Abstract

Electronic speckle photography offers a simple and fast technique for measuring in-plane displacement fields in solid and fluid mechanics. An improved algorithm is presented and analyzed by use of both computer-simulated speckle patterns and real experiments. The idea of the improved algorithm is to maximize the correlation between correlated subimages from different images by shifting one of them by nonintegral pixel values. The improved algorithm was found to determine displacement components with an uncertainty of less than 1% of a pixel and with negligible systematic errors in ideal experimental conditions.

© 1994 Optical Society of America

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References

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  1. A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 203–253.
    [CrossRef]
  2. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9–75.
    [CrossRef]
  3. M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1(3), 133–139 (1983).
    [CrossRef]
  4. T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
    [CrossRef]
  5. H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
    [CrossRef]
  6. P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
    [CrossRef]
  7. D. J. Chen, F. P. Chiang, “Optimal sampling and range of measurement in displacement-only laser-speckle correlation,” Exp. Mech. 32, 145–153 (1992).
    [CrossRef]
  8. D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Digital speckle-displacement measurement using a complex spectrum method,” Appl. Opt. 32, 1839–1849 (1993).
    [CrossRef] [PubMed]
  9. S. Noh, I. Yamaguchi, “Two-dimensional measurement of strain distribution by speckle correlation,” Jpn. J. Appl. Phys. 31, L1299–L1301 (1992).
    [CrossRef]
  10. I. Yamaguchi, S. Noh, “Deformation measurement by 2-D speckle correlation,” in Interferometry: Applications, G. Brown, W. P. Jeuptner, R. J. Pryputniewicz, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1756, 106–118 (1992).
  11. M. Sjödahl, L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 2278–2284 (1993).
    [CrossRef] [PubMed]
  12. M. Sjödahl, L. R. Benckert, “Systematic and random errors in electronic speckle photography,” submitted to Appl. Opt.
  13. J. M. Huntley, “Speckle photography fringe analysis: assessment of current algorithms,” Appl. Opt. 28, 4316–4322 (1989).
    [CrossRef] [PubMed]
  14. D. W. Li, F. P. Chiang, “Decorrelation functions in laser speckle photography,” J. Opt. Soc. Am. A 3, 1023–1031 (1986).
    [CrossRef]
  15. G. E. P. Box, W. G. Hunter, J. S. Hunter, Statistics for Experimenters (Wiley, New York, 1978).
  16. I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
    [CrossRef]
  17. M. Sjödahl, “Strain field measurements using electronic speckle photography: a comparison,” in Proceedings of the 10th International Conference on Experimental Mechanics (Balkema, Rotterdam, 1994).

1993 (3)

1992 (2)

S. Noh, I. Yamaguchi, “Two-dimensional measurement of strain distribution by speckle correlation,” Jpn. J. Appl. Phys. 31, L1299–L1301 (1992).
[CrossRef]

D. J. Chen, F. P. Chiang, “Optimal sampling and range of measurement in displacement-only laser-speckle correlation,” Exp. Mech. 32, 145–153 (1992).
[CrossRef]

1989 (2)

J. M. Huntley, “Speckle photography fringe analysis: assessment of current algorithms,” Appl. Opt. 28, 4316–4322 (1989).
[CrossRef] [PubMed]

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

1986 (1)

1985 (1)

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

1983 (1)

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1(3), 133–139 (1983).
[CrossRef]

1981 (1)

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
[CrossRef]

Benckert, L. R.

Box, G. E. P.

G. E. P. Box, W. G. Hunter, J. S. Hunter, Statistics for Experimenters (Wiley, New York, 1978).

Bruck, H. A.

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

Chao, Y. J.

P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
[CrossRef]

Chen, D. J.

D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Digital speckle-displacement measurement using a complex spectrum method,” Appl. Opt. 32, 1839–1849 (1993).
[CrossRef] [PubMed]

D. J. Chen, F. P. Chiang, “Optimal sampling and range of measurement in displacement-only laser-speckle correlation,” Exp. Mech. 32, 145–153 (1992).
[CrossRef]

Chiang, F. P.

Chu, T. C.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

Don, H. S.

Ennos, A. E.

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 203–253.
[CrossRef]

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9–75.
[CrossRef]

Hunter, J. S.

G. E. P. Box, W. G. Hunter, J. S. Hunter, Statistics for Experimenters (Wiley, New York, 1978).

Hunter, W. G.

G. E. P. Box, W. G. Hunter, J. S. Hunter, Statistics for Experimenters (Wiley, New York, 1978).

Huntley, J. M.

Li, D. W.

Luo, P. F.

P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
[CrossRef]

McNeill, S. R.

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1(3), 133–139 (1983).
[CrossRef]

Noh, S.

S. Noh, I. Yamaguchi, “Two-dimensional measurement of strain distribution by speckle correlation,” Jpn. J. Appl. Phys. 31, L1299–L1301 (1992).
[CrossRef]

I. Yamaguchi, S. Noh, “Deformation measurement by 2-D speckle correlation,” in Interferometry: Applications, G. Brown, W. P. Jeuptner, R. J. Pryputniewicz, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1756, 106–118 (1992).

Peters, W. H.

P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
[CrossRef]

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1(3), 133–139 (1983).
[CrossRef]

Ranson, W. F.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1(3), 133–139 (1983).
[CrossRef]

Sjödahl, M.

M. Sjödahl, L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 2278–2284 (1993).
[CrossRef] [PubMed]

M. Sjödahl, L. R. Benckert, “Systematic and random errors in electronic speckle photography,” submitted to Appl. Opt.

M. Sjödahl, “Strain field measurements using electronic speckle photography: a comparison,” in Proceedings of the 10th International Conference on Experimental Mechanics (Balkema, Rotterdam, 1994).

Sutton, M. A.

P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
[CrossRef]

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1(3), 133–139 (1983).
[CrossRef]

Tan, Y. S.

Wolters, W. J.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1(3), 133–139 (1983).
[CrossRef]

Yamaguchi, I.

S. Noh, I. Yamaguchi, “Two-dimensional measurement of strain distribution by speckle correlation,” Jpn. J. Appl. Phys. 31, L1299–L1301 (1992).
[CrossRef]

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
[CrossRef]

I. Yamaguchi, S. Noh, “Deformation measurement by 2-D speckle correlation,” in Interferometry: Applications, G. Brown, W. P. Jeuptner, R. J. Pryputniewicz, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1756, 106–118 (1992).

Appl. Opt. (3)

Exp. Mech. (4)

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–244 (1985).
[CrossRef]

H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

P. F. Luo, Y. J. Chao, M. A. Sutton, W. H. Peters, “Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision,” Exp. Mech. 33, 123–132 (1993).
[CrossRef]

D. J. Chen, F. P. Chiang, “Optimal sampling and range of measurement in displacement-only laser-speckle correlation,” Exp. Mech. 32, 145–153 (1992).
[CrossRef]

Image Vision Comput. (1)

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image Vision Comput. 1(3), 133–139 (1983).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

S. Noh, I. Yamaguchi, “Two-dimensional measurement of strain distribution by speckle correlation,” Jpn. J. Appl. Phys. 31, L1299–L1301 (1992).
[CrossRef]

Opt. Acta (1)

I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
[CrossRef]

Other (6)

M. Sjödahl, “Strain field measurements using electronic speckle photography: a comparison,” in Proceedings of the 10th International Conference on Experimental Mechanics (Balkema, Rotterdam, 1994).

G. E. P. Box, W. G. Hunter, J. S. Hunter, Statistics for Experimenters (Wiley, New York, 1978).

M. Sjödahl, L. R. Benckert, “Systematic and random errors in electronic speckle photography,” submitted to Appl. Opt.

I. Yamaguchi, S. Noh, “Deformation measurement by 2-D speckle correlation,” in Interferometry: Applications, G. Brown, W. P. Jeuptner, R. J. Pryputniewicz, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1756, 106–118 (1992).

A. E. Ennos, “Speckle interferometry,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 203–253.
[CrossRef]

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1975), pp. 9–75.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Principle of the algorithm; * indicates the cross correlation.

Fig. 2
Fig. 2

Random errors are introduced by the nonoverlapping edges of the two subimages.

Fig. 3
Fig. 3

Increase in the signal-to-noise ratio of the cross correlation obtained by image shifting. The correlation is normalized by the dc level. (a) Original cross-correlation surface. (b) The cross-correlation surface after the subimages are moved to optimal integral pixel values. (c) The cross-correlation surface after the subimages are shifted to optimal nonintegral pixel values.

Fig. 4
Fig. 4

Magnitude of the residual of each displacement component plotted against the number of iterations for two combinations of the following: average speckle size σ, subimage size n, and correlation γ. (a) σ = 2.4, n = 32, and γ = 1; (b) σ = 2.4, n = 32, and γ = 0.75.

Fig. 5
Fig. 5

Schematic of the simple experimental setup for electronic laser speckle photography.

Fig. 6
Fig. 6

Decrease in the random error for f# 26 and a subimage size of 32 pixels obtained in the experiment by the introduction of the improved algorithm.

Tables (2)

Tables Icon

Table 1 Results from Computer-Generated Speckle Simulations

Tables Icon

Table 2 Experiments with Real Laser Speckles and Pure Object Rotation

Equations (9)

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c ( p , q ) = F 1 ( H s 1 * H s 2 ) ,
u ( x , y ) = 1 P 2 p = 0 P 1 q = 0 P 1 c ( p , q ) × sin [ π ( x p ) ] sin [ π ( y q ) ] sin [ π ( x p ) / P ] sin [ π ( y q ) / P ] ,
e 0 . 66 σ / n ( 1 δ ) 2 ,
H shift ( p , q ) = H ( p , q ) exp [ 2 π ( k x q + k y p ) / m ] ; p , q = 0 , 1 , , m 1 ,
h shift ( i , j ) = | F 1 [ H shift ( p , q ) ] | ,
γ = [ ( θ sin θ ) / π ] 2 ,
θ = 2 cos 1 ( | d r | D ) ,
A ξ = a x L 0 [ x x 1 s x + x y 1 s y + Ω z 1 s y Ω y ( 1 s z + 1 ) ] , A ψ = a y L 0 [ y y 1 s y + x y 1 s x Ω z 1 s x Ω x ( 1 s z + 1 ) ] ,
e < f # / 25 n γ 2 ,

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