Optical Technique, Volume. 51, Issue 3, 282(2025)

The application and research progress of Zernike polynomials in the optimization of optical elements

ZHU Zhanke1,2, JI Fan3, and KE Xizheng1,2,3、*
Author Affiliations
  • 1Shaanxi Polytechnic Institute, School of Aeronautical Engineering, Xianyang 712000, China
  • 2Xianyang Key Laboratory of Intelligent Manufacturing Equipment Technology, Xianyang 712000, China
  • 3Xi’an University of Technology, School of Automation and Information Engineering, Xian 710048, China
  • show less
    References(32)

    [2] [2] Grant I, Stewart N, Padilla-Perez I A. Topographical measurements of water waves using the projection moire method[J]. Applied Optics,1990,29(28):3981—3983.

    [3] [3] Knauer M C, Kaminski J, Hausler G. Phase measuring deflectometry: a new approach to measure specular free-form surfaces[J]. Optical Metrology in Production Engineering,2004,5457:366—376.

    [4] [4] MacGovern A J, Wyant J C. Computer generated holograms for testing optical elements[J]. Applied optics,1971,10(3):619—624.

    [5] [5] Zhu J H, Zhang W H. Integrated layout design of supports and structures[J]. Computer Methods in Applied Mechanics and Engineering,2010,199(9-12):557—569.

    [6] [6] Zernike F. Diffraction theory of the cut procedure and its improved form, the phase contrast method[J]. Physica,1934,1(689-704):56.

    [9] [9] Niu K, Tian C. Zernike polynomials and their applications[J]. Journal of O Ptics,2022,24(12):123001.

    [10] [10] Mahajan V N. Zernike annular polynomials for imaging systems with annular pupils[J]. JOSA,1981,71(1):75—85.

    [11] [11] Wang J Y, Silva D E. Wave-front interpretation with Zernike polynomials[J]. Applied Optics,1980,19(9):1510—1518.

    [15] [15] Kim Y, Yang H S, Kim S W, et al. Alignment of off-axis optical system with multi mirrors using derivative of Zernike polynomial coefficient[J]. Optical System Alignment, Tolerancing, and Verification III,2009,7433(1):112—119.

    [17] [17] Kihm H, Yang H S. Design optimization of a 1-m lightweight mirror for a space telescope[J]. Optical Engineering,2013,52(9): 091806—091806.

    [19] [19] Liu C, Shang H, Zhao Y, et al. A new method to optimize the azimuth angle of elements in a projection lens[J]. Optics Communications,2016,381:365—370.

    [24] [24] Rao B V, Kiran M, Venkateswaran R, et al. Convex optical freeforms using fringe Zernike overlay approach for two-mirror and three-mirror telescopes for space applications[J]. Optics Communications,2023,541:129533.

    [27] [27] Zheng Z, Sun X, Liu X, et al. Design of reflective projection lens with Zernike polynomials surfaces[J]. Displays,2008,29(4):412—417.

    [37] [37] Xu N, Liu G, Zhao Y, et al. Ultrahigh-aspect-ratio beam generation with super-resolution spot[J]. Applied Physics Letters,2021,119(9):094101.

    [38] [38] Li W, Shi Y, Wang C, et al. Structural topology optimization of reflective mirror based on objective of wavefront aberration[J]. Machines,2022,10(11):1043.

    [39] [39] Liu Y, Rui Y, Zhao Z, et al. Topology optimization design of an active deformable mirror based on discrete orthogonal Zernike polynomials[J]. Symmetry,2022,14(11):2469(1)—2469(18).

    [41] [41] Liu Y, Zhang R, Han X, et al. Design and optical performance analysis of large-aperture optical windows for structural vibration reduction[C]∥Photonics. MDPI,2024,11(1): 86.

    [45] [45] Wang Z, Eng S H, Alameh K. Design and optimization of programmable lens array for adaptive optics[J]. Smart Structures, Devices, and Systems III,2007,6414(1):135—143.

    [46] [46] Liu Y, Ma J, Ma H, et al.Zernike aberration characteristics of precision conformal optical windows[C]∥Sixth International Symposium on Precision Engineering Measurements and Instrumentation.Hangzhou,China:SPIE,2010,7544:991—997.

    [47] [47] De Oliveira O G, de Lima Monteiro D W. Optimization of the hartmann-shack microlens array[J]. Optics and Lasers in Engineering,2011,49(4):521—525.

    [48] [48] Zhao H. Design of fore-optical system with zernike surface and high-speed for hyper-spectral imagers[C]∥International Conference on Control, Automation and Systems Engineering (CASE). Singapore:IEEE,2011:1—4.

    [49] [49] Long C S, Loveday P W, Forbes A. Zernike polynomial based Rayleigh-Ritz model of a piezoelectric unimorph deformable mirror[J].I nternational Journal of Mechanics and Materials in Design,2012,8:237—245.

    [51] [51] Zhang W, Zuo B, Chen S, et al. Design of fixed correctors used in conformal optical system based on diffractive optical elements[J]. Applied Optics,2013,52(3):461—466.

    [53] [53] Zhu H, Cui Q, Piao M, et al. Design of a dual-band MWIR/LWIR circular unobscured three-mirror optical system with Zernike polynomial surfaces[J]. Optical Design and Testing VI,2014,9272: 92720W.

    [54] [54] Yang T, Zhu J, Jin G. Nodal aberration properties of coaxial imaging systems using Zernike polynomial surfaces[J]. JOSA A,2015,32(5):822—836.

    [56] [56] Houzet J, Faure N, Larochette M, et al. Ultrafast laser spatial beam shaping based on Zernike polynomials for surface processing[J]. Optics Express,2016,24(6):6542—6552.

    [57] [57] Liu C, Gross H. Numerical optimization strategy for multi-lens imaging systems containing freeform surfaces[J]. Applied Optics,2018,57(20):5758—5768.

    [58] [58] Liu J, Chen X. Study on the relationship between surface error and optical performance for polymer optical lenses[J]. Optik,2019,194:163119.

    [60] [60] McCluskey K A, van Veen E N W, Cnossen J P, et al. Global correction of optical distortions in multicolor single-molecule microscopy using Zernike polynomial gradients[J]. Optics Express,2021,29(25):42251—42264.

    [61] [61] MiriRostami S R, Pinilla S, Shevkunov I, et al. Hybrid diffractive optics (DOE & refractive lens) for broadband EDoF imaging[J]. Electronic Imaging,2023,35(1):1—14.

    [64] [64] Puentes G, Minotti F. Spectral characterization of optical aberrations in fluidic lenses[J]. Front Phys,2024,11:1299393.

    [65] [65] Zhang S, Zhao X, Li D, et al. High-precision analysis of aberration contribution of Zernike freeform surface terms for non-zero field of view[J]. Optics Express,2024,32(3):3167—3183.

    Tools

    Get Citation

    Copy Citation Text

    ZHU Zhanke, JI Fan, KE Xizheng. The application and research progress of Zernike polynomials in the optimization of optical elements[J]. Optical Technique, 2025, 51(3): 282

    Download Citation

    EndNote(RIS)BibTexPlain Text
    Save article for my favorites
    Paper Information

    Category:

    Received: Sep. 26, 2024

    Accepted: May. 29, 2025

    Published Online: May. 29, 2025

    The Author Email: KE Xizheng (xzke@263.net)

    DOI:

    Topics