Use of implicitly defined optical surfaces for the design of imaging and illumination systems

This paper presents an approach that uses implicitly defined optical surfaces for designing imaging and illumination systems. In the standard aspheric optical surface, consisting of a conic with an even-order polynomial, the surface sagitta (sag), z, is defined explicitly as a function of the coordinates x and y. This standard aspheric surface is deemed useful for describing surfaces with small departures from a conic surface. However, optical surfaces with large departures from a conic are sometimes useful for current applications, such as null certification, conformal domes and windows, luminaires, and condenser design. The approach in this paper, which uses implicitly defined surfaces to describe highly aspheric surfaces, can be more general and easier to use for some situations. The sag z of an implicit surface is not defined directly, as it is in an explicit surface. Instead, it is defined indirectly in a more general form, as a function of x, y, and z. Because implicit functions have a more general form than explicit functions, they can better describe a variety of surfaces that cannot be easily described using the standard explicit aspheric surface. We show some examples of current interest.