Abstract

This paper presents a study of the combined use of a delta function and a Legendre polynomial series to represent the phase function of scattering particles. An approximation frame was developed by combining the requirement that conserving several moments of phase function and minimizing approximation errors within a specific scattering angle range, which is related to four parameters (M, M*, N_f , λ) and named G-δ-L approximation. The physical meaning of G-δ-L and its relationships with δ-M and δ-fit were analyzed. Tests were made to analyze the effects of different values of G-δ-L parameters and optical depths on absolute and relative errors of the scattering phase function and layer outcoming radiance. It is concluded that δ-M and δ-fit are specific cases of the G-δ-L and their advantages can be combined by G-δ-L with suitable parameters.

© 2015 Optical Society of America