The optical method of caustics, initially developed for recording abrupt plate slopes created by singularities in elastic stress fields, was extended to incorporate the study of the general case of any type of surface. A universal technique, based on the general theory of caustics developed in this paper, was formulated to study the topography of any surface from its corresponding caustics obtained by illuminating the surface by a parallel, convergent, or divergent light beam. The special case of an axisymmetric mirror with elliptical cross section, whose ellipticity varies from zero to infinity, was studied extensively to show the potentialities of the technique developed. It was shown that the caustics obtained are very sensitive to the particular form of the surface considered. From the procedure developed in this paper it was concluded that the method of caustics can be successfully used to record the topography of any surface with large or infinitesimal slopes.
© 1976 Optical Society of America
Equations on this page are rendered with MathJax. Learn more.