Abstract

A method for calculating the angular and optical depth dependencies of diffuse radiation in light scattering and absorbing particulate media is established. From the Lorenz–Mie theory, the coefficients involved in the expansion of the single particle phase function in terms of Legendre polynomials are obtained. Then the angular dependence of diffuse radiation is described by means of generalized phase functions, corresponding to the different scattering orders. The optical depth dependence is given in terms of weighting factors, which depend on average path-length parameters and forward-scattering ratios of the different scattering orders. Intensity patterns are obtained for different particle sizes, concentrations, and relative refractive indices, and the behavior of the forward and backward diffuse intensities in terms of optical depth is displayed. Comparisons with the forward-multiple-scattering theory of Hartel are carried out. A generalization of the Beer–Lambert law in the case of light-scattering materials is obtained from the present approach, which is derived from the radiative transfer equation.

© 1997 Optical Society of America

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