The point-characteristic function, wavefronts, and caustic of a spherical wave refracted by an arbitrary smooth surface.

The aim of this paper is to obtain expressions for the k-function, the wavefront train, and the caustic associated with the light rays refracted by an arbitrary smooth surface after being emitted by a point light source located at an arbitrary position in a three-dimensional homogeneous optical medium. The general results are applied to a parabolic refracting surface. For this case, we find that when the point light source is off the optical axis, the caustic locally has singularities of the hyperbolic umbilic type, while the refracted wavefront, at the caustic region, locally has singularities of the cusp ridge and swallowtail types.