One-way radiative transfer

We introduce the one-way radiative transfer equation (RTE) for modeling the transmission of a light beam incident normally on a slab composed of a uniform forward-peaked scattering medium. Unlike the RTE, which is formulated as a boundary value problem, the one-way RTE is formulated as an initial value problem. Consequently, the one-way RTE is much easier to solve. We discuss the relation of the one-way RTE to the Fokker–Planck, small-angle, and Fermi pencil beam approximations. Then, we validate the one-way RTE through systematic comparisons with RTE simulations for both the Henyey–Greenstein and screened Rutherford scattering phase functions over a broad range of albedo, anisotropy factor, optical thickness, and refractive index values. We find that the one-way RTE gives very good approximations for a broad range of optical property values for thin to moderately thick media that have moderately to sharply forward-peaked scattering. Specifically, we show that the error made by the one-way RTE decreases monotonically as the anisotropic factor increases and as the albedo increases. On the other hand, the error increases monotonically as the optical thickness increases and the refractive index mismatch at the boundary increases.