Abstract

A stereovision-assisted sub-aperture stitching (SAS) approach is proposed to solve the positioning problem of tested optics. The principle of stitching is analyzed and the overlapping calculation problem is simplified. Then, a binocular stereovision system is integrated into a test configuration. By measuring the coordinates of marks attached to the fixture in different positions, the stereovision system obtains the position and pose data of the optics to provide the initial values for optimization algorithm. The key benefit of stereovision is that the SAS test is easily performed without a precision positioning system. A simulation and practical examples are given to demonstrate the performance of this method. The stitching result shows good agreement with the full-aperture result.

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  1. J. G. Thunen and O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1982).
  2. W. M. Cheng and M. Chen, “Transformation and connection of subapertures in the multiaperture overlap-scanning technique for large optics tests,” Opt. Eng. 32(8), 1947–1950 (1993).
    [CrossRef]
  3. P. Murphy, J. Fleig, and G. Forbes, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J1–10 (2006).
  4. M. Tricard, P. Dumas, and G. Forbes, “Sub-aperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. X. K. Wang, L. H. Wang, L. H. Yin, B. Z. Zhang, D. Fan, and X. J. Zhang, “Measurement of large aspheric surfaces by annular subaperture stitching interferometry,” Chin. Opt. Lett. 5, 645–647 (2007).
  10. F. Granados-Agust$ian, J. F. Escobar-Romero, and A. Cornejo-Rodr$iaguez, “Testing Parabolic Surfaces with Annular Subaperture Interferograms,” Opt. Rev. 11(2), 82–86 (2004).
    [CrossRef]
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    [CrossRef]
  12. J. J. Li, H. Zhao, Q. Fu, P. F. Zhang, and X. Zhou, “New 3D high-accuracy optical coordinates measuring technique based on an infrared target and binocular stereo vision,” Proc. SPIE 7389, 7389251 (2009).

2009 (1)

J. J. Li, H. Zhao, Q. Fu, P. F. Zhang, and X. Zhou, “New 3D high-accuracy optical coordinates measuring technique based on an infrared target and binocular stereo vision,” Proc. SPIE 7389, 7389251 (2009).

2008 (1)

2007 (2)

2006 (1)

2005 (1)

M. Tricard, P. Dumas, and G. Forbes, “Sub-aperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[CrossRef]

2004 (1)

F. Granados-Agust$ian, J. F. Escobar-Romero, and A. Cornejo-Rodr$iaguez, “Testing Parabolic Surfaces with Annular Subaperture Interferograms,” Opt. Rev. 11(2), 82–86 (2004).
[CrossRef]

2003 (1)

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and spherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

2002 (1)

M. Sjödahl and B. F. Oreb, “Stitching interferometric measurement data for inspection of large optical components,” Opt. Eng. 41(2), 403–408 (2002).
[CrossRef]

1993 (1)

W. M. Cheng and M. Chen, “Transformation and connection of subapertures in the multiaperture overlap-scanning technique for large optics tests,” Opt. Eng. 32(8), 1947–1950 (1993).
[CrossRef]

1982 (1)

J. G. Thunen and O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1982).

Chen, M.

W. M. Cheng and M. Chen, “Transformation and connection of subapertures in the multiaperture overlap-scanning technique for large optics tests,” Opt. Eng. 32(8), 1947–1950 (1993).
[CrossRef]

Chen, S. Y.

Cheng, W. M.

W. M. Cheng and M. Chen, “Transformation and connection of subapertures in the multiaperture overlap-scanning technique for large optics tests,” Opt. Eng. 32(8), 1947–1950 (1993).
[CrossRef]

Cornejo-Rodr$iaguez, A.

F. Granados-Agust$ian, J. F. Escobar-Romero, and A. Cornejo-Rodr$iaguez, “Testing Parabolic Surfaces with Annular Subaperture Interferograms,” Opt. Rev. 11(2), 82–86 (2004).
[CrossRef]

Dai, Y. F.

Ding, L. Y.

Dumas, P.

M. Tricard, P. Dumas, and G. Forbes, “Sub-aperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[CrossRef]

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and spherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Escobar-Romero, J. F.

F. Granados-Agust$ian, J. F. Escobar-Romero, and A. Cornejo-Rodr$iaguez, “Testing Parabolic Surfaces with Annular Subaperture Interferograms,” Opt. Rev. 11(2), 82–86 (2004).
[CrossRef]

Fan, D.

Fleig, J.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and spherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Forbes, G.

M. Tricard, P. Dumas, and G. Forbes, “Sub-aperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[CrossRef]

Forbes, G. W.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and spherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Fu, Q.

J. J. Li, H. Zhao, Q. Fu, P. F. Zhang, and X. Zhou, “New 3D high-accuracy optical coordinates measuring technique based on an infrared target and binocular stereo vision,” Proc. SPIE 7389, 7389251 (2009).

Granados-Agust$ian, F.

F. Granados-Agust$ian, J. F. Escobar-Romero, and A. Cornejo-Rodr$iaguez, “Testing Parabolic Surfaces with Annular Subaperture Interferograms,” Opt. Rev. 11(2), 82–86 (2004).
[CrossRef]

Kwon, O. Y.

J. G. Thunen and O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1982).

Li, J. J.

J. J. Li, H. Zhao, Q. Fu, P. F. Zhang, and X. Zhou, “New 3D high-accuracy optical coordinates measuring technique based on an infrared target and binocular stereo vision,” Proc. SPIE 7389, 7389251 (2009).

Li, S. Y.

Murphy, P. E.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and spherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Oreb, B. F.

M. Sjödahl and B. F. Oreb, “Stitching interferometric measurement data for inspection of large optical components,” Opt. Eng. 41(2), 403–408 (2002).
[CrossRef]

Sjödahl, M.

M. Sjödahl and B. F. Oreb, “Stitching interferometric measurement data for inspection of large optical components,” Opt. Eng. 41(2), 403–408 (2002).
[CrossRef]

Thunen, J. G.

J. G. Thunen and O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1982).

Tricard, M.

M. Tricard, P. Dumas, and G. Forbes, “Sub-aperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[CrossRef]

Wang, L. H.

Wang, X. K.

Yin, L. H.

Zeng, S. Y.

Zhang, B. Z.

Zhang, P. F.

J. J. Li, H. Zhao, Q. Fu, P. F. Zhang, and X. Zhou, “New 3D high-accuracy optical coordinates measuring technique based on an infrared target and binocular stereo vision,” Proc. SPIE 7389, 7389251 (2009).

Zhang, X. J.

Zhao, H.

J. J. Li, H. Zhao, Q. Fu, P. F. Zhang, and X. Zhou, “New 3D high-accuracy optical coordinates measuring technique based on an infrared target and binocular stereo vision,” Proc. SPIE 7389, 7389251 (2009).

Zheng, Z. W.

Zhou, X.

J. J. Li, H. Zhao, Q. Fu, P. F. Zhang, and X. Zhou, “New 3D high-accuracy optical coordinates measuring technique based on an infrared target and binocular stereo vision,” Proc. SPIE 7389, 7389251 (2009).

Appl. Opt. (1)

Chin. Opt. Lett. (1)

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

M. Sjödahl and B. F. Oreb, “Stitching interferometric measurement data for inspection of large optical components,” Opt. Eng. 41(2), 403–408 (2002).
[CrossRef]

W. M. Cheng and M. Chen, “Transformation and connection of subapertures in the multiaperture overlap-scanning technique for large optics tests,” Opt. Eng. 32(8), 1947–1950 (1993).
[CrossRef]

Opt. Express (1)

Opt. Rev. (1)

F. Granados-Agust$ian, J. F. Escobar-Romero, and A. Cornejo-Rodr$iaguez, “Testing Parabolic Surfaces with Annular Subaperture Interferograms,” Opt. Rev. 11(2), 82–86 (2004).
[CrossRef]

Proc. SPIE (4)

J. J. Li, H. Zhao, Q. Fu, P. F. Zhang, and X. Zhou, “New 3D high-accuracy optical coordinates measuring technique based on an infrared target and binocular stereo vision,” Proc. SPIE 7389, 7389251 (2009).

J. G. Thunen and O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1982).

M. Tricard, P. Dumas, and G. Forbes, “Sub-aperture approaches for asphere polishing and metrology,” Proc. SPIE 5638, 284–299 (2005).
[CrossRef]

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and spherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Other (1)

P. Murphy, J. Fleig, and G. Forbes, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J1–10 (2006).

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Figures (8)

Fig. 1
Fig. 1

Principles of the SAS test. (a) sketch of the SAS test (top view); (b) the i-th sub-aperture in the global coordinate.

Fig. 2
Fig. 2

The overlapping calculation problem. (a) sketch of the projection on the X-Y plane; (b) sketch of the projection on the X-Z plane

Fig. 3
Fig. 3

Sketch of the stereovision system. (a) the relationship between the stereovision and global coordinate systems; (b) marked positions on the workstation.

Fig. 4
Fig. 4

The residual error map of the stitching result in two situations. (a) lattice; (b) without the stereovision system; (c) with the stereovision system.

Fig. 5
Fig. 5

Experimental setup. (a) the SAS test; (b) the electronic control platform.

Fig. 6
Fig. 6

The performance of the stereovision system. (a) errors in distance measurements (absolute max value 0.0701 mm); (b) errors in angle measurements (absolute max value 0.0371 degree).

Fig. 7
Fig. 7

Sphere test. (a) lattice; (b) stitching result without stereovision; (c) stitching result with stereovision (PV = 0.1091 wave, RMS = 0.0166 wave).

Fig. 8
Fig. 8

Cross-test. (a) full-aperture result (PV = 0.114wave, RMS = 0.017wave); (b) residual error (PV = 0.0478wave, RMS = 0.00825wave) (wave = 632.8nm).

Equations (5)

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[ X , Y , Z , 1 ] T = g i [ x , y , z , 1 ] T .
[ x , y , z ] = [ ( r b s + φ ) k u , ( r b s + φ ) k v , r t s ( r b s + φ ) 1 k 2 ( u 2 + v 2 ) ] ,
e r r o r i , j ( k ) = Z i , k Z j , k ,
min F = u 1 σ 2 + u 2 σ 0 2 ,
σ 0 2 = k = 1 N [ ( Z i , k Z 0 , k ) 2 + ( Z j , k Z 0 , k ) 2 ] / ( 2 N ) ,

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