Underwater refraction-polarization patterns of skylight perceived by aquatic animals through Snell's window of the flat water surface

The grass shrimp (Palaemonetes vulgaris) orients itself by means of the polarization pattern of the sky visible through Snell's window of the water surface. The celestial polarization pattern viewed from water is distorted and modified because of refraction and repolarization of skylight at the air-water interface. This work provides a quantitative account of the repolarization of skylight transmitted through a flat water surface. The degree and direction of linear polarization, the transmissivity and the shape of the refraction-polarization oval are calculated at the air-water interface as functions of the polarization characteristics and the incident angle of partially linearly polarized incoming light. Two-dimensional patterns of linear polarization ellipses and of the degree and direction of polarization of skylight are presented for different zenith distances of the sun. The corresponding underwater refraction-polarization patterns are computed. Transmissivity patterns of a flat water surface are calculated for unpolarized light of an overcast sky and for partially polarized light of clear skies as a function of the zenith distance of the sun. The role of these refraction-polarization patterns in orientation and polarization vision of the grass shrimp (P. vulgaris) and rainbow trout (Oncorhyncus mykiss) is reviewed. The effects of cloud cover, surface waves and water turbidity on the refraction-polarization patterns are briefly discussed.