Discrete scatterers and autocorrelations of multiply scattered light

Abstract

The intensity autocorrelation function of light backscattered from the surface of concentrated suspensions of small spheres is studied. In the past, calculations have been based on a model of light diffusing in a continuous medium, which, in order to agree with experiment, relies on rather unphysical, ad hoc assumptions about boundary conditions. Here, it is shown that for isotropic scatterers the discrete nature of the scatterers is very important in determining the autocorrelation function, a point that is neglected in the continuum diffusion model. In the case of highly anisotropic scatterers, a one-dimensional diffusion model does not suffice to describe a photon’s path, which is characterized both by a slowly changing direction and position. Numerical simulations that take into account the discrete nature of scattering events and the direction and position of scattered photons, give autocorrelation functions, that are close to those seen experimentally [D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 (1988)]. In addition, various limits of the autocorrelations are examined analytically.