Abstract

The effective scattering and absorption coefficients used to describe the optical properties of particulate materials in radiative transfer models are determined by the average path-length parameter of the diffuse radiation, as well as by the fraction of energy that each particle scatters into the forward and backward hemispheres relative to the direction of the impinging radiation. Until now, there were no well-established methods to calculate these parameters. We have devised an approach for evaluating average path-length parameters and forward-scattering ratios for both forward and backward diffuse radiation intensities. Single-scattering processes are described by Lorenz–Mie theory, and multiple-scattering effects have been taken into account by a generalization of Hartel theory. As a consequence of the formalism, the Kubelka–Munk scattering and absorption coefficients are explicitly related to average path-length parameters and forward-scattering ratios. These parameters display an optical depth dependence, characterized by values smoothly increasing or decreasing from the perpendicularly illuminated interface and saturation values at large optical depths.

© 1997 Optical Society of America

Forward average path-length parameter in four-flux radiative transfer models

William E. Vargas and Gunnar A. Niklasson
Appl. Opt. 36(16) 3735-3738 (1997)

Intensity of diffuse radiation in particulate media

William E. Vargas and Gunnar A. Niklasson
J. Opt. Soc. Am. A 14(9) 2253-2262 (1997)

Two-flux radiative transfer model under nonisotropic propagating diffuse radiation

William E. Vargas
Appl. Opt. 38(7) 1077-1085 (1999)

Generalized four-flux radiative transfer model

William E. Vargas
Appl. Opt. 37(13) 2615-2623 (1998)

Diffuse radiation intensity propagating through a particulate slab

William E. Vargas
J. Opt. Soc. Am. A 16(6) 1362-1372 (1999)