Analytic foundations of halo theory

Abstract

This article develops a unified approach to the computation of refraction ice crystal halos and their caustics. An explicit formula is given for the halo function, that is, the function that expresses points of light on the celestial sphere as a function of crystal orientation. Restricting the halo function to various subsets of its domain produces different halos. The caustic of a halo is the image of the set of singular points of the (suitably restricted) halo function. Computation of the kernel of the Jacobian of the unrestricted halo function leads to a general approach to the construction of caustics of arbitrary halos. The halos used as examples are circular halos, upper and lower tangent arcs, infralateral and supralateral arcs, Lowitz arcs, and parhelia. The above methods are used to generate computer plots of several of these halos and their caustics, together with the sets of crystal orientations responsible for the halos.