Tolerancing sub-aperture regions of optical surfaces using circular and elliptical Zernike polynomials

Chih Yu Huang, Richard Youngworth, Rongguang Liang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Zernike polynomials are orthogonal within a normalized circle. However, when optical surfaces are away from the stop, the beam size becomes smaller than the surfaces, and the full-aperture Zernike polynomials are not orthogonal inside the illuminated region. In this paper, we investigate a method of using Zernike polynomials to fit sub-aperture regions illuminated by the optical beam in order to retain orthogonality. The method works for both on-axis and off-axis conditions. In some special cases where the optical beam is not circular, we develop a user defined surface that utilizes elliptical Zernike polynomials for the fitting. Finally, we provide an example and discuss the importance of the sub-aperture fitting to tolerance assignment and analysis of the surface.

Original languageEnglish (US)
Title of host publicationOptical System Alignment, Tolerancing, and Verification VIII
EditorsRichard N. Youngworth, Jose Sasian
PublisherSPIE
ISBN (Electronic)9781628412222
DOIs
StatePublished - 2014
EventOptical System Alignment, Tolerancing, and Verification VIII - San Diego, United States
Duration: Aug 17 2014Aug 18 2014

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume9195
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X

Other

OtherOptical System Alignment, Tolerancing, and Verification VIII
CountryUnited States
CitySan Diego
Period8/17/148/18/14

Keywords

  • Elliptical Zernike polynomials
  • Orthogonality
  • Tolerancing
  • Zernike polynomials

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'Tolerancing sub-aperture regions of optical surfaces using circular and elliptical Zernike polynomials'. Together they form a unique fingerprint.

  • Cite this

    Huang, C. Y., Youngworth, R., & Liang, R. (2014). Tolerancing sub-aperture regions of optical surfaces using circular and elliptical Zernike polynomials. In R. N. Youngworth, & J. Sasian (Eds.), Optical System Alignment, Tolerancing, and Verification VIII [919506] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 9195). SPIE. https://doi.org/10.1117/12.2064787