Optical Design and Analysis with Structural Aberration Coefficients

Abstract

The use of dimensionless parameters is profitable in many fields of science and engineering. Structural aberration coefficients represent an effort to extend this benefit to optical design and analysis, as they are independent of scaling and therefore represent a system’s fundamental aberration characteristics through comparatively simple formulas. Useful design insight is gained by exploring their implications in imaging systems.This dissertation presents generalized structural coefficients for the image aberrations of an axially symmetric system to sixth order, the pupil aberrations of an axially symmetric system to fourth order, and the image aberrations of a plane symmetric system to fourth order. Basic analysis is demonstrated through the derivation of structural coefficients for simple optical components. Then, a detailed analysis of unobscured, freeform, two-mirror telescopes is presented to highlight the utility of this formalism in conducting trade-off studies. A table of general solutions prescribes freeform overlays and surface tilts to correct fourth-order aberrations, analogous to conic solutions in axially symmetric telescopes. Two novel unobscured design forms are introduced which possess remarkable aberration cancellation using axially symmetric mirrors. Additionally, two sixth-order solutions are presented, inspired by the Dall-Kirkham and Ritchey-Chrétien solutions. A novel freeform surface, the wave aberration polynomial (WAP), is derived directly from the bilateral symmetric wave aberration function (BSWAF) to enable the efficient design of complex freeform imaging systems. General methods for prescribing and optimizing starting geometries to final performance are presented, and some design examples are given to demonstrate the process. The mathematical form of the proposed freeform surface—compatible with all structural coefficient formalism presented in this dissertation—offers a synergy between the wave theory of aberrations and state-of-the-art optimization software.