Estimating surface orientation from microfacet Mueller matrix bidirectional reflectance distribution function models in outdoor passive imaging polarimetry

Representative examples from 3 years of measurements from JPL's ground-based multiangle spectropolarimetric imager (GroundMSPI) are compared to a Mueller matrix bidirectional reflectance distribution function (mmBRDF). This mmBRDF is used to model polarized light scattering from solar illuminated surfaces. The camera uses a photoelastic-modulator-based polarimetric imaging technique to measure linear Stokes parameters in three wavebands (470, 660, and 865 nm) with a ±0.005 uncertainty in degree of linear polarization. GroundMSPI measurements are made over a range of scattering angles determined from a fixed viewing geometry and varying sun positions over time. This microfacet mmBRDF model predicts an angle of the linear polarization that is consistently perpendicular to the scattering plane and therefore is only appropriate for rough surface types. The model is comprised of a volumetric reflection term plus a specular reflection term of Fresnel-reflecting microfacets. The following modifications to this mmBRDF model are evaluated: an apodizing shadowing function, a Bréon or Gaussian microfacet scattering density function, and treating the surface orientation as an additional model parameter in the specular reflection term. The root-mean-square error (RMSE) between the GroundMSPI measurements and these various forms of the microfacet mmBRDF model is reported. Four example scenes for which a shadowed-Bréon microfacet mmBRDF model yields realistic estimates of surface orientation, and the lowest RMSE among other model options are shown.