26 November 2012 Wavefront fitting with Zernike polynomials based on total variation regularization method
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The wavefront function can be achieved by fitting the optical surfaces date using Zernike polynomials because of the corresponding relation between Zernike polynomials and Seidel aberrations. In this paper, the reason of the stable solution cannot be achieved when proceed to fit wavefront by least square, Gram-Schmidt orthogonalization and Householder transformation is deduced in theory. The Zernike coefficients fitting method based total variation (TV) regularization is presented to resolve the instability of numerical solution because of there are errors in phase values obtained by optimization algorithm in Least Square, Gram-Schmidt orthogonalization and Householder transformation. The solving model of Zernike coefficients is developed, and the regularization term is introduced in solving model, then the L-curve method is applied to determine the regularization parameter and the modified steepest descent method is applied to solve Zernike coefficients. The simulation experiment shows that the proposed algorithm can be achieve the stable fitting coefficients with the error on fitting data.
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Lihong Lu, Lihong Lu, Qingyu Hou, Qingyu Hou, "Wavefront fitting with Zernike polynomials based on total variation regularization method", Proc. SPIE 8557, Optical Design and Testing V, 855725 (26 November 2012); doi: 10.1117/12.2001016; https://doi.org/10.1117/12.2001016


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