Integral equation method applied to radiative transfer in a 2-D absorbing–scattering refractive medium

In this paper, an investigation of radiative transfer in a rectangular medium with one-dimensional or two-dimensional graded index is presented. The integral equations of intensity moments are derived and then the cases of a cold medium exposed to diffuse irradiation at the left boundary are solved by the Nyström method. The results obtained by solving integral equations are in excellent agreement with those obtained by the Monte Carlo method and the discrete ordinates method. For the case with an increasing refractive index in the direction to the right boundary, the distribution of refractive index enhances the radiation in the direction to the right, and so the half-range flux toward the right boundary increases with the increase of the gradient of refractive index. Besides, the half-range flux toward the right boundary decreases as the position considered approaches the top or bottom boundary.