Abstract

A setup that permits full-field vibration amplitude and phase retrieval with digital Fresnel holography is presented. Full reconstruction of the vibration is achieved with a three-step stroboscopic holographic recording, and an extraction algorithm is proposed. The finite temporal width of the illuminating light is considered in an investigation of the distortion of the measured amplitude and phase. In particular, a theoretical analysis is proposed and compared with numerical simulations that show good agreement. Experimental results are presented for a loudspeaker under sinusoidal excitation; the mean quadratic velocity extracted from amplitude evaluation under two different measuring conditions is presented. Comparison with time averaging validates the full-field vibrometer.

© 2005 Optical Society of America

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  1. Th. Kreis, Holographic Interferometry—Principles and Methods, Vol. 1 of Akademie Verlag Series in Optical Metrology (Akademie Verlag, Berlin, 1996).
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    [CrossRef] [PubMed]
  4. G. Pedrini, H. J. Tiziani, “Digital double pulse holographic interferometry using Fresnel and image plane holograms,” Measurement 18, 251–260 (1995).
    [CrossRef]
  5. G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
    [CrossRef]
  6. C. Wagner, S. Seebacher, W. Osten, W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 28, 4812–4820 (1999).
    [CrossRef]
  7. I. Yamaguchi, J. Kato, S. Ohta, “Surface shape measurement by phase shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
    [CrossRef]
  8. F. Dubois, L. Joannes, J. C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” Appl. Opt. 38, 7085–7094 (1999).
    [CrossRef]
  9. P. Picart, E. Moisson, D. Mounier, “Twin sensitivity measurement by spatial multiplexing of digitally recorded holograms,” Appl. Opt. 42, 1947–1957 (2003).
    [CrossRef] [PubMed]
  10. R. L. Powell, K. A. Stetson, “Interferometric analysis by wavefront reconstruction,” J. Opt. Soc. Am. 55, 1593–1598 (1965).
    [CrossRef]
  11. P. Picart, J. Leval, D. Mounier, S. Gougeon, “Time averaged digital holography,” Opt. Lett. 28, 1900–1902 (2003).
    [CrossRef] [PubMed]
  12. P. Picart, J. Leval, D. Mounier, S. Gougeon, “Some opportunities for vibration analysis with time averaging in digital Fresnel holography,” Appl. Opt. 44, 337–343 (2005).
    [CrossRef] [PubMed]
  13. O. J. Lokberg, K. Hogmoen, “Use of modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
    [CrossRef]
  14. T. R. Moore, J. D. Kaplon, G. D. McDowall, K. A. Martin, “Vibrational modes of trumpet bells,” J. Sound Vib. 254, 777–786 (2002).
    [CrossRef]
  15. F. Pinard, B. Laine, H. Vach, “Musical quality assessment of clarinet Reeds using optical holography,” J. Acoust. Soc. Am. 113, 1736–1742 (2003).
    [CrossRef] [PubMed]
  16. N. Demoli, D. Vukicevic, “Detection of hidden stationary deformations of vibrating surfaces by use of time-averaged digital holographic interferometry,” Opt. Lett. 29, 2423–2425 (2004).
    [CrossRef] [PubMed]
  17. C. W. Sim, F. S. Chau, S. L. Toh, “Vibration analysis and non-destructive testing with real-time shearography,” Opt. Laser Technol. 27, 45–49 (1995).
    [CrossRef]
  18. F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, G. Mills, “Vibration analysis by phase-shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
    [CrossRef]
  19. D. N. Borza, “High-resolution time average electronic holography for vibration measurement,” Opt. Lasers Eng. 41, 515–527 (2004).
    [CrossRef]
  20. J. C. Pascal, X. Carniel, V. Chalvidan, P. Smigielski, “Determination of phase and magnitude of vibration for energy flow measurements in a plate using holographic interferometry,” Opt. Lasers Eng. 25, 343–360 (1996).
    [CrossRef]
  21. J. P. Chambard, V. Chalvidan, X. Carniel, J. C. Pascal, “Pulsed TV—holography recording for vibration analysis applications,” Opt. Lasers Eng. 28, 131–143 (2002).
    [CrossRef]
  22. S. Ellingsrud, O. J. Lokberg, “Full field amplitude and phase measurement of loudspeakers by using TV—holography and digital image processing,” J. Sound Vib. 168, 193–207 (1993).
    [CrossRef]
  23. A. F. Doval, C. Trillo, D. Cernadas, B. V. Dorrio, C. Lopez, J. L. Fernandez, M. Perez-Amor, “Measuring amplitude and phase of vibration with double exposure stroboscopic TV holography,” in Interferometry in Speckle Light—Theory and Applications, P. Jacquot, J. M. Fournier, eds. (Springer-Verlag, 2000), pp. 281–288.
    [CrossRef]
  24. D. J. Anderson, J. D. R. Valera, J. D. C. Jones, “Electronic speckle pattern interferometry using diode laser stroboscopic illumination,” Meas. Sci. Technol. 4, 982–987 (1993).
    [CrossRef]
  25. G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects,” Opt. Lasers Eng. 38, 117–129 (2002).
    [CrossRef]
  26. G. O. Rosvold, O. J. Lokberg, “Effect and use of exposure control in vibration analysis using TV holography,” Appl. Opt. 32, 684–691 (1993).
    [CrossRef] [PubMed]
  27. S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E 22, 289–292 (1989).
    [CrossRef]
  28. P. Picart, “Error analysis for a Mach Zehnder type speckle interferometer,” Opt. Lasers Eng. 35, 335–353 (2001).
    [CrossRef]
  29. H. J. von Martens, “Evaluation of uncertainty in measurements—problems and tools,” Opt. Lasers Eng. 38, 185–206 (2002).
    [CrossRef]

2005

2004

N. Demoli, D. Vukicevic, “Detection of hidden stationary deformations of vibrating surfaces by use of time-averaged digital holographic interferometry,” Opt. Lett. 29, 2423–2425 (2004).
[CrossRef] [PubMed]

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, G. Mills, “Vibration analysis by phase-shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[CrossRef]

D. N. Borza, “High-resolution time average electronic holography for vibration measurement,” Opt. Lasers Eng. 41, 515–527 (2004).
[CrossRef]

2003

2002

T. R. Moore, J. D. Kaplon, G. D. McDowall, K. A. Martin, “Vibrational modes of trumpet bells,” J. Sound Vib. 254, 777–786 (2002).
[CrossRef]

J. P. Chambard, V. Chalvidan, X. Carniel, J. C. Pascal, “Pulsed TV—holography recording for vibration analysis applications,” Opt. Lasers Eng. 28, 131–143 (2002).
[CrossRef]

G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects,” Opt. Lasers Eng. 38, 117–129 (2002).
[CrossRef]

H. J. von Martens, “Evaluation of uncertainty in measurements—problems and tools,” Opt. Lasers Eng. 38, 185–206 (2002).
[CrossRef]

2001

P. Picart, “Error analysis for a Mach Zehnder type speckle interferometer,” Opt. Lasers Eng. 35, 335–353 (2001).
[CrossRef]

I. Yamaguchi, J. Kato, S. Ohta, “Surface shape measurement by phase shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[CrossRef]

1999

F. Dubois, L. Joannes, J. C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” Appl. Opt. 38, 7085–7094 (1999).
[CrossRef]

C. Wagner, S. Seebacher, W. Osten, W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 28, 4812–4820 (1999).
[CrossRef]

1996

J. C. Pascal, X. Carniel, V. Chalvidan, P. Smigielski, “Determination of phase and magnitude of vibration for energy flow measurements in a plate using holographic interferometry,” Opt. Lasers Eng. 25, 343–360 (1996).
[CrossRef]

1995

C. W. Sim, F. S. Chau, S. L. Toh, “Vibration analysis and non-destructive testing with real-time shearography,” Opt. Laser Technol. 27, 45–49 (1995).
[CrossRef]

G. Pedrini, H. J. Tiziani, “Digital double pulse holographic interferometry using Fresnel and image plane holograms,” Measurement 18, 251–260 (1995).
[CrossRef]

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

1994

1993

S. Ellingsrud, O. J. Lokberg, “Full field amplitude and phase measurement of loudspeakers by using TV—holography and digital image processing,” J. Sound Vib. 168, 193–207 (1993).
[CrossRef]

D. J. Anderson, J. D. R. Valera, J. D. C. Jones, “Electronic speckle pattern interferometry using diode laser stroboscopic illumination,” Meas. Sci. Technol. 4, 982–987 (1993).
[CrossRef]

G. O. Rosvold, O. J. Lokberg, “Effect and use of exposure control in vibration analysis using TV holography,” Appl. Opt. 32, 684–691 (1993).
[CrossRef] [PubMed]

1989

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E 22, 289–292 (1989).
[CrossRef]

1976

O. J. Lokberg, K. Hogmoen, “Use of modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[CrossRef]

1972

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

1965

Anderson, D. J.

D. J. Anderson, J. D. R. Valera, J. D. C. Jones, “Electronic speckle pattern interferometry using diode laser stroboscopic illumination,” Meas. Sci. Technol. 4, 982–987 (1993).
[CrossRef]

Borza, D. N.

D. N. Borza, “High-resolution time average electronic holography for vibration measurement,” Opt. Lasers Eng. 41, 515–527 (2004).
[CrossRef]

Carniel, X.

J. P. Chambard, V. Chalvidan, X. Carniel, J. C. Pascal, “Pulsed TV—holography recording for vibration analysis applications,” Opt. Lasers Eng. 28, 131–143 (2002).
[CrossRef]

J. C. Pascal, X. Carniel, V. Chalvidan, P. Smigielski, “Determination of phase and magnitude of vibration for energy flow measurements in a plate using holographic interferometry,” Opt. Lasers Eng. 25, 343–360 (1996).
[CrossRef]

Cernadas, D.

A. F. Doval, C. Trillo, D. Cernadas, B. V. Dorrio, C. Lopez, J. L. Fernandez, M. Perez-Amor, “Measuring amplitude and phase of vibration with double exposure stroboscopic TV holography,” in Interferometry in Speckle Light—Theory and Applications, P. Jacquot, J. M. Fournier, eds. (Springer-Verlag, 2000), pp. 281–288.
[CrossRef]

Chalvidan, V.

J. P. Chambard, V. Chalvidan, X. Carniel, J. C. Pascal, “Pulsed TV—holography recording for vibration analysis applications,” Opt. Lasers Eng. 28, 131–143 (2002).
[CrossRef]

J. C. Pascal, X. Carniel, V. Chalvidan, P. Smigielski, “Determination of phase and magnitude of vibration for energy flow measurements in a plate using holographic interferometry,” Opt. Lasers Eng. 25, 343–360 (1996).
[CrossRef]

Chambard, J. P.

J. P. Chambard, V. Chalvidan, X. Carniel, J. C. Pascal, “Pulsed TV—holography recording for vibration analysis applications,” Opt. Lasers Eng. 28, 131–143 (2002).
[CrossRef]

Chau, F. S.

C. W. Sim, F. S. Chau, S. L. Toh, “Vibration analysis and non-destructive testing with real-time shearography,” Opt. Laser Technol. 27, 45–49 (1995).
[CrossRef]

Demoli, N.

Dorrio, B. V.

A. F. Doval, C. Trillo, D. Cernadas, B. V. Dorrio, C. Lopez, J. L. Fernandez, M. Perez-Amor, “Measuring amplitude and phase of vibration with double exposure stroboscopic TV holography,” in Interferometry in Speckle Light—Theory and Applications, P. Jacquot, J. M. Fournier, eds. (Springer-Verlag, 2000), pp. 281–288.
[CrossRef]

Doval, A. F.

A. F. Doval, C. Trillo, D. Cernadas, B. V. Dorrio, C. Lopez, J. L. Fernandez, M. Perez-Amor, “Measuring amplitude and phase of vibration with double exposure stroboscopic TV holography,” in Interferometry in Speckle Light—Theory and Applications, P. Jacquot, J. M. Fournier, eds. (Springer-Verlag, 2000), pp. 281–288.
[CrossRef]

Dubois, F.

Ellingsrud, S.

S. Ellingsrud, O. J. Lokberg, “Full field amplitude and phase measurement of loudspeakers by using TV—holography and digital image processing,” J. Sound Vib. 168, 193–207 (1993).
[CrossRef]

Fernandez, J. L.

A. F. Doval, C. Trillo, D. Cernadas, B. V. Dorrio, C. Lopez, J. L. Fernandez, M. Perez-Amor, “Measuring amplitude and phase of vibration with double exposure stroboscopic TV holography,” in Interferometry in Speckle Light—Theory and Applications, P. Jacquot, J. M. Fournier, eds. (Springer-Verlag, 2000), pp. 281–288.
[CrossRef]

Gougeon, S.

Hogmoen, K.

O. J. Lokberg, K. Hogmoen, “Use of modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[CrossRef]

Joannes, L.

Johansson, S.

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E 22, 289–292 (1989).
[CrossRef]

Jones, J. D. C.

D. J. Anderson, J. D. R. Valera, J. D. C. Jones, “Electronic speckle pattern interferometry using diode laser stroboscopic illumination,” Meas. Sci. Technol. 4, 982–987 (1993).
[CrossRef]

Juptner, W.

C. Wagner, S. Seebacher, W. Osten, W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 28, 4812–4820 (1999).
[CrossRef]

Jüptner, W.

Kaplon, J. D.

T. R. Moore, J. D. Kaplon, G. D. McDowall, K. A. Martin, “Vibrational modes of trumpet bells,” J. Sound Vib. 254, 777–786 (2002).
[CrossRef]

Kato, J.

I. Yamaguchi, J. Kato, S. Ohta, “Surface shape measurement by phase shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[CrossRef]

Kreis, Th.

Th. Kreis, Holographic Interferometry—Principles and Methods, Vol. 1 of Akademie Verlag Series in Optical Metrology (Akademie Verlag, Berlin, 1996).

Kronrod, M. A.

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Laine, B.

F. Pinard, B. Laine, H. Vach, “Musical quality assessment of clarinet Reeds using optical holography,” J. Acoust. Soc. Am. 113, 1736–1742 (2003).
[CrossRef] [PubMed]

Legros, J. C.

Leval, J.

Lokberg, O. J.

S. Ellingsrud, O. J. Lokberg, “Full field amplitude and phase measurement of loudspeakers by using TV—holography and digital image processing,” J. Sound Vib. 168, 193–207 (1993).
[CrossRef]

G. O. Rosvold, O. J. Lokberg, “Effect and use of exposure control in vibration analysis using TV holography,” Appl. Opt. 32, 684–691 (1993).
[CrossRef] [PubMed]

O. J. Lokberg, K. Hogmoen, “Use of modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[CrossRef]

Lopez, C.

A. F. Doval, C. Trillo, D. Cernadas, B. V. Dorrio, C. Lopez, J. L. Fernandez, M. Perez-Amor, “Measuring amplitude and phase of vibration with double exposure stroboscopic TV holography,” in Interferometry in Speckle Light—Theory and Applications, P. Jacquot, J. M. Fournier, eds. (Springer-Verlag, 2000), pp. 281–288.
[CrossRef]

Martin, K. A.

T. R. Moore, J. D. Kaplon, G. D. McDowall, K. A. Martin, “Vibrational modes of trumpet bells,” J. Sound Vib. 254, 777–786 (2002).
[CrossRef]

McDowall, G. D.

T. R. Moore, J. D. Kaplon, G. D. McDowall, K. A. Martin, “Vibrational modes of trumpet bells,” J. Sound Vib. 254, 777–786 (2002).
[CrossRef]

Merzlyakov, N. S.

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Mills, G.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, G. Mills, “Vibration analysis by phase-shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[CrossRef]

Moisson, E.

Moore, T. R.

T. R. Moore, J. D. Kaplon, G. D. McDowall, K. A. Martin, “Vibrational modes of trumpet bells,” J. Sound Vib. 254, 777–786 (2002).
[CrossRef]

Mounier, D.

Ohta, S.

I. Yamaguchi, J. Kato, S. Ohta, “Surface shape measurement by phase shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[CrossRef]

Osten, W.

C. Wagner, S. Seebacher, W. Osten, W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 28, 4812–4820 (1999).
[CrossRef]

Pascal, J. C.

J. P. Chambard, V. Chalvidan, X. Carniel, J. C. Pascal, “Pulsed TV—holography recording for vibration analysis applications,” Opt. Lasers Eng. 28, 131–143 (2002).
[CrossRef]

J. C. Pascal, X. Carniel, V. Chalvidan, P. Smigielski, “Determination of phase and magnitude of vibration for energy flow measurements in a plate using holographic interferometry,” Opt. Lasers Eng. 25, 343–360 (1996).
[CrossRef]

Pedrini, G.

G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects,” Opt. Lasers Eng. 38, 117–129 (2002).
[CrossRef]

G. Pedrini, H. J. Tiziani, “Digital double pulse holographic interferometry using Fresnel and image plane holograms,” Measurement 18, 251–260 (1995).
[CrossRef]

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

Perez-Amor, M.

A. F. Doval, C. Trillo, D. Cernadas, B. V. Dorrio, C. Lopez, J. L. Fernandez, M. Perez-Amor, “Measuring amplitude and phase of vibration with double exposure stroboscopic TV holography,” in Interferometry in Speckle Light—Theory and Applications, P. Jacquot, J. M. Fournier, eds. (Springer-Verlag, 2000), pp. 281–288.
[CrossRef]

Picart, P.

Pinard, F.

F. Pinard, B. Laine, H. Vach, “Musical quality assessment of clarinet Reeds using optical holography,” J. Acoust. Soc. Am. 113, 1736–1742 (2003).
[CrossRef] [PubMed]

Powell, R. L.

Predko, K. G.

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E 22, 289–292 (1989).
[CrossRef]

Rosvold, G. O.

Schedin, S.

G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects,” Opt. Lasers Eng. 38, 117–129 (2002).
[CrossRef]

Schnars, U.

Seebacher, S.

C. Wagner, S. Seebacher, W. Osten, W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 28, 4812–4820 (1999).
[CrossRef]

Sim, C. W.

C. W. Sim, F. S. Chau, S. L. Toh, “Vibration analysis and non-destructive testing with real-time shearography,” Opt. Laser Technol. 27, 45–49 (1995).
[CrossRef]

Smigielski, P.

J. C. Pascal, X. Carniel, V. Chalvidan, P. Smigielski, “Determination of phase and magnitude of vibration for energy flow measurements in a plate using holographic interferometry,” Opt. Lasers Eng. 25, 343–360 (1996).
[CrossRef]

Stetson, K. A.

Tiziani, H. J.

G. Pedrini, S. Schedin, H. J. Tiziani, “Pulsed digital holography combined with laser vibrometry for 3D measurements of vibrating objects,” Opt. Lasers Eng. 38, 117–129 (2002).
[CrossRef]

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

G. Pedrini, H. J. Tiziani, “Digital double pulse holographic interferometry using Fresnel and image plane holograms,” Measurement 18, 251–260 (1995).
[CrossRef]

Toh, S. L.

C. W. Sim, F. S. Chau, S. L. Toh, “Vibration analysis and non-destructive testing with real-time shearography,” Opt. Laser Technol. 27, 45–49 (1995).
[CrossRef]

Trillo, C.

A. F. Doval, C. Trillo, D. Cernadas, B. V. Dorrio, C. Lopez, J. L. Fernandez, M. Perez-Amor, “Measuring amplitude and phase of vibration with double exposure stroboscopic TV holography,” in Interferometry in Speckle Light—Theory and Applications, P. Jacquot, J. M. Fournier, eds. (Springer-Verlag, 2000), pp. 281–288.
[CrossRef]

Vach, H.

F. Pinard, B. Laine, H. Vach, “Musical quality assessment of clarinet Reeds using optical holography,” J. Acoust. Soc. Am. 113, 1736–1742 (2003).
[CrossRef] [PubMed]

Valera, J. D. R.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, G. Mills, “Vibration analysis by phase-shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[CrossRef]

D. J. Anderson, J. D. R. Valera, J. D. C. Jones, “Electronic speckle pattern interferometry using diode laser stroboscopic illumination,” Meas. Sci. Technol. 4, 982–987 (1993).
[CrossRef]

von Martens, H. J.

H. J. von Martens, “Evaluation of uncertainty in measurements—problems and tools,” Opt. Lasers Eng. 38, 185–206 (2002).
[CrossRef]

Vukicevic, D.

Wagner, C.

C. Wagner, S. Seebacher, W. Osten, W. Juptner, “Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology,” Appl. Opt. 28, 4812–4820 (1999).
[CrossRef]

Yamaguchi, I.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, G. Mills, “Vibration analysis by phase-shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[CrossRef]

I. Yamaguchi, J. Kato, S. Ohta, “Surface shape measurement by phase shifting digital holography,” Opt. Rev. 8, 85–89 (2001).
[CrossRef]

Yaroslavskii, L. P.

M. A. Kronrod, N. S. Merzlyakov, L. P. Yaroslavskii, “Reconstruction of a hologram with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Yokota, M.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, G. Mills, “Vibration analysis by phase-shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[CrossRef]

Zhang, F.

F. Zhang, J. D. R. Valera, I. Yamaguchi, M. Yokota, G. Mills, “Vibration analysis by phase-shifting digital holography,” Opt. Rev. 11, 297–299 (2004).
[CrossRef]

Zou, Y. L.

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

Appl. Opt.

J. Acoust. Soc. Am.

F. Pinard, B. Laine, H. Vach, “Musical quality assessment of clarinet Reeds using optical holography,” J. Acoust. Soc. Am. 113, 1736–1742 (2003).
[CrossRef] [PubMed]

J. Mod. Opt.

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

J. Opt. Soc. Am.

J. Phys. E

O. J. Lokberg, K. Hogmoen, “Use of modulated reference wave in electronic speckle pattern interferometry,” J. Phys. E 9, 847–851 (1976).
[CrossRef]

S. Johansson, K. G. Predko, “Performance of a phase-shifting speckle interferometer for measuring deformation and vibration,” J. Phys. E 22, 289–292 (1989).
[CrossRef]

J. Sound Vib.

S. Ellingsrud, O. J. Lokberg, “Full field amplitude and phase measurement of loudspeakers by using TV—holography and digital image processing,” J. Sound Vib. 168, 193–207 (1993).
[CrossRef]

T. R. Moore, J. D. Kaplon, G. D. McDowall, K. A. Martin, “Vibrational modes of trumpet bells,” J. Sound Vib. 254, 777–786 (2002).
[CrossRef]

Meas. Sci. Technol.

D. J. Anderson, J. D. R. Valera, J. D. C. Jones, “Electronic speckle pattern interferometry using diode laser stroboscopic illumination,” Meas. Sci. Technol. 4, 982–987 (1993).
[CrossRef]

Measurement

G. Pedrini, H. J. Tiziani, “Digital double pulse holographic interferometry using Fresnel and image plane holograms,” Measurement 18, 251–260 (1995).
[CrossRef]

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[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Error (%) for amplitude and phase for Rc = 1/50 (circles, numerical; curves, analytical).

Fig. 2
Fig. 2

Error (%) for amplitude and phase for Rc = 1/20 (circles, numerical; curves, analytical).

Fig. 3
Fig. 3

Error (%) for amplitude and phase for Rc = 1/17 (circles, numerical; curves, analytical).

Fig. 4
Fig. 4

Three-dimensional plot of criterion SdΔφm for amplitude distortion versus Rc and Δφm[%].

Fig. 5
Fig. 5

Three-dimensional plot of criterion S0 for amplitude distortion versus Rc and Δφm [rad].

Fig. 6
Fig. 6

Stroboscopic setup: DAC, digital-to-analog converter; VCO, voltage-controlled oscillator.

Fig. 7
Fig. 7

Experimental setup: L’s, lenses.

Fig. 8
Fig. 8

Vibration amplitude (left) and phase (right) at 2 kHz [rad].

Fig. 9
Fig. 9

Vibration amplitude (left) and phase (right) at 2.44 kHz [rad].

Fig. 10
Fig. 10

Vibration amplitude (left) and phase (right) at 3.88 Hz [rad].

Fig. 11
Fig. 11

Mean quadratic velocity of the membrane (*, experimental; solid curve, fitting curve).

Fig. 12
Fig. 12

Mean quadratic velocity after surface painting (*, experimental; solid curve, fitting curve).

Fig. 13
Fig. 13

Comparison between time-averaging and stroboscopic measurement (left, experimental; right, simulation).

Tables (3)

Tables Icon

Table 1 Statistics of Error in the First Simulation (%)

Tables Icon

Table 2 Statistics of Error in the Second Simulation (%)

Tables Icon

Table 3 Statistics of Error in the Last Simulation (%)

Equations (32)

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A ( x , y , t ) = A 0 ( x , y ) exp [ i ψ 0 ( x , y ) ] exp { i Δ φ m ( x , y ) × sin [ ω 0 t + φ 0 ( x , y ) ] } .
O ( x , y , d 0 , t ) = i exp ( i 2 π d 0 / λ ) λ d 0 exp [ i π λ d 0 ( x 2 + y 2 ) ] × - + - + A ( x , y , t ) exp [ i π λ d 0 ( x 2 + y 2 ) ] exp [ - 2 i π λ d 0 ( x x + y y ) ] d x d y .
H ( x , y , d 0 , t ) = O ( x , y d 0 t ) 2 + R ( x , y ) 2 + R * ( x , y ) O ( x , y , d 0 , t ) + R ( x , y ) O * ( x , y , d 0 , t ) .
H ( x , y , d 0 ) = t j t j + T H ( x , y , d 0 , t ) d t .
A + 1 R ( X , Y , d R , t j ) = i exp ( 2 i π d R / λ ) λ d R × exp [ i π λ d R ( X 2 + Y 2 ) ] × k = 0 k = K - 1 l = 0 l = L - 1 [ t j t j + T R * ( k p x , l p y ) × O ( k p x , l p y , d 0 , t ) d t ] × exp [ i π λ d R ( k 2 p x 2 + l 2 p y 2 ) ] × exp [ - 2 i π λ d R ( k X p x + l Y p y ) ] ,
A + 1 R ( x , y , - d 0 , t j ) N M λ 4 d 0 4 R * ( x , y ) × exp [ - i π λ d 0 ( u 0 2 + v 0 2 ) ] × t j t j + T A ( x - λ u 0 d 0 , y - λ v 0 d 0 , t ) d t .
t j t j + T exp [ i Δ φ m sin ( ω 0 t + φ 0 ) ] d t = T k J k ( Δ φ m ) × sinc ( k ω 0 T 2 ) exp [ i k ( ω 0 t j + φ 0 + ω 0 T 2 ) ] .
sinc ( k π T T 0 ) = 1 + P ( k π T T 0 ) ,
P ( x ) = n = 1 n = ( - 1 ) n x 2 n ( 2 n + 1 ) ! ,
t j t j + T exp [ i Δ φ m sin ( ω 0 t + φ 0 ) ] d t = T exp [ i Δ φ m sin ( ω 0 t j + φ 0 + ω 0 T 2 ) ] + T q j exp ( i Θ j ) ,
Θ j = arg { k = - k = + P ( k π T T 0 ) J k ( Δ φ m ) exp [ i k ( ω 0 t j + φ 0 + ω 0 T 2 ) ] } ,
q j = | { k = - k = + P ( k π T T 0 ) J k ( Δ φ m ) exp [ i k ( ω 0 t j + φ 0 + ω 0 T 2 ) ] | .
Δ φ j = Δ φ m sin ( ω 0 t j + φ 0 + ω 0 T / 2 ) ;
arg [ A + 1 R ( x , y , - d 0 , t j ) ] = - 2 i π ( u 0 x + v 0 y ) - i π λ d 0 ( u 0 2 + v 0 2 ) + ψ 0 ( x , y ) + Δ φ j ( x , y ) - arctan { q j ( x , y ) sin [ Δ φ j ( x , y ) - Θ j ( x , y ) ] 1 + q j ( x , y ) cos [ Δ φ j ( x , y ) - Θ j ( x , y ) ] } .
lim T / T 0 0 arg [ A + 1 R ( t j ) ] = ψ 0 + Δ φ m sin ( ω 0 t j + φ 0 ) ,             lim T / T 0 0 q j ( t j ) = 0.
arg [ A + 1 R ( t j ) ] = ψ j = ψ 0 + Δ φ m sin [ ω 0 t j + φ 0 + ( j - 1 ) π / 2 ] mod ( 2 π ) ,             j = 1 , 2 , 3 ,
Δ φ m ( x , y ) = ½ { Δ ψ 13 2 ( x , y ) + [ Δ ψ 23 ( x , y ) + Δ ψ 21 ( x , y ) ] 2 } 1 / 2 ,
φ 0 ( x , y ) = arctan [ Δ ψ 13 ( x , y ) Δ ψ 23 ( x , y ) + Δ ψ 21 ( x , y ) ] ,
d Δ φ m = Δ φ m Δ ψ 13 d Δ ψ 13 + Δ φ m Δ ψ 23 d Δ ψ 23 + Δ φ m Δ ψ 21 d Δ ψ 21 .
d ψ j - q j sin ( Δ φ j - Θ j ) 1 + q j cos ( Δ φ j - Θ j ) .
d ψ 1 = k = 0 k = + α 1 ( 2 k + 1 ) sin [ ( 2 k + 1 ) ( ω 0 t 1 + φ 0 + ω 0 T / 2 ) ] ,
d ψ 2 = k = 0 k = + ( - 1 ) k α 1 ( 2 k + 1 ) cos [ ( 2 k + 1 ) ( ω 0 t 1 + φ 0 + ω 0 T / 2 ) ] ,
α 1 k = - 2 T 0 0 T 0 q 1 ( t 1 ) sin [ Δ φ 1 ( t 1 ) - Θ 1 ( t 1 ) ] 1 + q 1 ( t 1 ) cos [ Δ φ 1 ( t 1 ) - Θ 1 ( t 1 ) ] × sin ( 2 π k T 0 t 1 ) d t 1 .
d Δ φ m = α 11 + k = 1 k = + [ α 1 ( 4 k + 1 ) - α 1 ( 4 k - 1 ) ] cos ( 4 k ω 0 t 1 + 4 k φ 0 + 2 k ω 0 T ) .
d φ 0 = 1 Δ φ m k = 0 k = + [ α 1 ( 4 k + 3 ) + α 1 ( 4 k + 5 ) ] × sin [ 2 ( 2 k + 2 ) ( ω 0 t 1 + φ 0 + ω o T / 2 ) ] .
S d Δ φ m = sgn ( α 11 ) { α 11 2 + 1 2 k = 1 k = + [ α 1 ( 4 k + 1 ) - α 1 ( 4 k - 1 ) ] 2 } 1 / 2 ,
S d φ 0 = 1 Δ φ m 2 { k = 0 k = + [ α 1 ( 4 k + 3 ) - α 1 ( 4 k + 5 ) ] 2 } 1 / 2 .
H a ( t j ) = k = 0 k = K p t j t j + T H ( t - k T 0 ) d t ,
A + 1 R ( x , y , - d 0 , t j ) ( K p + 1 ) N M λ 4 d 0 4 × R * ( x , y ) × exp [ - i π λ d 0 ( u 0 2 + v 0 2 ) ] { A 0 ( x , y ) × exp [ i ψ 0 ( x , y ) ] × t j t j + T exp [ i Δ φ m ( x , y , t ) ] d t } * δ ( x - λ u 0 d 0 , y - λ v 0 d 0 ) ,
u z ( x , y ) = λ 2 π 1 1 + cos θ Δ φ m ( x , y ) .
v z ( x , y , t ) = λ f 0 1 + cos θ Δ φ m ( x , y ) cos ( ω 0 t + φ 0 ) .
v 2 = 1 S T 0 S 0 T 0 v ( x , y , t ) 2 d t d x d y ,

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