Generalized four-flux radiative transfer model

General solutions for a four-flux radiative transfer model, derivedfrom the radiative transfer equation and based on Lorenz-Miescattering and absorption parameters, have been obtained. Forwardand backward average path-length parameters have been considered aswell as forward-scattering ratios for diffuse anisotropic radiationgoing into the forward and the backward hemispheres. The reportedsolutions are generalizations of those obtained by Maheu et al. [Appl. Opt. 23, 3353-3362(1984)]. Compared with the generalized solutions, numericalcalculations indicate that the delta-Eddington approximation and thestandard four-flux model of Maheu et al. overestimate thecollimated-diffuse reflectance of particulate coatings, whereas thesemodels give similar results in the case of collimated-diffusetransmittance.