Abstract

The departures from sphericity of a wavefront can be specified by either the wave aberration function or the transversal ray aberrations. Another possibility of specifying the departures from sphericity is by considering the envelope of a set of rays. Here we indicate that the analytical form of the caustic can be obtained readily from the wave aberration function or from the transversal ray aberrations. We show that the analytical form of the caustic and the parametric expressions for ray tracing are the particular solution and the general solution, respectively, of Clairaut's nonlinear differential equation.

© 1987 Optical Society of America