We present a computationally inexpensive analytical model for simulating celestial polarization patterns in variable conditions. We combine both the singularity theory of Dennis and Berry [1] and the intensity model of Perez [2] such that our single model describes 3 key sets of data: 1) The overhead distribution of the degree of polarization as well as the existence of neutral points in the sky; 2) the change in sky polarization as a function of the turbidity of the atmosphere; and 3) sky polarization patterns as a function of wavelength, calculated in this work from the ultraviolet (UV) to the near infra-red (IR). To verify the performance of our model we generate accurate reference data using a numerical radiative transfer model and statistical comparisons between these two methods demonstrate no significant difference in almost all situations. The development of our analytical model provides a novel method for efficiently calculating the overhead skylight polarization pattern. This provides a new tool of particular relevance for our understanding of animals that use the celestial polarization pattern as a source of visual information.
It is surprising that many insect species use only the ultraviolet (UV) component of the polarized skylight for orientation and navigation purposes, while both the intensity and the degree of polarization of light from the clear sky are lower in the UV than at longer (blue, green, red) wavelengths. Why have these insects chosen the UV part of the polarized skylight? This strange phenomenon is called the "UV-sky-pol paradox". Although earlier several speculations tried to resolve this paradox, they did this without any quantitative data. A theoretical and computational model has convincingly explained why it is advantageous for certain animals to detect celestial polarization in the UV. We performed a sky-polarimetric approach and built a polarized skylight sensor that models the processing of polarization signals by insect photoreceptors. Using this model sensor, we carried out measurements under clear and cloudy sky conditions. Our results showed that light from the cloudy sky has maximal degree of polarization in the UV. Furthermore, under both clear and cloudy skies the angle of polarization of skylight can be detected with a higher accuracy. By this, we corroborated empirically the soundness of the earlier computational resolution of the UV-sky-pol paradox.
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