Abstract

A direct correlation technique is used to calculate correlation fringe patterns from consecutive speckle patterns acquired with a dual-beam electronic speckle interferometer. Although more calculations are required than in standard image differencing routines, an advantage of the method is that the illumination over the surface of the object need not be uniform. In the method, Pearson’s coefficient of correlation between the intensities within a set of adjacent pixels is calculated. This has the added advantage of being directly related to the theoretical phase-dependent correlation. A mapping of this measure of correlation results in the correlation fringe pattern. Laboratory tests were carried out with in-plane translations ranging from 5 to 45 µm. The correlation calculations were carried out by using cells (square sets of pixels) in the raw speckle images with dimensions ranging from 2 pixels × 2 pixels to 19 pixels × 19 pixels. Both cell dimension and translation magnitude dependent decorrelation effects influence the quality of the correlation fringe patterns.

© 1997 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  5. A. E. Ennos, “Laser interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1989), pp. 203–253.
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    [CrossRef] [PubMed]
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    [CrossRef]
  9. J. N. Butters, J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E Sci. Instrum. 4, 277–279 (1971).
    [CrossRef]
  10. K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E Sci. Instrum. 8, 571–576 (1975).
    [CrossRef]
  11. O. J. Løkberg, K. Høgmoen, “Vibration phase mapping using electronic speckle pattern interferometry,” Appl. Opt. 15, 2701–2704 (1976).
    [CrossRef]
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    [CrossRef]
  13. C. Joenthan, B. M. Khorana, “Phase-measuring fiber optic electronic speckle pattern interferometer: phase step calibration and phase drift minimization,” Opt. Eng. 31, 315–321 (1992).
    [CrossRef]
  14. S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E Sci. Instrum. 22, 289–292 (1989).
    [CrossRef]
  15. J. Kato, I. Yamaguchi, Q. Ping, “Automatic deformation analysis by a TV speckle interferometer using a laser diode,” Appl. Opt. 32, 77–83 (1993).
    [CrossRef]
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    [CrossRef]
  18. R. Jones, C. Wykes, “De-correlation effects in speckle-pattern interferometry, 2. displacement dependent de-correlation and applications to the observation of machine-induced strain,” Opt. Acta 24, 533–550 (1977).
    [CrossRef]
  19. X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” Optik 90, 129–133 (1992).
  20. N. Zhu, F. P. Chang, “Vibration mode shape identification by digital speckle correlation (DISC),” Exp. Tech. 20, 17–19 (1996).
    [CrossRef]
  21. A. E. Ennos, “Laser interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1989), pp. 207–211.
  22. J. W. Goodman, “Statistical properties of laser speckle,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1989), pp. 21–26.
  23. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983), pp. 338–339.

1996

N. Zhu, F. P. Chang, “Vibration mode shape identification by digital speckle correlation (DISC),” Exp. Tech. 20, 17–19 (1996).
[CrossRef]

1994

1993

1992

C. Joenthan, B. M. Khorana, “Phase-measuring fiber optic electronic speckle pattern interferometer: phase step calibration and phase drift minimization,” Opt. Eng. 31, 315–321 (1992).
[CrossRef]

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” Optik 90, 129–133 (1992).

1989

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E Sci. Instrum. 22, 289–292 (1989).
[CrossRef]

1982

H. M. Pedersen, “Intensity correlation meterology: a comparative study,” Opt. Acta 29, 105–118 (1982).
[CrossRef]

1977

R. Jones, C. Wykes, “De-correlation effects in speckle-pattern interferometry, 2. displacement dependent de-correlation and applications to the observation of machine-induced strain,” Opt. Acta 24, 533–550 (1977).
[CrossRef]

1976

1975

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E Sci. Instrum. 8, 571–576 (1975).
[CrossRef]

1971

J. N. Butters, J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E Sci. Instrum. 4, 277–279 (1971).
[CrossRef]

1970

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of in-plane surface displacement by double-exposure speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E Sci. Instrum. 3, 214–218 (1970).
[CrossRef]

1969

Archbold, E.

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of in-plane surface displacement by double-exposure speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

Biedermann, K.

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E Sci. Instrum. 8, 571–576 (1975).
[CrossRef]

Burch, J. M.

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of in-plane surface displacement by double-exposure speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

Butters, J. N.

J. N. Butters, J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E Sci. Instrum. 4, 277–279 (1971).
[CrossRef]

Chang, F. P.

N. Zhu, F. P. Chang, “Vibration mode shape identification by digital speckle correlation (DISC),” Exp. Tech. 20, 17–19 (1996).
[CrossRef]

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, Berlin, 1989).

Diao, H. Y.

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” Optik 90, 129–133 (1992).

Ek, L.

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E Sci. Instrum. 8, 571–576 (1975).
[CrossRef]

Ennos, A. E.

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of in-plane surface displacement by double-exposure speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

A. E. Ennos, “Laser interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1989), pp. 207–211.

A. E. Ennos, “Laser interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1989), pp. 203–253.

Frankena, H. J.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1989), pp. 21–26.

Gorecki, C.

Høgmoen, K.

Jia, Z.

Z. Jia, “A study of the fracture process in cement-based materials using laser holographic and speckle interferometry,” Ph.D. thesis (Northwestern University, Evanston, Ill., 1994).

Joenthan, C.

C. Joenthan, B. M. Khorana, “Phase-measuring fiber optic electronic speckle pattern interferometer: phase step calibration and phase drift minimization,” Opt. Eng. 31, 315–321 (1992).
[CrossRef]

Johansson, S.

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E Sci. Instrum. 22, 289–292 (1989).
[CrossRef]

Jones, R.

R. Jones, C. Wykes, “De-correlation effects in speckle-pattern interferometry, 2. displacement dependent de-correlation and applications to the observation of machine-induced strain,” Opt. Acta 24, 533–550 (1977).
[CrossRef]

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983).

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983), Appendix E, p. 333.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983), pp. 338–339.

Kato, J.

Khorana, B. M.

C. Joenthan, B. M. Khorana, “Phase-measuring fiber optic electronic speckle pattern interferometer: phase step calibration and phase drift minimization,” Opt. Eng. 31, 315–321 (1992).
[CrossRef]

Leendertz, J. A.

J. N. Butters, J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E Sci. Instrum. 4, 277–279 (1971).
[CrossRef]

J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E Sci. Instrum. 3, 214–218 (1970).
[CrossRef]

Løkberg, O. J.

Pedersen, H. M.

H. M. Pedersen, “Intensity correlation meterology: a comparative study,” Opt. Acta 29, 105–118 (1982).
[CrossRef]

Peng, X.

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” Optik 90, 129–133 (1992).

Ping, Q.

Predko, K. G.

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E Sci. Instrum. 22, 289–292 (1989).
[CrossRef]

Sollid, J. E.

Tiziani, H.

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” Optik 90, 129–133 (1992).

van Haasteren, A. J. P.

Wykes, C.

R. Jones, C. Wykes, “De-correlation effects in speckle-pattern interferometry, 2. displacement dependent de-correlation and applications to the observation of machine-induced strain,” Opt. Acta 24, 533–550 (1977).
[CrossRef]

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983).

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983), pp. 338–339.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983), Appendix E, p. 333.

Yamaguchi, I.

Zhu, N.

N. Zhu, F. P. Chang, “Vibration mode shape identification by digital speckle correlation (DISC),” Exp. Tech. 20, 17–19 (1996).
[CrossRef]

Zou, Y. L.

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” Optik 90, 129–133 (1992).

Appl. Opt.

Exp. Tech.

N. Zhu, F. P. Chang, “Vibration mode shape identification by digital speckle correlation (DISC),” Exp. Tech. 20, 17–19 (1996).
[CrossRef]

J. Phys. E Sci. Instrum.

J. A. Leendertz, “Interferometric displacement measurement on scattering surfaces utilizing speckle effect,” J. Phys. E Sci. Instrum. 3, 214–218 (1970).
[CrossRef]

J. N. Butters, J. A. Leendertz, “A double exposure technique for speckle pattern interferometry,” J. Phys. E Sci. Instrum. 4, 277–279 (1971).
[CrossRef]

K. Biedermann, L. Ek, “A recording and display system for hologram interferometry with low resolution imaging devices,” J. Phys. E Sci. Instrum. 8, 571–576 (1975).
[CrossRef]

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E Sci. Instrum. 22, 289–292 (1989).
[CrossRef]

Opt. Acta

H. M. Pedersen, “Intensity correlation meterology: a comparative study,” Opt. Acta 29, 105–118 (1982).
[CrossRef]

R. Jones, C. Wykes, “De-correlation effects in speckle-pattern interferometry, 2. displacement dependent de-correlation and applications to the observation of machine-induced strain,” Opt. Acta 24, 533–550 (1977).
[CrossRef]

E. Archbold, J. M. Burch, A. E. Ennos, “Recording of in-plane surface displacement by double-exposure speckle photography,” Opt. Acta 17, 883–898 (1970).
[CrossRef]

Opt. Eng.

C. Joenthan, B. M. Khorana, “Phase-measuring fiber optic electronic speckle pattern interferometer: phase step calibration and phase drift minimization,” Opt. Eng. 31, 315–321 (1992).
[CrossRef]

Optik

X. Peng, H. Y. Diao, Y. L. Zou, H. Tiziani, “A novel approach to determine decorrelation effect in a dual-beam electronic speckle pattern interferometer,” Optik 90, 129–133 (1992).

Other

Z. Jia, “A study of the fracture process in cement-based materials using laser holographic and speckle interferometry,” Ph.D. thesis (Northwestern University, Evanston, Ill., 1994).

A. E. Ennos, “Laser interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1989), pp. 203–253.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983), Appendix E, p. 333.

J. C. Dainty, Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, Berlin, 1989).

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983).

A. E. Ennos, “Laser interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1989), pp. 207–211.

J. W. Goodman, “Statistical properties of laser speckle,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1989), pp. 21–26.

R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983), pp. 338–339.

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Figures (10)

Fig. 1
Fig. 1

Raw speckle patterns acquired, a, before and, b, after a 30-µm translation. Images include 756 horizontal × 486 vertical pixels and cover a range of 6.8 cm × 9.1 cm on the plate.

Fig. 2
Fig. 2

Fringe patterns obtained from the raw frames of Fig. 1 by, a, squaring the pixel-by-pixel difference; b, pixel averaging then frame subtraction, rectification, and taking of the square root; c, direct correlation.

Fig. 3
Fig. 3

Expected distribution of correlation amplitudes for perfect noise-free data.

Fig. 4
Fig. 4

Experimental geometry.

Fig. 5
Fig. 5

Details, a, vertically and, b, horizontally through the autocorrelation of Fig. 4a.

Fig. 6
Fig. 6

Histogram of intensities observed in a single raw speckle pattern acquired with the present experimental configuration.

Fig. 7
Fig. 7

Correlation fringe patterns for a 10-µm in-plane translation calculated with correlation cells of dimensions, a, 2 × 2; b, 5 × 5; c, 9 × 9; d, 19 × 19. Insets are the corresponding normalized correlation magnitude histograms with independent axes ranging from -0.1 to +1, the range of correlation values for the pixels in the image. Panels beneath each correlation image are the intensities observed along the horizontal profile indicated by the dotted lines through the centers of the images.

Fig. 8
Fig. 8

Contrast as a function of cell dimensions for different displacements.

Fig. 9
Fig. 9

Signal-to-noise ratio as a function of cell dimension for different displacements.

Fig. 10
Fig. 10

Correlation fringe patterns calculated with a 9 × 9 correlation cell size for translations of magnitude, a, 5 µm; b, 10 µm; c, 30 µm; d, 45 µm. Insets are the corresponding normalized correlation magnitude histograms with independent axes ranging from -0.1 to +1, the range of correlation values for pixels in the image. Panels beneath each correlation image are the intensities observed along the horizontal profile indicated by the dotted lines through the centers of the images.

Equations (7)

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

I1=I1+I2+2I1I2 cosΨ1-Ψ2
I2=I1+I2+2I1I2 cosΨ1-Ψ2+Δϕ,
ρ=I1I2-I1I2I12-I121/2I22-I221/2
ρ=½1+cosΔϕ.
Δϕ=2πλk1-k2·d,
r=1mmak1bk1-1mmak11mmbk1σaσb,
σa=1mmak12-1mmak121/2

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