient numerical methods for computing scattering kernels in radiative transfer, avoiding Legendre expansions and deriving a closed-form expression for the Henyey-Greenstein kernel using elliptic integrals.

Contribution

It presents rapidly convergent computational formulas for scattering kernels and derives a closed-form for the Henyey-Greenstein kernel using elliptic integrals, improving computational efficiency.

Findings

Developed exponentially convergent numerical integration rules.

Derived a closed-form expression for the Henyey-Greenstein kernel.

Enhanced computational methods for radiative transfer simulations.

Abstract

This note proposes rapidly convergent computational formulae for evaluating scattering kernels from radiative transfer theory. The approach used here does not rely on Legendre expansions, but rather uses exponentially convergent numerical integration rules. A closed form for the Henyey-Greenstein scattering kernel in terms of complete elliptic integrals is also derived.