Moonlight Polarization in a Hazy Sky — 2D Polarization Map

Moon Position

Moon elevation 32°

Moon azimuth 120°

Atmosphere

Haze / aerosol level 15%

Polarizing Filter

Filter transmission angle 0°

This is a top-down polar map of the whole sky: the center is the zenith (straight up), the outer rim is the horizon. Drag to pan, scroll/pinch to zoom, click any point to read it exactly.

Reading (last click)

Scattering angle θ

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Polarization degree

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E-vector angle

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Filter transmission

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The real physics

Each pixel in this map is a direction in the sky (radius = zenith distance from straight overhead, angle = compass azimuth). For every such direction the scattering angle θ from the Moon is computed with the spherical law of cosines, and the real single-scattering Rayleigh polarization law is applied:

P(θ) = sin²θ / (1 + cos²θ)

Saturation encodes degree of polarization (gray = unpolarized, vivid = strongly polarized), hue encodes the local E-vector axis, and brightness follows the Rayleigh phase function (1+cos²θ). Increasing haze scales P down toward zero everywhere, modeling how multiple scattering off aerosols destroys the clean single-scattering polarization signature. The filter slider applies the real partial-polarizer transmission law, (1−P)/2 + P·cos²(filter angle − local angle), dimming and brightening the map exactly as a rotating polarizing filter would over a real hazy moonlit sky.

zoom = 1.0×

Click the map to read a point

Moonlight Polarization in a Hazy Sky — 2D Polar Map