Abstract

The digital speckle correlation method (DSCM) has been widely used to resolve displacement and deformation gradient fields. The computational time and the computational accuracy are still two challenging problems faced in this area. In this paper, we introduce the radial basis function (RBF) interpolation method to DSCM and propose a method for displacement field analysis based on the combination of DSCM with RBF interpolation. We test the proposed method on two computer-simulated and two experimentally obtained deformation measurements and compare it with the widely used Newton– Raphson iteration (NR method). The experimental results demonstrate that our method performs better than the NR method in terms of both quantitative evaluation and visual quality. In addition, the total computational time of our method is considerably shorter than that of the NR method. Our method is particularly suitable for displacement field analysis of large regions.

© 2010 Optical Society of America

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References

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  1. W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental stress analysis,” Opt. Eng. 21, 427–431 (1982).
  2. T. F. Begemann, “Three-dimensional deformation field measurement with digital speckle correlation,” Appl. Opt. 42, 6783–6796 (2003).
    [CrossRef]
  3. E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Application of digital image correlation technique to dynamic measurement of the velocity field in the deformation zone in cold rolling,” Opt. Lasers Eng. 39, 479–488 (2003).
    [CrossRef]
  4. M. A. Sutton, J. J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).
  5. M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
    [CrossRef]
  6. S. Roux, J. Réthoré, and F. Hild, “Digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2D and 3D cracks,” J. Phys. D 42, 214004 (2009).
    [CrossRef]
  7. B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech. 41, 29–39(2001).
    [CrossRef]
  8. H. A. Bruck, S. R. McNeil, M. A. Sutton, and W. H. Peters, “Digital image correlation using Newton–Raphson method of partial differential correction,” Exp. Mech. 29, 261–267 (1989).
    [CrossRef]
  9. C. Q. Davis and D. M. Freeman, “Statistics of subpixel registration algorithms based on spatiotemporal gradients or block matching,” Opt. Eng. 37, 1290–1298 (1998).
    [CrossRef]
  10. P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation,” Opt. Eng. 40, 1613–1620 (2001).
    [CrossRef]
  11. D. J. Chen, F. P. Chiang, Y. S. Tan, and H. S. Don, “Digital speckle-displacement measurement using a complex spectrum method,” Appl. Opt. 32, 1839–1849 (1993).
    [CrossRef] [PubMed]
  12. H. Jin and H. Bruck, “Pointwise digital image correlation using genetic algorithms,” Exp. Tech. 29, 36–39 (2005).
    [CrossRef]
  13. M. C. Pitter, C. W. See, and M. G. Somekh, “Subpixel microscopic deformation analysis using correlation and artificial neural networks,” Opt. Express 8, 322–327 (2001).
    [CrossRef] [PubMed]
  14. B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
    [CrossRef]
  15. J. Zhang, G. Jin, S. Ma, and L. Meng, “Application of an improved subpixel registration algorithm on digital speckle correlation measurement,” Opt. Laser Technol. 35, 533–542(2003).
    [CrossRef]
  16. Z. Feng and R. E. Rowlands, “Continuous full-field representation and differentiation of three-dimensional experimental vector data,” Comput. Struct. 26, 979–990 (1987).
    [CrossRef]
  17. X. Dai, Y. C. Chan, and A. C. K. So, “Digital speckle correlation method based on wavelet-packet noise-reduction processing,” Appl. Opt. 38, 3474–3482 (1999).
    [CrossRef]
  18. M. D. Buhmann, Radial Basis Functions: Theory and Implementations (Cambridge U. Press, 2003).
    [CrossRef]
  19. G. B. Wright, “Radial basis function interpolation: numerical and analytical developments,” Ph.D. dissertation (University of Colorado, 2003).
  20. J. Duchon,  “Splines minimizing rotation-invariant semi-norms in Sobolev spaces,” Laboratoire de Mathematiques Appliquees. (Springer-Verlag, 1977), pp. 85–100.

2009 (2)

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

S. Roux, J. Réthoré, and F. Hild, “Digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2D and 3D cracks,” J. Phys. D 42, 214004 (2009).
[CrossRef]

2006 (1)

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
[CrossRef]

2005 (1)

H. Jin and H. Bruck, “Pointwise digital image correlation using genetic algorithms,” Exp. Tech. 29, 36–39 (2005).
[CrossRef]

2003 (3)

J. Zhang, G. Jin, S. Ma, and L. Meng, “Application of an improved subpixel registration algorithm on digital speckle correlation measurement,” Opt. Laser Technol. 35, 533–542(2003).
[CrossRef]

T. F. Begemann, “Three-dimensional deformation field measurement with digital speckle correlation,” Appl. Opt. 42, 6783–6796 (2003).
[CrossRef]

E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Application of digital image correlation technique to dynamic measurement of the velocity field in the deformation zone in cold rolling,” Opt. Lasers Eng. 39, 479–488 (2003).
[CrossRef]

2001 (3)

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech. 41, 29–39(2001).
[CrossRef]

M. C. Pitter, C. W. See, and M. G. Somekh, “Subpixel microscopic deformation analysis using correlation and artificial neural networks,” Opt. Express 8, 322–327 (2001).
[CrossRef] [PubMed]

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation,” Opt. Eng. 40, 1613–1620 (2001).
[CrossRef]

1999 (1)

1998 (1)

C. Q. Davis and D. M. Freeman, “Statistics of subpixel registration algorithms based on spatiotemporal gradients or block matching,” Opt. Eng. 37, 1290–1298 (1998).
[CrossRef]

1993 (1)

1989 (1)

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

1987 (1)

Z. Feng and R. E. Rowlands, “Continuous full-field representation and differentiation of three-dimensional experimental vector data,” Comput. Struct. 26, 979–990 (1987).
[CrossRef]

1982 (1)

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental stress analysis,” Opt. Eng. 21, 427–431 (1982).

Begemann, T. F.

Bornert, M.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

Brémand, F.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

Bruck, H.

H. Jin and H. Bruck, “Pointwise digital image correlation using genetic algorithms,” Exp. Tech. 29, 36–39 (2005).
[CrossRef]

Bruck, H. A.

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

Buhmann, M. D.

M. D. Buhmann, Radial Basis Functions: Theory and Implementations (Cambridge U. Press, 2003).
[CrossRef]

Chan, Y. C.

Chen, D. J.

Chiang, F. P.

Chrysochoos, A.

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech. 41, 29–39(2001).
[CrossRef]

Dai, F. L.

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
[CrossRef]

Dai, X.

Davis, C. Q.

C. Q. Davis and D. M. Freeman, “Statistics of subpixel registration algorithms based on spatiotemporal gradients or block matching,” Opt. Eng. 37, 1290–1298 (1998).
[CrossRef]

Don, H. S.

Doumalin, P.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

Duchon, J.

J. Duchon,  “Splines minimizing rotation-invariant semi-norms in Sobolev spaces,” Laboratoire de Mathematiques Appliquees. (Springer-Verlag, 1977), pp. 85–100.

Dupré, J. C.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

Fazzini, M.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

Feng, Z.

Z. Feng and R. E. Rowlands, “Continuous full-field representation and differentiation of three-dimensional experimental vector data,” Comput. Struct. 26, 979–990 (1987).
[CrossRef]

Freeman, D. M.

C. Q. Davis and D. M. Freeman, “Statistics of subpixel registration algorithms based on spatiotemporal gradients or block matching,” Opt. Eng. 37, 1290–1298 (1998).
[CrossRef]

Goodson, K. E.

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation,” Opt. Eng. 40, 1613–1620 (2001).
[CrossRef]

Grédiac, M.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

Hild, F.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

S. Roux, J. Réthoré, and F. Hild, “Digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2D and 3D cracks,” J. Phys. D 42, 214004 (2009).
[CrossRef]

Jin, G.

J. Zhang, G. Jin, S. Ma, and L. Meng, “Application of an improved subpixel registration algorithm on digital speckle correlation measurement,” Opt. Laser Technol. 35, 533–542(2003).
[CrossRef]

Jin, H.

H. Jin and H. Bruck, “Pointwise digital image correlation using genetic algorithms,” Exp. Tech. 29, 36–39 (2005).
[CrossRef]

Li, E. B.

E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Application of digital image correlation technique to dynamic measurement of the velocity field in the deformation zone in cold rolling,” Opt. Lasers Eng. 39, 479–488 (2003).
[CrossRef]

Ma, S.

J. Zhang, G. Jin, S. Ma, and L. Meng, “Application of an improved subpixel registration algorithm on digital speckle correlation measurement,” Opt. Laser Technol. 35, 533–542(2003).
[CrossRef]

McNeil, S. R.

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

Meng, L.

J. Zhang, G. Jin, S. Ma, and L. Meng, “Application of an improved subpixel registration algorithm on digital speckle correlation measurement,” Opt. Laser Technol. 35, 533–542(2003).
[CrossRef]

Mistou, S.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

Molimard, J.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

Muracciole, J. M.

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech. 41, 29–39(2001).
[CrossRef]

Némoz-Gaillard, M.

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech. 41, 29–39(2001).
[CrossRef]

Orteu, J. J.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

M. A. Sutton, J. J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

Pan, B.

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
[CrossRef]

Peters, W. H.

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

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental stress analysis,” Opt. Eng. 21, 427–431 (1982).

Pitter, M. C.

Ranson, W. F.

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental stress analysis,” Opt. Eng. 21, 427–431 (1982).

Réthoré, J.

S. Roux, J. Réthoré, and F. Hild, “Digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2D and 3D cracks,” J. Phys. D 42, 214004 (2009).
[CrossRef]

Robert, L.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

Roux, S.

S. Roux, J. Réthoré, and F. Hild, “Digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2D and 3D cracks,” J. Phys. D 42, 214004 (2009).
[CrossRef]

Rowlands, R. E.

Z. Feng and R. E. Rowlands, “Continuous full-field representation and differentiation of three-dimensional experimental vector data,” Comput. Struct. 26, 979–990 (1987).
[CrossRef]

Schreier, H.

M. A. Sutton, J. J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

See, C. W.

So, A. C. K.

Somekh, M. G.

Surrel, Y.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

Sutton, M. A.

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

M. A. Sutton, J. J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

Tan, Y. S.

Tieu, A. K.

E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Application of digital image correlation technique to dynamic measurement of the velocity field in the deformation zone in cold rolling,” Opt. Lasers Eng. 39, 479–488 (2003).
[CrossRef]

Vacher, P.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

Wattrisse, B.

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech. 41, 29–39(2001).
[CrossRef]

Wright, G. B.

G. B. Wright, “Radial basis function interpolation: numerical and analytical developments,” Ph.D. dissertation (University of Colorado, 2003).

Xie, H. M.

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
[CrossRef]

Xu, B. Q.

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
[CrossRef]

Yuen, W. Y. D.

E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Application of digital image correlation technique to dynamic measurement of the velocity field in the deformation zone in cold rolling,” Opt. Lasers Eng. 39, 479–488 (2003).
[CrossRef]

Zhang, J.

J. Zhang, G. Jin, S. Ma, and L. Meng, “Application of an improved subpixel registration algorithm on digital speckle correlation measurement,” Opt. Laser Technol. 35, 533–542(2003).
[CrossRef]

Zhou, P.

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation,” Opt. Eng. 40, 1613–1620 (2001).
[CrossRef]

Appl. Opt. (3)

Comput. Struct. (1)

Z. Feng and R. E. Rowlands, “Continuous full-field representation and differentiation of three-dimensional experimental vector data,” Comput. Struct. 26, 979–990 (1987).
[CrossRef]

Exp. Mech. (3)

M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac, F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher, and B. Wattrisse, “Assessment of digital image correlation measurement errors: methodology and results,” Exp. Mech. 49, 353–370 (2009).
[CrossRef]

B. Wattrisse, A. Chrysochoos, J. M. Muracciole, and M. Némoz-Gaillard, “Analysis of strain localization during tensile tests by digital image correlation,” Exp. Mech. 41, 29–39(2001).
[CrossRef]

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

Exp. Tech. (1)

H. Jin and H. Bruck, “Pointwise digital image correlation using genetic algorithms,” Exp. Tech. 29, 36–39 (2005).
[CrossRef]

J. Phys. D (1)

S. Roux, J. Réthoré, and F. Hild, “Digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2D and 3D cracks,” J. Phys. D 42, 214004 (2009).
[CrossRef]

Meas. Sci. Technol. (1)

B. Pan, H. M. Xie, B. Q. Xu, and F. L. Dai, “Performance of sub-pixel registration algorithms in digital image correlation,” Meas. Sci. Technol. 17, 1615–1621 (2006).
[CrossRef]

Opt. Eng. (3)

C. Q. Davis and D. M. Freeman, “Statistics of subpixel registration algorithms based on spatiotemporal gradients or block matching,” Opt. Eng. 37, 1290–1298 (1998).
[CrossRef]

P. Zhou and K. E. Goodson, “Subpixel displacement and deformation gradient measurement using digital image/speckle correlation,” Opt. Eng. 40, 1613–1620 (2001).
[CrossRef]

W. H. Peters and W. F. Ranson, “Digital imaging techniques in experimental stress analysis,” Opt. Eng. 21, 427–431 (1982).

Opt. Express (1)

Opt. Laser Technol. (1)

J. Zhang, G. Jin, S. Ma, and L. Meng, “Application of an improved subpixel registration algorithm on digital speckle correlation measurement,” Opt. Laser Technol. 35, 533–542(2003).
[CrossRef]

Opt. Lasers Eng. (1)

E. B. Li, A. K. Tieu, and W. Y. D. Yuen, “Application of digital image correlation technique to dynamic measurement of the velocity field in the deformation zone in cold rolling,” Opt. Lasers Eng. 39, 479–488 (2003).
[CrossRef]

Other (4)

M. A. Sutton, J. J. Orteu, and H. Schreier, Image Correlation for Shape, Motion and Deformation Measurements (Springer, 2009).

M. D. Buhmann, Radial Basis Functions: Theory and Implementations (Cambridge U. Press, 2003).
[CrossRef]

G. B. Wright, “Radial basis function interpolation: numerical and analytical developments,” Ph.D. dissertation (University of Colorado, 2003).

J. Duchon,  “Splines minimizing rotation-invariant semi-norms in Sobolev spaces,” Laboratoire de Mathematiques Appliquees. (Springer-Verlag, 1977), pp. 85–100.

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Figures (6)

Fig. 1
Fig. 1

Two-dimensional interpolation example. (a) The exact values of function and the interpolation points marked by “*.” (b) The evaluated values of the function by MATLAB cubic interpolation. (c) The evaluated values of function by RBF interpolation. (d) The absolute error of the MATLAB cubic interpolation. (e) The absolute error of the RBF interpolation.

Fig. 2
Fig. 2

Computer-simulated uniaxial tensile and its displacement field: (a) the reference speckle image, (b) the deformed speckle image, (c) the contour image of the displacement u by the NR method, and (d) the contour image of the displacement u by our method.

Fig. 3
Fig. 3

Computer-simulated rigid body rotation and its displacement field: (a) the reference speckle image, (b) the deformed speckle image, (c-1) the contour image of the displacement u by the NR method, (c-2) the contour image of the displacement v by the NR method, (d-1) the contour image of the displacement u by our method, and (d-2) the contour image of the displacement v by our method.

Fig. 4
Fig. 4

Experimentally obtained rigid body translation and its displacement field: (a) the reference speckle image, (b) the deformed speckle image, (c) the displacement in the x direction by the NR method, and (d) the displacement in the x direction by our method.

Fig. 5
Fig. 5

Experimentally obtained three-point bending and its displacement field: (a) the reference speckle image, (b) the deformed speckle image, (c-1) the contour image of the displacement u by the NR method, (c-2) the contour image of the displacement v by the NR method, (d-1) the contour image of the displacement u by our method, and (d-2) the contour image of the displacement v by our method.

Fig. 6
Fig. 6

Specimen of three-point bending.

Equations (23)

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

g ( x ) = f ( x + u ( x ) ) + η ( x ) ,
S ( x , y , u , v , u x , u y , v x , v y ) = i = 1 m j = 1 m [ f ( x , y ) g ( x * , y * ) ] i = 1 m j = 1 m f 2 ( x , y ) i = 1 m j = 1 m g 2 ( x * , y * ) ,
{ x * = x + u + u x Δ x + u y Δ y y * = y + v + v x Δ x + v y Δ y ,
Δ P i = H 1 ( P ) × ( P i ) ,
s ( X ) = i = 1 N w i ϕ ( X X i ) ,
s ( X i ) = f i , i = 1 , 2 , N .
[ A ] [ W ] = [ F ] ,
s ( X ) = i = 1 N w i ϕ ( X X i ) + k = 1 M c k p k ( X ) , X R d ,
j = 1 N c j p k ( X j ) = 0 , k = 1 , 2 , , M .
[ A P P T 0 ] [ W C ] = [ F 0 ] ,
[ ϕ 11 ϕ 12 ϕ 1 N 1 x 1 y 1 ϕ 21 ϕ 22 ϕ 2 N 1 x 2 y 2 ϕ N 1 ϕ N 2 ϕ N N 1 x N y N 1 1 1 0 0 0 x 1 x 2 x N 0 0 0 y 1 y 2 y N 0 0 0 ] [ w 1 w 2 w N c 1 c 2 c 3 ] = [ f 1 f 2 f N 0 0 0 ] .
F ( x , y ) = sin ( y ) × cos ( x ) , 0 x 2 π , 0 y 2 π .
I 1 [ i , j ] = 1 4 π a 2 I 0 k = 1 S [ erf ( i x k a ) erf ( i + 1 x k a ) ] × [ erf ( j y k a ) erf ( j + 1 y k a ) ] ,
I 2 [ i , j ] = 1 4 π a 2 I 0 J k = 1 S [ erf ( ξ 1 ξ 0 , k a ) erf ( ξ 2 ξ 0 , k a ) ] × [ erf ( η 1 η 0 , k a ) erf ( η 2 η 0 , k a ) ] ,
ξ 1 = ( 1 u x ) i u y j ,
ξ 2 = ( 1 u x ) ( i + 1 ) u y ( j + 1 ) ,
ξ 0 , k = x k + u 0 ,
η 1 = v x i + ( 1 v y ) j ,
η 2 = v x ( i + 1 ) + ( 1 v y ) ( j + 1 ) ,
η 0 , k = y k + v 0 ,
J = det | 1 u x u y v x 1 v y | ,
MSE = 1 M × N k = 1 M l = 1 N ( u ( k , l ) u 0 ( k , l ) ) 2 ,
T r = T NR T RBF ,

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