• Opto-Electronic Engineering
  • Vol. 46, Issue 5, 180273 (2019)
Sun Wenhan1、2、3, Wang Shuai1、2、*, He Xing1、2, Chen Xiaojun1、2、3, and Xu Bing1、2
Author Affiliations
  • 1[in Chinese]
  • 2[in Chinese]
  • 3[in Chinese]
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    DOI: 10.12086/oee.2019.180273 Cite this Article
    Sun Wenhan, Wang Shuai, He Xing, Chen Xiaojun, Xu Bing. Modal wavefront reconstruction to obtain Zernike coefficient with no cross coupling in lateral shearing measurement[J]. Opto-Electronic Engineering, 2019, 46(5): 180273 Copy Citation Text show less

    Abstract

    Modal cross coupling frequently occurs in modal approaches from wavefront gradient data such as lateral shearing measurement through Zernike circle polynomials, since the gradients of Zernike circle polynomials are not orthogonal. We use a modal approaches incorporating the Gram matrix, using the orthogonality of angular derivative of m≠0 modes with respect to weight function w(ρ)=ρ (polar coordinates), and the orthogonality of radial derivative of m=0 modes with respect to weight function w(ρ)=ρ(1-ρ2) (polar coordinates). The Gram matrix method needs no auxiliary vector functions. The Zernike coefficients can be obtained with no modal cross coupling. The simulation results are given, which indicate that the modal cross coupling is avoided by using Gram matrix method. This method can be easily extended to annulus, and the coefficients of Zernike annular polynomials with no modal cross coupling can be obtained.
    Sun Wenhan, Wang Shuai, He Xing, Chen Xiaojun, Xu Bing. Modal wavefront reconstruction to obtain Zernike coefficient with no cross coupling in lateral shearing measurement[J]. Opto-Electronic Engineering, 2019, 46(5): 180273
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