On the geometry of visual starbursts

The patterns observed by people when they look at stars are collectively called starbursts. Similar patterns are observed when viewing any distant object with sufficiently large pupils. We show here that starbursts are mainly curved, formed by the intersections of caustic surfaces, and associated with a wavefront emitted by a far object, with the retina. In particular, we derive the equations governing these caustic curves, present a few properties of their solutions, and compare the solutions with recent clinical observations. We further classify the starbursts into primary (the caustic curves themselves) and secondary (the diffraction patterns near the caustics).