Abstract

With the development of lens and mirror fabrication techniques, more and more aspherical surfaces have been used in optical systems. Using the conventional design methods, an aspherical surface is usually described by a conic formula plus some aspherical deformation terms which are a sum of even powers of the polar radial coordinate. The Taylor series of the conventional optics surface equation contains only the even order terms. A general question is why the equation of an optical surface should not also include odd order terms. Differential equation methods have been used extensively to design imaging and energy transfer systems. Normally, the differential equations for the surfaces cannot be solved in the closed forms. To carry out optical modeling, the resulting numerical surface data has been fit by a complete set of functions, such as general polynomials in which there are both even order and odd order terms. Studies on the aspherical surfaces used in reflecting microscopes, laser beam expanders, and soft x-ray projection lithography systems indicate the difficulties of the conventional optical surface formula to represent properly a generalized aspherical surface. Analysis of these results indicates that better performance can be achieved in these applications when the generalized aspherical surfaces are used.

© 1991 Optical Society of America