Meshfree Approximation Methods for Free-Form Surface Representation in Optical Design with Applications to Head-Worn Displays

In this paper, we summarize our initial experiences in designing head-worn displays with free-form optical surfaces. Typical optical surfaces implemented in raytrace codes today are functions mapping two dimensional vectors to real numbers. The majority of optical designs to date have relied on conic sections and polynomials as the functions of choice. The choice of conic sections is justified since conic sections are stigmatic surfaces under certain imaging geometries. The choice of polynomials from the point of view of surface description can be challenged. The advantage of using polynomials is that the wavefront aberration function is typically expanded in polynomials. Therefore, a polynomial surface description may link a designer’s understanding of wavefront aberrations and the surface description. The limitations of using multivariate polynomials are described by a theorem due to Mairhuber and Curtis from approximation theory. In our recent work, we proposed and applied radial basis functions to represent optical surfaces as an alternative to multivariate polynomials. We compare the polynomial descriptions to radial basis functions using the MTF criteria. The benefits of using radial basis functions for surface description are summarized in the context of specific magnifier systems, i.e., head-worn displays. They include, for example, the performance increase measured by the MTF, or the ability to increase the field of view or pupil size. Full-field displays are used for node placement within the field of view for the dual-element head-worn display.