Abstract

A high-speed optical measurement for the vibrating drumhead is presented and verified by experiment. A projected sinusoidal fringe pattern on the measured drumhead is dynamically deformed with the membrane vibration and grabbed by a high-speed camera. The shape deformation of the drumhead at each sampling instant can be recovered from this sequence of obtained fringe patterns. The membrane vibration of Chinese drum has been measured with a high speed sampling rate of 1,000 frames/sec. and a standard deviation of 0.075 mm. The restored vibration of the drumhead is also presented in an animation.

© 2005 Optical Society of America

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References

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  1. M. Takeda, K. Motoh, �??Fourier transform profilometry for the automatic measurement of 3D object shapes,�?? App. Opt. 22, 3977-3982 (1983).
    [CrossRef]
  2. Jian Li, Xian-Yu Su, Lu-Rong Guo, �??An improved Fourier transform profilometry for automatic measurement of 3D object shapes,�?? Opt. Eng. 29, 1439-1444 (1990).
    [CrossRef]
  3. Xianyu Su, Wenjing Chen, �??Fourier transform profilomitry: a review,�?? Opt. Laser in Eng. 35, 263-284 (2001).
    [CrossRef]
  4. Xianyu Su, Wenjing Chen, Qichan Zhang, Yiping Chao, �??Dynamic 3-D shape measurement method based on FTP�??, Opt. Laser Eng., 36, 49-64 (2001).
    [CrossRef]
  5. Qican Zhang, Xianyu Su, Wenjing Chen, Yiping Cao, Liqun Xiang, �??An Optical Real-time 3-D Measurement for Facial Shape and Movement,�?? in The 3rd International Conference on Photonics and Imaging in Biology and Medicine 2003, Qingming Luo, Britton Chance, eds., Proc. SPIE 5254, 214-221(2003).
  6. Qi-Can Zhang, Xian-Yu Su, �??An optical measurement of vortex shape at a free surface,�?? Opt. & Laser Tech. 34, 107-113 (2002).
    [CrossRef]
  7. M. Bertsch, �??Vibration patterns and sound analysis of the viennese timpani,�?? in Proceedigs of ISMA '2001 (International Symposium on Musical Acoustics), Nr. Perugia: Musical and Architectural Acoustics Lab. FSSG-CNR Venezia, eds., Proc. ISMA 2001 2, 281-284 (2001).
  8. Dan Russell, �??Vibrational Modes of a Circular Membrane,�?? <a href= "http://www.kettering.edu/~drussell/Demos/MembraneCircle/Circle.html">http://www.kettering.edu/~drussell/Demos/MembraneCircle/Circle.html</a>.
  9. ISVR - Institute of Sound and Vibration Research, University of Southampton, UK, �??Animations of Acoustic Waves,�?? <a href= "http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Web-standing-membrane.htm">http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Web-standing-membrane.htm</a>.
  10. T. R. Judge, P.J. Bryyanston-Cross, �??A review of phase unwrapping techniques in fringe analysis,�?? Opt. & Laser Eng. 21, 199-239 (1994).
    [CrossRef]
  11. Xianyu Su, Wenjing Chen, �??Reliability guided phase unwrapping algorithm-a review,�?? Opt. & Laser Eng. 42, 245-261 (2004).
    [CrossRef]
  12. Xian-Yu Su, �??Phase unwrapping techniques for 3D shape measurement,�?? in International Conference on Holography and Optical Information Processing (ICHOIP '96), Guoguang Mu, Guofan Jin and Glenn T. Sincerbox, eds., Proc. SPIE 2866, 460-465 (1996).
  13. Jie-Lin Li, Xian-Yu Su, Ji-Tao Li, �??Phase Unwrapping algorithm-based on reliability and edge-detection,�?? Opt. Eng. 36, 1685-1690 (1997).
    [CrossRef]
  14. Asundi, Wen-Sen Zhou, �??Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,�?? App. Opt. 38, 3556-3561 (1999).
    [CrossRef]

App. Opt. (2)

M. Takeda, K. Motoh, �??Fourier transform profilometry for the automatic measurement of 3D object shapes,�?? App. Opt. 22, 3977-3982 (1983).
[CrossRef]

Asundi, Wen-Sen Zhou, �??Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,�?? App. Opt. 38, 3556-3561 (1999).
[CrossRef]

Opt. & Laser Eng. (2)

T. R. Judge, P.J. Bryyanston-Cross, �??A review of phase unwrapping techniques in fringe analysis,�?? Opt. & Laser Eng. 21, 199-239 (1994).
[CrossRef]

Xianyu Su, Wenjing Chen, �??Reliability guided phase unwrapping algorithm-a review,�?? Opt. & Laser Eng. 42, 245-261 (2004).
[CrossRef]

Opt. & Laser Tech. (1)

Qi-Can Zhang, Xian-Yu Su, �??An optical measurement of vortex shape at a free surface,�?? Opt. & Laser Tech. 34, 107-113 (2002).
[CrossRef]

Opt. Eng. (2)

Jian Li, Xian-Yu Su, Lu-Rong Guo, �??An improved Fourier transform profilometry for automatic measurement of 3D object shapes,�?? Opt. Eng. 29, 1439-1444 (1990).
[CrossRef]

Jie-Lin Li, Xian-Yu Su, Ji-Tao Li, �??Phase Unwrapping algorithm-based on reliability and edge-detection,�?? Opt. Eng. 36, 1685-1690 (1997).
[CrossRef]

Opt. Laser Eng. (1)

Xianyu Su, Wenjing Chen, Qichan Zhang, Yiping Chao, �??Dynamic 3-D shape measurement method based on FTP�??, Opt. Laser Eng., 36, 49-64 (2001).
[CrossRef]

Opt. Laser in Eng. (1)

Xianyu Su, Wenjing Chen, �??Fourier transform profilomitry: a review,�?? Opt. Laser in Eng. 35, 263-284 (2001).
[CrossRef]

Proc. ISMA 2001 (1)

M. Bertsch, �??Vibration patterns and sound analysis of the viennese timpani,�?? in Proceedigs of ISMA '2001 (International Symposium on Musical Acoustics), Nr. Perugia: Musical and Architectural Acoustics Lab. FSSG-CNR Venezia, eds., Proc. ISMA 2001 2, 281-284 (2001).

Proc. SPIE (2)

Qican Zhang, Xianyu Su, Wenjing Chen, Yiping Cao, Liqun Xiang, �??An Optical Real-time 3-D Measurement for Facial Shape and Movement,�?? in The 3rd International Conference on Photonics and Imaging in Biology and Medicine 2003, Qingming Luo, Britton Chance, eds., Proc. SPIE 5254, 214-221(2003).

Xian-Yu Su, �??Phase unwrapping techniques for 3D shape measurement,�?? in International Conference on Holography and Optical Information Processing (ICHOIP '96), Guoguang Mu, Guofan Jin and Glenn T. Sincerbox, eds., Proc. SPIE 2866, 460-465 (1996).

Other (2)

Dan Russell, �??Vibrational Modes of a Circular Membrane,�?? <a href= "http://www.kettering.edu/~drussell/Demos/MembraneCircle/Circle.html">http://www.kettering.edu/~drussell/Demos/MembraneCircle/Circle.html</a>.

ISVR - Institute of Sound and Vibration Research, University of Southampton, UK, �??Animations of Acoustic Waves,�?? <a href= "http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Web-standing-membrane.htm">http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Web-standing-membrane.htm</a>.

Supplementary Material (2)

» Media 1: GIF (2501 KB)     
» Media 2: GIF (1582 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

Optical geometry of a FTP system.

Fig. 2.
Fig. 2.

Schematic diagram of the experimental setup.

Fig. 3.
Fig. 3.

The measured drumhead.

Fig. 4.
Fig. 4.

(2.44 MB) Movie of the deformed fringe.

Fig. 5.
Fig. 5.

Positions of the center point in vibration.

Fig. 6.
Fig. 6.

Profiles of the center rows of six sampling instants in one period.

Fig. 7.
Fig. 7.

Six mesh charts of the restored vibration shapes of the drumhead in one period. (1.54 MB) Movie of the whole restored vibration.

Equations (9)

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g 0 ( x , y ) = n = + A n r 0 ( x , y ) exp { i [ 2 n π f 0 x + n ϕ 0 ( x , y ) ] } .
g ( x , y , z ( t ) ) = n = + A n r ( x , y , t ) exp { i [ 2 n π f 0 x + n ϕ ( x , y , t ) ] } ( t = 1 , 2 , , m ) .
g ̂ ( x , y , z ( t ) ) = A 1 r ( x , y , t ) exp { i [ 2 π f 0 x + ϕ ( x , y , t ) ] } .
g ̂ 0 ( x , y ) = A 1 r 0 ( x , y ) exp { i [ 2 π f 0 x + ϕ 0 ( x , y ) ] } .
CD ¯ = d Z ( x , y , t ) [ l 0 Z ( x , y , t ) ] .
Δ ϕ ( x , y , t ) = ϕ ( x , y , t ) ϕ 0 ( x , y ) = 2 π f 0 ( BD ¯ BC ¯ ) = 2 π f 0 CD ¯ .
Z ( x , y , t ) = l 0 Δ ϕ ( x , y , t ) Δ ϕ ( x , y , t ) 2 π f 0 d .
Δ ϕ t ( x , y ) = ϕ ( x , y , t ) ϕ ( x , y , t 1 ) = arctg Im [ g ̂ ( x , y , t ) g ̂ * ( x , y , t 1 ) ] Re [ g ̂ ( x , y , t ) g ̂ * ( x , y , t 1 ) ] .
Φ uwk ( x , y , k ) = Φ uw 1 ( x , y , 1 ) + i = 1 k 1 Δ Φ i ( x , y ) .

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