We present the first high-resolution maps of Rayleigh behavior in clear and cloudy sky conditions measured by full-sky imaging polarimetry at the wavelengths of 650 nm (red), 550 nm (green), and 450 nm (blue) versus the solar elevation angle ${\theta }_s.$ Our maps display those celestial areas at which the deviation $\mathrm{\Delta }\alpha = |{\alpha }_{\mathrm{meas}}-\hspace{0.5em}{\alpha }_{\mathrm{Rayleigh}}|$ is below the threshold ${\alpha }_{\mathrm{thres}}=5°,$ where ${\alpha }_{\mathrm{meas}}$ is the angle of polarization of skylight measured by full-sky imaging polarimetry, and ${\alpha }_{\mathrm{Rayleigh}}$ is the celestial angle of polarization calculated on the basis of the single-scattering Rayleigh model. From these maps we derived the proportion r of the full sky for which the single-scattering Rayleigh model describes well (with an accuracy of $\mathrm{\Delta }\alpha =5°)$ the E-vector alignment of skylight. Depending on ${\theta }_s,$ r is high for clear skies, especially for low solar elevations $(40\%<r<70\%$ for ${\theta }_s\le \hspace{0.5em}13°).$ Depending on the cloud cover and the solar illumination, r decreases more or less under cloudy conditions, but sometimes its value remains remarkably high, especially at low solar elevations $(r_{max}=69\%$ for ${\theta }_s=0°).$ The proportion r of the sky that follows the Rayleigh model is usually higher for shorter wavelengths under clear as well as cloudy sky conditions. This partly explains why the shorter wavelengths are generally preferred by animals navigating by means of the celestial polarization. We found that the celestial E-vector pattern generally follows the Rayleigh pattern well, which is a fundamental hypothesis in the studies of animal orientation and human navigation (e.g., in aircraft flying near the geomagnetic poles and using a polarization sky compass) with the use of the celestial α pattern.

SUMMARY: The characteristic striped appearance of zebras has provoked much speculation about its function and why the pattern has evolved, but experimental evidence is scarce. Here, we demonstrate that a zebra-striped horse model attracts far fewer horseflies (tabanids) than either homogeneous black, brown, grey or white equivalents. Such biting flies are prevalent across Africa and have considerable fitness impact on potential mammalian hosts. Besides brightness, one of the likely mechanisms underlying this protection is the polarization of reflected light from the host animal. We show that the attractiveness of striped patterns to tabanids is also reduced if only polarization modulations (parallel stripes with alternating orthogonal directions of polarization) occur in horizontal or vertical homogeneous grey surfaces. Tabanids have been shown to respond strongly to linearly polarized light, and we demonstrate here that the light and dark stripes of a zebra’s coat reflect very different polarizations of light in a way that disrupts the attractiveness to tabanids. We show that the attractiveness to tabanids decreases with decreasing stripe width, and that stripes below a certain size are effective in not attracting tabanids. Further, we demonstrate that the stripe widths of zebra coats fall in a range where the striped pattern is most disruptive to tabanids. The striped coat patterns of several other large mammals may also function in reducing exposure to tabanids by similar mechanisms of differential brightness and polarization of reflected light. This work provides an experimentally supported explanation for the underlying mechanism leading to the selective advantage of a black-and-white striped coat pattern.

The distribution of polarization in the overcast sky has been practically unknown. Earlier the polarization of light from heavily overcast skies (when the Sun’s disc was invisible) has been measured only sporadically in some celestial points by point-source polarimetry. What kind of patterns of the degree p and angle α of linear polarization of light could develop after transmission through a thick layer of ice or water clouds? To answer this question, we measured the p and α patterns of numerous totally overcast skies on the Arctic Ocean and in Hungary by full-sky imaging polarimetry. We present here our finding that depending on the optical thickness of the cloud layer, the pattern of α of light transmitted through the ice or water clouds of totally overcast skies is qualitatively the same as the α pattern of the clear sky. Under overcast conditions the value of α is determined predominantly by scattering on cloud particles themselves. Nevertheless, the degrees of linear polarization of light from overcast skies were rather low $(p\le 16\%)$. Our results obtained under overcast conditions complete the earlier findings that the α pattern of the clear sky also appears in partly cloudy, foggy, and smoky skies. Our results show that the celestial distribution of the direction of polarization is a very robust pattern being qualitatively always the same under all possible sky conditions. This is of great importance for the orientation of polarization-sensitive animals based on sky polarization under conditions when the Sun is not visible.

White horses frequently suffer from malign skin cancer and visual deficiencies owing to their high sensitivity to the ultraviolet solar radiation. Furthermore, in the wild, white horses suffer a larger predation risk than dark individuals because they can more easily be detected. In spite of their greater vulnerability, white horses have been highly appreciated for centuries owing to their natural rarity. Here, we show that blood-sucking tabanid flies, known to transmit disease agents to mammals, are less attracted to white than dark horses. We also demonstrate that tabanids use reflected polarized light from the coat as a signal to find a host. The attraction of tabanids to mainly black and brown fur coats is explained by positive polarotaxis. As the host's colour determines its attractiveness to tabanids, this parameter has a strong influence on the parasite load of the host. Although we have studied only the tabanid–horse interaction, our results can probably be extrapolated to other host animals of polarotactic tabanids, as the reflection–polarization characteristics of the host's body surface are physically the same, and thus not species-dependent.

For elimination of the shortcomings of imaging polarimeters that take the necessary three pictures sequentially through linear-polarization filters, a three-lens, three-camera, full-sky imaging polarimeter was designed that takes the required pictures simultaneously. With this polarimeter, celestial polarization patterns can be measured even if rapid temporal changes occur in the sky: under cloudy sky conditions, or immediately after sunrise or prior to sunset. One of the possible applications of our polarimeter is the ground-based detection of clouds. With use of the additional information of the degree and the angle of polarization patterns of cloudy skies measured in the red (650 nm), green (550 nm), and blue (450 nm) spectral ranges, improved algorithms of radiometric cloud detection can be offered. We present a combined radiometric and polarimetric algorithm that performs the detection of clouds more efficiently and reliably as compared with an exclusively radiometric cloud-detection algorithm. The advantages and the limits of three-lens, three-camera, full-sky imaging polarimeters as well as the possibilities of improving our polarimetric cloud detection method are discussed briefly.