Abstract

We present a method to determine micro and nano in-plane displacements based on the phase singularities generated by application of directional wavelet transforms to speckle pattern images. The spatial distribution of the obtained phase singularities by the wavelet transform configures a network, which is characterized by two quasi-orthogonal directions. The displacement value is determined by identifying the intersection points of the network before and after the displacement produced by the tested object. The performance of this method is evaluated using simulated speckle patterns and experimental data. The proposed approach is compared with the optical vortex metrology and digital image correlation methods in terms of performance and noise robustness, and the advantages and limitations associated to each method are also discussed.

© 2013 Optical Society of America

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    [CrossRef]
  4. Y. Qiao, W. Wang, N. Minematsu, J. Liu, M. Takeda, and X. Tang, “A theory of phase singularities for image representation and its applications to object tracking and image matching,” IEEE Trans. Image Process. 18, 2153–2166 (2009).
    [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]

2009 (3)

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

Y. Qiao, W. Wang, N. Minematsu, J. Liu, M. Takeda, and X. Tang, “A theory of phase singularities for image representation and its applications to object tracking and image matching,” IEEE Trans. Image Process. 18, 2153–2166 (2009).
[CrossRef]

A. Federico and G. H. Kaufmann, “Robust phase recovery in temporal speckle pattern interferometry using a 3D directional wavelet transform,” Opt. Lett. 34, 2336–2338 (2009).
[CrossRef]

2008 (1)

2007 (1)

2006 (4)

2005 (1)

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
[CrossRef]

2000 (1)

M. V. Berry and M. R. Dennis, “Phase singularities in isotropic random waves,” Proc. R. Soc. A 456, 2059–2079 (2000).
[CrossRef]

1997 (1)

1993 (2)

1983 (1)

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

Antoine, J. P.

J. P. Antoine, R. Murenzi, P. Vandergheynst, and S. Twareque Ali, Two-Dimensional Wavelets and their Relatives (Cambridge University, 2004).

Asundi, A.

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

Benckert, L. R.

Berry, M. V.

M. V. Berry and M. R. Dennis, “Phase singularities in isotropic random waves,” Proc. R. Soc. A 456, 2059–2079 (2000).
[CrossRef]

Bo-qin, X.

B. Pan, X. Hui-min, X. Bo-qin, and D. Fu-long, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
[CrossRef]

Chen, D. J.

Chiang, F. P.

Dennis, M. R.

Don, H. S.

Equis, S.

S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6341, 381–386 (2006).
[CrossRef]

Federico, A.

Fu-long, D.

B. Pan, X. Hui-min, X. Bo-qin, and D. Fu-long, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
[CrossRef]

Hanson, S. G.

Hui-min, X.

B. Pan, X. Hui-min, X. Bo-qin, and D. Fu-long, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
[CrossRef]

Ishii, N.

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
[CrossRef]

Ishijima, R.

Jacquot, P.

S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6341, 381–386 (2006).
[CrossRef]

Kaufmann, G. H.

Liu, J.

Y. Qiao, W. Wang, N. Minematsu, J. Liu, M. Takeda, and X. Tang, “A theory of phase singularities for image representation and its applications to object tracking and image matching,” IEEE Trans. Image Process. 18, 2153–2166 (2009).
[CrossRef]

Matsuda, A.

McNeill, S. R.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

Minematsu, N.

Y. Qiao, W. Wang, N. Minematsu, J. Liu, M. Takeda, and X. Tang, “A theory of phase singularities for image representation and its applications to object tracking and image matching,” IEEE Trans. Image Process. 18, 2153–2166 (2009).
[CrossRef]

Miyamoto, Y.

W. Wang, T. Yokozeki, R. Ishijima, A. Wada, Y. Miyamoto, M. Takeda, and S. G. Hanson, “Optical vortex metrology for nanometric speckle displacement measurement,” Opt. Express 14, 10195–10206 (2006).
[CrossRef]

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
[CrossRef]

Murenzi, R.

J. P. Antoine, R. Murenzi, P. Vandergheynst, and S. Twareque Ali, Two-Dimensional Wavelets and their Relatives (Cambridge University, 2004).

Pan, B.

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

B. Pan, X. Hui-min, X. Bo-qin, and D. Fu-long, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
[CrossRef]

Peters, W. H.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

Qian, K.

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

Qiao, Y.

Y. Qiao, W. Wang, N. Minematsu, J. Liu, M. Takeda, and X. Tang, “A theory of phase singularities for image representation and its applications to object tracking and image matching,” IEEE Trans. Image Process. 18, 2153–2166 (2009).
[CrossRef]

Ranson, W. F.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

Sjödahl, M.

Sutton, M. A.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

Takeda, M.

Tan, Y. S.

Tang, X.

Y. Qiao, W. Wang, N. Minematsu, J. Liu, M. Takeda, and X. Tang, “A theory of phase singularities for image representation and its applications to object tracking and image matching,” IEEE Trans. Image Process. 18, 2153–2166 (2009).
[CrossRef]

Twareque Ali, S.

J. P. Antoine, R. Murenzi, P. Vandergheynst, and S. Twareque Ali, Two-Dimensional Wavelets and their Relatives (Cambridge University, 2004).

Vandergheynst, P.

J. P. Antoine, R. Murenzi, P. Vandergheynst, and S. Twareque Ali, Two-Dimensional Wavelets and their Relatives (Cambridge University, 2004).

Wada, A.

Wang, W.

Wolters, W. J.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

Xie, H.

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

Yokozeki, T.

Appl. Opt. (4)

IEEE Trans. Image Process. (1)

Y. Qiao, W. Wang, N. Minematsu, J. Liu, M. Takeda, and X. Tang, “A theory of phase singularities for image representation and its applications to object tracking and image matching,” IEEE Trans. Image Process. 18, 2153–2166 (2009).
[CrossRef]

Image Vis. Comput. (1)

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using improved digital correlation method,” Image Vis. Comput. 1, 133–139 (1983).
[CrossRef]

Meas. Sci. Technol. (2)

B. Pan, K. Qian, H. Xie, and A. Asundi, “Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review,” Meas. Sci. Technol. 20, 062001 (2009).
[CrossRef]

B. Pan, X. Hui-min, X. Bo-qin, and D. Fu-long, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
[CrossRef]

Opt. Commun. (1)

W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Phase singularities in analytic signal of white-light speckle pattern with application to micro-displacement measurement,” Opt. Commun. 248, 59–68 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. R. Soc. A (1)

M. V. Berry and M. R. Dennis, “Phase singularities in isotropic random waves,” Proc. R. Soc. A 456, 2059–2079 (2000).
[CrossRef]

Proc. SPIE (1)

S. Equis and P. Jacquot, “Simulation of speckle complex amplitude: advocating the linear model,” Proc. SPIE 6341, 381–386 (2006).
[CrossRef]

Other (1)

J. P. Antoine, R. Murenzi, P. Vandergheynst, and S. Twareque Ali, Two-Dimensional Wavelets and their Relatives (Cambridge University, 2004).

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