Utilizing the PReMA polarization metric to quantify surface roughness

We discovered a theoretical link between the reflectivity of a solid surface and the resulting polarization, and we are applying this discovery to advance the state-of-the-art of polarimetric remote sensing. At 45◦ incidence angle, a cloud of spectral points in the plot of polarization versus reflectivity collapses into a degenerate, 1-dimensional curve (termed the U-curve) that applies to all materials, both conductors and dielectrics, and starting from first principles, we have derived the analytic equations for the functions P(R) and the inverse, R(P). The curve shows an inverse relationship between polarization and reflectivity and provides a new theoretical underpinning to explain why dark objects are more polarizing than brighter ones. We claim that the U-curve represents the maximum achievable polarization for a surface of given reflectivity at 45◦ incidence. In this work, we measure the spectral polarization and reflectivity of a gold mirror and show that the data are coincident with the U-curve for the spectral region 400-2000 nm, validating the theory. In complementary work, we measure the spectral polarization and reflectivity of less smooth surfaces (copper, silver, crystalline minerals) and demonstrate that increasing surface roughness decreases polarization, moving the data points below the U-curve. We also measure surface roughness of the same materials using an optical profilometer and show that the quantified surface roughness is well correlated with the measured polarization when normalized by the U-curve. This new normalized polarization has been given the name PReMA, which stands for the Polarization Relative to the Maximum Achievable.