New treatment of strongly anisotropic scattering phase functions: The Delta-M+ method.

The treatment of strongly anisotropic scattering phase functions is still a challenge for accurate radiance computations. The new Delta-M+ method resolves this problem by introducing a reliable, fast, accurate, and easy-to-use Legendre expansion of the scattering phase function with modified moments. Delta-M+ is an upgrade of the widely-used Delta-M method that truncates the forward scattering peak with a Dirac delta function, where the '+' symbol indicates that it essentially matches moments beyond the first M terms. Compared with the original Delta-M method, Delta-M+ has the same computational efficiency, but for radiance computations the accuracy and stability have been increased dramatically.