General solutions for a four-flux radiative transfer model, derived from the radiative transfer equation and based on Lorenz–Mie scattering and absorption parameters, have been obtained. Forward and backward average path-length parameters have been considered as well as forward-scattering ratios for diffuse anisotropic radiation going into the forward and the backward hemispheres. The reported solutions are generalizations of those obtained by Maheu et al. [Appl. Opt. 23, 3353–3362 (1984)]. Compared with the generalized solutions, numerical calculations indicate that the δ-Eddington approximation and the standard four-flux model of Maheu et al. overestimate the collimated–diffuse reflectance of particulate coatings, whereas these models give similar results in the case of collimated–diffuse transmittance.
© 1998 Optical Society of America
Original Manuscript: August 25, 1997
Revised Manuscript: December 17, 1997
Published: May 1, 1998
William E. Vargas, "Generalized four-flux radiative transfer model," Appl. Opt. 37, 2615-2623 (1998)