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Title
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 image and pupil aberrations in systems with axial and plane symmetry. A detailed analysis of unobscured, freeform, two-mirror telescopes is outlined to highlight the utility of this formalism in conducting trade-off studies. Some notable results include: 1) a table of general solutions that prescribe freeform overlays and surface tilts to correct fourth-order aberrations, 2) two novel unobscured design forms that achieve remarkable aberration cancellation with axially symmetric mirrors, and 3) extended Dall-Kirkham and Ritchey-Chrétien solutions that consider sixth-order aberrations.
To enable the efficient design of more complex freeform imaging systems, a novel freeform surface called the wave aberration polynomial (WAP) is derived directly from the bilateral symmetric wave aberration function (BSWAF). General methods for prescribing starting geometries and optimizing them to finalized 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.