Discrete ordinate method for polarized light transport solution and subsurface BRDF computation

Abstract

Interest in polarization properties of rendered materials is growing, but so far discussions on polarization have been restricted only to surface reflection, and the reflection due to subsurface scattering is assumed to be unpolarized. Findings from other fields (e.g. optics and atmospheric science) show that volumetric interaction of light can contribute to polarization. We thus investigated the polarized nature of the radiance field due to subsurface scattering as a function of the thickness of the material layer for various types of materials. Though our computations show negligible polarization for material layers of high thickness, light reflected on thin layered materials show significant degrees of polarization. Consequently, polarization cannot be ignored for subsurface component of reflection from painted surfaces (particularly painted metal surfaces) or from coated materials. Reflection from such surfaces is computed by solving for light transport in the different paint layers. In this paper we employ the vector radiative transfer equation (VRTE), which is the polarized version of the radiative transfer equation, inside the material. We use and detail a discrete ordinate based method to solve the VRTE and use the solution to compute the polarized radiance field at the surface of the material layer. We generate the polarimetric BRDF from the solutions of the VRTE for incident irradiance with different polarizations. We validate our VRTE solution against a benchmark and demonstrate our results through renderings using the computed BRDF.