Polarized representation for depolarization-dominant materials

The light-matter interactions which occur in common indoor environments are strongly depolarizing, but the relatively small polarization attributes can be informative. This information is used in applications such as physics-based rendering and shape-from-polarization. Look-up table polarized bidirectional reflectance distribution functions (pBRDFs) for indoor materials are available, but closed-form representations are advantageous for their ease of use in both forward and inverse problems. First-surface Fresnel reflection, diffuse partial polarization, and ideal depolarization are popular terms used in closed-form pBRDF representations. The relative contributions of these terms are highly dependent on material, albedo/wavelength, and scattering geometry. Complicating matters further, current pBRDF representations incoherently combine Mueller matrices (MM) for Fresnel and polarized diffuse terms which couples into depolarization. In this work, a pBRDF representation is introduced where first-surface Fresnel reflection and diffuse polarization are coherently combined using Jones calculus to avoid affecting depolarization. The first-surface and diffuse reflection terms are combined using an analytic function which takes as input the scattering geometry as well as geometry-independent material parameters. Agreement with wide-field-of-view polarimetric measurements is demonstrated using the new pBRDF which has only six physically meaningful parameters: the scalar-valued depolarization parameter and average reflectance which are geometry-dependent and four geometry-independent material constants. In general, depolarization is described by nine parameters but a triply-degenerate (TD) model simplifies depolarization to a single parameter. To test this pBRDF representation, the material constants for a red 3D printed sphere are assumed and the geometry-dependent depolarization parameter is estimated from linear Stokes images. The geometry-averaged error of the depolarization parameter is 4.2% at 662 nm (high albedo) and 11.7% at 451 nm (low albedo). The error is inversely proportional to albedo and depolarization, so the TD-MM model is considered appropriate for depolarization-dominant materials. The robustness of the pBRDF representation is also demonstrated by comparing measured and extrapolated Mueller images of a Stanford bunny of the same red 3D printing material. The comparison is performed by using Mueller calculus to simulate polarimetric measurements based on the measured and extrapolated data.