Using polarization to estimate surface normals at air–water interfaces for correction of refraction in seafloor imaging

The retrieval of sea surface normal vectors using shape-from-polarization is investigated for the purpose of correcting for refraction at the water-air interface when imaging from above the water. In shallow clear water and overcast conditions, spectral longpass filtering (using a hard-coated 850 nm cut-on wavelength filter) is demonstrated to 1) avoid artifacts from the ground in the measured polarization state, and 2) reduce polarization from water-leaving radiance sufficiently to derive shape information exclusively from the polarization produced by specular reflection. The dependence of the method on meteorological conditions is studied. Measurements are performed with a commercial polarization filter array (PFA) camera. Due to the decreasing PFA efficiency towards the near-infrared, rigorous characterization and calibration measurements were performed and recommendations (e.g., on the f-number) elaborated. Overcoming the paraxial approximation, normal vectors are then retrieved with systematic errors of 0.1^∘ (image center) to 0.5^∘-0.8^∘ (edges/corners) for a flat water surface. An image of the sea floor corrected for surface refraction shows maximum displacements of 10-20 pixels only (corresponding to 0.25^∘) with respect to a validation image without water.