Abstract

A method, believed to be new, is introduced to evaluate displacement fields from the analysis of a deformed image compared with a reference image. In contrast to standard methods, which determine a piecewise constant displacement field, the present method gives direct access to spectral decomposition of the displacement field. A minimization procedure is derived and used twice: first, to determine an affine displacement field and, then, the spectral components of the residual displacement. Although the method is applicable to any space dimension, only cases dealing with one-dimensional signals are reported: First, a purely synthetic example is discussed to estimate the intrinsic performance of the method, and a second case deals with a profile extracted from a sample of compressed glass wool.

© 2002 Optical Society of America

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    [CrossRef]
  4. F. Hild, B. Raka, M. Baudequin, S. Roux, F. Cantelaube are preparing a manuscript to be called “Multi-scale displacement field measurements of compressed mineral wool samples by digital image correlation.”
  5. C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
    [CrossRef]
  6. L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A Solids 20, 169–187 (2001).
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  8. J. Desrues, J. Lanier, P. Stutz, “Localization of the deformation in tests on sand sample,” Eng. Fract. Mech. 21, 909–921 (1985).
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  20. H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV; Part I: Limitation of conventional techniques due to deformation of image patterns,” Exp. Fluids 15, 168–174 (1993).
  21. H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV. II. Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).
  22. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes (Cambridge University, Cambridge, Mass., 1992).
  23. P. Tokumaru, P. Dimotakis, “Image correlation velocimetry,” Exp. Fluids 19, 1–15 (1995).
    [CrossRef]
  24. B. Wagne, S. Roux, F. Hild are preparing a manuscript to be called “Spectral approach to displacement evaluation from image analysis.”
  25. E. Bouzereau, “A review of imaging velocimetry methods,” Internal Rep. (École Nationale Supérieure des Techniques Avancées, Palaiseau, France, 2000).
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    [CrossRef]
  28. M. Baudequin, G. Ryschenkow, S. Roux, “Nonlinear elastic behavior of light fibrous materials,” Eur. Phys. J. B 12, 157–162 (1999).
    [CrossRef]

2001 (1)

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A Solids 20, 169–187 (2001).
[CrossRef]

2000 (1)

L. Humbert, V. Valle, M. Cottron, “Experimental determination and empirical representation of out-of-plane displacements in a cracked elastic plate loaded in mode I,” Int. J. Solids Struct. 37, 5493–5504 (2000).
[CrossRef]

1999 (1)

M. Baudequin, G. Ryschenkow, S. Roux, “Nonlinear elastic behavior of light fibrous materials,” Eur. Phys. J. B 12, 157–162 (1999).
[CrossRef]

1995 (1)

P. Tokumaru, P. Dimotakis, “Image correlation velocimetry,” Exp. Fluids 19, 1–15 (1995).
[CrossRef]

1993 (3)

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]

H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV; Part I: Limitation of conventional techniques due to deformation of image patterns,” Exp. Fluids 15, 168–174 (1993).

H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV. II. Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).

1992 (1)

C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
[CrossRef]

1991 (1)

D. Choi, J. L. Thorpe, R. Hanna, “Image analysis to measure strain in wood and paper,” Wood Sci. Technol. 25, 251–262 (1991).
[CrossRef]

1985 (2)

J. Desrues, J. Lanier, P. Stutz, “Localization of the deformation in tests on sand sample,” Eng. Fract. Mech. 21, 909–921 (1985).
[CrossRef]

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 232–244 (1985).
[CrossRef]

1984 (1)

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, 133–139 (1983).
[CrossRef]

1981 (1)

P. Jacquot, P. K. Rastogi, “Influence of out-of-plane deformation and its elimination in white light speckle photography,” Opt. Lasers Eng. 2, 33–55 (1981).
[CrossRef]

1977 (1)

T. D. Dudderar, P. G. Simpkins, “Laser speckle photography in a fluid medium,” Nature (London) 270, 45–47 (1977).
[CrossRef]

Baudequin, M.

M. Baudequin, G. Ryschenkow, S. Roux, “Nonlinear elastic behavior of light fibrous materials,” Eur. Phys. J. B 12, 157–162 (1999).
[CrossRef]

F. Hild, B. Raka, M. Baudequin, S. Roux, F. Cantelaube are preparing a manuscript to be called “Multi-scale displacement field measurements of compressed mineral wool samples by digital image correlation.”

Berthaud, Y.

Y. Berthaud, J. Scholz, J. Thesing, “Méthodes optiques et acoustiques de mesures des caractéristiques mécaniques,” in Proceedings of Colloque national MECAMAT “Mécanismes et mécanique des grandes déformations,” (in French) (MECAMAT, Aussois, France, 1996), pp. 77–80.

Bouzereau, E.

E. Bouzereau, “A review of imaging velocimetry methods,” Internal Rep. (École Nationale Supérieure des Techniques Avancées, Palaiseau, France, 2000).

Brunet, M.

S. Mguil, F. Morestin, M. Brunet, “Mesure des déformations par corrélation directe d’images numériques,” in Photomécanique 98 (GAMAC, Paris, 1998), pp. 361–368 (in French).

Calloch, S.

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A Solids 20, 169–187 (2001).
[CrossRef]

Cantelaube, F.

F. Hild, B. Raka, M. Baudequin, S. Roux, F. Cantelaube are preparing a manuscript to be called “Multi-scale displacement field measurements of compressed mineral wool samples by digital image correlation.”

Chao, Y. J.

M. A. Sutton, S. R. McNeill, J. D. Helm, Y. J. Chao, “Advances in two-dimensional and three-dimensional computer vision,” in Photomechanics, P. K. Rastogi, ed., Top. Appl. Phys.77, 323–372 (2000).
[CrossRef]

Chen, D. J.

Chevalier, L.

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A Solids 20, 169–187 (2001).
[CrossRef]

Chiang, F. P.

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]

F. P. Chiang, Q. Wang, F. Lehman, “New developments in full-field strain measurements using speckles,” in Nontraditional Methods of Sensing Stress, Strain, and Damage in Materials and Structures, Special Technical Publications (American Society for Testing Materials, Philadelphia, Pa., 1997), Vol. 1318, pp. 156–169.

Choi, D.

D. Choi, J. L. Thorpe, R. Hanna, “Image analysis to measure strain in wood and paper,” Wood Sci. Technol. 25, 251–262 (1991).
[CrossRef]

Chu, T. C.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 232–244 (1985).
[CrossRef]

Coret, M.

F. Hild, J.-N. Périé, M. Coret, “Mesure de champs de déplacements 2D par corrélation d’images numériques: correli2D” (in French), Internal Rep. No. 230 (LMT-Cachan, Cachan, France, 1999).

Cottron, M.

L. Humbert, V. Valle, M. Cottron, “Experimental determination and empirical representation of out-of-plane displacements in a cracked elastic plate loaded in mode I,” Int. J. Solids Struct. 37, 5493–5504 (2000).
[CrossRef]

Dahnoun, A.

C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
[CrossRef]

Desrues, J.

J. Desrues, J. Lanier, P. Stutz, “Localization of the deformation in tests on sand sample,” Eng. Fract. Mech. 21, 909–921 (1985).
[CrossRef]

Dimotakis, P.

P. Tokumaru, P. Dimotakis, “Image correlation velocimetry,” Exp. Fluids 19, 1–15 (1995).
[CrossRef]

Don, H. S.

Dudderar, T. D.

T. D. Dudderar, P. G. Simpkins, “Laser speckle photography in a fluid medium,” Nature (London) 270, 45–47 (1977).
[CrossRef]

Fiedler, H.

H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV; Part I: Limitation of conventional techniques due to deformation of image patterns,” Exp. Fluids 15, 168–174 (1993).

H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV. II. Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes (Cambridge University, Cambridge, Mass., 1992).

G’Sell, C.

C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
[CrossRef]

Halliwell, N. A.

Hanna, R.

D. Choi, J. L. Thorpe, R. Hanna, “Image analysis to measure strain in wood and paper,” Wood Sci. Technol. 25, 251–262 (1991).
[CrossRef]

Helm, J. D.

M. A. Sutton, S. R. McNeill, J. D. Helm, Y. J. Chao, “Advances in two-dimensional and three-dimensional computer vision,” in Photomechanics, P. K. Rastogi, ed., Top. Appl. Phys.77, 323–372 (2000).
[CrossRef]

Hild, F.

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A Solids 20, 169–187 (2001).
[CrossRef]

F. Hild, B. Raka, M. Baudequin, S. Roux, F. Cantelaube are preparing a manuscript to be called “Multi-scale displacement field measurements of compressed mineral wool samples by digital image correlation.”

B. Wagne, S. Roux, F. Hild are preparing a manuscript to be called “Spectral approach to displacement evaluation from image analysis.”

F. Hild, J.-N. Périé, M. Coret, “Mesure de champs de déplacements 2D par corrélation d’images numériques: correli2D” (in French), Internal Rep. No. 230 (LMT-Cachan, Cachan, France, 1999).

Hiver, J.-M.

C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
[CrossRef]

Huang, H.

H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV; Part I: Limitation of conventional techniques due to deformation of image patterns,” Exp. Fluids 15, 168–174 (1993).

H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV. II. Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).

Humbert, L.

L. Humbert, V. Valle, M. Cottron, “Experimental determination and empirical representation of out-of-plane displacements in a cracked elastic plate loaded in mode I,” Int. J. Solids Struct. 37, 5493–5504 (2000).
[CrossRef]

Jacquot, P.

P. Jacquot, P. K. Rastogi, “Influence of out-of-plane deformation and its elimination in white light speckle photography,” Opt. Lasers Eng. 2, 33–55 (1981).
[CrossRef]

Lanier, J.

J. Desrues, J. Lanier, P. Stutz, “Localization of the deformation in tests on sand sample,” Eng. Fract. Mech. 21, 909–921 (1985).
[CrossRef]

Lehman, F.

F. P. Chiang, Q. Wang, F. Lehman, “New developments in full-field strain measurements using speckles,” in Nontraditional Methods of Sensing Stress, Strain, and Damage in Materials and Structures, Special Technical Publications (American Society for Testing Materials, Philadelphia, Pa., 1997), Vol. 1318, pp. 156–169.

Marco, Y.

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A Solids 20, 169–187 (2001).
[CrossRef]

McNeill, S. R.

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, 133–139 (1983).
[CrossRef]

M. A. Sutton, S. R. McNeill, J. D. Helm, Y. J. Chao, “Advances in two-dimensional and three-dimensional computer vision,” in Photomechanics, P. K. Rastogi, ed., Top. Appl. Phys.77, 323–372 (2000).
[CrossRef]

Merzkirch, W.

W. Merzkirch, Flow Visualization (Academic, New York, 1987).

Mguil, S.

S. Mguil, F. Morestin, M. Brunet, “Mesure des déformations par corrélation directe d’images numériques,” in Photomécanique 98 (GAMAC, Paris, 1998), pp. 361–368 (in French).

Morestin, F.

S. Mguil, F. Morestin, M. Brunet, “Mesure des déformations par corrélation directe d’images numériques,” in Photomécanique 98 (GAMAC, Paris, 1998), pp. 361–368 (in French).

Périé, J.-N.

F. Hild, J.-N. Périé, M. Coret, “Mesure de champs de déplacements 2D par corrélation d’images numériques: correli2D” (in French), Internal Rep. No. 230 (LMT-Cachan, Cachan, France, 1999).

Peters, W. H.

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, 133–139 (1983).
[CrossRef]

Petters, W. H.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 232–244 (1985).
[CrossRef]

Pickering, C. J. D.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes (Cambridge University, Cambridge, Mass., 1992).

Raka, B.

F. Hild, B. Raka, M. Baudequin, S. Roux, F. Cantelaube are preparing a manuscript to be called “Multi-scale displacement field measurements of compressed mineral wool samples by digital image correlation.”

Ranson, W. F.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 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, 133–139 (1983).
[CrossRef]

Rastogi, P. K.

P. Jacquot, P. K. Rastogi, “Influence of out-of-plane deformation and its elimination in white light speckle photography,” Opt. Lasers Eng. 2, 33–55 (1981).
[CrossRef]

Roux, S.

M. Baudequin, G. Ryschenkow, S. Roux, “Nonlinear elastic behavior of light fibrous materials,” Eur. Phys. J. B 12, 157–162 (1999).
[CrossRef]

B. Wagne, S. Roux, F. Hild are preparing a manuscript to be called “Spectral approach to displacement evaluation from image analysis.”

F. Hild, B. Raka, M. Baudequin, S. Roux, F. Cantelaube are preparing a manuscript to be called “Multi-scale displacement field measurements of compressed mineral wool samples by digital image correlation.”

Ryschenkow, G.

M. Baudequin, G. Ryschenkow, S. Roux, “Nonlinear elastic behavior of light fibrous materials,” Eur. Phys. J. B 12, 157–162 (1999).
[CrossRef]

Scholz, J.

Y. Berthaud, J. Scholz, J. Thesing, “Méthodes optiques et acoustiques de mesures des caractéristiques mécaniques,” in Proceedings of Colloque national MECAMAT “Mécanismes et mécanique des grandes déformations,” (in French) (MECAMAT, Aussois, France, 1996), pp. 77–80.

Simpkins, P. G.

T. D. Dudderar, P. G. Simpkins, “Laser speckle photography in a fluid medium,” Nature (London) 270, 45–47 (1977).
[CrossRef]

Souahi, A.

C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
[CrossRef]

Stutz, P.

J. Desrues, J. Lanier, P. Stutz, “Localization of the deformation in tests on sand sample,” Eng. Fract. Mech. 21, 909–921 (1985).
[CrossRef]

Sutton, M. A.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 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, 133–139 (1983).
[CrossRef]

M. A. Sutton, S. R. McNeill, J. D. Helm, Y. J. Chao, “Advances in two-dimensional and three-dimensional computer vision,” in Photomechanics, P. K. Rastogi, ed., Top. Appl. Phys.77, 323–372 (2000).
[CrossRef]

Tan, Y. S.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes (Cambridge University, Cambridge, Mass., 1992).

Thesing, J.

Y. Berthaud, J. Scholz, J. Thesing, “Méthodes optiques et acoustiques de mesures des caractéristiques mécaniques,” in Proceedings of Colloque national MECAMAT “Mécanismes et mécanique des grandes déformations,” (in French) (MECAMAT, Aussois, France, 1996), pp. 77–80.

Thorpe, J. L.

D. Choi, J. L. Thorpe, R. Hanna, “Image analysis to measure strain in wood and paper,” Wood Sci. Technol. 25, 251–262 (1991).
[CrossRef]

Tokumaru, P.

P. Tokumaru, P. Dimotakis, “Image correlation velocimetry,” Exp. Fluids 19, 1–15 (1995).
[CrossRef]

Valle, V.

L. Humbert, V. Valle, M. Cottron, “Experimental determination and empirical representation of out-of-plane displacements in a cracked elastic plate loaded in mode I,” Int. J. Solids Struct. 37, 5493–5504 (2000).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes (Cambridge University, Cambridge, Mass., 1992).

Wagne, B.

B. Wagne, S. Roux, F. Hild are preparing a manuscript to be called “Spectral approach to displacement evaluation from image analysis.”

Wang, J.

H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV; Part I: Limitation of conventional techniques due to deformation of image patterns,” Exp. Fluids 15, 168–174 (1993).

H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV. II. Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).

Wang, Q.

F. P. Chiang, Q. Wang, F. Lehman, “New developments in full-field strain measurements using speckles,” in Nontraditional Methods of Sensing Stress, Strain, and Damage in Materials and Structures, Special Technical Publications (American Society for Testing Materials, Philadelphia, Pa., 1997), Vol. 1318, pp. 156–169.

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, 133–139 (1983).
[CrossRef]

Appl. Opt. (2)

Eng. Fract. Mech. (1)

J. Desrues, J. Lanier, P. Stutz, “Localization of the deformation in tests on sand sample,” Eng. Fract. Mech. 21, 909–921 (1985).
[CrossRef]

Eur. J. Mech. A Solids (1)

L. Chevalier, S. Calloch, F. Hild, Y. Marco, “Digital image correlation used to analyze the multiaxial behavior of rubber-like materials,” Eur. J. Mech. A Solids 20, 169–187 (2001).
[CrossRef]

Eur. Phys. J. B (1)

M. Baudequin, G. Ryschenkow, S. Roux, “Nonlinear elastic behavior of light fibrous materials,” Eur. Phys. J. B 12, 157–162 (1999).
[CrossRef]

Exp. Fluids (3)

H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV; Part I: Limitation of conventional techniques due to deformation of image patterns,” Exp. Fluids 15, 168–174 (1993).

H. Huang, H. Fiedler, J. Wang, “Limitation and improvement of PIV. II. Particle image distortion, a novel technique,” Exp. Fluids 15, 263–273 (1993).

P. Tokumaru, P. Dimotakis, “Image correlation velocimetry,” Exp. Fluids 19, 1–15 (1995).
[CrossRef]

Exp. Mech. (1)

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Petters, “Applications of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 3, 232–244 (1985).
[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, 133–139 (1983).
[CrossRef]

Int. J. Solids Struct. (1)

L. Humbert, V. Valle, M. Cottron, “Experimental determination and empirical representation of out-of-plane displacements in a cracked elastic plate loaded in mode I,” Int. J. Solids Struct. 37, 5493–5504 (2000).
[CrossRef]

J. Mater. Sci. (1)

C. G’Sell, J.-M. Hiver, A. Dahnoun, A. Souahi, “Video-controlled tensile testing of polymers and metals beyond the necking point,” J. Mater. Sci. 27, 5031–5039 (1992).
[CrossRef]

Nature (London) (1)

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Opt. Lasers Eng. (1)

P. Jacquot, P. K. Rastogi, “Influence of out-of-plane deformation and its elimination in white light speckle photography,” Opt. Lasers Eng. 2, 33–55 (1981).
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Other (13)

W. Merzkirch, Flow Visualization (Academic, New York, 1987).

F. Hild, B. Raka, M. Baudequin, S. Roux, F. Cantelaube are preparing a manuscript to be called “Multi-scale displacement field measurements of compressed mineral wool samples by digital image correlation.”

A. Lagarde, ed., Proceedings of the IUTAM Symposium on Advanced Optical Methods and Applications in Solid Mechanics, in Vol. 82 of Solid Mechanics and its Applications (Kluwer, Dordrecht, The Netherlands, 2000).

M. A. Sutton, S. R. McNeill, J. D. Helm, Y. J. Chao, “Advances in two-dimensional and three-dimensional computer vision,” in Photomechanics, P. K. Rastogi, ed., Top. Appl. Phys.77, 323–372 (2000).
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Y. Berthaud, J. Scholz, J. Thesing, “Méthodes optiques et acoustiques de mesures des caractéristiques mécaniques,” in Proceedings of Colloque national MECAMAT “Mécanismes et mécanique des grandes déformations,” (in French) (MECAMAT, Aussois, France, 1996), pp. 77–80.

F. P. Chiang, Q. Wang, F. Lehman, “New developments in full-field strain measurements using speckles,” in Nontraditional Methods of Sensing Stress, Strain, and Damage in Materials and Structures, Special Technical Publications (American Society for Testing Materials, Philadelphia, Pa., 1997), Vol. 1318, pp. 156–169.

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B. Wagne, S. Roux, F. Hild are preparing a manuscript to be called “Spectral approach to displacement evaluation from image analysis.”

E. Bouzereau, “A review of imaging velocimetry methods,” Internal Rep. (École Nationale Supérieure des Techniques Avancées, Palaiseau, France, 2000).

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F. Hild, J.-N. Périé, M. Coret, “Mesure de champs de déplacements 2D par corrélation d’images numériques: correli2D” (in French), Internal Rep. No. 230 (LMT-Cachan, Cachan, France, 1999).

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[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Two artificial textures as generated from a random walk: dashed curve, f; solid curve, g.

Fig. 2
Fig. 2

Change in the rms error in displacement with the number of iterations. The first eight iterations correspond to the affine estimate of the displacement field. The subsequent 41 iterations are used to evaluate the Fourier modes of the displacement field.

Fig. 3
Fig. 3

Final displacement field compared with the prescribed field: solid curve, prescribed displacement (defined by using 30 Fourier modes); dashed curve, estimate obtained from the present method after 8 + 41 iterations (i.e., 95 Fourier modes). Note that the only significant error (bottom curve) between the prescribed and the computed displacement field is confined to the edges of the signal.

Fig. 4
Fig. 4

Schematic of the experimental setup. The region of interest, ROI, is acquired initially and after various contractions. An example of reference and deformed pictures of a glass wool sample (1008 × 1016 pixels, 8-bit digitization) is shown.

Fig. 5
Fig. 5

Two functions as measured on the reference and the deformed sample of glass wool: dashed curve, f; solid curve, g.

Fig. 6
Fig. 6

Superimposed profiles accounting for the displacement field as determined with 55 Fourier modes: dashed curve, f; solid curve, g; bottom curve, the difference f - g, i.e., an estimate of the error.

Fig. 7
Fig. 7

Displacement field estimated from the present method with 55 Fourier modes for the glass-wool sample (8 + 21 iterations) compared with the result of a DIC analysis with a ZOI of 64 pixels, which is totally independent: solid curve, present method; dashed curve, DIC analysis.

Fig. 8
Fig. 8

First determination of an affine displacement field using the first treatment discussed in Section 4 (eight iterations). For comparison purposes the displacement field is shown and is determined by a standard DIC technique, which is totally independent: solid curve, first determination; dashed curve, DIC analysis.

Equations (26)

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

gX=gx+uxfx.
g˜k=gk= gXexp2iπkXdX= fxexp2iπkx+ux1+uxdx,
g˜k=f˜k+ exp2iπkxfxux+2iπkuxdx.
g˜k=f˜k- exp2iπkxfxuxdx+exp2iπkxfxux0L,
H˜1k=1if kk10if k>k1,
f˜-g˜kH˜1k= exp2iπkxH˜1kfxuxdx-H˜1kexp2iπkxfxux0L.
Ux=12πKK2 ŨKexp-2iπKxdK.
f˜-g˜kH˜1k=KK2 ŨKf˜k-KH˜1kdK.
f˜-g˜kH˜1kKK2 ŨKf˜k-KH˜1k-KdK,
gxfx-Uxfx-fxUx.
kf˜-g˜kH˜1kf˜K-kH˜1K-kdk=KK2 ŨKk f˜k-KH˜1k-Kf˜K-k×H˜1K-kdkdK.
f-gˆxfˆx=Uxfˆ2x,
Ux=f-gˆxfˆxfˆ2x.
AŪ= gX-fX-ŪX2dX,
AŪ= |g˜k-f·-Ū·k|2dk.
V¯= gXfX-V¯dX,
AˆŪ= |g˜k-f·-Ū·k|2H˜1kdk.
Ū=12πKK2 ŨKexp-2iπKxdK.
f·-Ū·k=f˜k-KK2 ŨK×f˜k-KH˜1k-KdK.
AˆŪ= g˜-f˜k-KK2 ŨKf˜k-K×H˜1k-KdK2H˜1kdk,
KK2 ŨKk f˜K-kH˜1K-kf˜k-K×H˜1k-KdkdK=kf˜-g˜kH˜1kf˜K-k×H˜1K-kdk.
AW¯= g-fx-W¯xfx2dx,
MA=B,
A=a1a2,
Mij= fˆ2xxi+j-2dx,
Bi= f-gˆxfˆxxi-1dx,

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