Abstract

An alternative approach to fully automatic speckle-displacement measurement is described. Two speckle patterns of a specimen, one before and one after deformation, are captured by a CCD camera and registered by a frame grabber. Two series of small subimages are obtained by segmenting the two speckle patterns. The corresponding subimage pairs extracted from both series are analyzed pointwise. The interrogation of each subimage pair involves a two-step fast-Fourier transform. While the first-step fast-Fourier transform achieves a complex spectrum characterized by the local displacement information, the second-step one generates a signal peak in the second spectral domain that resolves the local displacement vector. A rough estimate of the displacement vector is achieved by detecting the maximum pixel of the discrete spectrum. A more accurate determination is attained by a subpixel-maximum determination through a biparabolic fitting near the signal peak. The u- and v-displacement fields are deduced by analyzing all subimage pairs. A large rigid-body displacement can be overcome by introducing an artificial rigid shift of the two speckle patterns toward each other before the numerical process. The technique retains all the advantages of optical speckle photography and provides an extended range of measurement. Dynamic incremental deformations can be inspected by registering more speckle patterns at many consecutive deformation stages by using a high-speed CCD camera. The system was applied successfully to the study of crack-tip deformation fields.

© 1993 Optical Society of America

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  1. J. M. Burch, J. M. J. Tokarski, “Production of multiple beam fringes from photographic scatters,” Opt. Acta 15, 101–111 (1968).
  2. 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]
  3. R. P. Khetan, F. P. Chiang, “Strain analysis by one-beam laser speckle interferometry: 1: Single aperture method,” Appl. Opt. 15, 2205–2215 (1976).
    [CrossRef] [PubMed]
  4. F. P. Chiang, R. P. Khetan, “Strain analysis by one-beam laser speckle interferometry. 2: Multiaperture method,” Appl. Opt. 18, 2175–2186 (1979).
    [CrossRef] [PubMed]
  5. V. J. Parks, “The range of speckle metrology,” Exp. Mech. 20, 181–191 (1980).
    [CrossRef]
  6. I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” Opt. Acta 28, 1359–1376 (1981).
    [CrossRef]
  7. F. P. Chiang, R. M. Juang, “Vibration analysis of plate and shell by laser speckle interferometry,” Opt. Acta 23, 997–1009 (1976).
    [CrossRef]
  8. F. P. Chiang, A. Asundi, “Interior displacement and strain measurement using white light speckles,” Appl. Opt. 19, 2254–2256 (1980).
  9. F. P. Chiang, A. Asundi, “A white light speckle method applied to the determination of stress intensity factor and displacement field around a crack tip,” Eng. Fract. Mech. 15, 115–121 (1981).
    [CrossRef]
  10. R. Jones, C. Wikes, Holographic and Speckle Interferometry (Cambridge U. Press, Cambridge, UK, 1983).
  11. R. J. Pryputniewicz, K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputnievicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 456–467 (1989).
  12. C. A. Sciammarella, M. A. Ahmadshahi, “Detection of fringe pattern information using a computer based method,” Experimental Stress Analysis, H. Wieringa, ed. (Nijhoff, Dordrecht, The Netherlands, 1986), pp. 359–368.
    [CrossRef]
  13. P. Hariharan, B. F. Oreb, N. Brown, “A digital phase measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
    [CrossRef]
  14. K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestr. Eval. 8, 69–76 (1989).
    [CrossRef]
  15. T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–44 (1985).
    [CrossRef]
  16. N. Takai, T. Asakura, “Vectorial measurements of speckle displacement by 2-D electronic correlation method,” Appl. Opt. 24, 660–665 (1985).
    [CrossRef] [PubMed]
  17. M. A. Hamed, “Object-motion measurements using pulse-echo acoustical speckle and two-dimensional correlation,” Exp. Mech. 27, 250–254(1987).
    [CrossRef]
  18. H. A. Bruck, S. R. McNeill, M. A. Sutton, W. H. Peters, “Digital image correlation using Newton–Raphson method of partial differential correlation,” Exp. Mech. 29, 261–267 (1989).
    [CrossRef]
  19. C. Lee, Y. J. Chao, M. A. Sutton, W. H. Peters, W. F. Rason, “Determination of plastic strains at notches by image-processing methods,” Exp. Mech. 29, 214–220 (1989).
    [CrossRef]
  20. 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]
  21. D. J. Chen, F. P. Chiang, “Computer speckle interferometry,” in Proceeding of International Conference on Hologram Interferometry and Speckle Metrology (Society for Experimental Mechanics, Baltimore, Md., 1990), pp. 49–58.
  22. D. J. Chen, F. P. Chiang, “Computer-aided speckle interferometry using spectral amplitude fringes,” Appl. Opt. 32, 225–236 (1993).
    [CrossRef] [PubMed]
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  24. J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” in Applications of Digital Image Processing, A. G. Tescher, ed. Proc. Soc. Photo-Opt. Instrum. Eng.119, 197–205 (1977).
  25. C. D. Kuglin, A. F. Blumenthal, J. J. Pearson, “Map-matching techniques for terminal guidance using Fourier phase information,” in Digital Processing of Aerial Images, E. L. Hall, T. F. Wiener, eds., Proc. Soc. Photo-Opt. Instrum. Eng.186, 21–29 (1979).
  26. P. E. Anuta, “Spatial registration of multispectral and multitemporal digital imagery using fast Fourier transform techniques,” IEEE Trans. Geosci. Electron. GE-8, 353–368 (1970).
    [CrossRef]
  27. D. J. Chen, S. Li, T. Y. Hsu, F. P. Chiang, “Range of measurement of computer aided speckle interferometry,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 922–931 (1991).
  28. F. P. Chiang, T. V. Hareesh, B. C. Liu, S. Li, “Optical analysis of HRR field,” Opt. Eng. 27, 625–629 (1988).
  29. S. Li, D. J. Chen, F. P. Chiang, “Experimental on elastic-plastic deformation field of a propagating crack studied by CASI and moiré,” in Proceedings of the Seventh International Congress on Experimental Mechanics (Society for Experimental Mechanics, Las Vegas, Nev., 1992), Vol. 2, pp. 1720–1725.
  30. A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), Vol. 1.
  31. C. K. Yuen, D. Fraser, Digital Spectral Analysis (Pitman, New York, 1979).
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  33. D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Computer aided speckle interferometry (CASI): Part II. An alternate approach using spectral amplitude and phase information,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 706–717 (1991).

1993 (1)

1992 (1)

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 (3)

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

C. Lee, Y. J. Chao, M. A. Sutton, W. H. Peters, W. F. Rason, “Determination of plastic strains at notches by image-processing methods,” Exp. Mech. 29, 214–220 (1989).
[CrossRef]

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestr. Eval. 8, 69–76 (1989).
[CrossRef]

1988 (1)

F. P. Chiang, T. V. Hareesh, B. C. Liu, S. Li, “Optical analysis of HRR field,” Opt. Eng. 27, 625–629 (1988).

1987 (1)

M. A. Hamed, “Object-motion measurements using pulse-echo acoustical speckle and two-dimensional correlation,” Exp. Mech. 27, 250–254(1987).
[CrossRef]

1985 (2)

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–44 (1985).
[CrossRef]

N. Takai, T. Asakura, “Vectorial measurements of speckle displacement by 2-D electronic correlation method,” Appl. Opt. 24, 660–665 (1985).
[CrossRef] [PubMed]

1982 (1)

P. Hariharan, B. F. Oreb, N. Brown, “A digital phase measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

1981 (2)

F. P. Chiang, A. Asundi, “A white light speckle method applied to the determination of stress intensity factor and displacement field around a crack tip,” Eng. Fract. Mech. 15, 115–121 (1981).
[CrossRef]

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

1980 (2)

V. J. Parks, “The range of speckle metrology,” Exp. Mech. 20, 181–191 (1980).
[CrossRef]

F. P. Chiang, A. Asundi, “Interior displacement and strain measurement using white light speckles,” Appl. Opt. 19, 2254–2256 (1980).

1979 (1)

1976 (2)

F. P. Chiang, R. M. Juang, “Vibration analysis of plate and shell by laser speckle interferometry,” Opt. Acta 23, 997–1009 (1976).
[CrossRef]

R. P. Khetan, F. P. Chiang, “Strain analysis by one-beam laser speckle interferometry: 1: Single aperture method,” Appl. Opt. 15, 2205–2215 (1976).
[CrossRef] [PubMed]

1970 (2)

P. E. Anuta, “Spatial registration of multispectral and multitemporal digital imagery using fast Fourier transform techniques,” IEEE Trans. Geosci. Electron. GE-8, 353–368 (1970).
[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]

1968 (1)

J. M. Burch, J. M. J. Tokarski, “Production of multiple beam fringes from photographic scatters,” Opt. Acta 15, 101–111 (1968).

Ahmadshahi, M. A.

C. A. Sciammarella, M. A. Ahmadshahi, “Detection of fringe pattern information using a computer based method,” Experimental Stress Analysis, H. Wieringa, ed. (Nijhoff, Dordrecht, The Netherlands, 1986), pp. 359–368.
[CrossRef]

Anuta, P. E.

P. E. Anuta, “Spatial registration of multispectral and multitemporal digital imagery using fast Fourier transform techniques,” IEEE Trans. Geosci. Electron. GE-8, 353–368 (1970).
[CrossRef]

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]

Asakura, T.

Asundi, A.

F. P. Chiang, A. Asundi, “A white light speckle method applied to the determination of stress intensity factor and displacement field around a crack tip,” Eng. Fract. Mech. 15, 115–121 (1981).
[CrossRef]

F. P. Chiang, A. Asundi, “Interior displacement and strain measurement using white light speckles,” Appl. Opt. 19, 2254–2256 (1980).

Blumenthal, A. F.

C. D. Kuglin, A. F. Blumenthal, J. J. Pearson, “Map-matching techniques for terminal guidance using Fourier phase information,” in Digital Processing of Aerial Images, E. L. Hall, T. F. Wiener, eds., Proc. Soc. Photo-Opt. Instrum. Eng.186, 21–29 (1979).

Brohinsky, W. R.

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestr. Eval. 8, 69–76 (1989).
[CrossRef]

Brown, N.

P. Hariharan, B. F. Oreb, N. Brown, “A digital phase measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

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 correlation,” Exp. Mech. 29, 261–267 (1989).
[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]

J. M. Burch, J. M. J. Tokarski, “Production of multiple beam fringes from photographic scatters,” Opt. Acta 15, 101–111 (1968).

Bushman, T.

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestr. Eval. 8, 69–76 (1989).
[CrossRef]

Chao, Y. J.

C. Lee, Y. J. Chao, M. A. Sutton, W. H. Peters, W. F. Rason, “Determination of plastic strains at notches by image-processing methods,” Exp. Mech. 29, 214–220 (1989).
[CrossRef]

Chen, D. J.

D. J. Chen, F. P. Chiang, “Computer-aided speckle interferometry using spectral amplitude fringes,” Appl. Opt. 32, 225–236 (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]

D. J. Chen, F. P. Chiang, “Computer speckle interferometry,” in Proceeding of International Conference on Hologram Interferometry and Speckle Metrology (Society for Experimental Mechanics, Baltimore, Md., 1990), pp. 49–58.

D. J. Chen, S. Li, T. Y. Hsu, F. P. Chiang, “Range of measurement of computer aided speckle interferometry,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 922–931 (1991).

D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Computer aided speckle interferometry (CASI): Part II. An alternate approach using spectral amplitude and phase information,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 706–717 (1991).

S. Li, D. J. Chen, F. P. Chiang, “Experimental on elastic-plastic deformation field of a propagating crack studied by CASI and moiré,” in Proceedings of the Seventh International Congress on Experimental Mechanics (Society for Experimental Mechanics, Las Vegas, Nev., 1992), Vol. 2, pp. 1720–1725.

Chiang, F. P.

D. J. Chen, F. P. Chiang, “Computer-aided speckle interferometry using spectral amplitude fringes,” Appl. Opt. 32, 225–236 (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]

F. P. Chiang, T. V. Hareesh, B. C. Liu, S. Li, “Optical analysis of HRR field,” Opt. Eng. 27, 625–629 (1988).

F. P. Chiang, A. Asundi, “A white light speckle method applied to the determination of stress intensity factor and displacement field around a crack tip,” Eng. Fract. Mech. 15, 115–121 (1981).
[CrossRef]

F. P. Chiang, A. Asundi, “Interior displacement and strain measurement using white light speckles,” Appl. Opt. 19, 2254–2256 (1980).

F. P. Chiang, R. P. Khetan, “Strain analysis by one-beam laser speckle interferometry. 2: Multiaperture method,” Appl. Opt. 18, 2175–2186 (1979).
[CrossRef] [PubMed]

R. P. Khetan, F. P. Chiang, “Strain analysis by one-beam laser speckle interferometry: 1: Single aperture method,” Appl. Opt. 15, 2205–2215 (1976).
[CrossRef] [PubMed]

F. P. Chiang, R. M. Juang, “Vibration analysis of plate and shell by laser speckle interferometry,” Opt. Acta 23, 997–1009 (1976).
[CrossRef]

D. J. Chen, S. Li, T. Y. Hsu, F. P. Chiang, “Range of measurement of computer aided speckle interferometry,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 922–931 (1991).

D. J. Chen, F. P. Chiang, “Computer speckle interferometry,” in Proceeding of International Conference on Hologram Interferometry and Speckle Metrology (Society for Experimental Mechanics, Baltimore, Md., 1990), pp. 49–58.

S. Li, D. J. Chen, F. P. Chiang, “Experimental on elastic-plastic deformation field of a propagating crack studied by CASI and moiré,” in Proceedings of the Seventh International Congress on Experimental Mechanics (Society for Experimental Mechanics, Las Vegas, Nev., 1992), Vol. 2, pp. 1720–1725.

D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Computer aided speckle interferometry (CASI): Part II. An alternate approach using spectral amplitude and phase information,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 706–717 (1991).

Chu, T. C.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–44 (1985).
[CrossRef]

Don, H. S.

D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Computer aided speckle interferometry (CASI): Part II. An alternate approach using spectral amplitude and phase information,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 706–717 (1991).

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]

Fraser, D.

C. K. Yuen, D. Fraser, Digital Spectral Analysis (Pitman, New York, 1979).

Golosman, S.

J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” in Applications of Digital Image Processing, A. G. Tescher, ed. Proc. Soc. Photo-Opt. Instrum. Eng.119, 197–205 (1977).

Hamed, M. A.

M. A. Hamed, “Object-motion measurements using pulse-echo acoustical speckle and two-dimensional correlation,” Exp. Mech. 27, 250–254(1987).
[CrossRef]

Hareesh, T. V.

F. P. Chiang, T. V. Hareesh, B. C. Liu, S. Li, “Optical analysis of HRR field,” Opt. Eng. 27, 625–629 (1988).

Hariharan, P.

P. Hariharan, B. F. Oreb, N. Brown, “A digital phase measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Hines, D. C.

J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” in Applications of Digital Image Processing, A. G. Tescher, ed. Proc. Soc. Photo-Opt. Instrum. Eng.119, 197–205 (1977).

Hsu, T. Y.

D. J. Chen, S. Li, T. Y. Hsu, F. P. Chiang, “Range of measurement of computer aided speckle interferometry,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 922–931 (1991).

Jones, R.

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

Juang, R. M.

F. P. Chiang, R. M. Juang, “Vibration analysis of plate and shell by laser speckle interferometry,” Opt. Acta 23, 997–1009 (1976).
[CrossRef]

Kak, A. C.

A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), Vol. 1.

Khetan, R. P.

Kuglin, C. D.

J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” in Applications of Digital Image Processing, A. G. Tescher, ed. Proc. Soc. Photo-Opt. Instrum. Eng.119, 197–205 (1977).

C. D. Kuglin, A. F. Blumenthal, J. J. Pearson, “Map-matching techniques for terminal guidance using Fourier phase information,” in Digital Processing of Aerial Images, E. L. Hall, T. F. Wiener, eds., Proc. Soc. Photo-Opt. Instrum. Eng.186, 21–29 (1979).

Lee, C.

C. Lee, Y. J. Chao, M. A. Sutton, W. H. Peters, W. F. Rason, “Determination of plastic strains at notches by image-processing methods,” Exp. Mech. 29, 214–220 (1989).
[CrossRef]

Li, S.

F. P. Chiang, T. V. Hareesh, B. C. Liu, S. Li, “Optical analysis of HRR field,” Opt. Eng. 27, 625–629 (1988).

S. Li, D. J. Chen, F. P. Chiang, “Experimental on elastic-plastic deformation field of a propagating crack studied by CASI and moiré,” in Proceedings of the Seventh International Congress on Experimental Mechanics (Society for Experimental Mechanics, Las Vegas, Nev., 1992), Vol. 2, pp. 1720–1725.

D. J. Chen, S. Li, T. Y. Hsu, F. P. Chiang, “Range of measurement of computer aided speckle interferometry,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 922–931 (1991).

Liu, B. C.

F. P. Chiang, T. V. Hareesh, B. C. Liu, S. Li, “Optical analysis of HRR field,” Opt. Eng. 27, 625–629 (1988).

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 correlation,” Exp. Mech. 29, 261–267 (1989).
[CrossRef]

Oreb, B. F.

P. Hariharan, B. F. Oreb, N. Brown, “A digital phase measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Parks, V. J.

V. J. Parks, “The range of speckle metrology,” Exp. Mech. 20, 181–191 (1980).
[CrossRef]

Pearson, J. J.

C. D. Kuglin, A. F. Blumenthal, J. J. Pearson, “Map-matching techniques for terminal guidance using Fourier phase information,” in Digital Processing of Aerial Images, E. L. Hall, T. F. Wiener, eds., Proc. Soc. Photo-Opt. Instrum. Eng.186, 21–29 (1979).

J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” in Applications of Digital Image Processing, A. G. Tescher, ed. Proc. Soc. Photo-Opt. Instrum. Eng.119, 197–205 (1977).

Peters, W. H.

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

C. Lee, Y. J. Chao, M. A. Sutton, W. H. Peters, W. F. Rason, “Determination of plastic strains at notches by image-processing methods,” Exp. Mech. 29, 214–220 (1989).
[CrossRef]

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–44 (1985).
[CrossRef]

Pryputniewicz, R. J.

R. J. Pryputniewicz, K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputnievicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 456–467 (1989).

Ranson, W. F.

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–44 (1985).
[CrossRef]

Rason, W. F.

C. Lee, Y. J. Chao, M. A. Sutton, W. H. Peters, W. F. Rason, “Determination of plastic strains at notches by image-processing methods,” Exp. Mech. 29, 214–220 (1989).
[CrossRef]

Rosenfeld, A.

A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), Vol. 1.

Sciammarella, C. A.

C. A. Sciammarella, M. A. Ahmadshahi, “Detection of fringe pattern information using a computer based method,” Experimental Stress Analysis, H. Wieringa, ed. (Nijhoff, Dordrecht, The Netherlands, 1986), pp. 359–368.
[CrossRef]

Stetson, K. A.

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestr. Eval. 8, 69–76 (1989).
[CrossRef]

R. J. Pryputniewicz, K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputnievicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 456–467 (1989).

Sutton, M. A.

C. Lee, Y. J. Chao, M. A. Sutton, W. H. Peters, W. F. Rason, “Determination of plastic strains at notches by image-processing methods,” Exp. Mech. 29, 214–220 (1989).
[CrossRef]

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

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–44 (1985).
[CrossRef]

Takai, N.

Tan, Y. S.

D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Computer aided speckle interferometry (CASI): Part II. An alternate approach using spectral amplitude and phase information,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 706–717 (1991).

Tokarski, J. M. J.

J. M. Burch, J. M. J. Tokarski, “Production of multiple beam fringes from photographic scatters,” Opt. Acta 15, 101–111 (1968).

Wahid, J.

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestr. Eval. 8, 69–76 (1989).
[CrossRef]

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H. W. Wessely, “Image correlation: Part II. Theoretical basis,” Rep. R-2057/2-PR (Rand Corporation, Santa Monica, Calif., 1976).

Wikes, C.

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

Yamaguchi, I.

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

Yu, F. T. S.

F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983).

Yuen, C. K.

C. K. Yuen, D. Fraser, Digital Spectral Analysis (Pitman, New York, 1979).

Appl. Opt. (5)

Eng. Fract. Mech. (1)

F. P. Chiang, A. Asundi, “A white light speckle method applied to the determination of stress intensity factor and displacement field around a crack tip,” Eng. Fract. Mech. 15, 115–121 (1981).
[CrossRef]

Exp. Mech. (6)

V. J. Parks, “The range of speckle metrology,” Exp. Mech. 20, 181–191 (1980).
[CrossRef]

M. A. Hamed, “Object-motion measurements using pulse-echo acoustical speckle and two-dimensional correlation,” Exp. Mech. 27, 250–254(1987).
[CrossRef]

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

C. Lee, Y. J. Chao, M. A. Sutton, W. H. Peters, W. F. Rason, “Determination of plastic strains at notches by image-processing methods,” Exp. Mech. 29, 214–220 (1989).
[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]

T. C. Chu, W. F. Ranson, M. A. Sutton, W. H. Peters, “Application of digital-image-correlation techniques to experimental mechanics,” Exp. Mech. 25, 232–44 (1985).
[CrossRef]

IEEE Trans. Geosci. Electron. (1)

P. E. Anuta, “Spatial registration of multispectral and multitemporal digital imagery using fast Fourier transform techniques,” IEEE Trans. Geosci. Electron. GE-8, 353–368 (1970).
[CrossRef]

J. Nondestr. Eval. (1)

K. A. Stetson, W. R. Brohinsky, J. Wahid, T. Bushman, “An electro-optic holography system with real-time arithmetic processing,” J. Nondestr. Eval. 8, 69–76 (1989).
[CrossRef]

Opt. Acta (4)

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

F. P. Chiang, R. M. Juang, “Vibration analysis of plate and shell by laser speckle interferometry,” Opt. Acta 23, 997–1009 (1976).
[CrossRef]

J. M. Burch, J. M. J. Tokarski, “Production of multiple beam fringes from photographic scatters,” Opt. Acta 15, 101–111 (1968).

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. Commun. (1)

P. Hariharan, B. F. Oreb, N. Brown, “A digital phase measurement system for real-time holographic interferometry,” Opt. Commun. 41, 393–396 (1982).
[CrossRef]

Opt. Eng. (1)

F. P. Chiang, T. V. Hareesh, B. C. Liu, S. Li, “Optical analysis of HRR field,” Opt. Eng. 27, 625–629 (1988).

Other (13)

S. Li, D. J. Chen, F. P. Chiang, “Experimental on elastic-plastic deformation field of a propagating crack studied by CASI and moiré,” in Proceedings of the Seventh International Congress on Experimental Mechanics (Society for Experimental Mechanics, Las Vegas, Nev., 1992), Vol. 2, pp. 1720–1725.

A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), Vol. 1.

C. K. Yuen, D. Fraser, Digital Spectral Analysis (Pitman, New York, 1979).

H. W. Wessely, “Image correlation: Part II. Theoretical basis,” Rep. R-2057/2-PR (Rand Corporation, Santa Monica, Calif., 1976).

D. J. Chen, F. P. Chiang, Y. S. Tan, H. S. Don, “Computer aided speckle interferometry (CASI): Part II. An alternate approach using spectral amplitude and phase information,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 706–717 (1991).

D. J. Chen, S. Li, T. Y. Hsu, F. P. Chiang, “Range of measurement of computer aided speckle interferometry,” in Second International Conference on Photomechanics and Speckle Metrology: Speckle Techniques, Birefringence Methods, and Applications to Solid Mechanics, F. Chiang, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1554A, 922–931 (1991).

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

R. J. Pryputniewicz, K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” in Laser Interferometry: Quantitative Analysis of Interferograms: Third in a Series, R. J. Pryputnievicz, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1162, 456–467 (1989).

C. A. Sciammarella, M. A. Ahmadshahi, “Detection of fringe pattern information using a computer based method,” Experimental Stress Analysis, H. Wieringa, ed. (Nijhoff, Dordrecht, The Netherlands, 1986), pp. 359–368.
[CrossRef]

D. J. Chen, F. P. Chiang, “Computer speckle interferometry,” in Proceeding of International Conference on Hologram Interferometry and Speckle Metrology (Society for Experimental Mechanics, Baltimore, Md., 1990), pp. 49–58.

F. T. S. Yu, Optical Information Processing (Wiley, New York, 1983).

J. J. Pearson, D. C. Hines, S. Golosman, C. D. Kuglin, “Video-rate image correlation processor,” in Applications of Digital Image Processing, A. G. Tescher, ed. Proc. Soc. Photo-Opt. Instrum. Eng.119, 197–205 (1977).

C. D. Kuglin, A. F. Blumenthal, J. J. Pearson, “Map-matching techniques for terminal guidance using Fourier phase information,” in Digital Processing of Aerial Images, E. L. Hall, T. F. Wiener, eds., Proc. Soc. Photo-Opt. Instrum. Eng.186, 21–29 (1979).

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Figures (8)

Fig. 1
Fig. 1

Schematic of data-acquisition and image-processing system.

Fig. 2
Fig. 2

Data-processing procedures: ωx, and ξ, η, spectral-domain coordinates.

Fig. 3
Fig. 3

Hypothetic optical transform process.

Fig. 4
Fig. 4

Typical signal peaks generated at (a) zero and (b) nonzero displacement locations.

Fig. 5
Fig. 5

Typical signal peaks obtained from a subimage pair when (a) α = 0.00, (b) α = 0.25, (c) α = 0.50, and (d) α = 1.00.

Fig. 6
Fig. 6

Subpixel-maximum detection of a signal peak (the high-lighted region is used in a biparabolic fitting).

Fig. 7
Fig. 7

Digital speckle patterns around a crack tip at (a) zero load, (b) load level 1, and (c) load level 2.

Fig. 8
Fig. 8

Displacement contours around a crack tip at (a) load level 1 and (b) load level 2. The upper and lower contour plots of (a) and (b) represent the u and v fields, respectively.

Equations (29)

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ψ ( f x , f y ) = ϕ 1 ( f x , f y ) - ϕ 2 ( f x , f y ) = 2 π v / ( λ f ) ,
h 1 ( x , y ) = h ( x , y ) , h 2 ( x , y ) = h ( x - u , y - v ) + n ( x , y ) ,
H 1 ( ω x , ω y ) = Δ h ( x , y ) exp [ - j 2 π ( x ω x + y ω y ) ] d x d y = H ( ω x , ω y ) exp [ j ϕ ( ω x , ω y ) ] , H 2 ( ω x , ω y ) = Δ [ h ( x - u , y - v ) + n ( x , y ) ] × exp [ - j 2 π ( x ω x + y ω y ) ] d x d y = H ( ω x , ω y ) exp { j [ ϕ ( ω x , ω y ) - 2 π ( u ω x + v ω y ) ] } + N ( ω x , ω y ) ,
F ( ω x , ω y ) = H 1 ( ω x , ω y ) H 2 * ( ω x , ω y ) / H 1 ( ω x , ω y ) H 2 ( ω x , ω y ) 1 - α
F ( ω x , ω y ) = H 1 ( ω x , ω y ) H 2 ( ω x , ω y ) α × exp { j [ ϕ 1 ( ω x , ω y ) - ϕ 2 ( ω x , ω y ) ] } ,
F ( ω x , ω y ) H ( ω x , ω y ) 2 α exp [ j 2 π ( u ω x + v ω y ) ] .
G ( ξ , η ) = Δ ω F ( ω x , ω y ) exp [ - j 2 π ( ω x ξ + ω y η ) ] d ω x d ω y Δ ω H ( ω x , ω y ) 2 α × exp { - j 2 π [ ω x ( ξ - u ) + ω y ( η - v ) ] } d ω x d ω y = G ¯ α ( ξ - u , η - v ) ,
G ¯ α ( ξ , η ) = Δ ω H ( ω x , ω y ) 2 α × exp [ - j 2 π ( ω x ξ + ω y η ) ] d ω x d ω y .
ξ = ξ - ξ 0 , η = η - η 0 .
ξ m = ξ m - ξ 0 , η m = η m - η 0 .
G f ( ξ , η ) = C 0 + C 1 ( ξ - ξ m ) + C 2 ( η - η m ) + C 3 ( ξ - ξ m ) 2 + C 4 ( η - η m ) 2 + C 5 ( ξ - ξ m ) ( η - η m ) + C 6 ( ξ - ξ m ) 3 + C 7 ( η - η m ) 3 + C 8 ( ξ - ξ m ) 2 ( η - η m ) + C 9 ( ξ - ξ m ) ( η - η m ) 2 + HOT ,
C 1 = C 2 = C 5 = C 6 = C 7 = C 8 = C 9 = 0 , C 3 = C 4 .
G f ( ξ , η ) = C 0 + C 3 [ ( ξ - ξ m ) 2 + ( η - η m ) 2 ] ,
G f ( ξ , η ) = c 0 + c 1 ξ + c 2 η + c 3 ( ξ 2 + η 2 ) ,
c 0 = C 0 + C 3 ( ξ m 2 + η m 2 ) , c 1 = - 2 C 3 ξ m , c 2 = - 2 C 3 η m , c 3 = C 3 .
[ c 0 c 1 c 2 c 3 ] = [ 27 / 175 0 0 - 1 / 35 0 1 / 50 0 0 0 0 1 / 50 0 - 1 / 35 0 0 1 / 140 ] × [ ξ = - 2 + 2 η = - 2 + 2 G ( ξ , η ) ξ = - 2 + 2 η = - 2 + 2 ξ G ( ξ , η ) ξ = - 2 + 2 η = - 2 + 2 η G ( ξ , η ) ξ = - 2 + 2 η = - 2 + 2 ( ξ 2 + η 2 ) G ( ξ , η ) ] .
ξ m = - c 1 / ( 2 c 3 ) , η m = - c 2 / ( 2 c 3 ) .
u = ξ m = ξ 0 + ξ m , v = η m = η 0 + η m .
δ i = 0.02 T ~ 0.05 T ,
δ 0 = 0.02 T 0 ~ 0.05 T 0 ,
δ = ξ = - K K η = - K K [ c 0 + c 1 ξ + c 2 η + c 3 ( ξ 2 + η 2 ) - G ( ξ , η ) ] 2 ,
δ / c i = 0 ,             i = 0 , , 3.
M k l = ξ = - K K η = - K K ξ k η l ,             k , l = 0 , , 4.
M k l = 0 ,             k or l odd ,
[ M 00 0 0 M 20 + M 02 0 M 20 0 0 0 0 M 02 0 M 20 + M 02 0 0 M 40 + 2 M 22 + M 04 ] [ c 0 c 1 c 2 c 3 ] = [ q 0 q 1 q 2 q 3 ] ,
[ q 0 q 1 q 2 q 3 ] = [ ξ = - K + K η = - K + K G ( ξ , η ) ξ = - K + K η = - K + K ξ G ( ξ , η ) ξ = - K + K η = - K + K η G ( ξ , η ) ξ = - K + K η = - K + K ( ξ 2 + η 2 ) G ( ξ , η ) ] .
[ c 0 c 1 c 2 c 3 ] = [ ( M 40 + 2 M 22 + M 04 ) / Δ 0 0 - ( M 20 + M 02 ) / Δ 0 1 / M 20 0 0 0 0 1 / M 02 0 - ( M 20 + M 02 ) / Δ 0 0 M 00 / Δ ] [ q 0 q 1 q 2 q 3 ] ,
Δ = M 00 ( M 40 + 2 M 22 + M 04 ) - ( M 20 + M 02 ) 2 .
[ c 0 c 1 c 2 c 3 ] = [ 27 / 175 0 0 - 1 / 35 0 1 / 50 0 0 0 0 1 / 50 0 - 1 / 35 0 0 1 / 140 ] × [ ξ = - 2 + 2 η = - 2 + 2 G ( ξ , η ) ξ = - 2 + 2 η = - 2 + 2 ξ G ( ξ , η ) ξ = - 2 + 2 η = - 2 + 2 η G ( ξ , η ) ξ = - 2 + 2 η ' = - 2 + 2 ( ξ 2 + η 2 ) G ( ξ , η ) ] .

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