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Frontiers of Optoelectronics

ISSN 2095-2759

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Front. Optoelectron.    2019, Vol. 12 Issue (2) : 180-189    https://doi.org/10.1007/s12200-018-0818-9
RESEARCH ARTICLE
Shape reconstruction of large optical surface with high-order terms in fringe reflection technique
Xiaoli JING1,2, Haobo CHENG1,2(), Yongfu WEN1,2()
1. School of Optics and Photonics, Beijing Institute of Technology, Beijing 100081, China
2. Shenzhen Research Institute, Beijing Institute of Technology, Shenzhen 518057, China
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Abstract

A fast and effective shape reconstruction method of large aspheric specular surfaces with high order terms is proposed in fringe reflection technique, which combines modal estimation with high-order finite-difference algorithm. The iterative equation with high-order truncation errors is derived for calculating the specular surface with large aperture based on high-order finite-difference algorithm. To achieve the wavefront estimation and improve convergence speed, the numerical orthogonal transformation method based on Zernike polynomials is implemented to obtain the initial iteration value. The reconstruction results of simulated surface identified the advantages of the proposed method. Furthermore, a freeform in illuminating system has been used to demonstrate the validity of the improved method in practical measurement. The results show that the proposed method has the advantages of making the reconstruction of different shape apertures accurate and rapid. In general, this method performs well in measuring large complex objects with high frequency information in practical measurement.
Keywords shape reconstruction      fringe reflection technique      Zernike orthogonal transformation      finite difference      measurement     
Corresponding Author(s): Haobo CHENG,Yongfu WEN   
Just Accepted Date: 27 July 2018   Online First Date: 03 September 2018    Issue Date: 03 July 2019
 Cite this article:   
Xiaoli JING,Haobo CHENG,Yongfu WEN. Shape reconstruction of large optical surface with high-order terms in fringe reflection technique[J]. Front. Optoelectron., 2019, 12(2): 180-189.
 URL:  
https://academic.hep.com.cn/foe/EN/10.1007/s12200-018-0818-9
https://academic.hep.com.cn/foe/EN/Y2019/V12/I2/180
Fig.1  Surface map of arbitrary surface
Fig.2  Slope map of arbitrary surface in (a) x and (b) y direction
Fig.3  Reconstruction error by (a) Legendre polynomials and (b) orthogonal Zernike polynomials
Fig.4  Slope map of freeform surface in (a) x and (b) y direction
Fig.5  Error map by (a) Southwell method, (b) Huang’s and (c) iterative high-order finite-difference method
reconstruction method PV/mm RMS/mm time/s
Southwell iteration 8.4 4.4 125
Huang’s 8.68 × 10−1 9.72 × 10−2 152
iterative high finite-difference 3.3 × 10−1 9 × 10−2 128
Tab.1  Analysis of 3D reconstruction results with three methods
Fig.6  Shape map of simulated surface
measured surface reconstruction method PV/mm RMS/mm time/s
arbitrary Southwell iteration 2.42 1.44 × 10−1 125
Zhou’s 1.8 1.12 × 10−1 26
Huang’s 3.80 × 10−1 4.08 × 10−2 141
Li’s 1.48 × 10−1 1.49 × 10−2 127
our 9.6 × 10−2 1.35 × 10−2 27
Tab.2  Analysis of 3D reconstruction results of measured surfaces under SNR= 30
Fig.7  Absolute errors of arbitrary surface using different methods. (a) SOR method based on Southwell geometry; (b) combined SOR with Legendre method proposed by Zhou; (c) iterative compensation method proposed by Huang; (d) iteration equation based on higher order integration method proposed by Li; (e) Legendre polynomials method; (f) our method
Fig.8  Error map by (a) Zernike polynomials, (b) Southwell iteration method, (c) our method and (d) reconstructed shape
tested surface reconstruction method PV/mm RMS/mm time/s
arbitrary (800 pixel × 800 pixel) Southwell iteration 1.42 8.39 × 10−1 101
our method 1.53 × 10−1 9.31 × 10−2 18
Tab.3  Comparison of reconstruction error of freeform surface by two methods
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