Regression analysis for wavefront fitting with Zernike polynomials

Bo Qi; Hongbin Chen; Jiaguang Ma; Nengli Dong

doi:10.1117/12.501144

22 December 2003 Regression analysis for wavefront fitting with Zernike polynomials

Bo Qi, Hongbin Chen, Jiaguang Ma, Nengli Dong

Proceedings Volume 5180, Optical Manufacturing and Testing V; (2003) https://doi.org/10.1117/12.501144
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

Many approaches to compute the wavefront of interferometer have been devised, for example least squares method, Gram-Schmidt method, covariance matrix method and SVD method, but one of the most interesting is based on the Zernike Polynomials. Zernike polynomials are ideal for fitting the measured data points in a wavefront to a two-dimensional polynomial, due to their orthogonal properties. The key problem of wavefront fitting is how to express exactly the whole wavefront. In established algorithms, the fixed mode number of Zernike polynomials is used, for example most analyzing software using 36 Zernike polynomials (i.e., Metropro of Zygo). When analyzing high spatial frequency aberrations, the analyzed result is not accurate. We develop a method of wavefront fitting with regression analysis. Regression analysis is the most widely used technique in statistics, and it is a statistical technique for investigating and modeling the relationship between variables. With stepwise regression we obtain the optimum combination of mode, and the wavefront can be exactly expressed.

Citation Download Citation

Bo Qi, Hongbin Chen, Jiaguang Ma, and Nengli Dong "Regression analysis for wavefront fitting with Zernike polynomials", Proc. SPIE 5180, Optical Manufacturing and Testing V, (22 December 2003); https://doi.org/10.1117/12.501144

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