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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Takeda and 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, and 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 and Wenjing Chen, “Fourier transform profilomitry: a review,” Opt. Laser in Eng. 35, 263–284 (2001).
    [CrossRef]
  4. Xianyu Su, Wenjing Chen, Qichan Zhang, and 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, and 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 and Britton Chance, eds., Proc. SPIE 5254, 214–221(2003).
  6. Qi-Can Zhang and 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. ISMA20012, 281–284 (2001).
  8. Dan Russell, “Vibrational Modes of a Circular Membrane,” http://www.kettering.edu/~drussell/Demos/MembraneCircle/Circle.html.
  9. ISVR - Institute of Sound and Vibration Research, University of Southampton, UK, “Animations of Acoustic Waves,” http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Web-standing-membrane.htm.
  10. T. R. Judge and P.J. Bryyanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. & Leaser Eng. 21, 199–239 (1994).
    [CrossRef]
  11. Xianyu Su and Wenjing Chen, “Reliability guided phase unwrapping algorithm-a review,” Opt. & Leaser 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, and Ji-Tao Li, “Phase Unwrapping algorithm-based on reliability and edge-detection,” Opt. Eng. 36, 1685–1690 (1997).
    [CrossRef]
  14. Asundi and Wen-Sen Zhou, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” App. Opt. 38, 3556–3561 (1999).
    [CrossRef]

2004 (1)

Xianyu Su and Wenjing Chen, “Reliability guided phase unwrapping algorithm-a review,” Opt. & Leaser Eng. 42, 245–261 (2004).
[CrossRef]

2003 (1)

Qican Zhang, Xianyu Su, Wenjing Chen, Yiping Cao, and 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 and Britton Chance, eds., Proc. SPIE 5254, 214–221(2003).

2002 (1)

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

2001 (2)

Xianyu Su and Wenjing Chen, “Fourier transform profilomitry: a review,” Opt. Laser in Eng. 35, 263–284 (2001).
[CrossRef]

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

1999 (1)

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

1997 (1)

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

1996 (1)

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).

1994 (1)

T. R. Judge and P.J. Bryyanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. & Leaser Eng. 21, 199–239 (1994).
[CrossRef]

1990 (1)

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

1983 (1)

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

Asundi,

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

Bertsch, M.

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. ISMA20012, 281–284 (2001).

Bryyanston-Cross, P.J.

T. R. Judge and P.J. Bryyanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. & Leaser Eng. 21, 199–239 (1994).
[CrossRef]

Cao, Yiping

Qican Zhang, Xianyu Su, Wenjing Chen, Yiping Cao, and 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 and Britton Chance, eds., Proc. SPIE 5254, 214–221(2003).

Chao, Yiping

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

Chen, Wenjing

Xianyu Su and Wenjing Chen, “Reliability guided phase unwrapping algorithm-a review,” Opt. & Leaser Eng. 42, 245–261 (2004).
[CrossRef]

Qican Zhang, Xianyu Su, Wenjing Chen, Yiping Cao, and 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 and Britton Chance, eds., Proc. SPIE 5254, 214–221(2003).

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

Xianyu Su and Wenjing Chen, “Fourier transform profilomitry: a review,” Opt. Laser in Eng. 35, 263–284 (2001).
[CrossRef]

Guo, Lu-Rong

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

Judge, T. R.

T. R. Judge and P.J. Bryyanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. & Leaser Eng. 21, 199–239 (1994).
[CrossRef]

Li, Jian

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

Li, Jie-Lin

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

Li, Ji-Tao

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

Motoh, K.

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

Perugia, Nr.

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. ISMA20012, 281–284 (2001).

Russell, Dan

Dan Russell, “Vibrational Modes of a Circular Membrane,” http://www.kettering.edu/~drussell/Demos/MembraneCircle/Circle.html.

Su, Xianyu

Xianyu Su and Wenjing Chen, “Reliability guided phase unwrapping algorithm-a review,” Opt. & Leaser Eng. 42, 245–261 (2004).
[CrossRef]

Qican Zhang, Xianyu Su, Wenjing Chen, Yiping Cao, and 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 and Britton Chance, eds., Proc. SPIE 5254, 214–221(2003).

Xianyu Su and Wenjing Chen, “Fourier transform profilomitry: a review,” Opt. Laser in Eng. 35, 263–284 (2001).
[CrossRef]

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

Su, Xian-Yu

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

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

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).

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

Takeda, M.

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

Xiang, Liqun

Qican Zhang, Xianyu Su, Wenjing Chen, Yiping Cao, and 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 and Britton Chance, eds., Proc. SPIE 5254, 214–221(2003).

Zhang, Qican

Qican Zhang, Xianyu Su, Wenjing Chen, Yiping Cao, and 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 and Britton Chance, eds., Proc. SPIE 5254, 214–221(2003).

Zhang, Qi-Can

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

Zhang, Qichan

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

Zhou, Wen-Sen

Asundi and 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 and K. Motoh, “Fourier transform profilometry for the automatic measurement of 3D object shapes,” App. Opt. 22, 3977–3982 (1983).
[CrossRef]

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

in International Conference on Holography and Optical Information Processing (ICHOIP ’96) (1)

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).

in The 3rd International Conference on Photonics and Imaging in Biology and Medicine 2003 (1)

Qican Zhang, Xianyu Su, Wenjing Chen, Yiping Cao, and 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 and Britton Chance, eds., Proc. SPIE 5254, 214–221(2003).

Opt. & Laser Tech. (1)

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

Opt. & Leaser Eng. (2)

T. R. Judge and P.J. Bryyanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. & Leaser Eng. 21, 199–239 (1994).
[CrossRef]

Xianyu Su and Wenjing Chen, “Reliability guided phase unwrapping algorithm-a review,” Opt. & Leaser Eng. 42, 245–261 (2004).
[CrossRef]

Opt. Eng. (2)

Jian Li, Xian-Yu Su, and 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, and 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, and 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 and Wenjing Chen, “Fourier transform profilomitry: a review,” Opt. Laser in Eng. 35, 263–284 (2001).
[CrossRef]

Other (3)

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. ISMA20012, 281–284 (2001).

Dan Russell, “Vibrational Modes of a Circular Membrane,” http://www.kettering.edu/~drussell/Demos/MembraneCircle/Circle.html.

ISVR - Institute of Sound and Vibration Research, University of Southampton, UK, “Animations of Acoustic Waves,” http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Web-standing-membrane.htm.

Supplementary Material (2)

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

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

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 ) .

Metrics