Optical parameters of disperse medium with large absorbing and scattering inclusions

Based on the radiative transfer theory for a simple model of a discrete system containing optically large inclusions, an analytical relationship is established between the absorption and scattering indices and phase function integral parameter of an elementary volume of the medium and the corresponding characteristics of inclusions. It is shown that, in order to retain the form of the Bouguer-Beer-Lambert law, i.e., direct proportionality between the above phenomenological parameters and volumetric concentration of inclusions, one must introduce certain correcting factors into the law. An analytical description of these corrections and their analysis are presented. It is established that the indices of the absorption, scattering, attenuation, and backscattering of an elementary volume of the medium with inclusions are always smaller than similar characteristics of the disperse system with homogeneously distributed absorbing and scattering centers of the same mass. The correcting coefficients for these indices always decrease with increasing optical dimensions of inclusions. The unusual behavior of the forward scattering index of a medium with inclusions, which may increase with their optical dimensions, is quantitatively interpreted. The conditions for this anomaly are found and its cause is shown to be related to the multiple scattering of light within the same inclusion.