Abstract

The out-of-plane vibration of a rough surface causes an in-plane vibration of its speckle pattern when observed with a defocused optical photographic system. If the frequency of the oscillations is high enough, a time-averaged specklegram is recorded from which the amplitude of the vibration can be estimated. The statistical character of speckle distributions along with the pixel sampling and intensity analog-to-digital conversion inherent to electronic cameras degrade the accuracy of the amplitude measurement to an extent that is analyzed and experimentally tested in this paper. The relations limiting the mutually competing metrological features of a defocused speckle system are also deduced mathematically.

© 2009 Optical Society of America

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References

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  1. H. Tiziani, “A study of the use of laser speckle to measure small tilts of optically rough surfaces accurately,” Opt. Commun. 5, 271-274 (1972).
    [CrossRef]
  2. H. Tiziani, “Vibration analysis and deformation measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, 1978), pp. 73-110.
  3. P. K. Rastogi, “techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. R. Sirohi, ed. (Marcel Dekker, 1993), pp. 41-98.
  4. D. A. Gregory, “Basic physical principles of defocused speckle photography: a tilt topology inspection technique,” Opt. Laser Technol. 8, 201-213 (1976).
    [CrossRef]
  5. D. A. Gregory, “Speckle scatter, affine geometry and tilt topology,” Opt. Commun. 20, 1-5 (1977).
    [CrossRef]
  6. D. A. Gregory, “Topological speckle and structural inspection,” in Speckle Metrology, R. K. Erf, ed. (Academic, 1978), pp. 183-223.
  7. F. P. Chiang and R. M. Juang, “Laser speckle interferometry for plate bending problems,” Appl. Opt. 15, 2199-2204 (1976).
    [CrossRef]
  8. A. E. Ennos and M. S. Virdee, “Laser speckle photography as a practical alternative to holographic interferometry fot measuring plate deformation,” Opt. Eng. 21, 478-482 (1982).
  9. F. P. Chiang and R. M. Juang, “Vibration analysis of plate and shell by laser speckle interferometry,” Opt. Acta 23, 997-1009 (1976).
  10. H. Schwieger and J. Banken, “Speckle photography for deformation analysis of bent plates,” Mater. Prüf. 27, 153-156(1985).
  11. M. Sjödahl, “Electronic speckle photography: measurement of in-plane strain fields through the use of defocused laser speckle,” Appl. Opt. 34, 5799-5808 (1995).
    [CrossRef]
  12. M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image. Vis. Comput. 1, 133-139 (1983).
  13. D. J. Chen, F. P. Chiang, Y. S. Tan, and H. D. Don, “Digital speckle-displacement measurement using a complex spectrum method,” Appl. Opt. 32, 1839-1849 (1993).
    [CrossRef]
  14. M. Sjödahl and L. R. Benckert, “Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy,” Appl. Opt. 32, 2278-2284 (1993).
  15. D. Amodio, G. B. Broggato, F. Campana, and G. M. Newaz, “Digital speckle correlation for strain measurement by image analysis,” Exp. Mech. 43, 396-402 (2003).
    [CrossRef]
  16. O. J. Lokberg, “ESPI, the ultimate holographic tool for vibration analysis?,” J. Acoust. Soc. Am. 75, 1783-1791 (1984).
    [CrossRef]
  17. W. O. Wong and K. T. Chan, “Quantitative vibration amplitude measurement with time-averaged digital speckle pattern interferometry,” Opt. Laser Technol. 30, 317-324 (1998).
    [CrossRef]
  18. M. C. Shellabear and J. R. Tyrer, “Application of ESPI to three-dimensional vibration measurements,” Opt. Laser Technol. 15, 43-56 (1991).
  19. P. Slangen, L. Berwart, C. Veuster, J. Gonlinval, and Y. Lion, “Digital speckle pattern interferometry: a fast procedure to detect and measure vibration mode shapes,” Opt. Lasers Eng. 25, 311-321 (1996).
    [CrossRef]
  20. K. Kang, K. Kim, and H. Lee, “Evaluation of elastic modulus of cantilever beam by TA-ESPI,” Opt. Lasers Technol. 39, 449-452 (2007).
    [CrossRef]
  21. N. Takai, “Contrast of time-averaged image speckle pattern for a vibrating object,” Opt. Commun. 25, 31-34 (1978).
    [CrossRef]
  22. G. S. Spagnolo, D. Paoletty, and P. Zanetti, “Local speckle correlation for vibration analysis,” Opt. Commun. 123, 41-48(1996).
    [CrossRef]
  23. W. O. Wong, “Vibration analysis by laser speckle correlation,” Opt. Lasers Eng. 28, 277-286 (1997).
    [CrossRef]
  24. J. Diazdelacruz, “Multiwindowed defocused electronic speckle photographic system for tilt measurement,” Appl. Opt. 44, 2250-2257 (2005).
    [CrossRef]
  25. J. Diazdelacruz, “Adaptive aperture defocused digital speckle photography,” Appl. Opt. 46, 6105-6112 (2007).
    [CrossRef]
  26. A. F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37, 326-329 (1981).
    [CrossRef]
  27. J. D. Briers and S. Webster, “Laser speckle contrast analysis: a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1, 174-179 (1996).
    [CrossRef]
  28. L. Keene and F. P. Chiang, “Real-time anti-node visualization of vibrating distributed systems in noisy environments using defocused laser speckle contrast analysis,” J. Sound Vib. 320, 472-481 (2009).
    [CrossRef]
  29. D. J. Burns and H. F. Helbig, “A system for automatic electrical and optical characterization of microelectromechanical devices,” J. Microelectromech. Syst. 8, 473-482 (1999).
    [CrossRef]
  30. S. Wang, B. Guan, G. Wang, and L. Qian, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
    [CrossRef]
  31. J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer Verlag, 1975), pp. 9-75.
  32. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 1991).

2009 (1)

L. Keene and F. P. Chiang, “Real-time anti-node visualization of vibrating distributed systems in noisy environments using defocused laser speckle contrast analysis,” J. Sound Vib. 320, 472-481 (2009).
[CrossRef]

2007 (3)

S. Wang, B. Guan, G. Wang, and L. Qian, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[CrossRef]

J. Diazdelacruz, “Adaptive aperture defocused digital speckle photography,” Appl. Opt. 46, 6105-6112 (2007).
[CrossRef]

K. Kang, K. Kim, and H. Lee, “Evaluation of elastic modulus of cantilever beam by TA-ESPI,” Opt. Lasers Technol. 39, 449-452 (2007).
[CrossRef]

2005 (1)

2003 (1)

D. Amodio, G. B. Broggato, F. Campana, and G. M. Newaz, “Digital speckle correlation for strain measurement by image analysis,” Exp. Mech. 43, 396-402 (2003).
[CrossRef]

1999 (1)

D. J. Burns and H. F. Helbig, “A system for automatic electrical and optical characterization of microelectromechanical devices,” J. Microelectromech. Syst. 8, 473-482 (1999).
[CrossRef]

1998 (1)

W. O. Wong and K. T. Chan, “Quantitative vibration amplitude measurement with time-averaged digital speckle pattern interferometry,” Opt. Laser Technol. 30, 317-324 (1998).
[CrossRef]

1997 (1)

W. O. Wong, “Vibration analysis by laser speckle correlation,” Opt. Lasers Eng. 28, 277-286 (1997).
[CrossRef]

1996 (3)

P. Slangen, L. Berwart, C. Veuster, J. Gonlinval, and Y. Lion, “Digital speckle pattern interferometry: a fast procedure to detect and measure vibration mode shapes,” Opt. Lasers Eng. 25, 311-321 (1996).
[CrossRef]

G. S. Spagnolo, D. Paoletty, and P. Zanetti, “Local speckle correlation for vibration analysis,” Opt. Commun. 123, 41-48(1996).
[CrossRef]

J. D. Briers and S. Webster, “Laser speckle contrast analysis: a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1, 174-179 (1996).
[CrossRef]

1995 (1)

1993 (2)

1991 (1)

M. C. Shellabear and J. R. Tyrer, “Application of ESPI to three-dimensional vibration measurements,” Opt. Laser Technol. 15, 43-56 (1991).

1985 (1)

H. Schwieger and J. Banken, “Speckle photography for deformation analysis of bent plates,” Mater. Prüf. 27, 153-156(1985).

1984 (1)

O. J. Lokberg, “ESPI, the ultimate holographic tool for vibration analysis?,” J. Acoust. Soc. Am. 75, 1783-1791 (1984).
[CrossRef]

1983 (1)

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image. Vis. Comput. 1, 133-139 (1983).

1982 (1)

A. E. Ennos and M. S. Virdee, “Laser speckle photography as a practical alternative to holographic interferometry fot measuring plate deformation,” Opt. Eng. 21, 478-482 (1982).

1981 (1)

A. F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37, 326-329 (1981).
[CrossRef]

1978 (1)

N. Takai, “Contrast of time-averaged image speckle pattern for a vibrating object,” Opt. Commun. 25, 31-34 (1978).
[CrossRef]

1977 (1)

D. A. Gregory, “Speckle scatter, affine geometry and tilt topology,” Opt. Commun. 20, 1-5 (1977).
[CrossRef]

1976 (3)

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

D. A. Gregory, “Basic physical principles of defocused speckle photography: a tilt topology inspection technique,” Opt. Laser Technol. 8, 201-213 (1976).
[CrossRef]

F. P. Chiang and R. M. Juang, “Laser speckle interferometry for plate bending problems,” Appl. Opt. 15, 2199-2204 (1976).
[CrossRef]

1972 (1)

H. Tiziani, “A study of the use of laser speckle to measure small tilts of optically rough surfaces accurately,” Opt. Commun. 5, 271-274 (1972).
[CrossRef]

Amodio, D.

D. Amodio, G. B. Broggato, F. Campana, and G. M. Newaz, “Digital speckle correlation for strain measurement by image analysis,” Exp. Mech. 43, 396-402 (2003).
[CrossRef]

Banken, J.

H. Schwieger and J. Banken, “Speckle photography for deformation analysis of bent plates,” Mater. Prüf. 27, 153-156(1985).

Benckert, L. R.

Berwart, L.

P. Slangen, L. Berwart, C. Veuster, J. Gonlinval, and Y. Lion, “Digital speckle pattern interferometry: a fast procedure to detect and measure vibration mode shapes,” Opt. Lasers Eng. 25, 311-321 (1996).
[CrossRef]

Briers, J. D.

J. D. Briers and S. Webster, “Laser speckle contrast analysis: a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1, 174-179 (1996).
[CrossRef]

A. F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37, 326-329 (1981).
[CrossRef]

Broggato, G. B.

D. Amodio, G. B. Broggato, F. Campana, and G. M. Newaz, “Digital speckle correlation for strain measurement by image analysis,” Exp. Mech. 43, 396-402 (2003).
[CrossRef]

Burns, D. J.

D. J. Burns and H. F. Helbig, “A system for automatic electrical and optical characterization of microelectromechanical devices,” J. Microelectromech. Syst. 8, 473-482 (1999).
[CrossRef]

Campana, F.

D. Amodio, G. B. Broggato, F. Campana, and G. M. Newaz, “Digital speckle correlation for strain measurement by image analysis,” Exp. Mech. 43, 396-402 (2003).
[CrossRef]

Chan, K. T.

W. O. Wong and K. T. Chan, “Quantitative vibration amplitude measurement with time-averaged digital speckle pattern interferometry,” Opt. Laser Technol. 30, 317-324 (1998).
[CrossRef]

Chen, D. J.

Chiang, F. P.

L. Keene and F. P. Chiang, “Real-time anti-node visualization of vibrating distributed systems in noisy environments using defocused laser speckle contrast analysis,” J. Sound Vib. 320, 472-481 (2009).
[CrossRef]

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

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

F. P. Chiang and R. M. Juang, “Laser speckle interferometry for plate bending problems,” Appl. Opt. 15, 2199-2204 (1976).
[CrossRef]

Diazdelacruz, J.

Don, H. D.

Ennos, A. E.

A. E. Ennos and M. S. Virdee, “Laser speckle photography as a practical alternative to holographic interferometry fot measuring plate deformation,” Opt. Eng. 21, 478-482 (1982).

Fercher, A. F.

A. F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37, 326-329 (1981).
[CrossRef]

Gonlinval, J.

P. Slangen, L. Berwart, C. Veuster, J. Gonlinval, and Y. Lion, “Digital speckle pattern interferometry: a fast procedure to detect and measure vibration mode shapes,” Opt. Lasers Eng. 25, 311-321 (1996).
[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, 1975), pp. 9-75.

Gregory, D. A.

D. A. Gregory, “Speckle scatter, affine geometry and tilt topology,” Opt. Commun. 20, 1-5 (1977).
[CrossRef]

D. A. Gregory, “Basic physical principles of defocused speckle photography: a tilt topology inspection technique,” Opt. Laser Technol. 8, 201-213 (1976).
[CrossRef]

D. A. Gregory, “Topological speckle and structural inspection,” in Speckle Metrology, R. K. Erf, ed. (Academic, 1978), pp. 183-223.

Guan, B.

S. Wang, B. Guan, G. Wang, and L. Qian, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[CrossRef]

Helbig, H. F.

D. J. Burns and H. F. Helbig, “A system for automatic electrical and optical characterization of microelectromechanical devices,” J. Microelectromech. Syst. 8, 473-482 (1999).
[CrossRef]

Juang, R. M.

F. P. Chiang and R. M. Juang, “Laser speckle interferometry for plate bending problems,” Appl. Opt. 15, 2199-2204 (1976).
[CrossRef]

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

Kang, K.

K. Kang, K. Kim, and H. Lee, “Evaluation of elastic modulus of cantilever beam by TA-ESPI,” Opt. Lasers Technol. 39, 449-452 (2007).
[CrossRef]

Keene, L.

L. Keene and F. P. Chiang, “Real-time anti-node visualization of vibrating distributed systems in noisy environments using defocused laser speckle contrast analysis,” J. Sound Vib. 320, 472-481 (2009).
[CrossRef]

Kim, K.

K. Kang, K. Kim, and H. Lee, “Evaluation of elastic modulus of cantilever beam by TA-ESPI,” Opt. Lasers Technol. 39, 449-452 (2007).
[CrossRef]

Lee, H.

K. Kang, K. Kim, and H. Lee, “Evaluation of elastic modulus of cantilever beam by TA-ESPI,” Opt. Lasers Technol. 39, 449-452 (2007).
[CrossRef]

Lion, Y.

P. Slangen, L. Berwart, C. Veuster, J. Gonlinval, and Y. Lion, “Digital speckle pattern interferometry: a fast procedure to detect and measure vibration mode shapes,” Opt. Lasers Eng. 25, 311-321 (1996).
[CrossRef]

Lokberg, O. J.

O. J. Lokberg, “ESPI, the ultimate holographic tool for vibration analysis?,” J. Acoust. Soc. Am. 75, 1783-1791 (1984).
[CrossRef]

McNeill, S. R.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image. Vis. Comput. 1, 133-139 (1983).

Newaz, G. M.

D. Amodio, G. B. Broggato, F. Campana, and G. M. Newaz, “Digital speckle correlation for strain measurement by image analysis,” Exp. Mech. 43, 396-402 (2003).
[CrossRef]

Paoletty, D.

G. S. Spagnolo, D. Paoletty, and P. Zanetti, “Local speckle correlation for vibration analysis,” Opt. Commun. 123, 41-48(1996).
[CrossRef]

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 1991).

Peters, W. H.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image. Vis. Comput. 1, 133-139 (1983).

Qian, L.

S. Wang, B. Guan, G. Wang, and L. Qian, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[CrossRef]

Ranson, W. F.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image. Vis. Comput. 1, 133-139 (1983).

Rastogi, P. K.

P. K. Rastogi, “techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. R. Sirohi, ed. (Marcel Dekker, 1993), pp. 41-98.

Schwieger, H.

H. Schwieger and J. Banken, “Speckle photography for deformation analysis of bent plates,” Mater. Prüf. 27, 153-156(1985).

Shellabear, M. C.

M. C. Shellabear and J. R. Tyrer, “Application of ESPI to three-dimensional vibration measurements,” Opt. Laser Technol. 15, 43-56 (1991).

Sjödahl, M.

Slangen, P.

P. Slangen, L. Berwart, C. Veuster, J. Gonlinval, and Y. Lion, “Digital speckle pattern interferometry: a fast procedure to detect and measure vibration mode shapes,” Opt. Lasers Eng. 25, 311-321 (1996).
[CrossRef]

Spagnolo, G. S.

G. S. Spagnolo, D. Paoletty, and P. Zanetti, “Local speckle correlation for vibration analysis,” Opt. Commun. 123, 41-48(1996).
[CrossRef]

Sutton, M. A.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image. Vis. Comput. 1, 133-139 (1983).

Takai, N.

N. Takai, “Contrast of time-averaged image speckle pattern for a vibrating object,” Opt. Commun. 25, 31-34 (1978).
[CrossRef]

Tan, Y. S.

Tiziani, H.

H. Tiziani, “A study of the use of laser speckle to measure small tilts of optically rough surfaces accurately,” Opt. Commun. 5, 271-274 (1972).
[CrossRef]

H. Tiziani, “Vibration analysis and deformation measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, 1978), pp. 73-110.

Tyrer, J. R.

M. C. Shellabear and J. R. Tyrer, “Application of ESPI to three-dimensional vibration measurements,” Opt. Laser Technol. 15, 43-56 (1991).

Veuster, C.

P. Slangen, L. Berwart, C. Veuster, J. Gonlinval, and Y. Lion, “Digital speckle pattern interferometry: a fast procedure to detect and measure vibration mode shapes,” Opt. Lasers Eng. 25, 311-321 (1996).
[CrossRef]

Virdee, M. S.

A. E. Ennos and M. S. Virdee, “Laser speckle photography as a practical alternative to holographic interferometry fot measuring plate deformation,” Opt. Eng. 21, 478-482 (1982).

Wang, G.

S. Wang, B. Guan, G. Wang, and L. Qian, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[CrossRef]

Wang, S.

S. Wang, B. Guan, G. Wang, and L. Qian, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[CrossRef]

Webster, S.

J. D. Briers and S. Webster, “Laser speckle contrast analysis: a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1, 174-179 (1996).
[CrossRef]

Wolters, W. J.

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image. Vis. Comput. 1, 133-139 (1983).

Wong, W. O.

W. O. Wong and K. T. Chan, “Quantitative vibration amplitude measurement with time-averaged digital speckle pattern interferometry,” Opt. Laser Technol. 30, 317-324 (1998).
[CrossRef]

W. O. Wong, “Vibration analysis by laser speckle correlation,” Opt. Lasers Eng. 28, 277-286 (1997).
[CrossRef]

Zanetti, P.

G. S. Spagnolo, D. Paoletty, and P. Zanetti, “Local speckle correlation for vibration analysis,” Opt. Commun. 123, 41-48(1996).
[CrossRef]

Appl. Opt. (6)

Exp. Mech. (1)

D. Amodio, G. B. Broggato, F. Campana, and G. M. Newaz, “Digital speckle correlation for strain measurement by image analysis,” Exp. Mech. 43, 396-402 (2003).
[CrossRef]

Image. Vis. Comput. (1)

M. A. Sutton, W. J. Wolters, W. H. Peters, W. F. Ranson, and S. R. McNeill, “Determination of displacements using an improved digital correlation method,” Image. Vis. Comput. 1, 133-139 (1983).

J. Acoust. Soc. Am. (1)

O. J. Lokberg, “ESPI, the ultimate holographic tool for vibration analysis?,” J. Acoust. Soc. Am. 75, 1783-1791 (1984).
[CrossRef]

J. Biomed. Opt. (1)

J. D. Briers and S. Webster, “Laser speckle contrast analysis: a nonscanning, full-field technique for monitoring capillary blood flow,” J. Biomed. Opt. 1, 174-179 (1996).
[CrossRef]

J. Microelectromech. Syst. (1)

D. J. Burns and H. F. Helbig, “A system for automatic electrical and optical characterization of microelectromechanical devices,” J. Microelectromech. Syst. 8, 473-482 (1999).
[CrossRef]

J. Sound Vib. (1)

L. Keene and F. P. Chiang, “Real-time anti-node visualization of vibrating distributed systems in noisy environments using defocused laser speckle contrast analysis,” J. Sound Vib. 320, 472-481 (2009).
[CrossRef]

Mater. Prüf. (1)

H. Schwieger and J. Banken, “Speckle photography for deformation analysis of bent plates,” Mater. Prüf. 27, 153-156(1985).

Opt. Acta (1)

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

Opt. Commun. (5)

H. Tiziani, “A study of the use of laser speckle to measure small tilts of optically rough surfaces accurately,” Opt. Commun. 5, 271-274 (1972).
[CrossRef]

D. A. Gregory, “Speckle scatter, affine geometry and tilt topology,” Opt. Commun. 20, 1-5 (1977).
[CrossRef]

N. Takai, “Contrast of time-averaged image speckle pattern for a vibrating object,” Opt. Commun. 25, 31-34 (1978).
[CrossRef]

G. S. Spagnolo, D. Paoletty, and P. Zanetti, “Local speckle correlation for vibration analysis,” Opt. Commun. 123, 41-48(1996).
[CrossRef]

A. F. Fercher and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Opt. Commun. 37, 326-329 (1981).
[CrossRef]

Opt. Eng. (1)

A. E. Ennos and M. S. Virdee, “Laser speckle photography as a practical alternative to holographic interferometry fot measuring plate deformation,” Opt. Eng. 21, 478-482 (1982).

Opt. Laser Technol. (3)

D. A. Gregory, “Basic physical principles of defocused speckle photography: a tilt topology inspection technique,” Opt. Laser Technol. 8, 201-213 (1976).
[CrossRef]

W. O. Wong and K. T. Chan, “Quantitative vibration amplitude measurement with time-averaged digital speckle pattern interferometry,” Opt. Laser Technol. 30, 317-324 (1998).
[CrossRef]

M. C. Shellabear and J. R. Tyrer, “Application of ESPI to three-dimensional vibration measurements,” Opt. Laser Technol. 15, 43-56 (1991).

Opt. Lasers Eng. (2)

P. Slangen, L. Berwart, C. Veuster, J. Gonlinval, and Y. Lion, “Digital speckle pattern interferometry: a fast procedure to detect and measure vibration mode shapes,” Opt. Lasers Eng. 25, 311-321 (1996).
[CrossRef]

W. O. Wong, “Vibration analysis by laser speckle correlation,” Opt. Lasers Eng. 28, 277-286 (1997).
[CrossRef]

Opt. Lasers Technol. (1)

K. Kang, K. Kim, and H. Lee, “Evaluation of elastic modulus of cantilever beam by TA-ESPI,” Opt. Lasers Technol. 39, 449-452 (2007).
[CrossRef]

Pattern Recogn. Lett. (1)

S. Wang, B. Guan, G. Wang, and L. Qian, “Measurement of sinusoidal vibration from motion blurred images,” Pattern Recogn. Lett. 28, 1029-1040 (2007).
[CrossRef]

Other (5)

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

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw-Hill, 1991).

D. A. Gregory, “Topological speckle and structural inspection,” in Speckle Metrology, R. K. Erf, ed. (Academic, 1978), pp. 183-223.

H. Tiziani, “Vibration analysis and deformation measurement,” in Speckle Metrology, R. K. Erf, ed. (Academic, 1978), pp. 73-110.

P. K. Rastogi, “techniques of displacement and deformation measurements in speckle metrology,” in Speckle Metrology, R. R. Sirohi, ed. (Marcel Dekker, 1993), pp. 41-98.

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Figures (8)

Fig. 1
Fig. 1

Optical arrangement: A laser source (LS) generates a beam that, after being reflected at mirrors M1 and M2, and going through a beam expander (BE) and a circular window of radius a at the illumination mask (IM), is scattered by a vibrating rough surface (VRS) and recorded by a CCD camera focused at infinity.

Fig. 2
Fig. 2

Graphical representation for 1 Q ( ζ / s ) as a function of the adimensional parameter ζ / s (vibration amplitude on the recording plane over speckle size).

Fig. 3
Fig. 3

Graphical representation for the standard deviation of the incremental contrast P sampled for different c / s ratios as a function of ζ / s .

Fig. 4
Fig. 4

Graphical representation for the expected value of the incremental contrast P as a function of ζ / s for different values of b / s .

Fig. 5
Fig. 5

Graphical representation for the relative uncertainty (standard deviation over expected value) of P as a function of ζ / s for different values of c / s and b / s = 0.095 .

Fig. 6
Fig. 6

Results for b / s = 0.095 . The expected value of the incremental contrast is plotted as a solid line. The stars, crosses, and circles represent the measured values for c / s = 9 , 13.5, and 18, respectively. For each c / s ratio, the incremental contrast was determined on three independent experiments for three ζ / s values.

Fig. 7
Fig. 7

Results for b / s = 0.31 . The expected value of the incremental contrast is plotted as a solid line. The stars, crosses, and circles represent the measured values for c / s = 9 , 13.5, and 18, respectively. For each c / s ratio, the incremental contrast was determined on three independent experiments for three ζ / s values.

Fig. 8
Fig. 8

Deviations for b / s = 0.095 . The theoretical standard deviation of the incremental contrast is plotted as a function of ζ / s for the three different c / s ratios (solid line, dash-dotted, and dashed for c / s = 9.0 , 13.5, and 18.0, respectively). The experimental errors appear as stars ( c / s = 9 ), crosses ( c / s = 13.5 ), and circles ( c / s = 18 ).

Equations (62)

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d x = 2 f α ,
d y = 2 f β ,
α ( t ) = θ cos 2 π ν t ,
ζ = 2 f θ ,
ξ ˙ = 2 π ν ζ sin 2 π ν t ,
h 2 ( ξ , η ) = h 1 ( ξ ) δ ( η ) ,
h 1 ( ξ ) = 1 π ζ 2 ξ 2
h 2 ( ξ , η ) d ξ d η = 1.
i ( x , y ) = i 0 ( x , y ) h 2 ( x , y )
R 0 ( ξ , η ) E ( i 0 ( x + ξ , y + η ) i 0 ( x , y ) ) = I 2 ( 1 + | μ ( ξ , η ) | 2 ) ,
μ ( ξ , η ) = λ f J 1 ( 2 π a ξ 2 + η 2 λ f ) π a ξ 2 + η 2 ,
s = j 1 , 1 λ f π a 1.2 λ f a .
R ( ξ , η ) = E ( i ( x + ξ , y + η ) i ( x , y ) ) ,
R ( ξ , η ) = h 2 ( ξ , η ) h 2 ( ξ , η ) R 0 ( ξ , η )
h 2 ( ξ , η ) h 2 ( ξ , η ) = [ h 1 ( ξ ) h 1 ( ξ ) ] δ ( η ) ,
R ( ξ , η ) = h 1 ( ξ ) h 1 ( ξ ) R 0 ( ξ , η ) .
H 1 ( ξ ) = 4 π 2 ( 2 ζ + | ξ | ) K ( 2 ζ | ξ | 2 ζ + | ξ | )
R ( ξ , η ) = H 1 ( ξ ) R 0 ( ξ , η ) .
C ( ξ , η ) = R ( ξ , η ) I 2 ,
C ( ξ , η ) = I 2 ( | μ ( ξ + u , η ) | 2 + 1 ) H 1 ( u ) d u I 2 ,
C ( ξ , η ) = I 2 | μ ( ξ + u , η ) | 2 H 1 ( u ) d u .
Q = C ( 0 , 0 ) I 2 ,
Q 2 = | μ ( u , 0 ) | 2 H 1 ( u ) d u
Q 2 = 8 π 2 0 1 1 ( 1 + w ) K ( 1 w 1 + w ) ( J 1 ( 4 j 1 , 1 ζ w s ) 2 j 1 , 1 ζ w s ) 2 d w ,
Q 2 = E ( i 2 ( x , y ) ) E 2 ( i ( x , y ) ) E 2 ( i ( x , y ) ) ,
c = D f 2 d .
P = 1 π c 2 I 2 ( c i 0 2 d S c i 2 d S ) ,
E ( P ) = Q 2 ( 0 ) Q 2 ( ζ s ) ,
E ( P ) = 1 8 π 2 0 1 1 ( 1 + w ) K ( 1 w 1 + w ) ( J 1 ( 4 j 1 , 1 ζ t s ) 2 j 1 , 1 ζ w s ) 2 d w .
i 2 2 I i I 2 ,
P = 2 π c 2 I c ( i 0 i ) d x d y
VAR ( P ) = 4 π 2 c 4 I 2 c c E ( [ i ( x , y ) i 0 ( x , y ) ] [ i ( x , y ) i 0 ( x , y ) ] ) d x d y d x d y .
VAR ( P ) = 4 π 2 c 4 c c { [ h 1 ( ξ ) h 1 ( ξ ) 2 h 1 ( ξ ) + δ ( ξ ) ] δ ( η ) } | μ ( ξ , η ) | 2 d x d y d x d y ,
VAR ( P ) = 4 π 2 c 4 c c [ G ( ξ ) ( | μ ( ξ , η ) | 2 ] d x d y d x d y ,
G ( ξ ) = H 1 ( ξ ) 2 h 1 ( ξ ) + δ ( ξ ) .
VAR ( P ) = 4 π c 2 [ G ( ξ ) | μ ( ξ , η ) | 2 ] L ( ξ , η ) d ξ d η .
i ( x , y ) = i ( x , y ) [ 1 b 2 Π ( x b ) Π ( y b ) ] = i 0 ( x , y ) h 1 ( x ) δ ( y ) [ 1 b 2 Π ( x b ) Π ( y b ) ] ,
E ( i 2 ) = E ( i ( x , y ) i ( x , y ) ) = R ( 0 , 0 ) ,
R ( x , y ) = 1 b 4 R 0 ( x , y ) { [ ( h 1 ( x ) h 1 ( x ) Π ( x b ) Π ( x b ) ] [ Π ( y b ) Π ( y b ) ] }
R ( x , y ) = 1 b 4 R 0 ( x , y ) { [ H 1 ( x ) Π ( x b ) Π ( x b ) ] [ Π ( y b ) Π ( y b ) ] } .
Λ ( x ) = { 1 | x | if    | x | 1 0 , otherwise .
1 b 2 Π ( x b ) Π ( x b ) = 1 b Λ ( x b ) ,
R ( x , y ) = 1 b 2 R 0 ( x , y ) { Λ ( x b ) Λ ( y b ) } H 1 ( x ) ,
E ( i 2 ) = 1 b 2 [ H 1 ( x ) Λ ( x b ) ] R 0 ( x , y ) Λ ( y b ) d x d y ,
Q 2 = 1 b 2 [ H 1 ( x ) Λ ( x b ) ] | μ ( x , y ) | 2 Λ ( y b ) d x d y .
E ( P ) = Q 2 ( 0 ) Q 2 ( ζ s ) ,
E ( P ) = 1 b 2 [ { δ ( x ) H 1 ( x ) } Λ ( x b ) ] | μ ( x , y ) | 2 Λ ( y b ) d x d y ,
s 20 f θ s 2 f .
e = f Δ d 2 c = D f d .
H ( t ) = 1 π 2 ζ + | t | ζ d x ( ζ x ) ( ζ + x ) ( ζ | t | + x ) ( ζ + | t | x )
H ( t ) = 4 π 2 ( 2 ζ + | t | ) K ( k ) ,
k = 2 ζ | t | 2 ζ + | t |
ξ = x | t | 2 ζ | t | 2 .
H ( t ) = 1 π 2 ( ζ + | t | 2 ) 1 1 d ξ ( 1 ξ 2 ) ( 1 k 2 ξ 2 ) = 4 π 2 ( 2 ζ + | t | ) 0 1 d ξ ( 1 ξ 2 ) ( 1 k 2 ξ 2 ) ,
J = 1 π 2 c 4 F ( x x , y y ) O ( c , x , y ) O ( c , x , y ) d x d y d x d y ,
L ( x , y ) = 2 π ( a cos x 2 + y 2 2 c x 2 + y 2 2 c 1 x 2 + y 2 4 c 2 )
J = 1 π c 2 F ( ξ , η ) L ( ξ , η ) d ξ d η .
{ ξ = x x η = y y ξ = x + x η = y + y ,
D ( ξ , η , ξ , η ) D ( x , y , x , y ) = 4 ,
J = 1 4 π 2 c 4 F ( ξ , η ) ( O ( c , ξ + ξ 2 , η + η 2 ) O ( c , ξ ξ 2 , η η 2 ) d ξ d η ) d ξ d η ,
A = 8 c 2 ( a cos ξ 2 + η 2 2 c ξ 2 + η 2 2 c 1 ξ 2 + η 2 4 c 2 )
R ( ξ ) = H ( ξ ) H ( ξ ) R 0 ( ξ ) ,

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