Abstract

Wave fronts in isotropic media can, by Huygens’ principle, be described as envelopes of circles. By using this fact and the appropriate elimination method, the exact algebraic expression for the anticaustics of all the usual optical surfaces in reflection and refraction are derived for a finite distance source. An anticaustic is a wave front of zero optical-path difference. Once the equation of the anticaustic is known, the equation of the parallel wave front corresponding to any optical path difference can be formally found by the same process, although this time the computations are considerably more difficult. By means of this new equation the wave front can be mapped at various instants during its propagation. What happens as the wave front contracts and approaches the focal region is of particular interest. That the cusps of the wave front map the caustic is thus beautifully illustrated. Intriguing conclusions can also be deduced from these algebraic wave-front equations.

© 1990 Optical Society of America