The formation of many ice crystal halos can be visualized in an appropriate coordinate system on the sphere. A given crystal orientation is first represented by a point on the sphere. When the same sphere is regarded as the celestial sphere, it is easy to find the point of light on the sphere that results from the given crystal orientation. The analysis gives crude information on intensities of halos, not just along the caustic curve but for the entire sky.
© 1979 Optical Society of America
Walter Tape, "Geometry of halo formation," J. Opt. Soc. Am. 69, 1122-1132 (1979)