On the extinction of radiation by a homogeneous but spatially correlated random medium

Exponential extinction of incoherent radiation intensity in a random medium (sometimes referred to as the Beer-Lambert law) arises early in the develo pment of several branches of science and underlies much of radiative transf er theory and propagation in turbid media with applications in astronomy, a tmospheric science, and oceanography. We adopt a stochastic approach to exp onential extinction and connect it to the underlying Poisson statistics of extinction events. We then show that when a dilute random medium is statist ically homogeneous but spatially correlated, the attenuation of incoherent radiation with depth is often slower than exponential. This occurs because spatial correlations among obstacles of the medium spread out the probabili ty distribution of photon extinction events. Therefore the probability of t ransmission (no extinction) is increased. (C) 2001 Optical Society of Ameri ca.