A transformation approach for aberration-mode coefficients of Walsh functions and Zernike polynomials

Shuai Wang; Ping Yang; Lizhi Dong; Bing Xu; Mingwu Ao

doi:10.1117/12.2065453

3 February 2015 A transformation approach for aberration-mode coefficients of Walsh functions and Zernike polynomials

Shuai Wang, Ping Yang, Lizhi Dong, Bing Xu, Mingwu Ao

Proceedings Volume 9255, XX International Symposium on High-Power Laser Systems and Applications 2014; 92553C (2015) https://doi.org/10.1117/12.2065453
Event: XX International Symposium on High Power Laser Systems and Applications, 2014, Chengdu, China

Abstract

Walsh functions have been modified and utilized as binary-aberration-mode basis which are especially suitable for representing discrete wavefronts. However, when wavefront sensing techniques based on binary-aberration-mode detection trying to reconstruct common wavefronts with continuous forms, the Modified Walsh functions are incompetent. The limited space resolution of Modified Walsh functions will leave substantial residual wavefronts. In order to sidestep the space-resolution problem of binary-aberration modes, it’s necessary to transform the Modified-Walsh-function expansion coefficients of wavefront to Zernike-polynomial coefficients and use Zernike polynomials to represent the wavefront to be reconstructed. For this reason, a transformation method for wavefront expansion coefficients of the two aberration modes is proposed. The principle of the transformation is the linear of wavefront expansion and the method of least squares. The numerical simulation demonstrates that the coefficient transformation with the transformation matrix is reliable and accurate.

Citation Download Citation

Shuai Wang, Ping Yang, Lizhi Dong, Bing Xu, and Mingwu Ao "A transformation approach for aberration-mode coefficients of Walsh functions and Zernike polynomials", Proc. SPIE 9255, XX International Symposium on High-Power Laser Systems and Applications 2014, 92553C (3 February 2015); https://doi.org/10.1117/12.2065453

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