Please wait a minute...

Frontiers of Optoelectronics

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
Download: PDF(6823 KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
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:  
http://journal.hep.com.cn/foe/EN/10.1007/s12200-018-0818-9
http://journal.hep.com.cn/foe/EN/Y2019/V12/I2/180
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
Xiaoli JING
Haobo CHENG
Yongfu WEN
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 × 101 9.72 × 102 152
iterative high finite-difference 3.3 × 101 9 × 102 128
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 × 101 125
Zhou’s 1.8 1.12 × 101 26
Huang’s 3.80 × 101 4.08 × 102 141
Li’s 1.48 × 101 1.49 × 102 127
our 9.6 × 102 1.35 × 102 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 × 101 101
our method 1.53 × 101 9.31 × 102 18
Tab.3  Comparison of reconstruction error of freeform surface by two methods
1 Y L Xiao, X Su, W Chen. Flexible geometrical calibration for fringe-reflection 3D measurement. Optics Letters, 2012, 37(4): 620–622
https://doi.org/10.1364/OL.37.000620 pmid: 22344126
2 T Zhou, K Chen, H Wei, Y Li. Improved method for rapid shape recovery of large specular surfaces based on phase measuring deflectometry. Applied Optics, 2016, 55(10): 2760–2770
https://doi.org/10.1364/AO.55.002760 pmid: 27139683
3 L Huang, M Idir, C Zuo, K Kaznatcheev, L Zhou, A Asundi. Comparison of two-dimensional integration methods for shape reconstruction from gradient data. Optics and Lasers in Engineering, 2015, 64: 1–11
https://doi.org/10.1016/j.optlaseng.2014.07.002
4 R H Hudgin. Wave-front reconstruction for compensated imaging. Journal of the Optical Society of America, 1977, 67(3): 375–378
https://doi.org/10.1364/JOSA.67.000375
5 D L Fried. Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements. Journal of the Optical Society of America, 1977, 67(3): 370–375
https://doi.org/10.1364/JOSA.67.000370
6 W H Southwell. Wave-front estimation from wave-front slope measurements. Journal of the Optical Society of America, 1980, 70(8): 998–1006
https://doi.org/10.1364/JOSA.70.000998
7 L Huang, A Asundi. Improvement of least-squares integration method with iterative compensations in fringe reflectometry. Applied Optics, 2012, 51(31): 7459–7465
https://doi.org/10.1364/AO.51.007459 pmid: 23128691
8 G Li, Y Li, K Liu, X Ma, H Wang. Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2013, 30(7): 1448–1459
https://doi.org/10.1364/JOSAA.30.001448 pmid: 24323162
9 J Campos, L P Yaroslavsky, A Moreno, M J Yzuel. Integration in the Fourier domain for restoration of a function from its slope: comparison of four methods. Optics Letters, 2002, 27(22): 1986–1988
https://doi.org/10.1364/OL.27.001986 pmid: 18033420
10 S W Bahk. Highly accurate wavefront reconstruction algorithms over broad spatial-frequency bandwidth. Optics Express, 2011, 19(20): 18997–19014
https://doi.org/10.1364/OE.19.018997 pmid: 21996841
11 J Matías Di Martino, J L Flores, F Pfeiffer, K Scherer, G A Ayubi, J A Ferrari. Phase retrieval from one partial derivative. Optics Letters, 2013, 38(22): 4813–4816
https://doi.org/10.1364/OL.38.004813 pmid: 24322139
12 S Ettl, J Kaminski, M C Knauer, G Häusler. Shape reconstruction from gradient data. Applied Optics, 2008, 47(12): 2091–2097
https://doi.org/10.1364/AO.47.002091 pmid: 18425183
13 P Bon, S Monneret, B Wattellier. Noniterative boundary-artifact-free wavefront reconstruction from its derivatives. Applied Optics, 2012, 51(23): 5698–5704
https://doi.org/10.1364/AO.51.005698 pmid: 22885583
14 H Zhang, S Han, S Liu, S Li, L Ji, X Zhang. 3D shape reconstruction of large specular surface. Applied Optics, 2012, 51(31): 7616–7625
https://doi.org/10.1364/AO.51.007616 pmid: 23128710
15 X Jing, H Cheng, Y Wen. Path integration guided with a quality map for shape reconstruction in the fringe reflection technique. Measurement Science & Technology, 2018, 29(4): 045011
https://doi.org/10.1088/1361-6501/aaa5ef
16 J Ye, W Wang, Z Gao, Z Liu, S Wang, P Benítez, J C Miñano, Q Yuan. Modal wavefront estimation from its slopes by numerical orthogonal transformation method over general shaped aperture. Optics Express, 2015, 23(20): 26208–26220
https://doi.org/10.1364/OE.23.026208 pmid: 26480134
Related articles from Frontiers Journals
[1] Di WU, Yu JIA, Li WANG, Yueqiang SUN. Ship hull flexure measurement based on integrated GNSS/LINS[J]. Front. Optoelectron., 2019, 12(3): 332-340.
[2] Kejia WANG, Xinyang GU, Jinsong LIU, Zhengang YANG, Shenglie WANG. Proposal for CEP measurement based on terahertz air photonics[J]. Front. Optoelectron., 2018, 11(4): 407-412.
[3] Xin ZHANG, Jiawen JIAN, Han JIN, Peipeng XU. Nested microring resonator with a doubled free spectral range for sensing application[J]. Front. Optoelectron., 2017, 10(2): 144-150.
[4] Chenwenji WANG,Peili LI,Yuying GAN,Di CAO,Xiaozheng QIAO,Chen HE. Cross-correlation frequency-resolved optical gating scheme based on a periodically poled lithium niobate waveguide for an optical arbitrary waveform measurement[J]. Front. Optoelectron., 2017, 10(1): 70-79.
[5] Ran YAO,Dawei ZHANG,Bing ZOU,Jian XU. Junction temperature measurement of alternating current light-emitting-diode by threshold voltage method[J]. Front. Optoelectron., 2016, 9(4): 555-559.
[6] Xu YE,Haobo CHENG,Zhichao DONG,Hon-Yuen TAM. Error compensation for three-dimensional profile measurement system[J]. Front. Optoelectron., 2015, 8(4): 402-412.
[7] Saeed OLYAEE, Zahra DASHTBAN, Muhammad Hussein DASHTBAN. Design and implementation of super-heterodyne nano-metrology circuits[J]. Front Optoelec, 2013, 6(3): 318-326.
[8] Zhaoyun ZHANG, Yang GAO, Wei SU. Laser self-mixing interferometer for MEMS dynamic measurement[J]. Front Optoelec, 2013, 6(2): 210-215.
[9] Jia WANG, Qingyan WANG, Mingqian ZHANG. Development and prospect of near-field optical measurements and characterizations[J]. Front Optoelec, 2012, 5(2): 171-181.
[10] Yunshan ZHANG, Chunqing GAO, Mingwei GAO, Yan ZHENG, Lei WANG, Ran WANG. A speed measurement system utilizing an injection-seeded Tm:YAG laser[J]. Front Optoelec Chin, 2011, 4(4): 411-414.
[11] Xi HUANG, Cui QIN, Xinliang ZHANG. High accuracy numerical solutions for band structures in strained quantum well semiconductor optical amplifiers[J]. Front Optoelec Chin, 2011, 4(3): 330-337.
[12] Feng CAO, Duan LIU, Jiang LIN, Bichun HU, Deming LIU. Absorption measurement of methane gas with broadband light source using fiber-optic sensor system[J]. Front Optoelec Chin, 2010, 3(4): 394-398.
[13] Jian LIU, Hao ZHANG, Bo LIU. Temperature measurement based on photonic crystal modal interferometer[J]. Front Optoelec Chin, 2010, 3(4): 418-422.
[14] Shaomin LI, Xiaoying LIU, Chong LIU. FBG sensing temperature characteristic and application in oil/gas down-hole measurement[J]. Front Optoelec Chin, 2009, 2(2): 233-238.
[15] Sihua FU, Xuejun LONG, Hui LIN, Qifeng YU. Fringe-contoured-window sine/cosine filter for saw-tooth phase maps in ESPI[J]. Front Optoelec Chin, 2008, 1(3-4): 345-351.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed