Abstract

This study proposes an algorithm based on the standard deviation in the temporal domain to remove influences from background noise and ambient disturbance and enhance the quality of images obtained using interferometric technology. From measurements of the first ten in-plane resonant frequencies and mode shapes of vibrating zirconate titanate (PZT) laminates, we investigated the resonant characteristics in both the U and V directions. The resulting interference fringes were used to quantify the vibration amplitude of PZT plates on a submicron scale. The resonant frequencies obtained using the proposed method are in excellent agreement with those obtained using the finite element method and an impedance analyzer.

© 2012 Optical Society of America

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References

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  1. R. B. Karabalin, S. C. Masmanidis, and M. L. Roukes, “Efficient parametric amplification in high and very high frequency piezoelectric nano electromechanical systems,” Appl. Phys. Lett. 97, 183101 (2010).
    [CrossRef]
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    [CrossRef]
  3. A. Gaitas, S. Gianchandani, and W. Zhu, “A piezo-thermal probe for thermo mechanical analysis,” Rev. Sci. Instrum. 82, 053701 (2011).
    [CrossRef]
  4. S. Adhikari, M. I. Friswell, and D. J. Inman, “Piezoelectric energy harvesting from broadband random vibrations,” Smart Mater. Struct. 18, 115005 (2009).
    [CrossRef]
  5. N. G. Elvin and A. A. Elvin, “A general equivalent circuit model for piezoelectric generators,” J. Intell. Mater. Syst. Struct. 20, 3–9 (2009).
    [CrossRef]
  6. C.-C. Ma, Y.-C. Lin, Y.-H. Huang, and H.-Y. Lin, “Experimental measurement and numerical analysis on resonant characteristics of cantilever plates for piezoceramic bimorphs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 227–239 (2007).
    [CrossRef]
  7. A. Krushynska, V. Meleshko, C. C. Ma, and Y. H. Huang, “Mode excitation efficiency for contour vibrations of piezoelectric resonators,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 2222–2238 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  12. C. Y. Chang and C. C. Ma, “Mode-shape measurement of piezoelectric plate using temporal speckle pattern interferometry and temporal standard deviation,” Opt. Lett. 36, 4281–4283 (2011).
    [CrossRef]
  13. J. Muñoz-Maciel, F. J. Casillas-Rodríguez, M. Mora-González, F. G. Peña-Lecona, V. M. Duran-Ramírez, and G. Gómez-Rosas, “Phase recovery from a single interferogram with closed fringes by phase unwrapping,” Appl. Opt. 50, 22–27 (2011).
    [CrossRef]

2011

A. Gaitas, S. Gianchandani, and W. Zhu, “A piezo-thermal probe for thermo mechanical analysis,” Rev. Sci. Instrum. 82, 053701 (2011).
[CrossRef]

A. Krushynska, V. Meleshko, C. C. Ma, and Y. H. Huang, “Mode excitation efficiency for contour vibrations of piezoelectric resonators,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 2222–2238 (2011).
[CrossRef]

C. Y. Chang and C. C. Ma, “Mode-shape measurement of piezoelectric plate using temporal speckle pattern interferometry and temporal standard deviation,” Opt. Lett. 36, 4281–4283 (2011).
[CrossRef]

J. Muñoz-Maciel, F. J. Casillas-Rodríguez, M. Mora-González, F. G. Peña-Lecona, V. M. Duran-Ramírez, and G. Gómez-Rosas, “Phase recovery from a single interferogram with closed fringes by phase unwrapping,” Appl. Opt. 50, 22–27 (2011).
[CrossRef]

2010

J. Xu, Y. Li, H. Wang, L. Chai, and Q. Xu, “Phase-shift extraction for phase-shifting interferometry by histogram of phase difference,” Opt. Express 18, 24368–24378(2010).
[CrossRef]

R. B. Karabalin, S. C. Masmanidis, and M. L. Roukes, “Efficient parametric amplification in high and very high frequency piezoelectric nano electromechanical systems,” Appl. Phys. Lett. 97, 183101 (2010).
[CrossRef]

2009

T. Wu, Z. Ding, K. Wang, M. Chen, and C. Wang, “Two-dimensional scanning realized by an asymmetry fiber cantilever driven by single piezo bender actuator for optical coherence tomography,” Opt. Express 17, 13819–13829 (2009).
[CrossRef]

P. Gao, B. Yao, N. Lindlein, K. Mantel, I. Harder, and E. Geist, “Phase-shift extraction for generalized phase-shifting interferometry,” Opt. Lett. 34, 3553–3555 (2009).
[CrossRef]

S. Adhikari, M. I. Friswell, and D. J. Inman, “Piezoelectric energy harvesting from broadband random vibrations,” Smart Mater. Struct. 18, 115005 (2009).
[CrossRef]

N. G. Elvin and A. A. Elvin, “A general equivalent circuit model for piezoelectric generators,” J. Intell. Mater. Syst. Struct. 20, 3–9 (2009).
[CrossRef]

2007

C.-C. Ma, Y.-C. Lin, Y.-H. Huang, and H.-Y. Lin, “Experimental measurement and numerical analysis on resonant characteristics of cantilever plates for piezoceramic bimorphs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 227–239 (2007).
[CrossRef]

2006

Adhikari, S.

S. Adhikari, M. I. Friswell, and D. J. Inman, “Piezoelectric energy harvesting from broadband random vibrations,” Smart Mater. Struct. 18, 115005 (2009).
[CrossRef]

Casillas-Rodríguez, F. J.

Chai, L.

Chang, C. Y.

Chen, M.

Ding, Z.

Duran-Ramírez, V. M.

Elvin, A. A.

N. G. Elvin and A. A. Elvin, “A general equivalent circuit model for piezoelectric generators,” J. Intell. Mater. Syst. Struct. 20, 3–9 (2009).
[CrossRef]

Elvin, N. G.

N. G. Elvin and A. A. Elvin, “A general equivalent circuit model for piezoelectric generators,” J. Intell. Mater. Syst. Struct. 20, 3–9 (2009).
[CrossRef]

Friswell, M. I.

S. Adhikari, M. I. Friswell, and D. J. Inman, “Piezoelectric energy harvesting from broadband random vibrations,” Smart Mater. Struct. 18, 115005 (2009).
[CrossRef]

Gaitas, A.

A. Gaitas, S. Gianchandani, and W. Zhu, “A piezo-thermal probe for thermo mechanical analysis,” Rev. Sci. Instrum. 82, 053701 (2011).
[CrossRef]

Gao, P.

Geist, E.

Gianchandani, S.

A. Gaitas, S. Gianchandani, and W. Zhu, “A piezo-thermal probe for thermo mechanical analysis,” Rev. Sci. Instrum. 82, 053701 (2011).
[CrossRef]

Gómez-Rosas, G.

Gusev, M. E.

Harder, I.

Huang, Y. H.

A. Krushynska, V. Meleshko, C. C. Ma, and Y. H. Huang, “Mode excitation efficiency for contour vibrations of piezoelectric resonators,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 2222–2238 (2011).
[CrossRef]

Huang, Y.-H.

C.-C. Ma, Y.-C. Lin, Y.-H. Huang, and H.-Y. Lin, “Experimental measurement and numerical analysis on resonant characteristics of cantilever plates for piezoceramic bimorphs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 227–239 (2007).
[CrossRef]

Inman, D. J.

S. Adhikari, M. I. Friswell, and D. J. Inman, “Piezoelectric energy harvesting from broadband random vibrations,” Smart Mater. Struct. 18, 115005 (2009).
[CrossRef]

Karabalin, R. B.

R. B. Karabalin, S. C. Masmanidis, and M. L. Roukes, “Efficient parametric amplification in high and very high frequency piezoelectric nano electromechanical systems,” Appl. Phys. Lett. 97, 183101 (2010).
[CrossRef]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley2005), Chap. 8.

Krushynska, A.

A. Krushynska, V. Meleshko, C. C. Ma, and Y. H. Huang, “Mode excitation efficiency for contour vibrations of piezoelectric resonators,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 2222–2238 (2011).
[CrossRef]

Li, Y.

Lin, H.-Y.

C.-C. Ma, Y.-C. Lin, Y.-H. Huang, and H.-Y. Lin, “Experimental measurement and numerical analysis on resonant characteristics of cantilever plates for piezoceramic bimorphs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 227–239 (2007).
[CrossRef]

Lin, Y.-C.

C.-C. Ma, Y.-C. Lin, Y.-H. Huang, and H.-Y. Lin, “Experimental measurement and numerical analysis on resonant characteristics of cantilever plates for piezoceramic bimorphs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 227–239 (2007).
[CrossRef]

Lindlein, N.

Ma, C. C.

A. Krushynska, V. Meleshko, C. C. Ma, and Y. H. Huang, “Mode excitation efficiency for contour vibrations of piezoelectric resonators,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 2222–2238 (2011).
[CrossRef]

C. Y. Chang and C. C. Ma, “Mode-shape measurement of piezoelectric plate using temporal speckle pattern interferometry and temporal standard deviation,” Opt. Lett. 36, 4281–4283 (2011).
[CrossRef]

Ma, C.-C.

C.-C. Ma, Y.-C. Lin, Y.-H. Huang, and H.-Y. Lin, “Experimental measurement and numerical analysis on resonant characteristics of cantilever plates for piezoceramic bimorphs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 227–239 (2007).
[CrossRef]

Mantel, K.

Masmanidis, S. C.

R. B. Karabalin, S. C. Masmanidis, and M. L. Roukes, “Efficient parametric amplification in high and very high frequency piezoelectric nano electromechanical systems,” Appl. Phys. Lett. 97, 183101 (2010).
[CrossRef]

Meleshko, V.

A. Krushynska, V. Meleshko, C. C. Ma, and Y. H. Huang, “Mode excitation efficiency for contour vibrations of piezoelectric resonators,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 2222–2238 (2011).
[CrossRef]

Mora-González, M.

Muñoz-Maciel, J.

Osten, W.

Pedrini, G.

Peña-Lecona, F. G.

Roukes, M. L.

R. B. Karabalin, S. C. Masmanidis, and M. L. Roukes, “Efficient parametric amplification in high and very high frequency piezoelectric nano electromechanical systems,” Appl. Phys. Lett. 97, 183101 (2010).
[CrossRef]

Wang, C.

Wang, H.

Wang, K.

Wu, T.

Xu, J.

Xu, Q.

Yao, B.

Zhu, W.

A. Gaitas, S. Gianchandani, and W. Zhu, “A piezo-thermal probe for thermo mechanical analysis,” Rev. Sci. Instrum. 82, 053701 (2011).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

R. B. Karabalin, S. C. Masmanidis, and M. L. Roukes, “Efficient parametric amplification in high and very high frequency piezoelectric nano electromechanical systems,” Appl. Phys. Lett. 97, 183101 (2010).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

C.-C. Ma, Y.-C. Lin, Y.-H. Huang, and H.-Y. Lin, “Experimental measurement and numerical analysis on resonant characteristics of cantilever plates for piezoceramic bimorphs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 227–239 (2007).
[CrossRef]

A. Krushynska, V. Meleshko, C. C. Ma, and Y. H. Huang, “Mode excitation efficiency for contour vibrations of piezoelectric resonators,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 58, 2222–2238 (2011).
[CrossRef]

J. Intell. Mater. Syst. Struct.

N. G. Elvin and A. A. Elvin, “A general equivalent circuit model for piezoelectric generators,” J. Intell. Mater. Syst. Struct. 20, 3–9 (2009).
[CrossRef]

Opt. Express

Opt. Lett.

Rev. Sci. Instrum.

A. Gaitas, S. Gianchandani, and W. Zhu, “A piezo-thermal probe for thermo mechanical analysis,” Rev. Sci. Instrum. 82, 053701 (2011).
[CrossRef]

Smart Mater. Struct.

S. Adhikari, M. I. Friswell, and D. J. Inman, “Piezoelectric energy harvesting from broadband random vibrations,” Smart Mater. Struct. 18, 115005 (2009).
[CrossRef]

Other

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley2005), Chap. 8.

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Figures (7)

Fig. 1.
Fig. 1.

Fringe analysis of in-plane vibration amplitude: local maxima and minima denote bright and dark fringes respectively.

Fig. 2.
Fig. 2.

Optical setup for time-averaged ESPI system for in-plane measurement.

Fig. 3.
Fig. 3.

Comparison of the first four in-plane mode shapes of the rectangular PZT laminate: experimental and FEM results.

Fig. 4.
Fig. 4.

Comparison of the fifth to seventh in-plane mode shapes of the rectangular PZT laminate: experimental and FEM results.

Fig. 5.
Fig. 5.

Comparison of the eighth to tenth in-plane mode shapes of the rectangular PZT laminate: experimental and FEM results.

Fig. 6.
Fig. 6.

Quantitative analysis of interferometric fringes: the third U direction mode.

Fig. 7.
Fig. 7.

Frequency-impedance curve obtained from impedance analyzer: local minima and maxima denote resonant and anti-resonant frequencies, respectively.

Tables (3)

Tables Icon

Table 1. Constants of Piezoelectric Material Used In This Study

Tables Icon

Table 2. Comparison of In-Plane Resonant Frequencies Obtained Using ESPI, FEM, and an Impedance Analyzer

Tables Icon

Table 3. Resonant Frequencies and EMCC Obtained Using an Impedance Analyzer

Equations (7)

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

Ii(x,y)=1τiτ(i+1)τI(x,y,t)dt=Io+IR+2IoIR(cosϕ+ψisinϕ)J0(ΓA),
Ii*=Ii2IoIR=Io+IR2IoIR+(cosϕ+ψisinϕ)J0(ΓA)=Ibg+(cosϕ+ψisinϕ)J0(ΓA),
I^*=1n1i=1n(Ii*I¯*)2=ψ^s|sinϕJ0(ΓA)|,
I¯*=1ni=1nIi*=Ibg+|(cosϕ+ψ¯ssinϕ)J0(ΓA)|,
ψ^s=1n1i=1n[ψiψ¯s],
ψ¯s=1ni=1nψi,
keff=fa2fr2fa2,

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