Aspherical surface profile fitting based on the relationship between polynomial and inner products

Xuemin Cheng; Yikang Yang; Qun Hao

doi:10.1117/1.OE.55.1.015105

26 January 2016 Aspherical surface profile fitting based on the relationship between polynomial and inner products

Xuemin Cheng, Yikang Yang, Qun Hao

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Optical Engineering, Vol. 55, Issue 1, 015105 (January 2016). https://doi.org/10.1117/1.OE.55.1.015105

Abstract

High-precision aspherical polynomial fitting is essential to image quality evaluation in optical design and optimization. However, conventional fitting methods cannot reach optimal fitting precision and may somehow induce numerical ill-conditioning, such as excessively high coefficients. For this reason, a projection from polynomial equations to vector space was here proposed such that polynomial solutions could be obtained based on matrix and vector operation, so avoiding the problem of excessive coefficients. The Newton–Raphson iteration method was used to search for optimal fitting of the spherical surface. The profile fitting test showed that the proposed approach was able to obtain results with high precision and small value, which solved the numerical ill-conditioning phenomenon effectively.

CC BY: © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Xuemin Cheng, Yikang Yang, and Qun Hao "Aspherical surface profile fitting based on the relationship between polynomial and inner products," Optical Engineering 55(1), 015105 (26 January 2016). https://doi.org/10.1117/1.OE.55.1.015105

Published: 26 January 2016

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