The Corrected Diffusion Approximation for Diagnostic Measurements
Friday, 19 August 2011: 14.30-15.15
Arnold Kim, University of California, Merced
We study the steady-state radiative transport equation when scattering is strong and absorption is weak. Through a systematic asymptotic analysis, we derive the diffusion approximation modeling the radiance deep in the interior of the domain. In addition, we derive a boundary layer solution that corrects the errors made by the diffusion approximation near boundaries. This corrected diffusion approximation leads to a better model for diagnostic measurements of scattered light. It is only slightly more complicated than the standard diffusion approximation, but still much simpler than solving the full radiative transport equation. We discuss also an extension of this theory that takes into account the polarization state of scattered light.