Sampling optimization and compact tabulation of isotropic polarized scattering

Realistic simulations of light-matter interactions can be enhanced by empirical polarized bidirectional reflectance distribution functions (pBRDFs), which consist of Mueller matrix (MM) measurements at discretely sampled scattering geometries. The goal of this work is to improve the efficiency of pBRDF representation and acquisition so that extensive libraries of materials found indoors can become readily available. Performing Mueller measurements at many scattering geometries and wavebands requires considerable acquisition time and storage resources. In this work, we introduce a cylindrical, rather than Cartesian, interpretation of the three angles that parameterize an isotropic pBRDF to reduce the volume of the pBRDF space. Furthermore, we exclude geometries that do not correspond to external reflection during tabulation. Together, these steps result in 63% fewer tabulated pBRDF samples while no information is lost because only redundant and non-physical geometries are excluded. We then utilize the compact representation to determine an efficient set of goniometric camera positions at which the pBRDF of a sphere should be sampled. For a given size of sphere and camera parameters of our polarimeter, we found a set of 92 goniometer positions, which samples 82% of the uniformly discretized scattering geometries at least once. We performed this optimized pBRDF sampling and tabulation for a 3D printed sphere. Our cylindrical coordinate representation is used to visualize the pBRDF as a function of scattering geometry.