Geometric optics is often described as tracing the paths of non-diffracting rays through an optical system. In paraxial limit, ray traces can be calculated using transfer matrices (colloquially, ABCD matrices), which are 2x2 acting on height and slope rays. A known limitation that they only work for elements centered normal to axis. this article, we provide improved 3x3 matrix method calculatin...

Geometric-optics singularities in the intensity profiles of refraction halos formed by randomly oriented ice crystals are softened by diffraction and decorated with fine supernumerary fringes. If the crystals have 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 ...