Abstract

Micrometer-scale rigid-body translations are determined from electronic speckle interferometric fringe patterns. An iterative minimum error procedure employs the relative fringe order of picked positions of fringe maxima and minima within a single interferogram to calculate the displacement field directly. The method does not calculate the displacement at a single point but relies on the assumption that the character, but not the magnitudes or directions, of the displacements over the viewing area of the interferogram is known. That is, a model of the displacements exists. On perfect, noise-free forward modeled fringe patterns calculated for an 8.0-μm displacement, the phase error is less than 2 × 10-6 fringe orders (1.3 × 10-5 rad) and probably results only from numerical noise in the inversion. On real fringe patterns obtained in electronic speckle interferometric experiments, mean phase errors are generally less than 5 × 10-5 fringe orders (3.2 × 10-4 rad), suggesting that the technique is robust despite errors resulting from speckle noise, lack of accuracy in positioning of experimental components, and image-distortion corrections.

© 1998 Optical Society of America

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References

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  1. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  2. R. Jones, C. Wykes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983).
  3. J. E. Sollid, “Holographic interferometry applied to measurements of small static displacements of diffusely reflecting surfaces,” Appl. Opt. 8, 1587–1595 (1969).
    [CrossRef] [PubMed]
  4. A. E. Ennos, “Measurement of in-plane surface strain by hologram interferometry,” J. Phys. E Sci. Instrum. 1(Series 2), 731–734 (1968).
    [CrossRef]
  5. A. Makino, D. Nelson, “Residual - stress determination by single axis holographic interferometry and hole drilling,” Exp. Mech. 34(1), 66–71 (1994).
    [CrossRef]
  6. S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E 22, 289–292 (1989).
    [CrossRef]
  7. 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]
  8. 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] [PubMed]
  9. J. C. Dainty, Laser Speckle and Related Phenomena, 2nd ed. (Springer-Verlag, Berlin, 1989).
  10. Z. Jia, “A study of the fracture process in cement-based materials using laser holographic and speckle interferometry,” Ph. D. dissertation (Northwestern University, Evanston, Ill., 1994).
  11. D. R. Schmitt, R. W. Hunt, “Optimization of fringe pattern calculation with direct correlations in speckle interferometry,” Appl. Opt. 36, 8848–8857 (1997).
    [CrossRef]
  12. 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]

1997 (1)

1994 (1)

A. Makino, D. Nelson, “Residual - stress determination by single axis holographic interferometry and hole drilling,” Exp. Mech. 34(1), 66–71 (1994).
[CrossRef]

1993 (1)

1992 (1)

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]

1989 (1)

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

1975 (1)

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]

1969 (1)

1968 (1)

A. E. Ennos, “Measurement of in-plane surface strain by hologram interferometry,” J. Phys. E Sci. Instrum. 1(Series 2), 731–734 (1968).
[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]

Dainty, J. C.

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

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.

A. E. Ennos, “Measurement of in-plane surface strain by hologram interferometry,” J. Phys. E Sci. Instrum. 1(Series 2), 731–734 (1968).
[CrossRef]

Hunt, R. W.

Jia, Z.

Z. Jia, “A study of the fracture process in cement-based materials using laser holographic and speckle interferometry,” Ph. D. dissertation (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 22, 289–292 (1989).
[CrossRef]

Jones, R.

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

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]

Makino, A.

A. Makino, D. Nelson, “Residual - stress determination by single axis holographic interferometry and hole drilling,” Exp. Mech. 34(1), 66–71 (1994).
[CrossRef]

Nelson, D.

A. Makino, D. Nelson, “Residual - stress determination by single axis holographic interferometry and hole drilling,” Exp. Mech. 34(1), 66–71 (1994).
[CrossRef]

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 22, 289–292 (1989).
[CrossRef]

Schmitt, D. R.

Sollid, J. E.

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Wykes, C.

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

Yamaguchi, I.

Appl. Opt. (3)

Exp. Mech. (1)

A. Makino, D. Nelson, “Residual - stress determination by single axis holographic interferometry and hole drilling,” Exp. Mech. 34(1), 66–71 (1994).
[CrossRef]

J. Phys. E (1)

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

J. Phys. E Sci. Instrum. (2)

A. E. Ennos, “Measurement of in-plane surface strain by hologram interferometry,” J. Phys. E Sci. Instrum. 1(Series 2), 731–734 (1968).
[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]

Opt. Eng. (1)

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]

Other (4)

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

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

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

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

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Figures (4)

Fig. 1
Fig. 1

Experimental and optical geometry.

Fig. 2
Fig. 2

Calculated fringe patterns for 8-μm displacements of a flat plate in the (a) +x direction, (b) +y direction, and (c) +z direction. The origin of the coordinate system lies at the center of the images that cover an area of 9.5 cm horizontally and 7.5 cm vertically. The source points are at S1 = -8.63, 0.12, -10.65 cm and S2 = 8.62, 0.16, -14.45 cm.

Fig. 3
Fig. 3

Sum of squares fringe order error versus trial fringe order assignments from 745 picked fringe points in Fig. 4(i).

Fig. 4
Fig. 4

Observed and filtered correlograms and best solution fringe simulations: (a) observed correlogram for a nominal 20-μm pure x-axis translation; (b) low-pass filter applied to (a) with picked fringe peaks and troughs; (c) forward calculations using a result of inversion and comparison with picked points (corrected for imaging distortions); (d) observed correlogram for a nominal 20-μm pure y-axis translation; (e) low-pass filter applied to (d) with picked fringe peaks and troughs; (f) forward calculations where the result of inversion and comparison with picked points (corrected for imaging distortions) is used; (g) observed correlogram for nominal -20-μm pure z-axis translation; (h) low-pass filter applied to (g) with picked fringe peaks and troughs; (i) forward calculations where the result of inversion and comparison with picked points (corrected for imaging distortions) is used.

Tables (1)

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Table 1 Results of Inversion for Translations

Equations (5)

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Δ ϕ = 2 π λ n ˆ 1 - n ˆ 2 · d ,
d x ,   y ,   z = u 1 i ˆ + u 2 j ˆ + u 3 k ˆ ,
N x ,   y ,   z = 1 λ K x ,   y ,   z · d x ,   y ,   z .
n n n - 1 / 2 n - 1 / 2 n - 1 = k x 1 k y 1 k z 1 k x j k y j k z j k x j + 1 k y j + 1 k z j + 1 k x k k y k k z k k x k + 1 k y k + 1 k z k + 1 u 1 u 2 u 3
d = K T K - 1 K T n ,

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