Abstract

The primary problem of conventional wavefront interferometers is limited dynamic range. Unknown free-form surface figure error with large amplitude or slope is not measurable for too dense or invisible fringes. To troubleshoot this problem, we propose adaptive wavefront interferometry (AWI). AWI utilizes a wavefront sensor-less adaptive optics (AO) subsystem to intelligently speculate and compensate the unknown free-form surface figure error. In this subsystem, adaptive null optics is utilized to iteratively generate adaptive wavefronts to compensate the unknown severe surface figure error. The adaptive null optics is close-loop controlled (i.e., wavefront sensor-less optimization algorithms are utilized to control it by real time monitoring the compensation effects to guarantee convergence of the iteration). Ultimately, invisible fringes turn into resolvable ones, and null test is further realized. To demonstrate the feasibility of AWI, we designed one spatial light modulator (SLM) based AWI modality as an example. The system is based on a commercial interferometer and is easy to establish. No other elements are required besides the SLM. Principle, simulation, and experiments for the SLM based AWI are demonstrated.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (1)

2017 (5)

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]

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[Crossref]

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[Crossref]

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[Crossref] [PubMed]

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[Crossref]

2016 (3)

2015 (1)

2014 (5)

2013 (2)

J. Zhu, T. Yang, and G. Jin, “Design method of surface contour for a freeform lens with wide linear field-of-view,” Opt. Express 21(22), 26080–26092 (2013).
[Crossref] [PubMed]

G. Tie, Y. Dai, C. Guan, S. Chen, and B. Song, “Research on subsurface defects of potassium dihydrogen phosphate crystals fabricated by single point diamond turning technique,” Opt. Eng. 52(3), 033401 (2013).
[Crossref]

2011 (1)

H. Yang and X. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43(3), 630–635 (2011).
[Crossref]

2010 (2)

M. Ares, S. Royo, I. Sergievskaya, and J. Riu, “Active optics null test system based on a liquid crystal programmable spatial light modulator,” Appl. Opt. 49(32), 6201–6206 (2010).
[Crossref] [PubMed]

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

2009 (2)

2008 (1)

2007 (2)

2006 (1)

2005 (1)

2004 (2)

2003 (1)

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

2002 (1)

2000 (1)

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).

1979 (1)

1970 (1)

Ares, M.

Bai, Y.

L. Zhang, D. Li, Y. Liu, Y. Bai, J. Li, and B. Yu, “Flexible interferometry for optical aspheric and free form surfaces,” Opt. Rev. 24(6), 677–685 (2017).
[Crossref]

Bauer, M.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Beverage, J.

Booth, M.

M. Booth, “Adaptive optical microscopy: the ongoing quest for a perfect image,” Light Sci. Appl. 3(4), e165 (2014).
[Crossref]

Booth, M. J.

Cao, Z.

Carhart, G. W.

Cashmore, M. T.

Cauwenberghs, G.

Chen, Q.

Chen, S.

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of large steep convex spheres,” Opt. Express 23(22), 29047–29058 (2015).
[Crossref] [PubMed]

S. Chen, C. Zhao, Y. Dai, and S. Li, “Reconfigurable optical null based on counter-rotating Zernike plates for test of aspheres,” Opt. Express 22(2), 1381–1386 (2014).
[Crossref] [PubMed]

G. Tie, Y. Dai, C. Guan, S. Chen, and B. Song, “Research on subsurface defects of potassium dihydrogen phosphate crystals fabricated by single point diamond turning technique,” Opt. Eng. 52(3), 033401 (2013).
[Crossref]

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.

Chong, S.

Cohen, M.

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).

Dai, Y.

de Groot, P. J.

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

DeVries, G.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Du, H.

Dumas, P.

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Fan, W.

Fleig, J.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Forbes, G.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Fuerschbach, K.

Gao, B.

Gao, F.

Gappinger, R. O.

Garbusi, E.

Gong, C.

Graves, L. R.

Greivenkamp, J. E.

Guan, C.

G. Tie, Y. Dai, C. Guan, S. Chen, and B. Song, “Research on subsurface defects of potassium dihydrogen phosphate crystals fabricated by single point diamond turning technique,” Opt. Eng. 52(3), 033401 (2013).
[Crossref]

Hall, S. R.

He, T.

He, Y.

Hilbert, R. S.

Hou, X.

Hu, H.

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

Hu, L.

Huang, L.

Idir, M.

Jiang, W.

Jiang, X.

Jin, G.

Kacperski, J.

Kim, D. W.

Kujawinska, M.

Kulawiec, A.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Li, D.

Li, J.

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]

L. Zhang, D. Li, Y. Liu, Y. Bai, J. Li, and B. Yu, “Flexible interferometry for optical aspheric and free form surfaces,” Opt. Rev. 24(6), 677–685 (2017).
[Crossref]

Li, S.

Li, X.

H. Yang and X. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43(3), 630–635 (2011).
[Crossref]

H. Yang, X. Li, C. Gong, and W. Jiang, “Restoration of turbulence-degraded extended object using the stochastic parallel gradient descent algorithm: numerical simulation,” Opt. Express 17(5), 3052–3062 (2009).
[Crossref] [PubMed]

Liang, R.

Liu, D.

Liu, Y.

Love, G. D.

Lu, J.

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

Luo, Y.

McPherson, C.

Miladinovich, D.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

Mu, Q.

Murphy, P.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Osten, W.

Peng, X.

Pruss, C.

E. Garbusi, C. Pruss, and W. Osten, “Interferometer for precise and flexible asphere testing,” Opt. Lett. 33(24), 2973–2975 (2008).
[Crossref] [PubMed]

C. Pruss and H. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233(1), 1–3 (2004).
[Crossref]

Ren, H.

Rimmer, M. P.

Riu, J.

Rolland, J. P.

Royo, S.

Sergievskaya, I.

Shafer, D. R.

Shen, Y.

Shi, T.

Song, B.

G. Tie, Y. Dai, C. Guan, S. Chen, and B. Song, “Research on subsurface defects of potassium dihydrogen phosphate crystals fabricated by single point diamond turning technique,” Opt. Eng. 52(3), 033401 (2013).
[Crossref]

Song, C.

Thompson, K. P.

Tian, C.

Tian, Y.

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

Tie, G.

G. Tie, Y. Dai, C. Guan, S. Chen, and B. Song, “Research on subsurface defects of potassium dihydrogen phosphate crystals fabricated by single point diamond turning technique,” Opt. Eng. 52(3), 033401 (2013).
[Crossref]

Tiziani, H.

C. Pruss and H. Tiziani, “Dynamic null lens for aspheric testing using a membrane mirror,” Opt. Commun. 233(1), 1–3 (2004).
[Crossref]

Tricard, M.

M. Tricard, A. Kulawiec, M. Bauer, G. DeVries, J. Fleig, G. Forbes, D. Miladinovich, and P. Murphy, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Ann. 59(1), 547–550 (2010).
[Crossref]

P. Murphy, G. Forbes, J. Fleig, P. Dumas, and M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14(5), 38–43 (2003).
[Crossref]

Vorontsov, M. A.

Wang, L.

Wu, F.

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, M.

Xuan, L.

Xue, J.

Xue, S.

S. Xue, S. Chen, Y. Tian, J. Lu, and H. Hu, “Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors,” Measurement 106, 79–87 (2017).
[Crossref]

S. Chen, S. Xue, Y. Dai, and S. Li, “Subaperture stitching test of large steep convex spheres,” Opt. Express 23(22), 29047–29058 (2015).
[Crossref] [PubMed]

Yang, H.

H. Yang and X. Li, “Comparison of several stochastic parallel optimization algorithms for adaptive optics system without a wavefront sensor,” Opt. Laser Technol. 43(3), 630–635 (2011).
[Crossref]

H. Yang, X. Li, C. Gong, and W. Jiang, “Restoration of turbulence-degraded extended object using the stochastic parallel gradient descent algorithm: numerical simulation,” Opt. Express 17(5), 3052–3062 (2009).
[Crossref] [PubMed]

Yang, L.

Yang, T.

Yang, Y.

Yu, B.

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]

L. Zhang, D. Li, Y. Liu, Y. Bai, J. Li, and B. Yu, “Flexible interferometry for optical aspheric and free form surfaces,” Opt. Rev. 24(6), 677–685 (2017).
[Crossref]

Zhang, L.

Zhao, C.

Zhao, W.

Zhou, S.

Zhu, J.

Appl. Opt. (11)

J. E. Greivenkamp, “Sub-Nyquist interferometry,” Appl. Opt. 26(24), 5245–5258 (1987).
[Crossref] [PubMed]

H. Du, C. Song, S. Li, M. Xu, and X. Peng, “Optimization technique for rolled edge control process based on the acentric tool influence functions,” Appl. Opt. 56(15), 4330–4337 (2017).
[Crossref] [PubMed]

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

R. S. Hilbert and M. P. Rimmer, “A variable refractive null lens,” Appl. Opt. 9(4), 849–852 (1970).
[Crossref] [PubMed]

D. R. Shafer, “Zoom null lens,” Appl. Opt. 18(22), 3863–3865 (1979).
[Crossref] [PubMed]

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]

M. T. Cashmore, S. R. Hall, and G. D. Love, “Traceable interferometry using binary reconfigurable holograms,” Appl. Opt. 53(24), 5353–5358 (2014).
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Supplementary Material (2)

NameDescription
» Visualization 1       This video shows the full process in the simulation to turn invisible fringes to resolvable fringes utilizing AWI.
» Visualization 2       This video shows the full process in the experiment to turn invisible fringes to resolvable fringes utilizing AWI.

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Figures (15)

Fig. 1
Fig. 1 Illustration of the SLM-based AWI for freeform surfaces with severe surface figure error. (a) The conventional test of a freeform surface utilizing a static null. (b) The full aperture interferogram of which the upper region cannot be resolved by the interferometer. (c) The surface figure error map of which the upper region is not available. (d) The SLM-based AWI for testing unknown severe local surface figure error. (e) The initial interferogram of the local region. (f) The final interferogram of the local region nulled by the SLM. (g) The surface figure error of the local region. (h) Full aperture surface figure error map stitching result.
Fig. 2
Fig. 2 Principle of encoding aberration based on optical hologram.
Fig. 3
Fig. 3 Flowchart of the SLM-based AWI.
Fig. 4
Fig. 4 Interferograms of the unknown large local surface figure error region within the work region of the SLM at the three steps of adaptive null algorithm. (a) The initial interferogram before fringes restoration step. (b) The interferogram after fringes restoration step. (c) The interferogram after dense fringes relaxation step. (d) The interferogram after phase conjugation algorithm.
Fig. 5
Fig. 5 Simulation conditions. (a) The simulated test wavefront reflected from the large figure error local region of the full aperture test surface and transmits through the static null. (b) The corresponding interferogram generated by Zemax. (c) The modified interferogram which simulates the practical interferogram acquired by the interferometer.
Fig. 6
Fig. 6 Interferograms during the fringe restoration optimization. (a)−(c) The fringes that have not been restored completely. (d) The fringes that have been restored completely.
Fig. 7
Fig. 7 Interferograms during the fringe relaxation optimization (see Visualization 1). (a)−(c) The fringes that have not been relaxed completely. (d) The final interferogram after fringe relaxation.
Fig. 8
Fig. 8 SLM-based AWI experiment setup to test a Φ61mm flat mirror with unknown severe local surface figure error.
Fig. 9
Fig. 9 Measurement results of WFD of SLM. (a) Interferogram of WFD of SLM, where the green dot-dash circle stands for the usually used apertures, with size of Φ26mm. (b) WFD map of SLM within the circular aperture.
Fig. 10
Fig. 10 Interference type CGH image encoding WFD phase with tilt carrier.
Fig. 11
Fig. 11 Measurement results after self-compensating WFD of SLM. (a) Interferogram of full aperture after self-compensating. (b) Residual error within the circular aperture after self-compensating.
Fig. 12
Fig. 12 Test results of measuring the test surface with interferometer directly. (a) Interferogram. (b) Corresponding surface figure error map.
Fig. 13
Fig. 13 Interferograms during SLM-based AWI test (see Visualization 2). (a) At initial. (b) After fringes restoration step. (c) After fringes relaxation step. (d) After phase conjugation step.
Fig. 14
Fig. 14 Test results by SLM-based AWI and on machine measurement. (a) The central Φ26mm circular local region surface figure error obtained by AWI. (b) Full aperture surface figure error obtained by AWI. (c) Full aperture surface figure error obtained by on machine measurement. (d) Difference map between the two test results.
Fig. 15
Fig. 15 On machine measurement based on an ultra-precision lathe.

Equations (13)

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z j,i = φ j,i + a i + b i u j,i + c i v j,i + s i φ j,i u j,i + t i φ j,i v j,i + δ i [ u j,i φ j,i v j,i v j,i φ j,i u j,i ], z j,k = φ j,k + a k + b k u j,k + c i v j,k + s k φ j,k u j,k + t k φ j,k v j,k + δ k [ u j,k φ j,k v j,k v j,k φ j,k u j,k ],
minF= jo=1 No ( z jo,i z jo,k ) 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.
J= J 1 + J 2 + J 3 = i A r ( 0 ) ,j A r ( 0 ) ( g i g j ) 2 /2+ i A n ( 0 ) ,j A n ( 0 ) ( g i g j ) 2 /2 + i A r ( 0 ) ,j A n ( 0 ) ( g i g j ) 2 .
J 1 = C M r ( 0 ) 2 E( Z 2 ),
J 3 = C M r ( 0 ) 1 C M n ( 0 ) 1 E( X 2 ),
J M r ( 0 ) ( 3 M r (0) 4 M (0) )/12.
J= i A (0) ( g i x ) 2 + ( g i y ) 2 .
W r3f =f( W uf , λФ/2π) ,
W ¯ r3f =f( W ¯ uf ,λ Ф ¯ /2π),
W u = W ¯ uf + W r3r .

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