Simulaiton of the rayleigh sky model using python.
Angle of Polarization (°) Angle $\alpha$ of polarization of $\vec{E}$ at any observable point $P$ can be found with:
$\alpha = arctan(\frac{sin(\theta)cos(\theta_s)-cos(\theta)cos(\varphi-\varphi_s)sin(\theta_s)}{sin(\varphi-\varphi_s)sin(\theta_s)})$
$\theta \to$ Angle from zenith to observed point $P$ (angle
complimentary to the elevation)
$\varphi \to$ Angle from $0°$ due north to observed point $P$ (same angle as the azimuth)
$\theta_s \to$ Angle from zenith to the sun (angle complimentary to the solar elevation)
$\varphi_s \to$ Angle from $0°$ due north to the sun (same angle as the solar azimuth)
Degree of Polarization (%) The degree of polarized light $\delta$ at any observable point $P$ can be found with:
$\delta = \frac{\delta_{max}sin^2(\gamma)}{1+cos^2(\gamma)}$
$\gamma \to$ Angular distance between the Sun and the observed point. Can be expressed as:
$\gamma = arccos(cos(\theta)cos(\theta_s)+sin(\theta)sin(\theta_s)cos(\varphi-\varphi_s))$
Image-registration-based solar meridian detection for accurate and robust polarization navigation
HEMISPHERICAL PROJECTION METHODS
