On the link between particle size and deviations from the Beer-Lambert-Bouguer law for direct transmission

Ballistic photon models of radiative transfer in discrete absorbing random media have demonstrated deviations from the Beer-Lambert-Bouguer law of exponential attenuation. A number of theoretical constructs to quantify the deviation from the Beer-Lambert-Bouguer law have appeared in the literature, several of which rely principally on a statistical measure related to the statistics of the absorber spatial positions alone. Here, we utilize a simple computational model to explore the interplay between the geometric size of the absorbing obstacles and the statistics governing the placement of the absorbers in the volume. We find that a description of the volume that depends on particle size and the spatial statistics of absorbers is not sufficient to fully characterize deviations from the Beer-Lambert-Bouguer law. Implications for future further theoretical and computational explorations of the problem are explored. (C) 2013 Elsevier Ltd. All rights reserved.