Opto-Electronic Engineering, Volume. 51, Issue 11, 240163-1(2024)

Surface characterization using Zernike polynomials

Jingyuan Liang1, Xiwen Li1, Chenghu Ke2, and Xizheng Ke1,3、*
Author Affiliations
  • 1School of Automation and Information Engineering, Xi'an University of Technology, Xi’an, Shaanxi 710048, China
  • 2School of Information Engineering, Xi’an University, Xi’an, Shaanxi 710048, China
  • 3Shaanxi Civil-Military Integration Key Laboratory of Intelligence Collaborative Networks, Xi’an, Shaanxi 710048, China
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    References(61)

    [1] Yang T, Duan Y Z, Cheng D W et al. Freeform imaging optical system design: theories, development, and applications[J]. Acta Opt Sin, 41, 0108001(2021).

    [2] Cheng D W, Chen H L, Wang Y T et al. Mathematical description and design methods of complex optical surfaces[J]. Acta Opt Sin, 43, 0822008(2023).

    [3] Niu K, Tian C. Zernike polynomials and their applications[J]. J Opt, 24, 123001(2022).

    [4] Yang H F, Jiang Z F. Research of Zernike modal wavefront reconstruction of 19-element Hartmann-Shack wavefront sensor[J]. Laser Technol, 29, 484-487(2005).

    [5] Wang C. Research on characterization function and application of free-form surface[D](2014).

    [6] Ye J F, Gao Z S, Liu X L et al. Freeform surfaces reconstruction based on Zernike polynomials and radial basis function[J]. Acta Opt Sin, 34, 0822003(2014).

    [7] Yang T, Wang Y D, Lü X et al. Design of Imaging and display systems combining freeform optics and holographic optical elements[J]. Acta Opt Sin, 44, 0900001(2024).

    [8] Lang C F. Studies on constraints of optimal design and manufacturing of Q-Type freeform surface[D](2022).

    [9] Forbes G W. Robust and fast computation for the polynomials of optics[J]. Opt Express, 18, 13851-13862(2010).

    [10] Ye J F. Research on the method and technique for characterizing freeform optical surface[D](2016).

    [11] Mahajan V N, Aftab M. Systematic comparison of the use of annular and Zernike circle polynomials for annular wavefronts[J]. Appl Opt, 49, 6489-6501(2010).

    [12] Kaya I, Thompson K P, Rolland J P. Edge clustered fitting grids for φ-polynomial characterization of freeform optical surfaces[J]. Opt Express, 19, 26962-26974(2011).

    [13] Svechnikov M V, Chkhalo N I, Toropov M N et al. Resolving capacity of the circular Zernike polynomials[J]. Opt Express, 23, 14677-14694(2015).

    [14] Mahajan V N. Zernike annular polynomials and optical aberrations of systems with annular pupils[J]. Appl Opt, 33, 8125-8127(1994).

    [15] Mahajan V N, Dai G M. Orthonormal polynomials for hexagonal pupils[J]. Opt Lett, 31, 2462-2464(2006).

    [16] Mahajan V N, Dai G M. Orthonormal polynomials in wavefront analysis: analytical solution[J]. J Opt Soc Am A, 24, 2994-3016(2007).

    [17] Dai G M, Mahajan V N. Orthonormal polynomials in wavefront analysis: error analysis[J]. Appl Opt, 47, 3433-3445(2008).

    [18] Ferreira C, López J L, Navarro R et al. Orthogonal basis with a conicoid first mode for shape specification of optical surfaces[J]. Opt Express, 24, 5448-5462(2016).

    [20] Area I, Dimitrov D K, Godoy E. Recursive computation of generalised Zernike polynomials[J]. J Comput Appl Math, 312, 58-64(2017).

    [21] Ares M, Royo S. Comparison of cubic B-spline and Zernike-fitting techniques in complex wavefront reconstruction[J]. Appl Opt, 45, 6954-6964(2006).

    [22] Kaya I, Thompson K P, Rolland J P. Comparative assessment of freeform polynomials as optical surface descriptions[J]. Opt Express, 20, 22683-22691(2012).

    [23] Rahbar K, Faez K, Kakhki E A. Phase wavefront aberration modeling using Zernike and pseudo-Zernike polynomials[J]. J Opt Soc Am A, 30, 1988-1993(2013).

    [24] Trevino J P, Gómez‐Correa J E, Iskander D R et al. Zernike vs. Bessel circular functions in visual optics[J]. Ophthalmic Physiol Opt, 33, 394-402(2013).

    [25] Badar I, Hellmann C, Wyrowski F. Wavefront phase representation by Zernike and spline models: a comparison[J]. J Opt Soc Am A, 38, 1178-1186(2021).

    [26] Raasch T W, Su L J, Yi A. Whole-surface characterization of progressive addition lenses[J]. Optom Vis Sci, 88, E217-E226(2011).

    [27] Ivanova T V, Zavgorodniĭ D S. Zernike-polynomial description of the deformation of a known surface profile with a noncircularly symmetric shape[J]. J Opt Technol, 88, 8-13(2021).

    [28] Omidi P, Cayless A, Langenbucher A. Evaluation of optimal Zernike radial degree for representing corneal surfaces[J]. PLoS One, 17, e0269119(2022).

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

    [30] Li X Y, Jiang W H. Modal description of wavefront aberration in non-circle apertures[J]. Chin J Lasers, B11, 259-266(2002).

    [31] Wang Q F, Cheng D W, Wang Y T. Description of free-form optical curved surface using two-variable orthogonal polynomials[J]. Acta Opt Sin, 32, 0922002(2012).

    [32] Li M Y, Li D H, Wang Q H et al. Wavefront reconstruction with orthonormal polynomials in a Square Area[J]. Chin J Lasers, 39, 1108011(2012).

    [33] Zhao Q, Wang Y, Wang P et al. Construction method of non-circular pupil Zernike orthogonal basis in wavefront reconstruction[J]. Opt Tech, 43, 228-233(2017).

    [34] Yan J Z, Lei F, Zhou B F et al. Algorithms for wavefront fitting using Zernike polynomial[J]. Opt Precis Eng, 7, 119-128(1999).

    [35] Mo W D. The reseach into the method to fit interferogram with Zernike polynomials[J]. High Speed Photog Photonics, 20, 389-396(1991).

    [36] Mo W D. The principle of fitting Interferogram with Zernike polynomials[J]. J Air Force Eng Univ (Nat Sci Ed), 3, 35-38(2002).

    [37] Zhang W, Liu J F, Long F N et al. Study on wavefront fitting using Zernike polynomials[J]. Opt Tech, 31, 675-678(2005).

    [38] Sun X Z, Su X Y, Jing H L. The influence of sampling points on the precision of curved surface fitting based on Zernike polynomials[J]. Opt Instrum, 30, 6-10(2008).

    [39] Xie S L. Sampling point number in curved surface fitting with Zernike polynomials[J]. J Appl Opt, 31, 943-949(2010).

    [40] Feng J, Bai Y, Xing T W. Fitting accuracy of wavefront using Zernike polynomials[J]. Electro-Opt Technol Appl, 26, 31-34(2011).

    [41] Guo L X, Wei J J, Tang P. Fitting simulation and precision of mirror surface with Zernike circular polynomial[J]. Opt Optoelectron Technol, 16, 56-62(2018).

    [42] Han L, Tian A L, Nie F M et al. Algorithm for three-dimensional surface reconstruction of fringe reflection using Zernike polynomial[J]. J Xi'an Technol Univ, 39, 137-144(2019).

    [43] Wei X Y, Yu X. An optical wavefront seuing and reconstruction method based on Zernike polynomials[J]. Acta Opt Sin, 14, 718-723(1994).

    [44] Zhang Q, Jiang W H, Xu B. Reconstruction of turbulent optical wavefront realized by Zernike polynomial[J]. Opto-Electron Eng, 25, 15-19(1998).

    [45] Luo Z F, Chen H X, Ding L. Wavefront measurement and reconstruction of small phase-distortion on laser beam[J]. Laser J, 27, 35-36(2006).

    [46] Zhang H, Lu J D, Liu R et al. Design of uniform square spot Lens based on smooth optimization of Zernike polynomials[J]. Laser Optoelectron Prog, 55, 102202(2018).

    [47] Yang D Q, Tao Y H, Zhao G L et al. Rapid simulation of atmospheric turbulence degradation images based on neural networks[J]. Spacecr Recovery Remote Sens, 44, 57-67(2023).

    [48] Mo W D. Error and precision evaluation of a system for Inspecting surface of optical plane[J]. Acta Opt Sin, 23, 879-883(2003).

    [49] Yang J W, Huang Q L, Han Y M. Application and simulation in fitting optical surface with Zernike polynomial[J]. Spacecr Recovery Remote Sens, 31, 49-55(2010).

    [50] Pang Z H, Fan X W, Ma Z et al. Free-form optical elements corrected aberrations of optical system[J]. Acta Opt Sin, 36, 0522001(2016).

    [51] Guan S, Wang C, Tong S F et al. Optical antenna design of off-axis two-mirror reflective telescope with freeform surface for space laser communication[J]. Infrared Laser Eng, 46, 1205002(2017).

    [52] Xiang B B, Wang C S, Lian P Y. Effect of surface error distribution and aberration on electromagnetic performance of a reflector antenna[J]. Int J Antennas Propagation, 2019, 5062545(2019).

    [53] Shi Y C, Yan H D, Gong P et al. Topology optimization design method for supporting structures of optical reflective mirrors based on Zernike coefficient optimization model[J]. Acta Photonica Sin, 49, 0622001(2020).

    [54] Zhou T, Hao Q, Hu Y et al. An optimization method of deformable mirror shape design for freeform surface partial compensation interferometry[J]. Opt Tech, 47, 257-264(2021).

    [55] Yan J H, Hu Z J, Zhu D Y et al. Design of compact off-axis three-mirror afocal system based on freeform surface[J]. Acta Photonica Sin, 51, 0511002(2022).

    [56] Xie B F, Zhao X, Tao S S et al. Application of freeform surface in aberration compensation of femtosecond laser filamentation system[J]. Acta Opt Sin, 43, 0822020(2023).

    [57] Han J Z, Zhao S J, Feng A W et al. Design of compact and broadband imaging spectrometer based on free-form surface[J]. Acta Opt Sin, 43, 1422002(2023).

    [58] Zhang Q, Lü B D, Jiang W H. Zernike model wavefront reconstruction for annular field[J]. High Power Laser Part Beams, 12, 306-310(2000).

    [59] Wang Q T, Tong S F, Xu Y H. On simulation and verification of the atmospheric turbulent phase screen with Zernike polynomials[J]. Infrared Laser Eng, 42, 1907-1911(2013).

    [60] Wu J L, Ke X Z. Adaptive optics correction of wavefront sensorless[J]. Laser Optoelectron Prog, 55, 030103(2018).

    [61] Zhang H M, Li X Y. Numerical simulation of wavefront phase screen distorted by atmospheric turbulence[J]. Opto-Electron Eng, 33, 14-19(2006).

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    Jingyuan Liang, Xiwen Li, Chenghu Ke, Xizheng Ke. Surface characterization using Zernike polynomials[J]. Opto-Electronic Engineering, 2024, 51(11): 240163-1

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    Paper Information

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    Received: Jul. 12, 2024

    Accepted: Oct. 26, 2024

    Published Online: Jan. 24, 2025

    The Author Email: Xizheng Ke (柯熙政)

    DOI:10.12086/oee.2024.240163

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