Wave front equation, caustics, and wave aberration function of simple lenses and mirrors.

Using the condition of constant optical path length for rays passing through an optical system, an equation for the wave front is presented in a simplified form. The wave front equation has been explicitly evaluated for a plane wave incident on a spherical reflector or a plano-convex lens. Then, the principal radii of curvature of the reflected or refracted wave front, evaluated directly from the wave front equation, are shown to locate the caustic surfaces of the optical system. From the wave front equation, a closed form expression for the wave aberration function for a plane wave reflected by a spherical mirror or a plano-corvex lens has been evaluated and compared to the results obtained from third-order aberration theory.