Abstract

A fully automated algorithm was developed for the recording and analysis of vibrating objects with the help of digital speckle pattern interferometry utilizing continuous-wave laser light. A series of measurements were performed with increasing force inducing vibration to allow the spatial distribution of vibration amplitude to be reconstructed on the object’s surface. The developed algorithm uses Hilbert transformation for an independent, quantitative evaluation of the Bessel function at every point of the investigated surface. The procedure does not require phase modulation, and thus can be implemented within any, even the simplest, DSPI apparatus. The proposed deformation analysis is fast and computationally inexpensive.

© 2012 Optical Society of America

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References

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  1. K. D. Hinsch, G. Gülker, and H. Helmers, “Checkup for aging artwork—optical tools to monitor mechanical behaviour,” Opt. Lasers Eng. 45, 578–588 (2007).
    [CrossRef]
  2. S. Mirza, P. Singh, R. Kumar, A. L. Vyas, and C. Shakher, “Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform,” Opt. Lasers Eng. 44, 41–55 (2006).
    [CrossRef]
  3. H. Van der Auweraer, H. Steinbichler, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Industrial applications of pulsed-laser ESPI vibration analysis,” in Proceedings of the International Modal Analysis Conference IMAC (2001), Vol. 1, pp. 490–496.
  4. N. Akhter, H. C. Jung, H. Chang, and K. Kim, “Location of delamination in laminated composite plates by pulsed laser holography,” Opt. Lasers Eng. 47, 584–588 (2009).
    [CrossRef]
  5. J. V. Araújo dos Santos, H. M. R. Lopes, M. Vaz, C. M. MotaSoares, C. A. MotaSoares, and M. J. M. de Freitas, “Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography,” Compos. Struct. 76, 272–281 (2006).
    [CrossRef]
  6. G. Coppotelli, R. Di Conza, F. Mastroddi, R. Pascual, and M. A. Caponero, “Damage identification in composite plates by dynamic displacement measurements,” in Proceedings of the International Conference on Noise and Vibration Engineering (ISMA, 2004), pp. 417–432.
  7. J. M. Huntley, “Automated analysis of speckle interferogtrams,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 59–139.
  8. A. Davila, P. D. Ruiz, G. H. Kaufmann, and J. M. Huntley, “Measurement of sub-surface delaminations in carbon fibre composites using high-speed phase-shifted speckle interferometry and temporal phase unwrapping,” Opt. Lasers Eng. 40, 447–458 (2003).
    [CrossRef]
  9. C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, “Speckle interferometry with temporal phase evaluation for measuring large-object deformation,” Appl. Opt. 37, 2608–2614 (1998).
    [CrossRef]
  10. H. Van der Auweraer, H. Steinbichler, S. Vanlanduit, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Application of stroboscopic and pulsed-laser electronic speckle pattern interferometry (ESPI) to modal analysis problems,” Meas. Sci. Technol. 13, 451 (2002).
    [CrossRef]
  11. J. D. R. Valera, J. D. C. Jones, O. J. Løkberg, C. H. Buckberry, and D. P. Towers, “Bimodal vibration analysis with stroboscopic heterodyned ESPI,” Meas. Sci. Technol. 8, 648 (1997).
    [CrossRef]
  12. K. A. Stetson and W. R. Brohinsky, “Fringe-shifting technique for numerical analysis of time-average holograms of vibrating objects,” J. Opt. Soc. Am. A 5, 1472–1476 (1988).
    [CrossRef]
  13. 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]
  14. D. N. Borza, “Full-field vibration amplitude recovery from high-resolution time-averaged speckle interferograms and digital holograms by regional inverting of the Bessel function,” Opt. Lasers Eng. 44, 747–770 (2006).
    [CrossRef]
  15. L. Lasyk, M. Łukomski, and Ł. Bratasz, “Simple digital speckle pattern interferometer (DSPI) for investigation of art objects,” Opt. Appl. 41, 687–700 (2011).
  16. R. J. Pryputniewicz and K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” Proc. SPIE 1162, 456–467 (1989).
    [CrossRef]
  17. S. L. Hahn, Hilbert Transforms in Signal Processing (Artech House, 1996).

2011 (1)

L. Lasyk, M. Łukomski, and Ł. Bratasz, “Simple digital speckle pattern interferometer (DSPI) for investigation of art objects,” Opt. Appl. 41, 687–700 (2011).

2009 (1)

N. Akhter, H. C. Jung, H. Chang, and K. Kim, “Location of delamination in laminated composite plates by pulsed laser holography,” Opt. Lasers Eng. 47, 584–588 (2009).
[CrossRef]

2007 (1)

K. D. Hinsch, G. Gülker, and H. Helmers, “Checkup for aging artwork—optical tools to monitor mechanical behaviour,” Opt. Lasers Eng. 45, 578–588 (2007).
[CrossRef]

2006 (3)

S. Mirza, P. Singh, R. Kumar, A. L. Vyas, and C. Shakher, “Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform,” Opt. Lasers Eng. 44, 41–55 (2006).
[CrossRef]

J. V. Araújo dos Santos, H. M. R. Lopes, M. Vaz, C. M. MotaSoares, C. A. MotaSoares, and M. J. M. de Freitas, “Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography,” Compos. Struct. 76, 272–281 (2006).
[CrossRef]

D. N. Borza, “Full-field vibration amplitude recovery from high-resolution time-averaged speckle interferograms and digital holograms by regional inverting of the Bessel function,” Opt. Lasers Eng. 44, 747–770 (2006).
[CrossRef]

2003 (1)

A. Davila, P. D. Ruiz, G. H. Kaufmann, and J. M. Huntley, “Measurement of sub-surface delaminations in carbon fibre composites using high-speed phase-shifted speckle interferometry and temporal phase unwrapping,” Opt. Lasers Eng. 40, 447–458 (2003).
[CrossRef]

2002 (1)

H. Van der Auweraer, H. Steinbichler, S. Vanlanduit, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Application of stroboscopic and pulsed-laser electronic speckle pattern interferometry (ESPI) to modal analysis problems,” Meas. Sci. Technol. 13, 451 (2002).
[CrossRef]

1998 (2)

C. Joenathan, B. Franze, P. Haible, and H. J. Tiziani, “Speckle interferometry with temporal phase evaluation for measuring large-object deformation,” Appl. Opt. 37, 2608–2614 (1998).
[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]

1997 (1)

J. D. R. Valera, J. D. C. Jones, O. J. Løkberg, C. H. Buckberry, and D. P. Towers, “Bimodal vibration analysis with stroboscopic heterodyned ESPI,” Meas. Sci. Technol. 8, 648 (1997).
[CrossRef]

1989 (1)

R. J. Pryputniewicz and K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” Proc. SPIE 1162, 456–467 (1989).
[CrossRef]

1988 (1)

Akhter, N.

N. Akhter, H. C. Jung, H. Chang, and K. Kim, “Location of delamination in laminated composite plates by pulsed laser holography,” Opt. Lasers Eng. 47, 584–588 (2009).
[CrossRef]

Borza, D. N.

D. N. Borza, “Full-field vibration amplitude recovery from high-resolution time-averaged speckle interferograms and digital holograms by regional inverting of the Bessel function,” Opt. Lasers Eng. 44, 747–770 (2006).
[CrossRef]

Bratasz, L.

L. Lasyk, M. Łukomski, and Ł. Bratasz, “Simple digital speckle pattern interferometer (DSPI) for investigation of art objects,” Opt. Appl. 41, 687–700 (2011).

Brohinsky, W. R.

Buckberry, C. H.

J. D. R. Valera, J. D. C. Jones, O. J. Løkberg, C. H. Buckberry, and D. P. Towers, “Bimodal vibration analysis with stroboscopic heterodyned ESPI,” Meas. Sci. Technol. 8, 648 (1997).
[CrossRef]

Caponero, M. A.

G. Coppotelli, R. Di Conza, F. Mastroddi, R. Pascual, and M. A. Caponero, “Damage identification in composite plates by dynamic displacement measurements,” in Proceedings of the International Conference on Noise and Vibration Engineering (ISMA, 2004), pp. 417–432.

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]

Chang, H.

N. Akhter, H. C. Jung, H. Chang, and K. Kim, “Location of delamination in laminated composite plates by pulsed laser holography,” Opt. Lasers Eng. 47, 584–588 (2009).
[CrossRef]

Coppotelli, G.

G. Coppotelli, R. Di Conza, F. Mastroddi, R. Pascual, and M. A. Caponero, “Damage identification in composite plates by dynamic displacement measurements,” in Proceedings of the International Conference on Noise and Vibration Engineering (ISMA, 2004), pp. 417–432.

Davila, A.

A. Davila, P. D. Ruiz, G. H. Kaufmann, and J. M. Huntley, “Measurement of sub-surface delaminations in carbon fibre composites using high-speed phase-shifted speckle interferometry and temporal phase unwrapping,” Opt. Lasers Eng. 40, 447–458 (2003).
[CrossRef]

de Freitas, M. J. M.

J. V. Araújo dos Santos, H. M. R. Lopes, M. Vaz, C. M. MotaSoares, C. A. MotaSoares, and M. J. M. de Freitas, “Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography,” Compos. Struct. 76, 272–281 (2006).
[CrossRef]

Di Conza, R.

G. Coppotelli, R. Di Conza, F. Mastroddi, R. Pascual, and M. A. Caponero, “Damage identification in composite plates by dynamic displacement measurements,” in Proceedings of the International Conference on Noise and Vibration Engineering (ISMA, 2004), pp. 417–432.

Franze, B.

Freymann, R.

H. Van der Auweraer, H. Steinbichler, S. Vanlanduit, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Application of stroboscopic and pulsed-laser electronic speckle pattern interferometry (ESPI) to modal analysis problems,” Meas. Sci. Technol. 13, 451 (2002).
[CrossRef]

H. Van der Auweraer, H. Steinbichler, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Industrial applications of pulsed-laser ESPI vibration analysis,” in Proceedings of the International Modal Analysis Conference IMAC (2001), Vol. 1, pp. 490–496.

Gülker, G.

K. D. Hinsch, G. Gülker, and H. Helmers, “Checkup for aging artwork—optical tools to monitor mechanical behaviour,” Opt. Lasers Eng. 45, 578–588 (2007).
[CrossRef]

Haberstok, C.

H. Van der Auweraer, H. Steinbichler, S. Vanlanduit, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Application of stroboscopic and pulsed-laser electronic speckle pattern interferometry (ESPI) to modal analysis problems,” Meas. Sci. Technol. 13, 451 (2002).
[CrossRef]

H. Van der Auweraer, H. Steinbichler, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Industrial applications of pulsed-laser ESPI vibration analysis,” in Proceedings of the International Modal Analysis Conference IMAC (2001), Vol. 1, pp. 490–496.

Hahn, S. L.

S. L. Hahn, Hilbert Transforms in Signal Processing (Artech House, 1996).

Haible, P.

Helmers, H.

K. D. Hinsch, G. Gülker, and H. Helmers, “Checkup for aging artwork—optical tools to monitor mechanical behaviour,” Opt. Lasers Eng. 45, 578–588 (2007).
[CrossRef]

Hinsch, K. D.

K. D. Hinsch, G. Gülker, and H. Helmers, “Checkup for aging artwork—optical tools to monitor mechanical behaviour,” Opt. Lasers Eng. 45, 578–588 (2007).
[CrossRef]

Huntley, J. M.

A. Davila, P. D. Ruiz, G. H. Kaufmann, and J. M. Huntley, “Measurement of sub-surface delaminations in carbon fibre composites using high-speed phase-shifted speckle interferometry and temporal phase unwrapping,” Opt. Lasers Eng. 40, 447–458 (2003).
[CrossRef]

J. M. Huntley, “Automated analysis of speckle interferogtrams,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 59–139.

Joenathan, C.

Jones, J. D. C.

J. D. R. Valera, J. D. C. Jones, O. J. Løkberg, C. H. Buckberry, and D. P. Towers, “Bimodal vibration analysis with stroboscopic heterodyned ESPI,” Meas. Sci. Technol. 8, 648 (1997).
[CrossRef]

Jung, H. C.

N. Akhter, H. C. Jung, H. Chang, and K. Kim, “Location of delamination in laminated composite plates by pulsed laser holography,” Opt. Lasers Eng. 47, 584–588 (2009).
[CrossRef]

Kaufmann, G. H.

A. Davila, P. D. Ruiz, G. H. Kaufmann, and J. M. Huntley, “Measurement of sub-surface delaminations in carbon fibre composites using high-speed phase-shifted speckle interferometry and temporal phase unwrapping,” Opt. Lasers Eng. 40, 447–458 (2003).
[CrossRef]

Kim, K.

N. Akhter, H. C. Jung, H. Chang, and K. Kim, “Location of delamination in laminated composite plates by pulsed laser holography,” Opt. Lasers Eng. 47, 584–588 (2009).
[CrossRef]

Kumar, R.

S. Mirza, P. Singh, R. Kumar, A. L. Vyas, and C. Shakher, “Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform,” Opt. Lasers Eng. 44, 41–55 (2006).
[CrossRef]

Lasyk, L.

L. Lasyk, M. Łukomski, and Ł. Bratasz, “Simple digital speckle pattern interferometer (DSPI) for investigation of art objects,” Opt. Appl. 41, 687–700 (2011).

Linet, V.

H. Van der Auweraer, H. Steinbichler, S. Vanlanduit, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Application of stroboscopic and pulsed-laser electronic speckle pattern interferometry (ESPI) to modal analysis problems,” Meas. Sci. Technol. 13, 451 (2002).
[CrossRef]

H. Van der Auweraer, H. Steinbichler, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Industrial applications of pulsed-laser ESPI vibration analysis,” in Proceedings of the International Modal Analysis Conference IMAC (2001), Vol. 1, pp. 490–496.

Løkberg, O. J.

J. D. R. Valera, J. D. C. Jones, O. J. Løkberg, C. H. Buckberry, and D. P. Towers, “Bimodal vibration analysis with stroboscopic heterodyned ESPI,” Meas. Sci. Technol. 8, 648 (1997).
[CrossRef]

Lopes, H. M. R.

J. V. Araújo dos Santos, H. M. R. Lopes, M. Vaz, C. M. MotaSoares, C. A. MotaSoares, and M. J. M. de Freitas, “Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography,” Compos. Struct. 76, 272–281 (2006).
[CrossRef]

Lukomski, M.

L. Lasyk, M. Łukomski, and Ł. Bratasz, “Simple digital speckle pattern interferometer (DSPI) for investigation of art objects,” Opt. Appl. 41, 687–700 (2011).

Mastroddi, F.

G. Coppotelli, R. Di Conza, F. Mastroddi, R. Pascual, and M. A. Caponero, “Damage identification in composite plates by dynamic displacement measurements,” in Proceedings of the International Conference on Noise and Vibration Engineering (ISMA, 2004), pp. 417–432.

Mirza, S.

S. Mirza, P. Singh, R. Kumar, A. L. Vyas, and C. Shakher, “Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform,” Opt. Lasers Eng. 44, 41–55 (2006).
[CrossRef]

MotaSoares, C. A.

J. V. Araújo dos Santos, H. M. R. Lopes, M. Vaz, C. M. MotaSoares, C. A. MotaSoares, and M. J. M. de Freitas, “Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography,” Compos. Struct. 76, 272–281 (2006).
[CrossRef]

MotaSoares, C. M.

J. V. Araújo dos Santos, H. M. R. Lopes, M. Vaz, C. M. MotaSoares, C. A. MotaSoares, and M. J. M. de Freitas, “Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography,” Compos. Struct. 76, 272–281 (2006).
[CrossRef]

Pascual, R.

G. Coppotelli, R. Di Conza, F. Mastroddi, R. Pascual, and M. A. Caponero, “Damage identification in composite plates by dynamic displacement measurements,” in Proceedings of the International Conference on Noise and Vibration Engineering (ISMA, 2004), pp. 417–432.

Pryputniewicz, R. J.

R. J. Pryputniewicz and K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” Proc. SPIE 1162, 456–467 (1989).
[CrossRef]

Ruiz, P. D.

A. Davila, P. D. Ruiz, G. H. Kaufmann, and J. M. Huntley, “Measurement of sub-surface delaminations in carbon fibre composites using high-speed phase-shifted speckle interferometry and temporal phase unwrapping,” Opt. Lasers Eng. 40, 447–458 (2003).
[CrossRef]

Santos, J. V. Araújo dos

J. V. Araújo dos Santos, H. M. R. Lopes, M. Vaz, C. M. MotaSoares, C. A. MotaSoares, and M. J. M. de Freitas, “Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography,” Compos. Struct. 76, 272–281 (2006).
[CrossRef]

Shakher, C.

S. Mirza, P. Singh, R. Kumar, A. L. Vyas, and C. Shakher, “Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform,” Opt. Lasers Eng. 44, 41–55 (2006).
[CrossRef]

Singh, P.

S. Mirza, P. Singh, R. Kumar, A. L. Vyas, and C. Shakher, “Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform,” Opt. Lasers Eng. 44, 41–55 (2006).
[CrossRef]

Steinbichler, H.

H. Van der Auweraer, H. Steinbichler, S. Vanlanduit, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Application of stroboscopic and pulsed-laser electronic speckle pattern interferometry (ESPI) to modal analysis problems,” Meas. Sci. Technol. 13, 451 (2002).
[CrossRef]

H. Van der Auweraer, H. Steinbichler, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Industrial applications of pulsed-laser ESPI vibration analysis,” in Proceedings of the International Modal Analysis Conference IMAC (2001), Vol. 1, pp. 490–496.

Stetson, K. A.

R. J. Pryputniewicz and K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” Proc. SPIE 1162, 456–467 (1989).
[CrossRef]

K. A. Stetson and W. R. Brohinsky, “Fringe-shifting technique for numerical analysis of time-average holograms of vibrating objects,” J. Opt. Soc. Am. A 5, 1472–1476 (1988).
[CrossRef]

Storer, D.

H. Van der Auweraer, H. Steinbichler, S. Vanlanduit, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Application of stroboscopic and pulsed-laser electronic speckle pattern interferometry (ESPI) to modal analysis problems,” Meas. Sci. Technol. 13, 451 (2002).
[CrossRef]

H. Van der Auweraer, H. Steinbichler, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Industrial applications of pulsed-laser ESPI vibration analysis,” in Proceedings of the International Modal Analysis Conference IMAC (2001), Vol. 1, pp. 490–496.

Tiziani, H. J.

Towers, D. P.

J. D. R. Valera, J. D. C. Jones, O. J. Løkberg, C. H. Buckberry, and D. P. Towers, “Bimodal vibration analysis with stroboscopic heterodyned ESPI,” Meas. Sci. Technol. 8, 648 (1997).
[CrossRef]

Valera, J. D. R.

J. D. R. Valera, J. D. C. Jones, O. J. Løkberg, C. H. Buckberry, and D. P. Towers, “Bimodal vibration analysis with stroboscopic heterodyned ESPI,” Meas. Sci. Technol. 8, 648 (1997).
[CrossRef]

Van der Auweraer, H.

H. Van der Auweraer, H. Steinbichler, S. Vanlanduit, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Application of stroboscopic and pulsed-laser electronic speckle pattern interferometry (ESPI) to modal analysis problems,” Meas. Sci. Technol. 13, 451 (2002).
[CrossRef]

H. Van der Auweraer, H. Steinbichler, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Industrial applications of pulsed-laser ESPI vibration analysis,” in Proceedings of the International Modal Analysis Conference IMAC (2001), Vol. 1, pp. 490–496.

Vanlanduit, S.

H. Van der Auweraer, H. Steinbichler, S. Vanlanduit, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Application of stroboscopic and pulsed-laser electronic speckle pattern interferometry (ESPI) to modal analysis problems,” Meas. Sci. Technol. 13, 451 (2002).
[CrossRef]

Vaz, M.

J. V. Araújo dos Santos, H. M. R. Lopes, M. Vaz, C. M. MotaSoares, C. A. MotaSoares, and M. J. M. de Freitas, “Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography,” Compos. Struct. 76, 272–281 (2006).
[CrossRef]

Vyas, A. L.

S. Mirza, P. Singh, R. Kumar, A. L. Vyas, and C. Shakher, “Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform,” Opt. Lasers Eng. 44, 41–55 (2006).
[CrossRef]

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]

Appl. Opt. (1)

Compos. Struct. (1)

J. V. Araújo dos Santos, H. M. R. Lopes, M. Vaz, C. M. MotaSoares, C. A. MotaSoares, and M. J. M. de Freitas, “Damage localization in laminated composite plates using mode shapes measured by pulsed TV holography,” Compos. Struct. 76, 272–281 (2006).
[CrossRef]

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

Meas. Sci. Technol. (2)

H. Van der Auweraer, H. Steinbichler, S. Vanlanduit, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Application of stroboscopic and pulsed-laser electronic speckle pattern interferometry (ESPI) to modal analysis problems,” Meas. Sci. Technol. 13, 451 (2002).
[CrossRef]

J. D. R. Valera, J. D. C. Jones, O. J. Løkberg, C. H. Buckberry, and D. P. Towers, “Bimodal vibration analysis with stroboscopic heterodyned ESPI,” Meas. Sci. Technol. 8, 648 (1997).
[CrossRef]

Opt. Appl. (1)

L. Lasyk, M. Łukomski, and Ł. Bratasz, “Simple digital speckle pattern interferometer (DSPI) for investigation of art objects,” Opt. Appl. 41, 687–700 (2011).

Opt. Laser Technol. (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]

Opt. Lasers Eng. (5)

D. N. Borza, “Full-field vibration amplitude recovery from high-resolution time-averaged speckle interferograms and digital holograms by regional inverting of the Bessel function,” Opt. Lasers Eng. 44, 747–770 (2006).
[CrossRef]

N. Akhter, H. C. Jung, H. Chang, and K. Kim, “Location of delamination in laminated composite plates by pulsed laser holography,” Opt. Lasers Eng. 47, 584–588 (2009).
[CrossRef]

A. Davila, P. D. Ruiz, G. H. Kaufmann, and J. M. Huntley, “Measurement of sub-surface delaminations in carbon fibre composites using high-speed phase-shifted speckle interferometry and temporal phase unwrapping,” Opt. Lasers Eng. 40, 447–458 (2003).
[CrossRef]

K. D. Hinsch, G. Gülker, and H. Helmers, “Checkup for aging artwork—optical tools to monitor mechanical behaviour,” Opt. Lasers Eng. 45, 578–588 (2007).
[CrossRef]

S. Mirza, P. Singh, R. Kumar, A. L. Vyas, and C. Shakher, “Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform,” Opt. Lasers Eng. 44, 41–55 (2006).
[CrossRef]

Proc. SPIE (1)

R. J. Pryputniewicz and K. A. Stetson, “Measurement of vibration patterns using electro-optic holography,” Proc. SPIE 1162, 456–467 (1989).
[CrossRef]

Other (4)

S. L. Hahn, Hilbert Transforms in Signal Processing (Artech House, 1996).

H. Van der Auweraer, H. Steinbichler, C. Haberstok, R. Freymann, D. Storer, and V. Linet, “Industrial applications of pulsed-laser ESPI vibration analysis,” in Proceedings of the International Modal Analysis Conference IMAC (2001), Vol. 1, pp. 490–496.

G. Coppotelli, R. Di Conza, F. Mastroddi, R. Pascual, and M. A. Caponero, “Damage identification in composite plates by dynamic displacement measurements,” in Proceedings of the International Conference on Noise and Vibration Engineering (ISMA, 2004), pp. 417–432.

J. M. Huntley, “Automated analysis of speckle interferogtrams,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001), pp. 59–139.

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Figures (6)

Fig. 1.
Fig. 1.

Analysis of sound-induced vibrations of paint layer delaminated from a wooden support (Specimen 1); (a) interferogram obtained for a surface vibrating with different amplitudes; (b) results of fitting the function to chosen pixels marked in (a); (c) reconstruction of vibration amplitude. A detailed description of the specimen, experimental procedure and data analysis is provided in Subsection 4.B.

Fig. 2.
Fig. 2.

Bessel function J0 (solid curve) approximated by cosine function (dotted curve). Below 1 approximation by square function (dashed curve) is presented.

Fig. 3.
Fig. 3.

Calibration of the loudspeaker used in the measurements. The dashed line shows the limit of a linear relationship between voltage and sound intensity.

Fig. 4.
Fig. 4.

Specimen 1: reconstruction of the spatial distribution of the vibration amplitude of the sound-induced (10.9 kHz) vibration of a ground layer delaminated from the wooden board; (a) three-dimensional (3D) maps of the vibration amplitude reconstructed by fitting the function to experimentally obtained data; (b) 3D map of the vibration amplitude reconstructed using the Hilbert transformation or the square function fitting to experimentally obtained data for large or small vibration amplitudes, respectively. Analysis was performed for the interferogram presented in Fig. 1(a).

Fig. 5.
Fig. 5.

Specimen 2: analysis of the sound-induced (5 kHz) vibration of a ground layer delaminated from a wooden board, (a) photograph of the specimen—the analyzed area is marked on the surface; (b) the interferogram obtained by subtracting images recorded for the vibrating and still surfaces; (c) two-dimensional and (d) 3D map of vibration amplitude reconstructed using the Hilbert transformation or the square function fitting for large or small vibration amplitudes, respectively.

Fig. 6.
Fig. 6.

Aged specimen of painted wood—an analysis of sound-induced (11.3 kHz) vibration of a design layer delaminated from a wooden support, (a) photograph of the specimen—the analyzed area is marked on the surface; (b) the interferogram obtained by subtracting images recorded for vibrating and still surfaces; (c) a 3D map of vibration amplitude reconstructed using the Hilbert transformation or the square function fitting for large or small vibration amplitudes respectively.

Equations (9)

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I=Ir+Io+2IrIocos(φd+φr+Δφ),
I=Ir+Io+2IrIocos(φ)Jo(4πλa0),
I=A+BJ0(a0C).
I(0)I(π)=4IrIocos(φ)J0(4πλa0).
(I0(0)I0(π))2+(I0(π2)I0(3π2))2=Abs[4IrIoJ0(4πλa0)].
signJ0(4πλa0)=sign{[Is(0)Is(π)]*[Iv(0)Iv(π)]+[Is(π2)Is(3π2)]*[Iv(π2)Iv(3π2)]},
y=2IrIoJ0(4πλa0),
θ(p)=tan1[y˜(p)y(p)],
a0(p)=λ4π[θ(p)+π4].

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