When observing a distant point source of light through a water droplet adhering to a pane of glass near one's eye or the scattering of light from raindrops, one often sees optical caustics. In this paper, diffraction integrals are used to investigate these caustics. The caustic shapes are related to divergences in the stationary phase method for approximating the diffraction integrals. These divergences correspond to the coalescing of two or more geometrical light rays in ray optics or the coalescing of two or more regions of stationary phase in wave optics. The number of coalescing light rays is related to a polynomial approximation of the phase function in the diffraction integral. Also, the relation between the shape of the resulting caustic and the elementary caustic forms of the catastrophe optics classification scheme is described.