Azimuthally dependent radiative transfer in a slab with variable refractive index

Applying Fourier series expansion and a discrete ordinates method, we obtain accurate solutions of azimuthally dependent radiative transfer in an anisotropically scattering slab with variable refractive index and oblique irradiation. It is found that in a slab with a positive gradient of refractive index the optical distance traveled by incident rays decreases, and thus the value of transmittance increases. Besides, the increase of gradient of refractive index enhances the above effect. Influence of the optical thickness, scattering albedo and phase function of the medium, the incident angle of irradiation and the spatial variation of refractive index on the angular distribution of bidirectional reflectance is also investigated.