Abstract

Time-averaged in-line digital holography is applied for vibration analysis. In particular, by use of a double-exposure approach, simultaneous determination of vibration mode shape and mean static state deformation during a vibration cycle are obtained. The subtraction of two numerically reconstructed digital holograms recorded at the same resonant frequency but with a small difference in amplitude shows the mixing of Bessel-type time-averaged fringes owing to vibration and of the double-exposure fringes owing to differences in the mean deformation of the object. It is shown that separation of these fringe patterns can be readily accomplished numerically. An experimental demonstration of this effect by use of in-line digital holography for relatively small membranes is demonstrated.

© 2006 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2005 (3)

2004 (1)

2003 (3)

C. H. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, "Effects of the fill factor of CCD pixels on digital holograms: comment on the papers 'Frequency analysis of digital holography' and 'Frequency analysis of digital holography with reconstruction by convolution,"' Opt. Eng. 42, 2768-2771 (2003).
[CrossRef]

N. Demoli, J. Mestrovic, and I. Sovic, "Subtraction digital holography," Appl. Opt. 42, 798-804 (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 (2)

U. Schnars and W. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).

I. Yamaguchi, T. Matsumura, and J. Kato, "Phase-shifting color digital holography," Opt. Lett. 27, 1108-1110 (2002).
[CrossRef]

2001 (1)

L. Xu, X. Peng, A. Asundi, and J. Miao, "Hybrid holographic microscope for interferometric measurement of microstructures," Opt. Eng. 40, 2533-2539 (2001).
[CrossRef]

2000 (2)

G. Pedrini, H. J. Tiziani, and M. E. Gusev, "Pulsed digital holographic interferometry with 694- and 347-nm wavelengths," Appl. Opt. 39, 246-249 (2000).
[CrossRef]

L. Xu, J. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214-3219 (2000).
[CrossRef]

1997 (1)

T. M. Kreis and W. Juptner, "Suppression of dc term in digital holography," Opt. Eng. 36, 2357-2360 (1997).
[CrossRef]

1994 (1)

1984 (1)

O. J. Lokberg, "ESPI--the ultimate holographic tool for vibration analysis?" J. Acoust. Soc. Am. 76, 1783-1791 (1984).
[CrossRef]

Asundi, A.

L. Xu, X. Peng, A. Asundi, and J. Miao, "Hybrid holographic microscope for interferometric measurement of microstructures," Opt. Eng. 40, 2533-2539 (2001).
[CrossRef]

L. Xu, J. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214-3219 (2000).
[CrossRef]

Colomb, T.

Cuche, E.

Demoli, I.

Demoli, N.

Depeursinge, C.

Emery, Y.

Gougeon, S.

Guo, C. H.

C. H. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, "Effects of the fill factor of CCD pixels on digital holograms: comment on the papers 'Frequency analysis of digital holography' and 'Frequency analysis of digital holography with reconstruction by convolution,"' Opt. Eng. 42, 2768-2771 (2003).
[CrossRef]

Gusev, M. E.

Juptner, W.

U. Schnars and W. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).

T. M. Kreis and W. Juptner, "Suppression of dc term in digital holography," Opt. Eng. 36, 2357-2360 (1997).
[CrossRef]

U. Schnars and W. Juptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994).
[CrossRef] [PubMed]

Kato, J.

Kreis, T. M.

T. M. Kreis and W. Juptner, "Suppression of dc term in digital holography," Opt. Eng. 36, 2357-2360 (1997).
[CrossRef]

Leval, J.

Lokberg, O. J.

O. J. Lokberg, "ESPI--the ultimate holographic tool for vibration analysis?" J. Acoust. Soc. Am. 76, 1783-1791 (1984).
[CrossRef]

Magistretti, P. J.

Marquet, P.

Matsumura, T.

Mestrovic, J.

Miao, J.

L. Xu, X. Peng, A. Asundi, and J. Miao, "Hybrid holographic microscope for interferometric measurement of microstructures," Opt. Eng. 40, 2533-2539 (2001).
[CrossRef]

L. Xu, J. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214-3219 (2000).
[CrossRef]

Mounier, D.

Pedrini, G.

Peng, X.

L. Xu, X. Peng, A. Asundi, and J. Miao, "Hybrid holographic microscope for interferometric measurement of microstructures," Opt. Eng. 40, 2533-2539 (2001).
[CrossRef]

Picart, P.

Rappaz, B.

Rong, Z. Y.

C. H. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, "Effects of the fill factor of CCD pixels on digital holograms: comment on the papers 'Frequency analysis of digital holography' and 'Frequency analysis of digital holography with reconstruction by convolution,"' Opt. Eng. 42, 2768-2771 (2003).
[CrossRef]

Schnars, U.

U. Schnars and W. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).

U. Schnars and W. Juptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179-181 (1994).
[CrossRef] [PubMed]

Sovic, I.

Tiziani, H. J.

Vukicevic, D.

Wang, H. T.

C. H. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, "Effects of the fill factor of CCD pixels on digital holograms: comment on the papers 'Frequency analysis of digital holography' and 'Frequency analysis of digital holography with reconstruction by convolution,"' Opt. Eng. 42, 2768-2771 (2003).
[CrossRef]

Xu, L.

L. Xu, X. Peng, A. Asundi, and J. Miao, "Hybrid holographic microscope for interferometric measurement of microstructures," Opt. Eng. 40, 2533-2539 (2001).
[CrossRef]

L. Xu, J. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214-3219 (2000).
[CrossRef]

Yamaguchi, I.

Zhang, L.

C. H. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, "Effects of the fill factor of CCD pixels on digital holograms: comment on the papers 'Frequency analysis of digital holography' and 'Frequency analysis of digital holography with reconstruction by convolution,"' Opt. Eng. 42, 2768-2771 (2003).
[CrossRef]

Appl. Opt. (4)

J. Acoust. Soc. Am. (1)

O. J. Lokberg, "ESPI--the ultimate holographic tool for vibration analysis?" J. Acoust. Soc. Am. 76, 1783-1791 (1984).
[CrossRef]

Meas. (1)

U. Schnars and W. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).

Opt. Eng. (4)

L. Xu, X. Peng, A. Asundi, and J. Miao, "Hybrid holographic microscope for interferometric measurement of microstructures," Opt. Eng. 40, 2533-2539 (2001).
[CrossRef]

L. Xu, J. Miao, and A. Asundi, "Properties of digital holography based on in-line configuration," Opt. Eng. 39, 3214-3219 (2000).
[CrossRef]

T. M. Kreis and W. Juptner, "Suppression of dc term in digital holography," Opt. Eng. 36, 2357-2360 (1997).
[CrossRef]

C. H. Guo, L. Zhang, Z. Y. Rong, and H. T. Wang, "Effects of the fill factor of CCD pixels on digital holograms: comment on the papers 'Frequency analysis of digital holography' and 'Frequency analysis of digital holography with reconstruction by convolution,"' Opt. Eng. 42, 2768-2771 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

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Figures (5)

Fig. 1
Fig. 1

(a) In-line digital holographic setup for vibration measurement. (b) Schematic of the vibrating membrane.

Fig. 2
Fig. 2

Subtracted wave fields of membranes vibrating at the same frequency but different amplitudes, showing mixing of the vibration and mean static deformation fringes. Vibration frequencies are (a) 2.0, (b) 5.25, (c) 6.0, and (d) 7.75 kHz.

Fig. 3
Fig. 3

Vibration mode patterns at frequencies (a) 2.0, (b) 5.25, (c) 6.0, and (d) 7.75 kHz.

Fig. 4
Fig. 4

Subtraction of phase gives the fringe pattern that corresponds to mean static deformation during a change in vibration amplitudes.

Fig. 5
Fig. 5

Mean static deformation at two amplitudes of a stationary plate.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

z ( x , y , t ) = z ( x , y ) cos ω t ,
O ( x , y , t ) = O 0 ( x , y ) exp [ i ϕ 0 ( x , y ) ] ×  exp { i [ K · z ( x , y , t ) ] } ,
H ( ξ , η ) = | O ( ξ , η ) | 2 + | R ( ξ , η ) | 2 + O * ( ξ , η ) R ( ξ , η ) + O ( ξ , η ) R * ( ξ , η ) .
H ( m , n ) = [ H ( ξ , η )  rect ( ξ α Δ ξ , η β Δ η ) ] ×  rect ( ξ M Δ ξ , η N Δ η ) comb ( ξ Δ ξ , η Δ η ) ,
U ( x , y ) = J [ H ( m , n ) R ( m , n ) g ( m , n ) ] .
U ( x , y ) = O 0 ( x , y ) exp [ i ϕ ( x , y ) ] J 0 [ K z ( x , y ) ] + U ,
O 1 ( x , y , t ) = O 0 ( x , y ) exp [ i ϕ 1 ( x , y ) ] ×  exp { i [ K z 1 ( x , y , t ) ] } ,
O 2 ( x , y , t ) = O 0 ( x , y ) exp [ i ϕ 2 ( x , y ) ] ×  exp { i [ K z 2 ( x , y , t ) ] } .
U 1 ( x , y ) = O 0 ( x , y ) exp [ i ϕ 1 ( x , y ) ] J 0 [ K z 1 ( x , y ) ] + U 1 ,
U 2 ( x , y ) = O 0 ( x , y ) exp [ i ϕ 2 ( x , y ) ] J 0 [ K z 2 ( x , y ) ] + U 2 .
( U 1 U 2 ) = O 0 ( x , y ) { exp [ i ϕ 1 ( x , y ) ] × J 0 [ K z 1 ( x , y ) ] exp [ i ϕ 2 ( x , y ) ] × J 0 [ K z 2 ( x , y ) ] } ,
I = | ( U 1 U 2 ) | 2 = | O 0 ( x , y ) { exp [ i ϕ 1 ( x , y ) ] ×  J 0 [ K z 1 ( x , y ) ] exp [ i ϕ 2 ( x , y ) ] ×  J 0 [ K z 2 ( x , y ) ] } | 2 .
Δ I = | U 1 | 2 | U 2 | 2
= O 0     2 ( x , y ) { J 0     2 [ K z 1 ( x , y ) ] J 0     2 [ K z 2 ( x , y ) ] } ,
Δ ϕ = ϕ 1 ( x , y ) ϕ 2 ( x , y ) .

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