Diffusing-Light Spectroscopies Beyond the Diffusion Limit: The Role of Ballistic Transport and Anisotropic Scattering

Diffuse transmission and diffusing-wave spectroscopy (DWS) can be used to probe the structure and dynamics of opaque materials such as colloids, foams, and sand. A crucial step is to model photon transport as a diffusion process. This approach is acceptable for optically thick samples, far into the limit of strong multiple scattering; however, it becomes increasingly inaccurate for thinner samples for several reasons. Here, we correct for two of these defects. By modeling photon propagation by a telegrapher equation with suitable boundary conditions, we can account for the ballistic transport of photons at finite speed between successive scattering events. By introducing a discontinuity in the photon concentration at the source point, and then averaging over a range of penetration depths, we can account for the fact that photons usually scatter anisotropically into the forward direction, rather than being completely randomized at each event. The accuracy of our approach is tested by comparison both with random walk computer simulations and with experiments on specially designed suspensions of polystyrene spheres. We find that our predictions extend the utility of diffuse transmission to slabs of all thicknesses and of DWS to slabs down to about two transport mean free paths. Disciplines Physical Sciences and Mathematics | Physics Comments At the time of publication, author Douglas J. Durian was affiliated with University of California, Los Angeles. Currently, he is a faculty member at the Physics Department at the University of Pennsylvania. This journal article is available at ScholarlyCommons: https://repository.upenn.edu/physics_papers/624 Diffusing-light spectroscopies beyond the diffusion limit: The role of ballistic transport and anisotropic scattering P.-A. Lemieux, M. U. Vera, and D. J. Durian Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1547 ~Received 14 October 1997 ! Diffuse transmission and diffusing-wave spectroscopy ~DWS! can be used to probe the structure and dynamics of opaque materials such as colloids, foams, and sand. A crucial step is to model photon transport as a diffusion process. This approach is acceptable for optically thick samples, far into the limit of strong multiple scattering; however, it becomes increasingly inaccurate for thinner samples for several reasons. Here, we correct for two of these defects. By modeling photon propagation by a telegrapher equation with suitable boundary conditions, we can account for the ballistic transport of photons at finite speed between successive scattering events. By introducing a discontinuity in the photon concentration at the source point, and then averaging over a range of penetration depths, we can account for the fact that photons usually scatter anisotropically into the forward direction, rather than being completely randomized at each event. The accuracy of our approach is tested by comparison both with random walk computer simulations and with experiments on specially designed suspensions of polystyrene spheres. We find that our predictions extend the utility of diffuse transmission to slabs of all thicknesses and of DWS to slabs down to about two transport mean free paths. @S1063-651X~98!11604-5# PACS number ~s!: 82.70. 2y, 05.40. 1j, 42.62.Fi