Dr. Haotian Chen Profile

Dr. Haotian Chen

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Proceedings Article | 15 February 2024 Paper

Zernike polynomials fitting of arbitrary shape wavefront

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

Proceedings Volume 13069, 1306912 (2024) https://doi.org/10.1117/12.3023145

KEYWORDS: Wavefronts, Zernike polynomials, Matrices, Interferometers, Optical components, Data processing, Optical surfaces

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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.

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