@inproceedings{e85dfda95e4c4b4ca9daae5087b6572e,
title = "Tolerancing sub-aperture regions of optical surfaces using circular and elliptical Zernike polynomials",
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.",
keywords = "Elliptical Zernike polynomials, Orthogonality, Tolerancing, Zernike polynomials",
author = "Huang, {Chih Yu} and Richard Youngworth and Rongguang Liang",
note = "Publisher Copyright: {\textcopyright} 2014 SPIE.; Optical System Alignment, Tolerancing, and Verification VIII ; Conference date: 17-08-2014 Through 18-08-2014",
year = "2014",
doi = "10.1117/12.2064787",
language = "English (US)",
series = "Proceedings of SPIE - The International Society for Optical Engineering",
publisher = "SPIE",
editor = "Youngworth, {Richard N.} and Jose Sasian",
booktitle = "Optical System Alignment, Tolerancing, and Verification VIII",
}