SUPERNUMERARY ICE-CRYSTAL HALOS

Geometric-optics singularities in the intensity profiles of refraction halos formed by randomly oriented ice crystals are softened by diffra ction and decorated with fine supernumerary fringes. If the crystals h ave a fixed symmetry axis (as in parhelia), the geometric singularity is a square-root divergence, as in the rainbow. However, the universal curve that describes diffraction is different from the rainbow's Airy function, with weak maxima (supernumerary fringes) on the geometrical ly dark region inside the halo (and even fainter fringes outside); the se are much smaller than their counterparts on the light side of rainb ows. If the crystals have no preferred orientation (as in the 22-degre es halo), the geometric singularity is a step. In this case the univer sal diffraction function has no maxima, and its supernumeraries are sh oulders rather than maxima. The low contrast of the fringes is probabl y the main reason why supernumerary halos are rarely if ever seen.