Light scattering from a sphere on or near an interface

Abstract

The light scattering problem of a sphere on or near a plane surface is solved using an extension of Mie theory. The approach taken is to solve the boundary conditions at the sphere and at the surface simultaneously and develop the scattering amplitude and Mueller scattering matrices. This is performed by projecting the fields in the half space region not including the sphere multiplied by an appropriate Fresnel reflection coefficient onto the half space region including the sphere. An assumption is made that the scattered fields from the sphere, reflecting off the surface and interacting with the sphere, are incident on the surface at near-normal incidence. The exact solution is asymptotically approached when either the sphere is a large distance from the surface or the conductivity of the medium behind the surface approaches infinity. The solution is greatly simplified in the asymptotic limit when the sphere is small compared with the wavelength. Comparisons are made between the experimental Mueller matrices of a contaminated surface and matrices predicted using this simplified system. Comparisons are also made between experimental BRDFs and those predicted using the sphere-surface scattering theory.