Polarized radiation deep in an atmosphere

The polarized radiation field components I and Q deep within an optically semi-infinite, homogeneous atmosphere containing no interior sources are examined for the Rayleigh-Cabannes (Rayleigh plus isotropic) scattering model that depends on the single scattering albedo and the depolarization factor. Five different parameters are considered as a function of the albedo: the asymptotic attenuation coefficient common to both radiation components and, for each polarization component, the outward-to-inward flux ratio and the mean cosine of the radiance. These parameters depend only very weakly on the amount of depolarization in the atmosphere, which indicates that any inversion algorithm for inferring the depolarization factor and the single scattering albedo will be extremely ill-conditioned.