Abstract

An anticaustic is the zero optical path wavefront corresponding to a given refracting or reflecting surface and a point source. The term anticaustic was coined by Jakob I Bernoulli in the 1690s. Anticaustics were introduced as they were easier to deal with mathematically than caustics. Anticaustics represent a curious case of interesting and possibly useful knowledge that fell into oblivion only to be resurrected much later but not without misconceptions. The anticaustics associated with the useful surfaces when the point sources are at finite distances are Descartes ovals or degeneracies thereof. The algebraic derivation of this fact is given. While mentioned briefly in textbooks in the context of stigmatic images, Descartes ovals are rapidly dismissed as being no more than curiosities. Yet they have many interesting properties. They are rarely represented correctly, i.e., as two nested closed loops, and the fact (known to Descartes) that a given oval has three foci, not two, is never mentioned. These properties and their optical consequences are reviewed. It should be noted that this is an example of wavefront tracing although very limited since only one surface is involved.

© 1988 Optical Society of America