• Opto-Electronic Engineering
  • Vol. 51, Issue 11, 240163-1 (2024)
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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    DOI: 10.12086/oee.2024.240163 Cite this Article
    Jingyuan Liang, Xiwen Li, Chenghu Ke, Xizheng Ke. Surface characterization using Zernike polynomials[J]. Opto-Electronic Engineering, 2024, 51(11): 240163-1 Copy Citation Text show less
    3D plots of the first 20 Zernike polynomials
    Fig. 1. 3D plots of the first 20 Zernike polynomials
    Wavefront plots of aberrations and their corresponding Zernike polynomials
    Fig. 2. Wavefront plots of aberrations and their corresponding Zernike polynomials
    曲面表征函数与方法优势缺点
    Zernike多项式正交,与经典相差一一对应,解析波前等对局部凸起难以精确表征,高阶项计算复杂
    Q型正交多项式正交,加工可控性强,适合表征全局特性等高阶计算复杂,尚未广泛集成到计算机软件当中
    XY多项式设计自由度高,适合表征全局特性等非正交,不可解析波前
    径向基函数局部表征能力强非正交
    NURBS函数局部表征能力强,构造灵活非正交,构造复杂
    Table 1. Comparison of common characterization functions: advantages and disadvantages
    项数Zernike多项式像差
    Z11平移
    Z2ρcos(θ)X轴倾斜
    Z3ρsin(θ)Y轴倾斜
    Z4ρ2cos2θ初级像散 (090)
    Z52ρ21离焦
    Z6ρ2sin2θ初级像散 (±45轴)
    Z7ρ3cos3θ初级三叶草 (X-轴)
    Z8(3ρ32ρ)cosθ初级慧差 (X-轴)
    Z9(3ρ32ρ)sinθ初级慧差 (Y-轴)
    Table 2. Correspondence between the first 9 Zernike polynomials and optical aberrations[5]
    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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