The origin of the bands is still somewhat controversial. The most accepted theory seems to be Codona's (1986): http://adsabs.harvard.edu/full/1986A%26A...164..415C …
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The basic idea seems to be in two parts. (1) For a point light source, low-altitude turbulence will cause refraction, and so ...
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differential illumination across different parts of the ground. (2) Integrating over a crescent shape we still get that differential illmn.
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Wish I had a better understanding of (a) why the scale of the bands is centimeters; (b) why integration over a crescent preserves bands, but
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integration over full disk does not; and (c) what sets the scale for the variation in illumination.
End of conversation
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