Abstract

The adaptive wavefront interferometer (AWI) we have reported recently is utilized to test in-process surfaces with severe surface figure error which is beyond dynamic range of conventional interferometers [S. Xue, S. Chen, Z. Fan, and D. Zhai, Opt. Express 26, 21910 (2018).]. However, it shows low intelligence when Monte-Carlo simulation is conducted to apply AWI on various surface figure error. In some simulation cases, the unresolvable fringes keep still or cannot be turned into completely resolvable fringes. To troubleshoot this issue, we studied AWIs in a general framework of global optimization for the first time. Under this framework, we explained that three optimization issues contribute to the poor performance of AWI. On this basis, we proposed a machine vision and genetic algorithm combined method (MV-GA) to control AWI to realize efficient and robust tests of various surface figure error. Monte-Carlo simulation and experiment verify the robustness has been greatly enhanced.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Adaptive wavefront interferometry for unknown free-form surfaces

Shuai Xue, Shanyong Chen, Zhanbin Fan, and Dede Zhai
Opt. Express 26(17) 21910-21928 (2018)

Obtaining the phase of an interferogram by use of an evolution strategy: Part I.

Sergio Vázquez-Montiel, Juan Jaime Sánchez-Escobar, and Olac Fuentes
Appl. Opt. 41(17) 3448-3452 (2002)

Efficient use of hybrid Genetic Algorithms in the gain optimization of distributed Raman amplifiers

B. Neto, A. L. J Teixeira, N. Wada, and P. S. André
Opt. Express 15(26) 17520-17528 (2007)

References

  • View by:
  • |
  • |
  • |

  1. D. Malacara, Optical Shop Testing (Wiley, 2007).
  2. S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (2017).
    [Crossref]
  3. J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26(24), 5245–5258 (1987).
    [Crossref] [PubMed]
  4. S. Xue, S. Chen, Z. Fan, and D. Zhai, “Adaptive wavefront interferometry for unknown free-form surfaces,” Opt. Express 26(17), 21910–21928 (2018).
    [Crossref] [PubMed]
  5. L. Huang, H. Choi, W. Zhao, L. R. Graves, and D. W. Kim, “Adaptive interferometric null testing for unknown freeform optics metrology,” Opt. Lett. 41(23), 5539–5542 (2016).
    [Crossref] [PubMed]
  6. F. Shih, Image Processing and Mathematical Morphology: Fundamentals and Applications (CRC, 2009).
  7. M. Locatelli, “On the multilevel structure of global optimization problems,” Comput. Optim. Appl. 30(1), 5–22 (2005).
    [Crossref]
  8. R. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66(3), 207–211 (1976).
    [Crossref]
  9. M. Locatelli and F. Schoen, Global Optimization - Theory, Algorithms, and Applications (SIAM, 2013).
  10. S. Sivanandam and S. Deepa, Introduction to Genetic Algorithms (Springer, 2008).
  11. S. Lim, A. Sultan, M. Sulaiman, A. Mustapha, and K. Leong, “Crossover and mutation operators of genetic algorithms,” Int. J. Mach. Learn. Comput. 7(1), 9–12 (2017).
    [Crossref]
  12. S. Xue, S. Chen, G. Tie, and Y. Tian, “Adaptive null interferometric test using spatial light modulator for free-form surfaces,” Opt. Express 27(6), 8414–8428 (2019).
    [Crossref]
  13. G. Berger and J. Petter, “Non-contact metrology of aspheric surfaces based on MWLI technology,” Proc. SPIE 8884, 88840V (2013).
    [Crossref]
  14. D. Wolpert and W. Macready, “No free lunch theorems for optimization,” IEEE Trans. Evol. Comput. 1(1), 67–82 (1997).
    [Crossref]
  15. G. Xu, “An adaptive parameter tuning of particle swarm optimization algorithm,” Appl. Math. Comput. 219(9), 4560–4569 (2013).
    [Crossref]
  16. K. Creath, “Holographic contour and deformation measurement using a 1.4 million element detector array,” Appl. Opt. 28(11), 2170–2175 (1989).
    [Crossref] [PubMed]
  17. P.J. de Groot, “Long-wavelength laser diode interferometer for surface flatness measurement,” Proc. SPIE 2248, 136–140 (1994).
    [Crossref]
  18. K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).
  19. E. Garbusi, C. Pruss, and W. Osten, “Interferometer for precise and flexible asphere testing,” Opt. Lett. 33(24), 2973–2975 (2008).
    [Crossref] [PubMed]
  20. J. Peng, D. Chen, H. Guo, J. Zhong, and Y. Yu, “Variable optical null based on a yawing CGH for measuring steep acylindrical surface,” Opt. Express 26(16), 20306–20318 (2018).
    [Crossref] [PubMed]
  21. S. Xue, S. Chen, and G. Tie, “Near-null interferometry using an aspheric null lens generating a broad range of variable spherical aberration for flexible test of aspheres,” Opt. Express 26(24), 31172–31189 (2018).
    [Crossref] [PubMed]
  22. C. Tian, Y. Yang, T. Wei, and Y. Zhuo, “Nonnull interferometer simulation for aspheric testing based on ray tracing,” Appl. Opt. 50(20), 3559–3569 (2011).
    [Crossref] [PubMed]
  23. Q. Hao, S. Wang, Y. Hu, H. Cheng, M. Chen, and T. Li, “Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements,” Appl. Opt. 55(35), 9992–10001 (2016).
    [Crossref] [PubMed]
  24. Y. He, L. Huang, X. Hou, W. Fan, and R. Liang, “Modeling near-null testing method of a freeform surface with a deformable mirror compensator,” Appl. Opt. 56(33), 9132–9138 (2017).
    [Crossref] [PubMed]
  25. L. Zhang, S. Zhou, D. Li, Y. Liu, T. He, B. Yu, and J. Li, “Pure adaptive interferometer for free form surfaces metrology,” Opt. Express 26(7), 7888–7898 (2018).
    [Crossref] [PubMed]

2019 (1)

2018 (4)

2017 (3)

S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (2017).
[Crossref]

S. Lim, A. Sultan, M. Sulaiman, A. Mustapha, and K. Leong, “Crossover and mutation operators of genetic algorithms,” Int. J. Mach. Learn. Comput. 7(1), 9–12 (2017).
[Crossref]

Y. He, L. Huang, X. Hou, W. Fan, and R. Liang, “Modeling near-null testing method of a freeform surface with a deformable mirror compensator,” Appl. Opt. 56(33), 9132–9138 (2017).
[Crossref] [PubMed]

2016 (2)

2013 (2)

G. Xu, “An adaptive parameter tuning of particle swarm optimization algorithm,” Appl. Math. Comput. 219(9), 4560–4569 (2013).
[Crossref]

G. Berger and J. Petter, “Non-contact metrology of aspheric surfaces based on MWLI technology,” Proc. SPIE 8884, 88840V (2013).
[Crossref]

2011 (1)

2008 (1)

2005 (1)

M. Locatelli, “On the multilevel structure of global optimization problems,” Comput. Optim. Appl. 30(1), 5–22 (2005).
[Crossref]

1997 (1)

D. Wolpert and W. Macready, “No free lunch theorems for optimization,” IEEE Trans. Evol. Comput. 1(1), 67–82 (1997).
[Crossref]

1994 (1)

P.J. de Groot, “Long-wavelength laser diode interferometer for surface flatness measurement,” Proc. SPIE 2248, 136–140 (1994).
[Crossref]

1989 (1)

1987 (1)

1985 (1)

K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).

1976 (1)

Berger, G.

G. Berger and J. Petter, “Non-contact metrology of aspheric surfaces based on MWLI technology,” Proc. SPIE 8884, 88840V (2013).
[Crossref]

Chen, D.

Chen, M.

Chen, S.

Cheng, H.

Cheng, Y.

K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).

Choi, H.

Creath, K.

K. Creath, “Holographic contour and deformation measurement using a 1.4 million element detector array,” Appl. Opt. 28(11), 2170–2175 (1989).
[Crossref] [PubMed]

K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).

de Groot, P.J.

P.J. de Groot, “Long-wavelength laser diode interferometer for surface flatness measurement,” Proc. SPIE 2248, 136–140 (1994).
[Crossref]

Fan, W.

Fan, Z.

Garbusi, E.

Graves, L. R.

Greivenkamp, J. E.

Guo, H.

Hao, Q.

He, T.

He, Y.

Hou, X.

Hu, Y.

Huang, L.

Kim, D. W.

Leong, K.

S. Lim, A. Sultan, M. Sulaiman, A. Mustapha, and K. Leong, “Crossover and mutation operators of genetic algorithms,” Int. J. Mach. Learn. Comput. 7(1), 9–12 (2017).
[Crossref]

Li, D.

Li, J.

Li, T.

Liang, R.

Lim, S.

S. Lim, A. Sultan, M. Sulaiman, A. Mustapha, and K. Leong, “Crossover and mutation operators of genetic algorithms,” Int. J. Mach. Learn. Comput. 7(1), 9–12 (2017).
[Crossref]

Liu, Y.

Locatelli, M.

M. Locatelli, “On the multilevel structure of global optimization problems,” Comput. Optim. Appl. 30(1), 5–22 (2005).
[Crossref]

Macready, W.

D. Wolpert and W. Macready, “No free lunch theorems for optimization,” IEEE Trans. Evol. Comput. 1(1), 67–82 (1997).
[Crossref]

Mustapha, A.

S. Lim, A. Sultan, M. Sulaiman, A. Mustapha, and K. Leong, “Crossover and mutation operators of genetic algorithms,” Int. J. Mach. Learn. Comput. 7(1), 9–12 (2017).
[Crossref]

Noll, R.

Osten, W.

Peng, J.

Petter, J.

G. Berger and J. Petter, “Non-contact metrology of aspheric surfaces based on MWLI technology,” Proc. SPIE 8884, 88840V (2013).
[Crossref]

Pruss, C.

Shi, F.

S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (2017).
[Crossref]

Sulaiman, M.

S. Lim, A. Sultan, M. Sulaiman, A. Mustapha, and K. Leong, “Crossover and mutation operators of genetic algorithms,” Int. J. Mach. Learn. Comput. 7(1), 9–12 (2017).
[Crossref]

Sultan, A.

S. Lim, A. Sultan, M. Sulaiman, A. Mustapha, and K. Leong, “Crossover and mutation operators of genetic algorithms,” Int. J. Mach. Learn. Comput. 7(1), 9–12 (2017).
[Crossref]

Tian, C.

Tian, Y.

Tie, G.

Wang, S.

Wei, T.

Wolpert, D.

D. Wolpert and W. Macready, “No free lunch theorems for optimization,” IEEE Trans. Evol. Comput. 1(1), 67–82 (1997).
[Crossref]

Wyant, J.

K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).

Xu, G.

G. Xu, “An adaptive parameter tuning of particle swarm optimization algorithm,” Appl. Math. Comput. 219(9), 4560–4569 (2013).
[Crossref]

Xue, S.

Yang, Y.

Yu, B.

Yu, Y.

Zhai, D.

S. Xue, S. Chen, Z. Fan, and D. Zhai, “Adaptive wavefront interferometry for unknown free-form surfaces,” Opt. Express 26(17), 21910–21928 (2018).
[Crossref] [PubMed]

S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (2017).
[Crossref]

Zhang, L.

Zhao, W.

Zhong, J.

Zhou, S.

Zhuo, Y.

Appl. Math. Comput. (1)

G. Xu, “An adaptive parameter tuning of particle swarm optimization algorithm,” Appl. Math. Comput. 219(9), 4560–4569 (2013).
[Crossref]

Appl. Opt. (5)

Comput. Optim. Appl. (1)

M. Locatelli, “On the multilevel structure of global optimization problems,” Comput. Optim. Appl. 30(1), 5–22 (2005).
[Crossref]

IEEE Trans. Evol. Comput. (1)

D. Wolpert and W. Macready, “No free lunch theorems for optimization,” IEEE Trans. Evol. Comput. 1(1), 67–82 (1997).
[Crossref]

Int. J. Mach. Learn. Comput. (1)

S. Lim, A. Sultan, M. Sulaiman, A. Mustapha, and K. Leong, “Crossover and mutation operators of genetic algorithms,” Int. J. Mach. Learn. Comput. 7(1), 9–12 (2017).
[Crossref]

Int. J. Opt. (1)

K. Creath, Y. Cheng, and J. Wyant, “Contouring aspheric surfaces using two-wavelength phase-shifting interferometry,” Int. J. Opt. 32(12), 1455–1464 (1985).

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

S. Xue, S. Chen, D. Zhai, and F. Shi, “Quasi-absolute surface figure test with two orthogonal transverse spatial shifts,” Opt. Commun. 389, 133–143 (2017).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Proc. SPIE (2)

P.J. de Groot, “Long-wavelength laser diode interferometer for surface flatness measurement,” Proc. SPIE 2248, 136–140 (1994).
[Crossref]

G. Berger and J. Petter, “Non-contact metrology of aspheric surfaces based on MWLI technology,” Proc. SPIE 8884, 88840V (2013).
[Crossref]

Other (4)

D. Malacara, Optical Shop Testing (Wiley, 2007).

F. Shih, Image Processing and Mathematical Morphology: Fundamentals and Applications (CRC, 2009).

M. Locatelli and F. Schoen, Global Optimization - Theory, Algorithms, and Applications (SIAM, 2013).

S. Sivanandam and S. Deepa, Introduction to Genetic Algorithms (Springer, 2008).

Supplementary Material (6)

NameDescription
» Visualization 1       The interferogram containing invisible fringes keep nearly still from the beginning to the end in one simulation of adaptive wavefront interferometer.
» Visualization 2       Interferogram containing invisible fringes can be improved, however, the fringes can never be completely resolvable in one simulation of adaptive wavefront interferometer.
» Visualization 3       Objective function map
» Visualization 4       Typical search process of a MV-GA simulation trial in which fringes are completely restored
» Visualization 5       The typical evolution process of interferograms corresponding to the best individual of different generations in experiment of using MV-GA to control AWI.
» Visualization 6       The typical failed search process in an experiment of using SSD-SPGD to control AWI.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (17)

Fig. 1
Fig. 1 Principle of the SLM-based AWI for freeform surfaces with severe surface figure error.
Fig. 2
Fig. 2 Fringes evolution in one simulation that non-convergence issue appears. (a) beginning of the search, (b)-(g) during the search, (h) end of the search.
Fig. 3
Fig. 3 Fringes evolution in one simulation that local-convergence issue appears. (a) beginning of the search, (b)-(g) during the search, and (h) end of the search.
Fig. 4
Fig. 4 Variation of the objective function value with iteration number for the non-convergence and local-convergence issue.
Fig. 5
Fig. 5 Machine vision method to automatically segment the interferogram into resolvable fringes sub-region and unresolvable fringes sub-region. (a) A typical 8-bit interferogram during the search process. (b), (c), and (d) are the binary image which can distinguish the unresolvable fringes sub-region (black region) from the resolvable fringes sub-region (white region) after threshold segmentation, region filling operation, and opening operation, respectively.
Fig. 6
Fig. 6 Relation of wavefront error slope with the unresolvable fringes sub-region. (a) wavefront error, (b) pixels with wavefront slope larger than a half wave per pixel are identified, (c) and (d) are interferogram corresponding to (a).
Fig. 7
Fig. 7 Typical landscape of fpn(Z).
Fig. 8
Fig. 8 Flowchart of the control process of using GA in AWIs.
Fig. 9
Fig. 9 Flowchart of the control process of using MV-GA in AWIs.
Fig. 10
Fig. 10 The objective function values when search is finished for every trail of MV-GA and SSD-SPGD.
Fig. 11
Fig. 11 Variation of the mean value & standard derivation of the 500 trials’ objective function values with generation number for MV-GA method.
Fig. 12
Fig. 12 Variation of the mean value & standard derivation of the 500 trials’ objective function values with iteration number for SSD-SPGD method.
Fig. 13
Fig. 13 The initial fringes (a), restored fringes(p), and some fringes during the search process (b-o) captured from Visualization 3.
Fig. 14
Fig. 14 The experiment apparatus of the MV-GA controlled AWI.
Fig. 15
Fig. 15 The interferogram corresponds to the central Φ26mm circular region of the test surface.
Fig. 16
Fig. 16 Fringes evolution in one experiment using MV-GA. (a) beginning of the search, (b)-(g) during the search, and (h) end of the search.
Fig. 17
Fig. 17 The surface figure error measurement results by (a) MV-GA AWI, and (b) LuphoScan 260. (c) shows the point-to-point difference between (a) and (b).

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

min ZA f( Z ),
p t (i,j)={ 0 if p(i,j)< T gl ,and | grad p(i,j) |< T ggn 1 otherwise ,
A={ ( z 4 , z 5 , z 6 ,, z n )| z i ( B l , B u ),i=4,5,6,},
Z v t+1 =a Z w t +(1a) Z v t , Z w t+1 =a Z v t +(1a) Z w t ,
z k i t+1,v ={ z k i t,v +Δ(t, B u z k i t,v ) if a random digit is 0, z k i t,v Δ(t, z k i t,v B l ) if a random digit is 1,
Δ(t,y)=y(1 r (1 t T ) 2 ),
Z (k+1) = Z (k) +γδJδ Z (k) ,
δJ=J( Z (k) +δ Z (k) )J( Z (k) ),
J= all(i,j) ( g i g j ) 2 /2.

Metrics