Abstract

This study proposes an image processing method to improve the quality of interference fringes in mode-shape measurement using temporal speckle pattern interferometry. A vibrating piezoelectric plate at resonance was investigated, and the full-field optical information was saved as a sequence of images. According to derived statistical properties, an algorithm was developed to remove noise from both the background and disturbance, resulting in high-resolution images of excellent quality. In addition, the resonant frequency and mode shape obtained using the proposed algorithm demonstrate excellent agreement with theoretical results obtained by the finite element method.

© 2011 Optical Society of America

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  1. G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2011 (1)

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

2010 (2)

2009 (5)

H. Nguyen-Xuan and T. Nguyen-Thoi, Commun. Numer. Methods Eng. 25, 882 (2009).
[CrossRef]

F. P. Chiang, Opt. Lasers Eng. 47, 274 (2009).
[CrossRef]

Y. H. Huang and C. C. Ma, Smart Mater. Struc. 18, 085017 (2009).
[CrossRef]

Y. H. Huang and C. C. Ma, Sens. Actuators A 149, 320 (2009).
[CrossRef]

A. Federico and G. H. Kaufmann, Opt. Lett. 34, 2336 (2009).
[CrossRef] [PubMed]

2008 (2)

D. Braess and M. Kaltenbacher, Int. J. Numer. Methods Eng. 73, 147 (2008).
[CrossRef]

P. Jacquot, Strain 44, 57 (2008).
[CrossRef]

1996 (1)

Alekseenko, I.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Bavigadda, V.

Braess, D.

D. Braess and M. Kaltenbacher, Int. J. Numer. Methods Eng. 73, 147 (2008).
[CrossRef]

Chiang, F. P.

F. P. Chiang, Opt. Lasers Eng. 47, 274 (2009).
[CrossRef]

Federico, A.

Gaspar, J.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2000).

Huang, Y. H.

Y. H. Huang and C. C. Ma, Sens. Actuators A 149, 320 (2009).
[CrossRef]

Y. H. Huang and C. C. Ma, Smart Mater. Struc. 18, 085017 (2009).
[CrossRef]

Hwang, C. H.

Jacquot, P.

P. Jacquot, Strain 44, 57 (2008).
[CrossRef]

Jallapuram, R.

Kaltenbacher, M.

D. Braess and M. Kaltenbacher, Int. J. Numer. Methods Eng. 73, 147 (2008).
[CrossRef]

Kaufmann, G. H.

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley, 2005).

Lin, S. Y.

Ma, C. C.

Y. H. Huang and C. C. Ma, Sens. Actuators A 149, 320 (2009).
[CrossRef]

Y. H. Huang and C. C. Ma, Smart Mater. Struc. 18, 085017 (2009).
[CrossRef]

Mihaylova, E.

Mujumdar, S.

Nguyen-Thoi, T.

H. Nguyen-Xuan and T. Nguyen-Thoi, Commun. Numer. Methods Eng. 25, 882 (2009).
[CrossRef]

Nguyen-Xuan, H.

H. Nguyen-Xuan and T. Nguyen-Thoi, Commun. Numer. Methods Eng. 25, 882 (2009).
[CrossRef]

Osten, W.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Paul, O.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Pedrini, G.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Schmidt, M. E.

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Toal, V.

Uppu, R.

Wang, W. C.

Appl. Opt. (1)

Commun. Numer. Methods Eng. (1)

H. Nguyen-Xuan and T. Nguyen-Thoi, Commun. Numer. Methods Eng. 25, 882 (2009).
[CrossRef]

Int. J. Numer. Methods Eng. (1)

D. Braess and M. Kaltenbacher, Int. J. Numer. Methods Eng. 73, 147 (2008).
[CrossRef]

Opt. Eng. (1)

G. Pedrini, J. Gaspar, M. E. Schmidt, I. Alekseenko, O. Paul, and W. Osten, Opt. Eng. 50, 101504 (2011).
[CrossRef]

Opt. Lasers Eng. (1)

F. P. Chiang, Opt. Lasers Eng. 47, 274 (2009).
[CrossRef]

Opt. Lett. (3)

Sens. Actuators A (1)

Y. H. Huang and C. C. Ma, Sens. Actuators A 149, 320 (2009).
[CrossRef]

Smart Mater. Struc. (1)

Y. H. Huang and C. C. Ma, Smart Mater. Struc. 18, 085017 (2009).
[CrossRef]

Strain (1)

P. Jacquot, Strain 44, 57 (2008).
[CrossRef]

Other (2)

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley, 2005).

J. W. Goodman, Statistical Optics (Wiley, 2000).

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Figures (3)

Fig. 1
Fig. 1

Fringe analysis of in-plane vibration amplitude.

Fig. 2
Fig. 2

TSPI setup for in-plane measurement.

Fig. 3
Fig. 3

Comparison of the eighth in-plane mode: mode shape in (a) the U direction and (b) the V direction obtained using FEM; mode shape in (c) the U direction and (d) the V direction obtained using the proposed method.

Equations (8)

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

I i ( x , y ) = I o ( x , y ) + I R ( x , y ) + 2 I o I R | cos ( ϕ ( x , y ) + ψ i ( x , y ) ) J 0 ( Γ A ( x , y ) ) | ,
ψ i ( x , y ) = 1 τ i τ ( i + 1 ) τ ψ ( x , y , t ) f ( ψ ( x , y , t ) ) d t ,
ψ ¯ s = 1 n i = 1 n ψ i ,
ψ ^ s = 1 n 1 i = 1 n ( | ψ i | | ψ ¯ s | ) 2 .
I i = I o + I R + 2 I o I R | ( cos ϕ + ψ i sin ϕ ) J 0 ( Γ A ) |
I i * = I b g + | ( cos ϕ + ψ i sin ϕ ) J 0 ( Γ A ) | .
I ^ * = 1 n 1 i = 1 n ( I i * I ¯ * ) 2 = ψ ^ s | sin ϕ J 0 ( Γ A ) | ,
I ¯ * = 1 n i = 1 n I i * = I b g + | ( cos ϕ + ψ ¯ s sin ϕ ) J 0 ( Γ A ) | ,

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