An analytical model for skylight polarization pattern with multiple scattering

To solve the issues in the modeling of skylight polarization, we build a new analytical model of skylight polarization patterns, which is based on the classic Rayleigh scattering and takes into consideration the multiple scattering properties of atmospheric particles, especially the aerosol. In this paper, we first build the model by the combination of single Rayleigh scattering and classic Perez sky models. Then we analyze the influence of secondary scattering by solving scattering phase function of different particle sizes and components of aerosol in OPAC data. Finally, the integral function for secondary scattering is simplified with the preferences of scattering phase function in forward direction. Compared with the Rayleigh model, our model can depict the existence of neutral points in the sky. The comparisons between our model and the measured results of clear sky further validate that the model not only exhibits characters of measured skylight polarization, such as the variation tendency, neutral points and the pattern symmetry, but also consists with the acquired values than the single scattering model; for example, the degree of similarity of polarization can be up to 75%.