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

Chih-Yu Huang; Richard Youngworth; Rongguang Liang

doi:10.1117/12.2064787

19 September 2014 Tolerancing sub-aperture regions of optical surfaces using circular and elliptical Zernike polynomials

Chih-Yu Huang, Richard Youngworth, Rongguang Liang

Author Affiliations +

Proceedings Volume 9195, Optical System Alignment, Tolerancing, and Verification VIII; 919506 (2014) https://doi.org/10.1117/12.2064787
Event: SPIE Optical Engineering + Applications, 2014, San Diego, California, United States

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.

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Chih-Yu Huang, Richard Youngworth, and Rongguang Liang "Tolerancing sub-aperture regions of optical surfaces using circular and elliptical Zernike polynomials", Proc. SPIE 9195, Optical System Alignment, Tolerancing, and Verification VIII, 919506 (19 September 2014); https://doi.org/10.1117/12.2064787

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