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23 February 2006 Effective algorithm based on household transformation for wavefront fitting
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A precise algorithm for wavefront fitting using Zernike polynomial is studied which can be applied in the digital wavefront processing. The polynomial coefficients of Zernike can be obtained through solution of overdetermined Ax = W equations by means of Household transformation. Differing from the conventional method of direct constructing normal equation group or the Gram-Schmidt orthogonalization, the new algorithm which utilizing Householder transformation orthogonalizes and triangulate the matrix of overdetermined equations set, and solve the coefficients. It is a healthy fitting algorithm, and computational error which is introduced in the process of constructing normal equation group can be avoided in the new algorithm. It has been proved to be an efficacious algorithm with characteristic of good stability and easy implementation.
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Yongguo Li, Jianqiang Zhu, and Xiaojun Cao "Effective algorithm based on household transformation for wavefront fitting", Proc. SPIE 6150, 2nd International Symposium on Advanced Optical Manufacturing and Testing Technologies: Optical Test and Measurement Technology and Equipment, 61504H (23 February 2006);

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