Abstract

Measuring deformation of vibrating specimens whose dimensions are in the submillimeter range introduces a number of difficulties using laser interferometry. Normal interferometry is not suitable because of a phase ambiguity problem. In addition, the noise effect is much more serious in the measurement of small objects because a high-magnification lens is used. We present a method for full-field measurement of displacement, velocity, and acceleration of a vibrating miniature object based on image-plane digital holographic microscopy. A miniature cantilever beam is excited by a piezoelectric transducer stage with a sinusoidal configuration. A sequence of digital holograms is captured using a high-speed digital holographic microscope. Windowed Fourier analysis is applied in the spatial and spatiotemporal domains to extract the displacement, velocity and acceleration. The result shows that a combination of image-plane digital holographic microscopy and windowed Fourier analyses can be used to study vibration without encountering a phase ambiguity problem, and one can obtain instantaneous kinematic parameters on each point.

© 2009 Optical Society of America

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    [CrossRef]
  2. M. Kujawinska, “Modern optical measurement station for micro-materials and micro-elements studies,” Sens. Actuators A 99, 144-153 (2002).
    [CrossRef]
  3. L. Yang and P. Colbourne, “Digital laser microinterferometer and its applications,” Opt. Eng. 42, 1417-1426 (2003).
    [CrossRef]
  4. S. H. Wang, C. Quan, and C. J. Tay, “A genetic optical interferometric inspection on micro-deformation,” Optik (Jena) 115 (11-12), 564-568 (2004).
  5. S. H. Wang, C. J. Tay, C. Quan, and H. M. Shang, “Determination of deflection and Young's modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279-1286(2001).
    [CrossRef]
  6. F. Dubois, O. Monnom, C. Yourassowsky, and J. C. Legros, “Border processing in digital holography by extension of the digital hologram and reduction of the higher spatial frequencies,” Appl. Opt. 41, 2621-2626 (2002).
    [CrossRef] [PubMed]
  7. S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane vibrations of MEMS with (sub)nanometer resolution,” J. Micromech. Microeng. 14 (9), S97-S101 (2004).
    [CrossRef]
  8. R. Jozwicki, M. Kujavinska, and K. Patorski, “Application of lasers in precise measurement of microelements,” Proc. SPIE 5229, 266-274 (2003).
    [CrossRef]
  9. P. Castellini, M. Martarelli, and E. P. Tomasini. “Laser Doppler vibrometry: development of advanced solutions answering to technology's needs,” Mech. Syst. Signal Process. 20, 1265-1285 (2006).
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    [CrossRef]
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    [CrossRef]
  13. H. J. Tiziani, “Spectral and temporal phase evaluation for interferometry and speckle applications,” in Trends in Optical Nondestructive Testing and Inspection, P. K. Rastogi and D. Inaudi, eds. (Elsevier Science, 2000), pp. 323-343.
    [CrossRef]
  14. G. H. Kaufmann and G. E. Galizzi, “Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and the Fourier transform methods,” Appl. Opt. 41, 7254-7263 (2002).
    [CrossRef] [PubMed]
  15. Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780-2787 (2004).
    [CrossRef]
  16. V. D. Madjarova, H. Kadona, and S. Toyooka, “Dynamic electronic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform,” Opt. Express 11 (6), 617-623 (2003).
    [CrossRef] [PubMed]
  17. S. Equis and P. Jacquot, “The empirical mode decomposition: a must-have tool in speckle interferometry?,” Opt. Express 17 (2), 611-613 (2009).
    [CrossRef] [PubMed]
  18. G. H. Kaufmann, “Phase measurement in temporal speckle pattern interferometry using the Fouier transform method with and without a temporal carrier,” Opt. Commun. 217, 141-149 (2003).
    [CrossRef]
  19. Y. Fu, C. J. Tay, C. Quan, and H. Miao, “Wavelet analysis of speckle patterns with a temporal carrier,” Appl. Opt. 44, 959-965 (2005).
    [CrossRef] [PubMed]
  20. J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
    [CrossRef]
  21. G. Pedrini, H. Tiziani, and Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199-219 (1997).
    [CrossRef]
  22. P. Picart, J. Leval, D. Mounier, and S. Gougeon, “Time-averaged digital holography,” Opt. Lett. 28, 1900-1902 (2003).
    [CrossRef] [PubMed]
  23. Y. Fu, R. M. Groves, G. Pedrini, and W. Osten, “Kinematic and deformation parameter measurement by spatiotemporal analysis of an interferogram sequence,” Appl. Opt. 46, 8645-8655 (2007).
    [CrossRef] [PubMed]
  24. Y. Fu, G. Pedrini, and W. Osten, “Vibration measurement by temporal Fourier analyses of digital hologram sequence,” Appl. Opt. 46, 5719-5727 (2007).
    [CrossRef] [PubMed]
  25. K. Qian, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304-317 (2007).
    [CrossRef]
  26. K. Qian, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695-2702 (2004).
    [CrossRef]
  27. L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046-5051 (2001).
    [CrossRef]
  28. E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994-7001(1999).
    [CrossRef]
  29. D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. 43, 6536-6544 (2004).
    [CrossRef]
  30. F. Charriere, A. Marian, F. Montfort, J. Kuhn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31, 178-180 (2006).
    [CrossRef] [PubMed]
  31. B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52-A61 (2008).
    [CrossRef] [PubMed]
  32. G. Pedrini, W. Osten, and M. E. Gusev, “High-speed digital holographic interferometry for vibration measurement,” Appl. Opt. 45, 3456-3462 (2006).
    [CrossRef] [PubMed]
  33. U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).
  34. S. Mallat, A Wavelet Tour of Signal Processing (Academic, 1998).
  35. K. Qian, Y. Fu, Q. Liu, H. S. Seah, and A. Asundi, “Generalized three-dimensional windowed Fourier transform for fringe analysis,” Opt. Lett. 31, 2121-2123 (2006).
    [CrossRef] [PubMed]
  36. H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205-210 (1999).
    [CrossRef]
  37. K. Qian, T. H. N. Le, F. Lin, and H. S. Seah, “Comparative analysis on some filters for wrapped phase maps,” Appl. Opt. 46, 7412-7418 (2007).
    [CrossRef]
  38. G. Cloud, Optical Methods of Engineering Analysis (Cambridge U. Press, 1998).
  39. M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, “Wavelet processing of interferometric signal and fringe patterns,” Proc. SPIE 3813, 692-702 (1999).
    [CrossRef]

2009 (1)

2008 (2)

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44 (1), 57-69 (2008).
[CrossRef]

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52-A61 (2008).
[CrossRef] [PubMed]

2007 (4)

2006 (4)

2005 (1)

2004 (5)

K. Qian, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695-2702 (2004).
[CrossRef]

D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. 43, 6536-6544 (2004).
[CrossRef]

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780-2787 (2004).
[CrossRef]

S. H. Wang, C. Quan, and C. J. Tay, “A genetic optical interferometric inspection on micro-deformation,” Optik (Jena) 115 (11-12), 564-568 (2004).

S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane vibrations of MEMS with (sub)nanometer resolution,” J. Micromech. Microeng. 14 (9), S97-S101 (2004).
[CrossRef]

2003 (5)

R. Jozwicki, M. Kujavinska, and K. Patorski, “Application of lasers in precise measurement of microelements,” Proc. SPIE 5229, 266-274 (2003).
[CrossRef]

L. Yang and P. Colbourne, “Digital laser microinterferometer and its applications,” Opt. Eng. 42, 1417-1426 (2003).
[CrossRef]

G. H. Kaufmann, “Phase measurement in temporal speckle pattern interferometry using the Fouier transform method with and without a temporal carrier,” Opt. Commun. 217, 141-149 (2003).
[CrossRef]

V. D. Madjarova, H. Kadona, and S. Toyooka, “Dynamic electronic speckle pattern interferometry (DESPI) phase analyses with temporal Hilbert transform,” Opt. Express 11 (6), 617-623 (2003).
[CrossRef] [PubMed]

P. Picart, J. Leval, D. Mounier, and S. Gougeon, “Time-averaged digital holography,” Opt. Lett. 28, 1900-1902 (2003).
[CrossRef] [PubMed]

2002 (3)

2001 (2)

S. H. Wang, C. J. Tay, C. Quan, and H. M. Shang, “Determination of deflection and Young's modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279-1286(2001).
[CrossRef]

L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046-5051 (2001).
[CrossRef]

1999 (4)

J. M. Huntley, G. H. Kaufmann, and D. Kerr, “Phase-shifted dynamic speckle pattern interferometry at 1 kHz,” Appl. Opt. 38, 6556-6563 (1999).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994-7001(1999).
[CrossRef]

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205-210 (1999).
[CrossRef]

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, “Wavelet processing of interferometric signal and fringe patterns,” Proc. SPIE 3813, 692-702 (1999).
[CrossRef]

1997 (1)

G. Pedrini, H. Tiziani, and Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199-219 (1997).
[CrossRef]

1982 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Aebischer, H. A.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205-210 (1999).
[CrossRef]

Asundi, A.

Asundi, A. K.

Bosseboeuf, A.

S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane vibrations of MEMS with (sub)nanometer resolution,” J. Micromech. Microeng. 14 (9), S97-S101 (2004).
[CrossRef]

Carl, D.

Castellini, P.

P. Castellini, M. Martarelli, and E. P. Tomasini. “Laser Doppler vibrometry: development of advanced solutions answering to technology's needs,” Mech. Syst. Signal Process. 20, 1265-1285 (2006).
[CrossRef]

Charriere, F.

Chen, L. J.

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780-2787 (2004).
[CrossRef]

Cherbuliez, M.

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, “Wavelet processing of interferometric signal and fringe patterns,” Proc. SPIE 3813, 692-702 (1999).
[CrossRef]

Cloud, G.

G. Cloud, Optical Methods of Engineering Analysis (Cambridge U. Press, 1998).

Colbourne, P.

L. Yang and P. Colbourne, “Digital laser microinterferometer and its applications,” Opt. Eng. 42, 1417-1426 (2003).
[CrossRef]

Colomb, T.

Cuche, E.

de Lega, X. Colonna

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, “Wavelet processing of interferometric signal and fringe patterns,” Proc. SPIE 3813, 692-702 (1999).
[CrossRef]

Depeursinge, C.

Dubois, F.

Equis, S.

Fu, Y.

Galizzi, G. E.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Gougeon, S.

Groves, R. M.

Gusev, M. E.

Huntley, J. M.

J. M. Huntley, G. H. Kaufmann, and D. Kerr, “Phase-shifted dynamic speckle pattern interferometry at 1 kHz,” Appl. Opt. 38, 6556-6563 (1999).
[CrossRef]

J. M. Huntley, “Challenges in phase unwrapping,” in Trends in Optical Nondestructive Testing and Inspection, P. K. Rastogi and D. Inaudi, eds. (Elsevier Science, 2000), pp. 37-44.
[CrossRef]

Ina, H.

Jacquot, P.

S. Equis and P. Jacquot, “The empirical mode decomposition: a must-have tool in speckle interferometry?,” Opt. Express 17 (2), 611-613 (2009).
[CrossRef] [PubMed]

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44 (1), 57-69 (2008).
[CrossRef]

M. Cherbuliez, P. Jacquot, and X. Colonna de Lega, “Wavelet processing of interferometric signal and fringe patterns,” Proc. SPIE 3813, 692-702 (1999).
[CrossRef]

Jozwicki, R.

R. Jozwicki, M. Kujavinska, and K. Patorski, “Application of lasers in precise measurement of microelements,” Proc. SPIE 5229, 266-274 (2003).
[CrossRef]

Jueptner, W.

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

Kadona, H.

Kaufmann, G. H.

Kemper, B.

Kerr, D.

Kobayashi, S.

Kuhn, J.

Kujavinska, M.

R. Jozwicki, M. Kujavinska, and K. Patorski, “Application of lasers in precise measurement of microelements,” Proc. SPIE 5229, 266-274 (2003).
[CrossRef]

Kujawinska, M.

M. Kujawinska, “Modern optical measurement station for micro-materials and micro-elements studies,” Sens. Actuators A 99, 144-153 (2002).
[CrossRef]

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Le, T. H. N.

Legros, J. C.

Leval, J.

Lin, F.

Liu, Q.

Madjarova, V. D.

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing (Academic, 1998).

Marian, A.

Marquet, P.

Martarelli, M.

P. Castellini, M. Martarelli, and E. P. Tomasini. “Laser Doppler vibrometry: development of advanced solutions answering to technology's needs,” Mech. Syst. Signal Process. 20, 1265-1285 (2006).
[CrossRef]

Miao, H.

Miao, J.

Monnom, O.

Montfort, F.

Mounier, D.

Osten, W.

Patorski, K.

R. Jozwicki, M. Kujavinska, and K. Patorski, “Application of lasers in precise measurement of microelements,” Proc. SPIE 5229, 266-274 (2003).
[CrossRef]

Pedrini, G.

Peng, X.

Petitgrand, S.

S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane vibrations of MEMS with (sub)nanometer resolution,” J. Micromech. Microeng. 14 (9), S97-S101 (2004).
[CrossRef]

Picart, P.

Qian, K.

Quan, C.

Y. Fu, C. J. Tay, C. Quan, and H. Miao, “Wavelet analysis of speckle patterns with a temporal carrier,” Appl. Opt. 44, 959-965 (2005).
[CrossRef] [PubMed]

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780-2787 (2004).
[CrossRef]

S. H. Wang, C. Quan, and C. J. Tay, “A genetic optical interferometric inspection on micro-deformation,” Optik (Jena) 115 (11-12), 564-568 (2004).

S. H. Wang, C. J. Tay, C. Quan, and H. M. Shang, “Determination of deflection and Young's modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279-1286(2001).
[CrossRef]

Schnars, U.

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

Seah, H. S.

Shang, H. M.

S. H. Wang, C. J. Tay, C. Quan, and H. M. Shang, “Determination of deflection and Young's modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279-1286(2001).
[CrossRef]

Takeda, M.

Tay, C. J.

Y. Fu, C. J. Tay, C. Quan, and H. Miao, “Wavelet analysis of speckle patterns with a temporal carrier,” Appl. Opt. 44, 959-965 (2005).
[CrossRef] [PubMed]

S. H. Wang, C. Quan, and C. J. Tay, “A genetic optical interferometric inspection on micro-deformation,” Optik (Jena) 115 (11-12), 564-568 (2004).

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780-2787 (2004).
[CrossRef]

S. H. Wang, C. J. Tay, C. Quan, and H. M. Shang, “Determination of deflection and Young's modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279-1286(2001).
[CrossRef]

Tiziani, H.

G. Pedrini, H. Tiziani, and Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199-219 (1997).
[CrossRef]

Tiziani, H. J.

H. J. Tiziani, “Spectral and temporal phase evaluation for interferometry and speckle applications,” in Trends in Optical Nondestructive Testing and Inspection, P. K. Rastogi and D. Inaudi, eds. (Elsevier Science, 2000), pp. 323-343.
[CrossRef]

Tomasini, E. P.

P. Castellini, M. Martarelli, and E. P. Tomasini. “Laser Doppler vibrometry: development of advanced solutions answering to technology's needs,” Mech. Syst. Signal Process. 20, 1265-1285 (2006).
[CrossRef]

Toyooka, S.

von Bally, G.

Waldner, S.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205-210 (1999).
[CrossRef]

Wang, S. H.

S. H. Wang, C. Quan, and C. J. Tay, “A genetic optical interferometric inspection on micro-deformation,” Optik (Jena) 115 (11-12), 564-568 (2004).

S. H. Wang, C. J. Tay, C. Quan, and H. M. Shang, “Determination of deflection and Young's modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279-1286(2001).
[CrossRef]

Wernicke, G.

Xu, L.

Yang, L.

L. Yang and P. Colbourne, “Digital laser microinterferometer and its applications,” Opt. Eng. 42, 1417-1426 (2003).
[CrossRef]

Yourassowsky, C.

Zou, Y.

G. Pedrini, H. Tiziani, and Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199-219 (1997).
[CrossRef]

Appl. Opt. (13)

F. Dubois, O. Monnom, C. Yourassowsky, and J. C. Legros, “Border processing in digital holography by extension of the digital hologram and reduction of the higher spatial frequencies,” Appl. Opt. 41, 2621-2626 (2002).
[CrossRef] [PubMed]

G. H. Kaufmann and G. E. Galizzi, “Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and the Fourier transform methods,” Appl. Opt. 41, 7254-7263 (2002).
[CrossRef] [PubMed]

J. M. Huntley, G. H. Kaufmann, and D. Kerr, “Phase-shifted dynamic speckle pattern interferometry at 1 kHz,” Appl. Opt. 38, 6556-6563 (1999).
[CrossRef]

Y. Fu, C. J. Tay, C. Quan, and H. Miao, “Wavelet analysis of speckle patterns with a temporal carrier,” Appl. Opt. 44, 959-965 (2005).
[CrossRef] [PubMed]

K. Qian, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695-2702 (2004).
[CrossRef]

L. Xu, X. Peng, J. Miao, and A. K. Asundi, “Studies of digital microscopic holography with applications to microstructure testing,” Appl. Opt. 40, 5046-5051 (2001).
[CrossRef]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl. Opt. 38, 6994-7001(1999).
[CrossRef]

D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high-resolution living-cell analysis,” Appl. Opt. 43, 6536-6544 (2004).
[CrossRef]

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47, A52-A61 (2008).
[CrossRef] [PubMed]

G. Pedrini, W. Osten, and M. E. Gusev, “High-speed digital holographic interferometry for vibration measurement,” Appl. Opt. 45, 3456-3462 (2006).
[CrossRef] [PubMed]

Y. Fu, R. M. Groves, G. Pedrini, and W. Osten, “Kinematic and deformation parameter measurement by spatiotemporal analysis of an interferogram sequence,” Appl. Opt. 46, 8645-8655 (2007).
[CrossRef] [PubMed]

Y. Fu, G. Pedrini, and W. Osten, “Vibration measurement by temporal Fourier analyses of digital hologram sequence,” Appl. Opt. 46, 5719-5727 (2007).
[CrossRef] [PubMed]

K. Qian, T. H. N. Le, F. Lin, and H. S. Seah, “Comparative analysis on some filters for wrapped phase maps,” Appl. Opt. 46, 7412-7418 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

J. Micromech. Microeng. (1)

S. Petitgrand and A. Bosseboeuf, “Simultaneous mapping of out-of-plane vibrations of MEMS with (sub)nanometer resolution,” J. Micromech. Microeng. 14 (9), S97-S101 (2004).
[CrossRef]

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

S. H. Wang, C. J. Tay, C. Quan, and H. M. Shang, “Determination of deflection and Young's modulus of a micro-beam by means of interferometry,” Meas. Sci. Technol. 12, 1279-1286(2001).
[CrossRef]

Mech. Syst. Signal Process. (1)

P. Castellini, M. Martarelli, and E. P. Tomasini. “Laser Doppler vibrometry: development of advanced solutions answering to technology's needs,” Mech. Syst. Signal Process. 20, 1265-1285 (2006).
[CrossRef]

Opt. Commun. (2)

G. H. Kaufmann, “Phase measurement in temporal speckle pattern interferometry using the Fouier transform method with and without a temporal carrier,” Opt. Commun. 217, 141-149 (2003).
[CrossRef]

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205-210 (1999).
[CrossRef]

Opt. Eng. (2)

Y. Fu, C. J. Tay, C. Quan, and L. J. Chen, “Temporal wavelet analysis for deformation and velocity measurement in speckle interferometry,” Opt. Eng. 43, 2780-2787 (2004).
[CrossRef]

L. Yang and P. Colbourne, “Digital laser microinterferometer and its applications,” Opt. Eng. 42, 1417-1426 (2003).
[CrossRef]

Opt. Express (1)

Opt. Express (1)

Opt. Lasers Eng. (2)

K. Qian, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304-317 (2007).
[CrossRef]

G. Pedrini, H. Tiziani, and Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199-219 (1997).
[CrossRef]

Opt. Lett. (3)

Optik (Jena) (1)

S. H. Wang, C. Quan, and C. J. Tay, “A genetic optical interferometric inspection on micro-deformation,” Optik (Jena) 115 (11-12), 564-568 (2004).

Proc. SPIE (2)

R. Jozwicki, M. Kujavinska, and K. Patorski, “Application of lasers in precise measurement of microelements,” Proc. SPIE 5229, 266-274 (2003).
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Sens. Actuators A (1)

M. Kujawinska, “Modern optical measurement station for micro-materials and micro-elements studies,” Sens. Actuators A 99, 144-153 (2002).
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Strain (1)

P. Jacquot, “Speckle interferometry: a review of the principal methods in use for experimental mechanics applications,” Strain 44 (1), 57-69 (2008).
[CrossRef]

Other (5)

J. M. Huntley, “Challenges in phase unwrapping,” in Trends in Optical Nondestructive Testing and Inspection, P. K. Rastogi and D. Inaudi, eds. (Elsevier Science, 2000), pp. 37-44.
[CrossRef]

H. J. Tiziani, “Spectral and temporal phase evaluation for interferometry and speckle applications,” in Trends in Optical Nondestructive Testing and Inspection, P. K. Rastogi and D. Inaudi, eds. (Elsevier Science, 2000), pp. 323-343.
[CrossRef]

U. Schnars and W. Jueptner, Digital Holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

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Figures (6)

Fig. 1
Fig. 1

(a) Schematic layout of the experimental setup and (b) specimen of a miniature cantilever beam with white-light illumination and the imaging area.

Fig. 2
Fig. 2

(a) Typical digital hologram obtained on a cantilever beam; (b) spectrum of the obtained digital hologram; (c) typical original wrapped phase map indicating the relative displacement of the beam and the area of interest.

Fig. 3
Fig. 3

Sequence of original wrapped phase maps and the phase maps after WFT filtering.

Fig. 4
Fig. 4

(a) Wrapped phase map in a spatiotemporal plane; (b) unwrapped phase map showing the displacement variation in the spatiotemporal plane; (c) displacement distributions of the cantilever beam at different instants; (d) instantaneous displacements of two points on the cantilever beam.

Fig. 5
Fig. 5

(a) Phase map of the velocity variation in the spatiotemporal plane; (b) typical velocity distributions on the cantilever beam; (c) instantaneous velocities of two points on the cantilever beam.

Fig. 6
Fig. 6

Instantaneous acceleration of two points on the cantilever beam.

Equations (6)

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I H ( x , y ) = | R H ( x , y ) | 2 + | U H ( x , y ) | 2 + R H ( x , y ) U H * ( x , y ) + R H * ( x , y ) U H ( x , y ) ,
f max = 2 λ sin ( θ max 2 ) ,
Δ ϕ = 2 π z λ S ,
Δ ϕ = arctan Im ( U ( x , y ; t n ) U * ( x , y ; t 1 ) ) Re ( U ( x , y ; t n ) U * ( x , y ; t 1 ) ) ,
S C p ( u , ξ ) = s 2 A ( u ) exp ( j [ φ ( u ) ξ u ] ) ( g ^ ( s [ ξ φ ( u ) ] ) + ε ( u , ξ ) ) ,
ξ ( u ) = φ ( u ) ,

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