Opto-Electronic Engineering, Volume. 46, Issue 5, 180273(2019)

Modal wavefront reconstruction to obtain Zernike coefficient with no cross coupling in lateral shearing measurement

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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    References(26)

    [1] [1] Rimmer M P. Method for evaluating lateral shearing interfero-grams[J]. Applied Optics, 1974, 13(3): 623–629.

    [2] [2] Harbers G, Kunst P J, Leibbrandt G W R. Analysis of lateral shearing interferograms by use of Zernike polynomials[J]. Ap-plied Optics, 1996, 35(31): 6162–6172.

    [3] [3] Shen W, Chang M W, Wan D S. Zernike polynomial fitting of lateral shearing interferometry[J]. Optical Engineering, 1997, 36(36): 905–913.

    [4] [4] Hunt B R. Matrix formulation of the reconstruction of phase values from phase differences[J]. Journal of the Optical Society of America, 1979, 69(3): 393–399.

    [6] [6] Tyson R. Principles of Adaptive Optics[M]. 3rd ed. London: CRC Press, 2010: 111–176.

    [7] [7] Zhang Q, Jiang W H, Xu B. Reconstruction of turbulent optical wavefront realized by Zernike polynomial[J]. Opto-Electronic Engineering, 1998, 25(6): 15–19.

    [8] [8] Xian H, Li H G, Jiang W H, et al. Measurement of the wavefront phase of a laser beam with Hartmann-Shack sensor[J]. Op-to-Electronic Engineering, 1995, 22(2): 38–45.

    [9] [9] Zhang R, Yang J S, Tian Y, et al. Wavefront phase recovery from the plenoptic camera[J]. Opto-Electronic Engineering, 2013, 40(2): 32–39.

    [10] [10] Cubalchini R. Modal wave-front estimation from phase deriva-tive measurements[J]. Journal of the Optical Society of America, 1979, 69(7): 972–977.

    [11] [11] Herrmann J. Cross coupling and aliasing in modal wave-front estimation[J]. Journal of the Optical Society of America, 1981, 71(8): 989–992.

    [12] [12] Huang S Y, Xi F J, Liu C H, et al. Eigenfunctions of Laplacian for phase estimation from wavefront gradient or curvature sensing[J]. Optics Communications, 2011, 284(12): 2781–2783.

    [13] [13] Huang S Y, Xi F J, Liu C H, et al. Phase retrieval on annular and annular sector pupils by using the eigenfunction method to solve the transport of intensity equation[J]. Journal of the Opt-ical Society of America A, 2012, 29(4): 513–520.

    [14] [14] Huang S Y, Yu N, Xi F J, et al. Modal wavefront reconstruction with Zernike polynomials and eigenfunctions of Laplacian[J]. Optics Communications, 2013, 288: 7–12.

    [15] [15] Gavrielides A. Vector polynomials orthogonal to the gradient of Zernike polynomials[J]. Optics Letters, 1982, 7(11): 526–528.

    [16] [16] Zhao C Y, Burge J H. Orthonormal vector polynomials in a unit circle, Part I: basis set derived from gradients of Zernike poly-nomials[J]. Optics Express, 2007, 15(26): 18014–18024.

    [17] [17] Zhao C Y, Burge J H. Orthonormal vector polynomials in a unit circle, Part II: completing the basis set[J]. Optics Express, 2008, 16(9): 6586–6591.

    [18] [18] Mahajan V N, Acosta E. Vector polynomials for direct analysis of circular wavefront slope data[J]. Journal of the Optical So-ciety of America A, 2017, 34(10): 1908–1913.

    [19] [19] Sun W H, Wang S, He X, et al. Jacobi circle and annular poly-nomials: modal wavefront reconstruction from wavefront gra-dient[J]. Journal of the Optical Society of America A, 2018, 35(7): 1140–1148.

    [20] [20] Horn R A, Johnson C R. Matrix Analysis[M]. Cambridge: Cam-bridge University Press, 1990: 407.

    [21] [21] Mahajan V N. Zernike circle polynomials and optical aberra-tions of systems with circular pupils[J]. Applied Optics, 1994, 33(34): 8121–8124.

    [22] [22] Zernike F. Diffraction theory of the knife-edge test and its im-proved form, the phase-contrast method[J]. Monthly Notices of the Royal Astronomical Society, 2002, 94(2): 377–384.

    [23] [23] Born M, Wolf E. Principles of Optics[M]. 7th ed. Cambridge: Cambridge University Press, 1999: 905–910.

    [24] [24] Wang Z X, Guo D R. Special Functions[M]. Singapore: World Scientific, 1989: 139, 169–173.

    [25] [25] Andrews G E, Askey R, Roy R. Special Functions[M]. Cam-bridge: Cambridge University Press, 1999: 94.

    [26] [26] Mahajan V N. Zernike annular polynomials and optical aberra-tions of systems with annular pupils[J]. Applied Optics, 1994, 33(34): 8125–8127.

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    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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    Paper Information

    Category: Article

    Received: May. 23, 2018

    Accepted: --

    Published Online: Jul. 25, 2019

    The Author Email: Shuai Wang (wangshuai@ioe.an.cn)

    DOI:10.12086/oee.2019.180273

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