Radiance and polarization in the diffusion region with an arbitrary scattering phase matrix

•The radiance and polarization in a diffusion region with an arbitrary scattering matrix have been numerically obtained.•The expansion order in terms of the GSFs is highly depending on the single-scattering albedo of the scattering medium.

Radiance and polarization patterns in an optically deep region, the so-called diffusion region or asymptotic region, of a homogeneous atmosphere or ocean, depend mainly on the scattering phase matrix and the single-scattering albedo of the medium. The radiance and polarization properties in the diffusion region for an arbitrary scattering phase matrix can be obtained in terms of a series of the generalized spherical functions. The number of terms is closely related to the single-scattering albedo of the medium. If the medium is conservative, the radiance is isotropic in conjunction with no polarization. If the single-scattering albedo is close to 1, several terms are sufficient to obtain the patterns, in which the degree of polarization feature is less than 1%. If the medium is highly absorptive, more expansion terms are required to obtain the diffusion patterns. The examples of simulated radiance and polarization patterns for Rayleigh scattering, Henyey–Greenstein–Rayleigh scattering, and haze L and cloud C1 scattering, defined by Deirmendjian, are calculated.