The research proposes arbitrary shaped aperture wavefront fitting (ASAWF) for arbitrary shaped aperture wavefront fitting and aberration removing. It departs from the traditional Zernike polynomials only ideal for wavefront reconstruction of circular wavefronts but not non-circular wavefronts. The approach preserves the orthogonality of the Zernike polynomials in arbitrary shaped aperture wavefronts and addresses the coefficient coupling problems of the non-circular shaped aperture wavefront fitting known adversely affecting aberration removal. The ASAWF method is used to fit non-circular regions with an orthogonal matrix using the modified Gram–Schmidt orthogonalization technique with QR decomposition and point cloud. The ASAWF method is employed to fit the arbitrary shaped aperture wavefront, including elliptical, square, and irregular shape wavefronts. The proposed method is confirmed through numerical simulation and experimental data demonstrating the effectiveness of wavefront reconstruction and aberration removal.
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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