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 publicationProceedings of SPIE - The International Society for Optical Engineering
PublisherSPIE
Volume9195
ISBN (Print)9781628412222
DOIs
StatePublished - 2014
EventOptical System Alignment, Tolerancing, and Verification VIII - San Diego, United States
Duration: Aug 17 2014Aug 18 2014

Other

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

Fingerprint

Zernike Polynomials
Tolerancing
polynomials
apertures
Polynomials
orthogonality
Orthogonality
Tolerance
Circle
Assignment

Keywords

  • Elliptical Zernike polynomials
  • Orthogonality
  • Tolerancing
  • Zernike polynomials

ASJC Scopus subject areas

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

Cite this

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

Tolerancing sub-aperture regions of optical surfaces using circular and elliptical Zernike polynomials. / Huang, Chih Yu; Youngworth, Richard; Liang, Rongguang.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 9195 SPIE, 2014. 919506.

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

Huang, CY, Youngworth, R & Liang, R 2014, Tolerancing sub-aperture regions of optical surfaces using circular and elliptical Zernike polynomials. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 9195, 919506, SPIE, Optical System Alignment, Tolerancing, and Verification VIII, San Diego, United States, 8/17/14. https://doi.org/10.1117/12.2064787
Huang CY, Youngworth R, Liang R. Tolerancing sub-aperture regions of optical surfaces using circular and elliptical Zernike polynomials. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 9195. SPIE. 2014. 919506 https://doi.org/10.1117/12.2064787
Huang, Chih Yu ; Youngworth, Richard ; Liang, Rongguang. / Tolerancing sub-aperture regions of optical surfaces using circular and elliptical Zernike polynomials. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 9195 SPIE, 2014.
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