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Proceedings Paper

Wavefront fitting with Zernike polynomials based on total variation regularization method
Author(s): Lihong Lu; Qingyu Hou
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Paper Abstract

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.

Paper Details

Date Published: 26 November 2012
PDF: 8 pages
Proc. SPIE 8557, Optical Design and Testing V, 855725 (26 November 2012); doi: 10.1117/12.2001016
Show Author Affiliations
Lihong Lu, Tianjin Polytechnic Univ. (China)
Qingyu Hou, Harbin Institute of Technology (China)

Published in SPIE Proceedings Vol. 8557:
Optical Design and Testing V
Yongtian Wang; Chunlei Du; Hong Hua; Kimio Tatsuno; H. Paul Urbach, Editor(s)

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