Abstract

A new technique capable of monitoring two-dimensional vibration fringe patterns in real-time is presented. It is based on optical reconstructing of time-averaged digital holograms. Recording of the holograms is realized in a quasi-Fourier off-axis setup whilst reconstructing in an extended Fourier transform setup capable of spatial filtering of the hologram reconstructions. The effectiveness of the proposed device, tested on a silicon wafer, was verified by performing operations such as monitoring of vibration modes, adjusting the hologram recording parameters, or searching for resonant frequencies. Additionally, mode beating between two distant vibration frequencies is observed and reported. The proposed technique is suitable for various scientific and industrial applications.

© 2006 Optical Society of America

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2005 (4)

N. Demoli and I. Demoli, "Measuring surface vibrations of musical instruments using an inexpensive digital holography device," Opt. Eng. 44, 09050213 (2005).
[CrossRef]

M. L. Jakobsen, H. E. Larsen, and S. G. Hanson, "Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements," J. Opt. A: Pure Appl. Opt. 7, S303-S307 (2005).
[CrossRef]

N. Demoli and I. Demoli, "Dynamic modal characterization of musical instruments using digital holography," Opt. Express 13, 4812-4817 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-13-4812.
[CrossRef] [PubMed]

P. Picart, J. Leval, J. Pascal, J. Boileau, M. Grill, J. Breteau, B. Gautier, and S. Gillet, "2D full field vibration analysis with multiplexed digital holograms," Opt. Express 13, 8882-8892 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-22-8882.
[CrossRef] [PubMed]

2004 (3)

C.-C. Ma and C.-H. Huang, "Experimental whole-field interferometry for transverse vibration of plates," J. Sound Vib. 271, 493-506 (2004).
[CrossRef]

P. Ferraro, S. DeNicola, A. Finizio, G. Pierattini, and G. Coppola, "Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method," Appl. Phys. Lett. 85, 2709-2711 (2004).
[CrossRef]

N. Demoli and 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]

2003 (2)

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

M. Reinstaedtler, U. Rabe, V. Scherer, J. A. Turner, and W. Arnold, "Imaging of flexural and torsional resonance modes of atomic force microscopy cantilevers using optical interferometry," Surf. Sci. 532-535, 1152-1158 (2003).
[CrossRef]

2002 (1)

2000 (2)

M. Sutkowski and M. Kujawinska, "Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms," Opt. Lasers Eng. 33, 191-201 (2000).
[CrossRef]

S. Prakash, S. Upadhyay, and C. Shakher, "Real time out-of-plane vibration measurement using Talbot interferometry," Opt. Lasers Eng. 34, 251-259 (2000).
[CrossRef]

1998 (1)

1997 (1)

1986 (1)

N. Demoli, "Coherent pattern recognition using a two-stage spatial prefiltering procedure," Optik 72, 102-108 (1986).

1985 (1)

1971 (1)

J. N. Butters and J. A. Leendertz, "Holographic and video techniques applied to engineering measurements," Meas. Control 4, 349-354 (1971).

1965 (1)

Abe, K.

Arnold, W.

M. Reinstaedtler, U. Rabe, V. Scherer, J. A. Turner, and W. Arnold, "Imaging of flexural and torsional resonance modes of atomic force microscopy cantilevers using optical interferometry," Surf. Sci. 532-535, 1152-1158 (2003).
[CrossRef]

Band, Y.

Boileau, J.

Breteau, J.

Butters, J. N.

J. N. Butters and J. A. Leendertz, "Holographic and video techniques applied to engineering measurements," Meas. Control 4, 349-354 (1971).

Chin, T.

Coppola, G.

P. Ferraro, S. DeNicola, A. Finizio, G. Pierattini, and G. Coppola, "Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method," Appl. Phys. Lett. 85, 2709-2711 (2004).
[CrossRef]

Dahms, U.

Demoli, I.

N. Demoli and I. Demoli, "Measuring surface vibrations of musical instruments using an inexpensive digital holography device," Opt. Eng. 44, 09050213 (2005).
[CrossRef]

N. Demoli and I. Demoli, "Dynamic modal characterization of musical instruments using digital holography," Opt. Express 13, 4812-4817 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-13-4812.
[CrossRef] [PubMed]

Demoli, N.

DeNicola, S.

P. Ferraro, S. DeNicola, A. Finizio, G. Pierattini, and G. Coppola, "Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method," Appl. Phys. Lett. 85, 2709-2711 (2004).
[CrossRef]

Ferraro, P.

P. Ferraro, S. DeNicola, A. Finizio, G. Pierattini, and G. Coppola, "Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method," Appl. Phys. Lett. 85, 2709-2711 (2004).
[CrossRef]

Finizio, A.

P. Ferraro, S. DeNicola, A. Finizio, G. Pierattini, and G. Coppola, "Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method," Appl. Phys. Lett. 85, 2709-2711 (2004).
[CrossRef]

Fukushima, S.

Gautier, B.

Gillet, S.

Gougeon, S.

Grill, M.

Gruber, H.

Hanson, S. G.

M. L. Jakobsen, H. E. Larsen, and S. G. Hanson, "Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements," J. Opt. A: Pure Appl. Opt. 7, S303-S307 (2005).
[CrossRef]

Heller, D.

Huang, C.-H.

C.-C. Ma and C.-H. Huang, "Experimental whole-field interferometry for transverse vibration of plates," J. Sound Vib. 271, 493-506 (2004).
[CrossRef]

Jakobsen, M. L.

M. L. Jakobsen, H. E. Larsen, and S. G. Hanson, "Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements," J. Opt. A: Pure Appl. Opt. 7, S303-S307 (2005).
[CrossRef]

Kafri, O.

Ko, J.-Y.

Kujawinska, M.

M. Sutkowski and M. Kujawinska, "Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms," Opt. Lasers Eng. 33, 191-201 (2000).
[CrossRef]

Kurokawa, T.

Larsen, H. E.

M. L. Jakobsen, H. E. Larsen, and S. G. Hanson, "Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements," J. Opt. A: Pure Appl. Opt. 7, S303-S307 (2005).
[CrossRef]

Leendertz, J. A.

J. N. Butters and J. A. Leendertz, "Holographic and video techniques applied to engineering measurements," Meas. Control 4, 349-354 (1971).

Leval, J.

Lim, T.-S.

Ma, C.-C.

C.-C. Ma and C.-H. Huang, "Experimental whole-field interferometry for transverse vibration of plates," J. Sound Vib. 271, 493-506 (2004).
[CrossRef]

Mounier, D.

Otsuka, K.

Pascal, J.

Picart, P.

Pierattini, G.

P. Ferraro, S. DeNicola, A. Finizio, G. Pierattini, and G. Coppola, "Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method," Appl. Phys. Lett. 85, 2709-2711 (2004).
[CrossRef]

Powel, R. L.

Prakash, S.

S. Prakash, S. Upadhyay, and C. Shakher, "Real time out-of-plane vibration measurement using Talbot interferometry," Opt. Lasers Eng. 34, 251-259 (2000).
[CrossRef]

Rabe, U.

M. Reinstaedtler, U. Rabe, V. Scherer, J. A. Turner, and W. Arnold, "Imaging of flexural and torsional resonance modes of atomic force microscopy cantilevers using optical interferometry," Surf. Sci. 532-535, 1152-1158 (2003).
[CrossRef]

Reinstaedtler, M.

M. Reinstaedtler, U. Rabe, V. Scherer, J. A. Turner, and W. Arnold, "Imaging of flexural and torsional resonance modes of atomic force microscopy cantilevers using optical interferometry," Surf. Sci. 532-535, 1152-1158 (2003).
[CrossRef]

Sano, M.

Scherer, V.

M. Reinstaedtler, U. Rabe, V. Scherer, J. A. Turner, and W. Arnold, "Imaging of flexural and torsional resonance modes of atomic force microscopy cantilevers using optical interferometry," Surf. Sci. 532-535, 1152-1158 (2003).
[CrossRef]

Shakher, C.

S. Prakash, S. Upadhyay, and C. Shakher, "Real time out-of-plane vibration measurement using Talbot interferometry," Opt. Lasers Eng. 34, 251-259 (2000).
[CrossRef]

Stetson, K. A.

Sutkowski, M.

M. Sutkowski and M. Kujawinska, "Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms," Opt. Lasers Eng. 33, 191-201 (2000).
[CrossRef]

Takeda, M.

Turner, J. A.

M. Reinstaedtler, U. Rabe, V. Scherer, J. A. Turner, and W. Arnold, "Imaging of flexural and torsional resonance modes of atomic force microscopy cantilevers using optical interferometry," Surf. Sci. 532-535, 1152-1158 (2003).
[CrossRef]

Upadhyay, S.

S. Prakash, S. Upadhyay, and C. Shakher, "Real time out-of-plane vibration measurement using Talbot interferometry," Opt. Lasers Eng. 34, 251-259 (2000).
[CrossRef]

Vukicevic, D.

Walling, J.

Wernicke, G.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

P. Ferraro, S. DeNicola, A. Finizio, G. Pierattini, and G. Coppola, "Recovering image resolution in reconstructing digital off-axis holograms by Fresnel-transform method," Appl. Phys. Lett. 85, 2709-2711 (2004).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (1)

M. L. Jakobsen, H. E. Larsen, and S. G. Hanson, "Optical spatial filtering velocimetry sensor for sub-micron, in-plane vibration measurements," J. Opt. A: Pure Appl. Opt. 7, S303-S307 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Sound Vib. (1)

C.-C. Ma and C.-H. Huang, "Experimental whole-field interferometry for transverse vibration of plates," J. Sound Vib. 271, 493-506 (2004).
[CrossRef]

Meas. Control (1)

J. N. Butters and J. A. Leendertz, "Holographic and video techniques applied to engineering measurements," Meas. Control 4, 349-354 (1971).

Opt. Eng. (1)

N. Demoli and I. Demoli, "Measuring surface vibrations of musical instruments using an inexpensive digital holography device," Opt. Eng. 44, 09050213 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (2)

S. Prakash, S. Upadhyay, and C. Shakher, "Real time out-of-plane vibration measurement using Talbot interferometry," Opt. Lasers Eng. 34, 251-259 (2000).
[CrossRef]

M. Sutkowski and M. Kujawinska, "Application of liquid crystal (LC) devices for optoelectronic reconstruction of digitally stored holograms," Opt. Lasers Eng. 33, 191-201 (2000).
[CrossRef]

Opt. Lett. (3)

Optik (1)

N. Demoli, "Coherent pattern recognition using a two-stage spatial prefiltering procedure," Optik 72, 102-108 (1986).

Surf. Sci. (1)

M. Reinstaedtler, U. Rabe, V. Scherer, J. A. Turner, and W. Arnold, "Imaging of flexural and torsional resonance modes of atomic force microscopy cantilevers using optical interferometry," Surf. Sci. 532-535, 1152-1158 (2003).
[CrossRef]

Other (3)

P. Hariharan, Optical Holography: Principles, Techniques, and Applications, 2nd ed. (Cambridge University Press, Cambridge, 1996).

Dantec Ettemeyer (2006), http://www.dantec-ettemeyer.com/pdf/PDF-new/F-Q-501-RTMM-05-002-EN.pdf.

Holoeye PhotonicsAG  (2006), http://www.holoeye.com/slm_technology.html.

Supplementary Material (3)

» Media 1: AVI (1842 KB)     
» Media 2: AVI (1842 KB)     
» Media 3: AVI (1842 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Scheme of the experimental device. (VBS) variable beam splitter; (M) mirror; (L) lens; (Col.) collimator; (LS) loudspeaker; (A) aperture; (FTL) Fourier transform lens; (SF) spatial filter.

Fig. 2.
Fig. 2.

Optical rec onstructions of the wafer at rest (0 Hz) and at the resonant frequencies.

Fig. 3.
Fig. 3.

Same as in Fig. 2. obtained by numerical reconstructing.

Fig. 4.
Fig. 4.

(1.8 MB) Movie of the static pattern obtained for the frequencies (220 × 1980) Hz.

Fig. 5.
Fig. 5.

(1.8 MB) Movie of the mode beating obtained for the frequencies (220 + 1978) Hz.

Fig. 6.
Fig. 6.

(1.8 MB) Movie of the mode beating obtained for the frequencies (220 + 1976) Hz.

Equations (6)

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E ξ η exp [ i 2 π λd ( ξX + ηY ) ] FT { s x y J 0 [ 4 π λ h x y ] exp [ i ( π λd ) ( x 2 + y 2 ) ] } ,
E CCD m Δ ξ , n Δ η [ E ξ η rect ( ξ α Δ ξ , η β Δ η ) ] comb ( ξ Δξ , η Δη ) rect ( ξ M Δ ξ , η N Δ η ) ,
U num x y = FT 1 { E CCD ( m Δ ξ , n Δ η ) } ,
U num x y ( { δ ( x X , y Y ) s x y J 0 [ 4 π λ h x y ] } sin c ( α Δ ξ λd x , β Δ η λd y ) ) comb ( Δ ξ λd x , Δ η λd y ) sin c ( M Δ ξ λd x , N Δ η λd y )
E LCD m Δ ξ , n Δ η rect ( ξ M Δξ , η N Δη ) × { [ E CCD m Δ ξ , n Δ η comb ( ξ Δξ , η Δη ) rect ( ξ M Δ ξ , η N Δ η ) ] rect ( ξ α Δξ , η β Δη ) }
U o p t ( x , y ) sin c ( M Δ ξ λ f x , N Δ η λ f y ) { [ U n u m ( x , y ) c o m b ( Δ ξ λ f x , Δ η λ f y ) sin c ( M Δ ξ λ f x , N Δ η λ f y ) ] sin c ( α Δ ξ λ f x , β Δ η λ f y ) }

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