Abstract

A novel iterative algorithm for subaperture stitching interferometry for general surfaces is presented. It is based on the alternating optimization technique and the successive linearization method. The computer-aided-design model of the tested surface is used to determine the overlapping region precisely. Subapertures are simultaneously stitched by minimizing deviations among them as well as deviations from the nominal surface. Precise prior knowledge of the six degrees-of-freedom nulling and alignment motion is no longer required.

© 2005 Optical Society of America

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  1. C. Kim, J. Wyant, “Subaperture test of a large flat or a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981).
  2. J. G. Thunen, O. Y. Kwon, “Full aperture testing with subaperture test optics,” Proc. SPIE 351, 19–27 (1982).
    [CrossRef]
  3. W. W. Chow, G. N. Lawrence, “Method for subaperture testing interferogram reduction,” Opt. Lett. 8, 468–470 (1983).
    [CrossRef] [PubMed]
  4. S. C. Jensen, W. W. Chow, G. N. Lawrence, “Subaperture testing approaches: a comparison,” Appl. Opt. 23, 740–745 (1984).
    [CrossRef] [PubMed]
  5. T. W. Stuhlinger, “Subaperture optical testing: experimental verification,” Proc. SPIE 656, 118–127 (1986).
    [CrossRef]
  6. M. Y. Chen, W. M. Cheng, C. W. Wang, “Multiaperture overlap-scanning technique for large-aperture test,” Proc. SPIE 1553, 626–635 (1991).
    [CrossRef]
  7. W. M. Cheng, M. Y. Chen, “Transformation and connection of subapertures in the multiaperture overlap-scanning technique for large optics tests,” Opt. Eng. (Bellingham) 32, 1947–1950 (1993).
    [CrossRef]
  8. W. M. Cheng, Y. L. Lin, M. Y. Chen, “Accuracy analysis of multiaperture overlap-scanning technique (MAOST),” Proc. SPIE 2003, 283–288 (1993).
    [CrossRef]
  9. M. Otsubo, K. Okada, J. Tsujiuchi, “Measurement of large plane surface shape with interferometric aperture synthesis,” Proc. SPIE 1720, 444–447 (1992).
    [CrossRef]
  10. M. Otsubo, K. Okada, J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. (Bellingham) 33, 608–613 (1994).
    [CrossRef]
  11. M. Y. Chen, D. Z. Wu, “Multiaperture overlap-scanning technique for moire metrology,” Proc. SPIE 2861, 107–112 (1996).
    [CrossRef]
  12. M. Bray, “Stitching interferometer for large plano optics using a standard interferometer,” Proc. SPIE 3134, 39–50 (1997).
    [CrossRef]
  13. S. H. Tang, “Stitching: high-spatial-resolution microsurface measurements over large areas,” Proc. SPIE 3479, 43–49 (1998).
    [CrossRef]
  14. J. C. Wyant, J. Schmit, “Large field of view, high spatial resolution, surface measurements,” Int. J. Mach. Tools Manuf. 38, 691–698 (1998).
    [CrossRef]
  15. M. A. Schmucker, J. Schmit, “Selection process for sequentially combining multiple sets of overlapping surface profile interferometric data to produce a continuous composite map,” U.S. patent 5,991,461 (November 23, 1999).
  16. M. Bray, “Stitching interferometer for large optics: recent developments of a system,” Proc. SPIE 3492, 946–955 (1999).
    [CrossRef]
  17. M. Bray, “Stitching interferometry and absolute surface shape metrology: similarities,” Proc. SPIE 4501, 375–383 (2001).
    [CrossRef]
  18. M. Sjöedahl, B. F. Oreb, “Stitching interferometric measurement data for inspection of large optical components,” Opt. Eng. (Bellingham) 41, 403–408 (2002).
    [CrossRef]
  19. L. Assoufid, M. Bray, J. Qian, D. M. Shu, “3-D surface profile measurements of large x-ray synchrotron radiation mirrors using stitching interferometry,” Proc. SPIE 4782, 21–28 (2002).
    [CrossRef]
  20. Y. J. Yu, M. Y. Chen, “Correlative stitching interferometer and its key techniques,” Proc. SPIE 4777, 382–393 (2002).
    [CrossRef]
  21. M. Y. Chen, H. W. Guo, Y. J. Yu, H. T. He, “Recent developments of multi-aperture overlap-scanning technique,” Proc. SPIE 5180, 393–401 (2003).
    [CrossRef]
  22. P. Murphy, G. Forbes, J. Fleig, P. Dumas, M. Tricard, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14, May 2003, pp. 38–43.
    [CrossRef]
  23. J. Fleig, P. Dumas, P. E. Murphy, G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
    [CrossRef]
  24. H. T. He, H. W. Guo, Y. J. Yu, M. Y. Chen, “Novel connection method based on virtual cylinder for three-dimensional surface measurement,” Acta Opt. Sin. 24, 978–982 (2004) (in Chinese).
  25. M. Bray, “Stitching interferometry: recent results and absolute calibration,” Proc. SPIE 5252, 305–313 (2004).
    [CrossRef]
  26. R. D. Day, T. A. Beery, G. N. Lawrence, “Sphericity measurements of full spheres using subaperture optical testing techniques,” Proc. SPIE 661, 334–341 (1986).
    [CrossRef]
  27. G. N. Lawrence, R. D. Day, “Interferometric characterization of full spheres: data reduction techniques,” Appl. Opt. 26, 4875–4882 (1987).
    [CrossRef] [PubMed]
  28. Y. M. Liu, G. N. Lawrence, C. L. Koliopoulo, “Subaperture testing of aspheres with annular zones,” Appl. Opt. 27, 4504–4513 (1988).
    [CrossRef] [PubMed]
  29. M. J. Tronolone, J. F. Fleig, C. S. Huang, J. H. Bruning, “Method of testing aspherical optical surfaces with an interferometer,” U.S. patent 5,416,586 (May 16, 1995).
  30. R. Murray, Z. X. Li, S. S. Sastry, A Mathematical Introduction to Robotics Manipulation (CRC Press, 1994).
  31. Z. X. Li, J. B. Gou, Y. X. Chu, “Geometric algorithm for workpiece localization,” IEEE Trans. Rob. Autom. 14, 864–878 (1998).
    [CrossRef]
  32. G. H. Gloub, C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996), Section 12.1.

2004

H. T. He, H. W. Guo, Y. J. Yu, M. Y. Chen, “Novel connection method based on virtual cylinder for three-dimensional surface measurement,” Acta Opt. Sin. 24, 978–982 (2004) (in Chinese).

M. Bray, “Stitching interferometry: recent results and absolute calibration,” Proc. SPIE 5252, 305–313 (2004).
[CrossRef]

2003

M. Y. Chen, H. W. Guo, Y. J. Yu, H. T. He, “Recent developments of multi-aperture overlap-scanning technique,” Proc. SPIE 5180, 393–401 (2003).
[CrossRef]

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

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

2002

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

L. Assoufid, M. Bray, J. Qian, D. M. Shu, “3-D surface profile measurements of large x-ray synchrotron radiation mirrors using stitching interferometry,” Proc. SPIE 4782, 21–28 (2002).
[CrossRef]

Y. J. Yu, M. Y. Chen, “Correlative stitching interferometer and its key techniques,” Proc. SPIE 4777, 382–393 (2002).
[CrossRef]

2001

M. Bray, “Stitching interferometry and absolute surface shape metrology: similarities,” Proc. SPIE 4501, 375–383 (2001).
[CrossRef]

1999

M. Bray, “Stitching interferometer for large optics: recent developments of a system,” Proc. SPIE 3492, 946–955 (1999).
[CrossRef]

1998

S. H. Tang, “Stitching: high-spatial-resolution microsurface measurements over large areas,” Proc. SPIE 3479, 43–49 (1998).
[CrossRef]

J. C. Wyant, J. Schmit, “Large field of view, high spatial resolution, surface measurements,” Int. J. Mach. Tools Manuf. 38, 691–698 (1998).
[CrossRef]

Z. X. Li, J. B. Gou, Y. X. Chu, “Geometric algorithm for workpiece localization,” IEEE Trans. Rob. Autom. 14, 864–878 (1998).
[CrossRef]

1997

M. Bray, “Stitching interferometer for large plano optics using a standard interferometer,” Proc. SPIE 3134, 39–50 (1997).
[CrossRef]

1996

M. Y. Chen, D. Z. Wu, “Multiaperture overlap-scanning technique for moire metrology,” Proc. SPIE 2861, 107–112 (1996).
[CrossRef]

1994

M. Otsubo, K. Okada, J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. (Bellingham) 33, 608–613 (1994).
[CrossRef]

1993

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

W. M. Cheng, Y. L. Lin, M. Y. Chen, “Accuracy analysis of multiaperture overlap-scanning technique (MAOST),” Proc. SPIE 2003, 283–288 (1993).
[CrossRef]

1992

M. Otsubo, K. Okada, J. Tsujiuchi, “Measurement of large plane surface shape with interferometric aperture synthesis,” Proc. SPIE 1720, 444–447 (1992).
[CrossRef]

1991

M. Y. Chen, W. M. Cheng, C. W. Wang, “Multiaperture overlap-scanning technique for large-aperture test,” Proc. SPIE 1553, 626–635 (1991).
[CrossRef]

1988

1987

1986

T. W. Stuhlinger, “Subaperture optical testing: experimental verification,” Proc. SPIE 656, 118–127 (1986).
[CrossRef]

R. D. Day, T. A. Beery, G. N. Lawrence, “Sphericity measurements of full spheres using subaperture optical testing techniques,” Proc. SPIE 661, 334–341 (1986).
[CrossRef]

1984

1983

1982

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

1981

C. Kim, J. Wyant, “Subaperture test of a large flat or a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981).

Assoufid, L.

L. Assoufid, M. Bray, J. Qian, D. M. Shu, “3-D surface profile measurements of large x-ray synchrotron radiation mirrors using stitching interferometry,” Proc. SPIE 4782, 21–28 (2002).
[CrossRef]

Beery, T. A.

R. D. Day, T. A. Beery, G. N. Lawrence, “Sphericity measurements of full spheres using subaperture optical testing techniques,” Proc. SPIE 661, 334–341 (1986).
[CrossRef]

Bray, M.

M. Bray, “Stitching interferometry: recent results and absolute calibration,” Proc. SPIE 5252, 305–313 (2004).
[CrossRef]

L. Assoufid, M. Bray, J. Qian, D. M. Shu, “3-D surface profile measurements of large x-ray synchrotron radiation mirrors using stitching interferometry,” Proc. SPIE 4782, 21–28 (2002).
[CrossRef]

M. Bray, “Stitching interferometry and absolute surface shape metrology: similarities,” Proc. SPIE 4501, 375–383 (2001).
[CrossRef]

M. Bray, “Stitching interferometer for large optics: recent developments of a system,” Proc. SPIE 3492, 946–955 (1999).
[CrossRef]

M. Bray, “Stitching interferometer for large plano optics using a standard interferometer,” Proc. SPIE 3134, 39–50 (1997).
[CrossRef]

Bruning, J. H.

M. J. Tronolone, J. F. Fleig, C. S. Huang, J. H. Bruning, “Method of testing aspherical optical surfaces with an interferometer,” U.S. patent 5,416,586 (May 16, 1995).

Chen, M. Y.

H. T. He, H. W. Guo, Y. J. Yu, M. Y. Chen, “Novel connection method based on virtual cylinder for three-dimensional surface measurement,” Acta Opt. Sin. 24, 978–982 (2004) (in Chinese).

M. Y. Chen, H. W. Guo, Y. J. Yu, H. T. He, “Recent developments of multi-aperture overlap-scanning technique,” Proc. SPIE 5180, 393–401 (2003).
[CrossRef]

Y. J. Yu, M. Y. Chen, “Correlative stitching interferometer and its key techniques,” Proc. SPIE 4777, 382–393 (2002).
[CrossRef]

M. Y. Chen, D. Z. Wu, “Multiaperture overlap-scanning technique for moire metrology,” Proc. SPIE 2861, 107–112 (1996).
[CrossRef]

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

W. M. Cheng, Y. L. Lin, M. Y. Chen, “Accuracy analysis of multiaperture overlap-scanning technique (MAOST),” Proc. SPIE 2003, 283–288 (1993).
[CrossRef]

M. Y. Chen, W. M. Cheng, C. W. Wang, “Multiaperture overlap-scanning technique for large-aperture test,” Proc. SPIE 1553, 626–635 (1991).
[CrossRef]

Cheng, W. M.

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

W. M. Cheng, Y. L. Lin, M. Y. Chen, “Accuracy analysis of multiaperture overlap-scanning technique (MAOST),” Proc. SPIE 2003, 283–288 (1993).
[CrossRef]

M. Y. Chen, W. M. Cheng, C. W. Wang, “Multiaperture overlap-scanning technique for large-aperture test,” Proc. SPIE 1553, 626–635 (1991).
[CrossRef]

Chow, W. W.

Chu, Y. X.

Z. X. Li, J. B. Gou, Y. X. Chu, “Geometric algorithm for workpiece localization,” IEEE Trans. Rob. Autom. 14, 864–878 (1998).
[CrossRef]

Day, R. D.

G. N. Lawrence, R. D. Day, “Interferometric characterization of full spheres: data reduction techniques,” Appl. Opt. 26, 4875–4882 (1987).
[CrossRef] [PubMed]

R. D. Day, T. A. Beery, G. N. Lawrence, “Sphericity measurements of full spheres using subaperture optical testing techniques,” Proc. SPIE 661, 334–341 (1986).
[CrossRef]

Dumas, P.

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

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

Fleig, J.

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

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

Fleig, J. F.

M. J. Tronolone, J. F. Fleig, C. S. Huang, J. H. Bruning, “Method of testing aspherical optical surfaces with an interferometer,” U.S. patent 5,416,586 (May 16, 1995).

Forbes, G.

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

Forbes, G. W.

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

Gloub, G. H.

G. H. Gloub, C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996), Section 12.1.

Gou, J. B.

Z. X. Li, J. B. Gou, Y. X. Chu, “Geometric algorithm for workpiece localization,” IEEE Trans. Rob. Autom. 14, 864–878 (1998).
[CrossRef]

Guo, H. W.

H. T. He, H. W. Guo, Y. J. Yu, M. Y. Chen, “Novel connection method based on virtual cylinder for three-dimensional surface measurement,” Acta Opt. Sin. 24, 978–982 (2004) (in Chinese).

M. Y. Chen, H. W. Guo, Y. J. Yu, H. T. He, “Recent developments of multi-aperture overlap-scanning technique,” Proc. SPIE 5180, 393–401 (2003).
[CrossRef]

He, H. T.

H. T. He, H. W. Guo, Y. J. Yu, M. Y. Chen, “Novel connection method based on virtual cylinder for three-dimensional surface measurement,” Acta Opt. Sin. 24, 978–982 (2004) (in Chinese).

M. Y. Chen, H. W. Guo, Y. J. Yu, H. T. He, “Recent developments of multi-aperture overlap-scanning technique,” Proc. SPIE 5180, 393–401 (2003).
[CrossRef]

Huang, C. S.

M. J. Tronolone, J. F. Fleig, C. S. Huang, J. H. Bruning, “Method of testing aspherical optical surfaces with an interferometer,” U.S. patent 5,416,586 (May 16, 1995).

Jensen, S. C.

Kim, C.

C. Kim, J. Wyant, “Subaperture test of a large flat or a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981).

Koliopoulo, C. L.

Kwon, O. Y.

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

Lawrence, G. N.

Li, Z. X.

Z. X. Li, J. B. Gou, Y. X. Chu, “Geometric algorithm for workpiece localization,” IEEE Trans. Rob. Autom. 14, 864–878 (1998).
[CrossRef]

R. Murray, Z. X. Li, S. S. Sastry, A Mathematical Introduction to Robotics Manipulation (CRC Press, 1994).

Lin, Y. L.

W. M. Cheng, Y. L. Lin, M. Y. Chen, “Accuracy analysis of multiaperture overlap-scanning technique (MAOST),” Proc. SPIE 2003, 283–288 (1993).
[CrossRef]

Liu, Y. M.

Murphy, P.

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

Murphy, P. E.

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

Murray, R.

R. Murray, Z. X. Li, S. S. Sastry, A Mathematical Introduction to Robotics Manipulation (CRC Press, 1994).

Okada, K.

M. Otsubo, K. Okada, J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. (Bellingham) 33, 608–613 (1994).
[CrossRef]

M. Otsubo, K. Okada, J. Tsujiuchi, “Measurement of large plane surface shape with interferometric aperture synthesis,” Proc. SPIE 1720, 444–447 (1992).
[CrossRef]

Oreb, B. F.

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

Otsubo, M.

M. Otsubo, K. Okada, J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. (Bellingham) 33, 608–613 (1994).
[CrossRef]

M. Otsubo, K. Okada, J. Tsujiuchi, “Measurement of large plane surface shape with interferometric aperture synthesis,” Proc. SPIE 1720, 444–447 (1992).
[CrossRef]

Qian, J.

L. Assoufid, M. Bray, J. Qian, D. M. Shu, “3-D surface profile measurements of large x-ray synchrotron radiation mirrors using stitching interferometry,” Proc. SPIE 4782, 21–28 (2002).
[CrossRef]

Sastry, S. S.

R. Murray, Z. X. Li, S. S. Sastry, A Mathematical Introduction to Robotics Manipulation (CRC Press, 1994).

Schmit, J.

J. C. Wyant, J. Schmit, “Large field of view, high spatial resolution, surface measurements,” Int. J. Mach. Tools Manuf. 38, 691–698 (1998).
[CrossRef]

M. A. Schmucker, J. Schmit, “Selection process for sequentially combining multiple sets of overlapping surface profile interferometric data to produce a continuous composite map,” U.S. patent 5,991,461 (November 23, 1999).

Schmucker, M. A.

M. A. Schmucker, J. Schmit, “Selection process for sequentially combining multiple sets of overlapping surface profile interferometric data to produce a continuous composite map,” U.S. patent 5,991,461 (November 23, 1999).

Shu, D. M.

L. Assoufid, M. Bray, J. Qian, D. M. Shu, “3-D surface profile measurements of large x-ray synchrotron radiation mirrors using stitching interferometry,” Proc. SPIE 4782, 21–28 (2002).
[CrossRef]

Sjöedahl, M.

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

Stuhlinger, T. W.

T. W. Stuhlinger, “Subaperture optical testing: experimental verification,” Proc. SPIE 656, 118–127 (1986).
[CrossRef]

Tang, S. H.

S. H. Tang, “Stitching: high-spatial-resolution microsurface measurements over large areas,” Proc. SPIE 3479, 43–49 (1998).
[CrossRef]

Thunen, J. G.

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

Tricard, M.

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

Tronolone, M. J.

M. J. Tronolone, J. F. Fleig, C. S. Huang, J. H. Bruning, “Method of testing aspherical optical surfaces with an interferometer,” U.S. patent 5,416,586 (May 16, 1995).

Tsujiuchi, J.

M. Otsubo, K. Okada, J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. (Bellingham) 33, 608–613 (1994).
[CrossRef]

M. Otsubo, K. Okada, J. Tsujiuchi, “Measurement of large plane surface shape with interferometric aperture synthesis,” Proc. SPIE 1720, 444–447 (1992).
[CrossRef]

Van Loan, C. F.

G. H. Gloub, C. F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, 1996), Section 12.1.

Wang, C. W.

M. Y. Chen, W. M. Cheng, C. W. Wang, “Multiaperture overlap-scanning technique for large-aperture test,” Proc. SPIE 1553, 626–635 (1991).
[CrossRef]

Wu, D. Z.

M. Y. Chen, D. Z. Wu, “Multiaperture overlap-scanning technique for moire metrology,” Proc. SPIE 2861, 107–112 (1996).
[CrossRef]

Wyant, J.

C. Kim, J. Wyant, “Subaperture test of a large flat or a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981).

Wyant, J. C.

J. C. Wyant, J. Schmit, “Large field of view, high spatial resolution, surface measurements,” Int. J. Mach. Tools Manuf. 38, 691–698 (1998).
[CrossRef]

Yu, Y. J.

H. T. He, H. W. Guo, Y. J. Yu, M. Y. Chen, “Novel connection method based on virtual cylinder for three-dimensional surface measurement,” Acta Opt. Sin. 24, 978–982 (2004) (in Chinese).

M. Y. Chen, H. W. Guo, Y. J. Yu, H. T. He, “Recent developments of multi-aperture overlap-scanning technique,” Proc. SPIE 5180, 393–401 (2003).
[CrossRef]

Y. J. Yu, M. Y. Chen, “Correlative stitching interferometer and its key techniques,” Proc. SPIE 4777, 382–393 (2002).
[CrossRef]

Acta Opt. Sin.

H. T. He, H. W. Guo, Y. J. Yu, M. Y. Chen, “Novel connection method based on virtual cylinder for three-dimensional surface measurement,” Acta Opt. Sin. 24, 978–982 (2004) (in Chinese).

Appl. Opt.

IEEE Trans. Rob. Autom.

Z. X. Li, J. B. Gou, Y. X. Chu, “Geometric algorithm for workpiece localization,” IEEE Trans. Rob. Autom. 14, 864–878 (1998).
[CrossRef]

Int. J. Mach. Tools Manuf.

J. C. Wyant, J. Schmit, “Large field of view, high spatial resolution, surface measurements,” Int. J. Mach. Tools Manuf. 38, 691–698 (1998).
[CrossRef]

J. Opt. Soc. Am.

C. Kim, J. Wyant, “Subaperture test of a large flat or a fast aspheric surface,” J. Opt. Soc. Am. 71, 1587 (1981).

Opt. Eng. (Bellingham)

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

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

M. Otsubo, K. Okada, J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. (Bellingham) 33, 608–613 (1994).
[CrossRef]

Opt. Lett.

Opt. Photonics News

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

Proc. SPIE

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

M. Bray, “Stitching interferometry: recent results and absolute calibration,” Proc. SPIE 5252, 305–313 (2004).
[CrossRef]

R. D. Day, T. A. Beery, G. N. Lawrence, “Sphericity measurements of full spheres using subaperture optical testing techniques,” Proc. SPIE 661, 334–341 (1986).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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Other

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Figures (5)

Fig. 1
Fig. 1

Lattice of a paraboloid surface.

Fig. 2
Fig. 2

Overlapping calculation.

Fig. 3
Fig. 3

Alternating iterations.

Fig. 4
Fig. 4

Map of isolines of the subapertures and stitched full aperture.

Fig. 5
Fig. 5

Track of iterations.

Tables (1)

Tables Icon

Table 1 Comparison between the Initial and the Resultant Configurations

Equations (35)

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W = { w j , i R 3 j = 1 , , N i ; i = 1 , , s } ,
g * = { g i * SE ( 3 ) i = 1 , , s } ,
SE ( 3 ) = { exp ( t = 1 6 m t ξ ̂ t ) } ,
ξ ̂ = [ ω ̂ v 0 0 ]
SE ( 3 ) G 0 = { g G 0 = exp ( m ̂ ) G 0 } ,
se ( 3 ) = M G 0 .
G 0 = { exp ( m 6 ξ ̂ 6 ) } ,
SE ( 3 ) G 0 = { g G 0 = exp ( t = 1 5 m t ξ ̂ t ) G 0 } .
d ( j , i ) = w j , i x j , i , n j , i ,
e j o , k = d j o , k d j o , i .
min f = μ 1 RMS 2 + μ 2 RMS o 2 ,
RMS 2 = i = 1 s j = 1 N i g i 1 w j , i x j , i , n j , i 2 i = 1 s N i .
RMS o 2 = i = 1 s 1 k = i + 1 s j o = 1 N o i k ( g k 1 w j o , k i k x j o , k i k , n j o , k i k g i 1 w j o , i i k x j o , k i k , n j o , k i k ) 2 N o ,
G 1 = { exp ( t = 1 r m t , 1 η ̂ t ) G 0 } .
g 1 l + 1 = g 1 l exp ( t = 1 r m t , 1 η ̂ ) g 1 l ( I + t = 1 r m t , 1 η ̂ ) ,
g i l + 1 = g i l exp ( t = 1 6 m t , i ξ ̂ ) g 1 l ( I + t = 1 6 m t , i ξ ̂ ) ,
i = 2 , , s ,
A m = b ,
s.t. m α ,
min f = μ 1 [ j = 1 N i ( d j , 1 t = 1 r m t , 1 n j , 1 T η ̂ t x j , 1 ) 2 + i = 2 s j = 1 N i ( d j , i t = 1 6 m t , i n j , i T ξ ̂ t x j , i ) 2 ] i = 1 s N i + μ 2 k = 2 s j o = 1 N o 1 k ( d j o , k 1 k d j o , 1 1 k t = 1 6 m t , k n j o , k T 1 k ξ ̂ t x j o , k 1 k + t = 1 r m t , 1 n j o , k T 1 k η ̂ t x j o , k 1 k ) 2 N o + μ 2 i = 2 s 1 k = i + 1 s j o = 1 N o i k ( d j o , k i k d j o , i i k t = 1 6 m t , k n j o , k T i k ξ ̂ t x j o , k i k + t = 1 6 m t , 1 n j o , k T i k ξ ̂ t x j o , k i k ) 2 N o .
A 1 = ( a j , t 1 ) = { λ 1 n j , 1 T η ̂ t x j , 1 1 t r 0 otherwise } ,
b 1 = ( λ 1 d j , 1 ) ,
j = 1 , , N 1 ; t = 1 , , v ,
A i = ( a j , t i ) = { λ 1 n j , i T ξ ̂ t r 6 ( i 2 ) x j , i r + 6 ( i 2 ) + 1 t r + 6 ( i 1 ) 0 otherwise } ,
b i = ( λ 1 d j , i ) ,
j = 1 , , N i ; t = 1 , , v ; i = 2 , , s ,
A o 1 k = ( a j o , t 1 k ) = { λ 2 n j o , k T 1 k η ̂ t x j o , k 1 k t r λ 2 n j o , k T 1 k ξ ̂ t r 6 ( k 2 ) x j o , k 1 k r + 6 ( k 2 ) + 1 t r + 6 ( k 1 ) 0 otherwise } ,
b o 1 k = ( λ 2 ( d j o , k 1 k d j o , 1 1 k ) ) ,
j o = 1 , , N 1 k o ; t = 1 , , v ; k = 2 , , s ,
A o i k = ( a j o , t i k ) = { λ 2 n j o , k T i k ξ ̂ t r 6 ( i 2 ) x j o , k i k r + 6 ( i 2 ) + 1 t r + 6 ( i 1 ) λ 2 n j o , k T i k ξ ̂ t r 6 ( k 2 ) x j o , k i k r + 6 ( k 2 ) + 1 t r + 6 ( k 1 ) 0 otherwise } ,
b o i k = [ λ 2 ( d j o , k i k d j o , i i k ) ] ,
j o = 1 , , N i k o ; t = 1 , , v ; i = 2 , , s 1 ; k = i + 1 , , s .
A = [ A 1 T , A 2 T , , A s T , , ( A o i k ) T , , ( A o ( s 1 ) s ) T ] T ,
b = [ b 1 , b 2 , , b s , , b o i k , , b o ( s 1 ) s ] T .
min A m b 2 .

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