Zernike polynomials fitting of arbitrary shape wavefront

Xuanyu Chai; Xingyu Lin; Haotian Chen; Qingyong Wei; Yingjie Yu

doi:10.1117/12.3023145

15 February 2024 Zernike polynomials fitting of arbitrary shape wavefront

Xuanyu Chai, Xingyu Lin, Haotian Chen, Qingyong Wei, Yingjie Yu

Proceedings Volume 13069, International Conference on Optical and Photonic Engineering (icOPEN 2023); 1306912 (2024) https://doi.org/10.1117/12.3023145
Event: International Conference on Optical and Photonic Engineering (icOPEN 2023), 2023, Singapore, Singapore

Abstract

Zernike polynomials are a complete set of continuous functions orthogonal on the unit circle, commonly used for wavefront fitting and analyzing wavefront properties. Zernike polynomials have the special properties of orthogonality and normalization within the unit circle, which makes them widely used in wavefront fitting and reconstruction. In addition to circular pupils and circular elements, non-circular shapes such as squares ellipses are usually found in optical systems. For non-circular wavefronts the Zernike polynomials lose their orthogonality, which also leads to coefficient coupling thus affecting the effectiveness of aberration removal. This paper presents the method based on the Gram–Schmidt orthogonalization technique to orthogonalize Zernike circular polynomials over the non-circular region through a series of matrix transformations. The proposed method can obtain Zernike wavefront fitting results for arbitrary shape wavefront without deriving the corresponding set of polynomials. Separate wavefront fits were conducted utilizing various wavefront shapes, and the results were analyzed. The fitting of non-circular wavefronts is realized in experiment using orthogonal Zernike matrix, which verifies the effectiveness of the proposed method.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Xuanyu Chai, Xingyu Lin, Haotian Chen, Qingyong Wei, and Yingjie Yu "Zernike polynomials fitting of arbitrary shape wavefront", Proc. SPIE 13069, International Conference on Optical and Photonic Engineering (icOPEN 2023), 1306912 (15 February 2024); https://doi.org/10.1117/12.3023145

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