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

Abstract

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.

Mayflies are least attracted to vertical polarization: A polarotactic reaction helping to avoid unsuitable habitats

“…This polarization feature arises from the following: The reflection-polarization characteristics of the water surface are determined by two light components: (1) light reflected from the water surface, and (2) light originating from below the water surface. Component 1 is usually horizontally polarized because of reflection polarization of sunlight/moonlight and skylight from the air-water interface [8], while component 2 is always vertically polarized due to the refraction polarization of subsurface light at the water-air interface [10]. If component 1 or 2 dominates, the net polarization of water-returned light is horizontally or vertically polarized, respectively.…”

Polarization Patterns of Transmitted Celestial Light under Wavy Water Surfaces

“…Coulson indicated that the single Rayleigh scattering model can effectively describe the polarized skylight in theory [43]. However, considering the atmospheric disturbances such as multiple scattering, ground reflection, aerosol and the anisotropic of molecules, we compute the skylight polarization patterns using the semi-empirical Rayleigh scattering model [7,43], which is expressed as below.…”

“…Then, we can describe the variation of the polarization when light passes through the air-water interface using the Mueller matrix, and the Mueller matrix of refraction at an interface can be derived using Fresnel's formulas and is shown in Equation (6) [7].…”

“…In a theoretical study, Kattawar numerically simulated the polarization of transmitted light under water with Rayleigh scattering approximation [29]. Horvath computed the polarization pattern of the Rayleigh scattering skylight refracted from a flat water surface without taking the wave water and the intensity distribution of skylight into account [7]. Horvath and his colleagues confined their investigation to the flat water surface; their calculation might be instructive as a first order approximation of the real refracted polarization pattern.…”

“…Many of the hydro-ecological processes are assumed to be independent of the polarization of the light field [4]. As the polarization in nature is realized that it can be utilized by many animals to determine geographic direction [5,6], which gives great inspiration to explore underwater polarization and the polarization response of aquatic animals [7]. The occurrence and pattern of light polarization in aquatic environments becomes a subject of wide potential relevance to various problems in oceanography and limnology.…”