Journal
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION
Volume 32, Issue 10, Pages 1836-1847Publisher
OPTICAL SOC AMER
DOI: 10.1364/JOSAA.32.001836
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Funding
- II-VI Foundation
- NASA Graduate Student Researchers Program (GSRP)
- National Science Foundation (NSF) [EECS-1002179]
- New York State Foundation for Science, Technology and Innovation (NYSTAR) [C050070]
- U.S. Department of Energy (DOE) [DE-EE0006033]
- Directorate For Engineering
- Div Of Industrial Innovation & Partnersh [1338877, 1338898] Funding Source: National Science Foundation
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Previous papers have shown how, for rotationally symmetric optical imaging systems, nodes in the field dependence of the wavefront aberration function develop when a rotationally symmetric optical surface within an imaging optical system is decentered and/or tilted. In this paper, we show how Shack's vector product (SVP) can be used to express the wavefront aberration function and to define vectors in terms of the Zernike polynomials. The wavefront aberration function is then expressed in terms of the Zernike vectors. It is further shown that SVP fits within the framework of two-dimensional geometric algebra (GA). Within the GA framework, an equation for the third-order node locations for the binodal astigmatism term that emerge in the presence of tilts and decenters is then demonstrated. A computer model of a three-mirror telescope system is used to demonstrate the validity of the mathematical development. (C) 2015 Optical Society of America
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