Abstract

A 1 cm long, low-finesse fiber-optic cavity was used as a transducer for the vibrations of the soundboard of an acoustic guitar and of a violin. The reflected light is detected and then amplified and recorded using conventional audio instrumentation. The fiber-optic pickup is found to have a high response range in both amplitude (up to 100μm displacement) and audio frequency (DC to 20kHz) and good linearity up to a displacement of 225μm. The audio noise is found to arise from the fiber-optic cables and, to a lesser extent, from the laser and laser driver.

© 2010 Optical Society of America

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References

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  1. H. P. Loock, W. S. Hopkins, C. Morris-Blair, R. Resendes, J. Saari, and N. R. Trefiak, “Recording the sound of musical instruments with FBGs: the photonic pickup,” Appl. Opt. 48, 2735-2741 (2009).
    [CrossRef] [PubMed]
  2. B. Sorazu, G. Thursby, B. Culshaw, F. Dong, S. G. Pierce, Y. Yang, and D. Betz, “Optical generation and detection of ultrasound,” Strain 39, 111-114 (2003).
    [CrossRef]
  3. M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
    [CrossRef]
  4. N. E. Fisher, J. Surowiec, D. J. Webb, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “In-fibre Bragg gratings for ultrasonic medical applications,” Meas. Sci. Technol. 8, 1050-1054 (1997).
    [CrossRef]
  5. N. Takahashi, K. Tetsumura, and S. Takahashi, “Underwater acoustic sensor using optical fiber Bragg grating as detecting element,” Jpn. J. Appl. Phys. 38, 1 (1999).
    [CrossRef]
  6. N. Takahashi, K. Yoshimura, S. Takahashi, and K. Imamura, “Development of an optical fiber hydrophone with fiber Bragg grating,” Ultrasonics 38, 581-585 (2000).
    [CrossRef] [PubMed]
  7. N. Takahashi, A. Hirose, and S. Takahashi, “Underwater acoustic sensor with fiber Bragg grating,” Opt. Rev. 4, 691-694(1997).
    [CrossRef]
  8. Q. X. Yang, J. Barnes, H. P. Loock, and D. Pedersen, “Time-resolved photoacoustic spectroscopy using fiber Bragg grating acoustic transducers,” Opt. Commun. 276, 97-106(2007).
    [CrossRef]
  9. Q. X. Yang, H. P. Loock, I. Kozin, and D. Pedersen, “Fiber Bragg grating photoacoustic detector for liquid chromatography,” Analyst (Amsterdam) 133, 1567-1572 (2008).
  10. G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Interrogation of FBG-based strain sensors by means of laser radio-frequency modulation techniques,” J. Opt. A Pure Appl. Opt. 8, S507-S513 (2006).
    [CrossRef]
  11. G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Fiber Bragg-grating strain sensor interrogation using laser radio-frequency modulation,” Opt. Express 13, 2377-2384 (2005).
    [CrossRef] [PubMed]
  12. B. Lissak, A. Arie, and M. Tur, “Highly sensitive dynamic strain measurements by locking lasers to fiber Bragg gratings,” Opt. Lett. 23, 1930-1932 (1998).
    [CrossRef]
  13. J. H. Chow, D. E. McClelland, M. B. Gray, and I. C. M. Littler, “Demonstration of a passive subpicostrain fiber strain sensor,” Opt. Lett. 30, 1923-1925 (2005).
    [CrossRef] [PubMed]
  14. http://www.chem.queensu.ca/people/faculty/loock/.

2009 (1)

2008 (1)

Q. X. Yang, H. P. Loock, I. Kozin, and D. Pedersen, “Fiber Bragg grating photoacoustic detector for liquid chromatography,” Analyst (Amsterdam) 133, 1567-1572 (2008).

2007 (1)

Q. X. Yang, J. Barnes, H. P. Loock, and D. Pedersen, “Time-resolved photoacoustic spectroscopy using fiber Bragg grating acoustic transducers,” Opt. Commun. 276, 97-106(2007).
[CrossRef]

2006 (1)

G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Interrogation of FBG-based strain sensors by means of laser radio-frequency modulation techniques,” J. Opt. A Pure Appl. Opt. 8, S507-S513 (2006).
[CrossRef]

2005 (2)

2003 (1)

B. Sorazu, G. Thursby, B. Culshaw, F. Dong, S. G. Pierce, Y. Yang, and D. Betz, “Optical generation and detection of ultrasound,” Strain 39, 111-114 (2003).
[CrossRef]

2000 (1)

N. Takahashi, K. Yoshimura, S. Takahashi, and K. Imamura, “Development of an optical fiber hydrophone with fiber Bragg grating,” Ultrasonics 38, 581-585 (2000).
[CrossRef] [PubMed]

1999 (2)

M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
[CrossRef]

N. Takahashi, K. Tetsumura, and S. Takahashi, “Underwater acoustic sensor using optical fiber Bragg grating as detecting element,” Jpn. J. Appl. Phys. 38, 1 (1999).
[CrossRef]

1998 (1)

1997 (2)

N. E. Fisher, J. Surowiec, D. J. Webb, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “In-fibre Bragg gratings for ultrasonic medical applications,” Meas. Sci. Technol. 8, 1050-1054 (1997).
[CrossRef]

N. Takahashi, A. Hirose, and S. Takahashi, “Underwater acoustic sensor with fiber Bragg grating,” Opt. Rev. 4, 691-694(1997).
[CrossRef]

Arie, A.

Barnes, J.

Q. X. Yang, J. Barnes, H. P. Loock, and D. Pedersen, “Time-resolved photoacoustic spectroscopy using fiber Bragg grating acoustic transducers,” Opt. Commun. 276, 97-106(2007).
[CrossRef]

Bennion, I.

M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
[CrossRef]

N. E. Fisher, J. Surowiec, D. J. Webb, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “In-fibre Bragg gratings for ultrasonic medical applications,” Meas. Sci. Technol. 8, 1050-1054 (1997).
[CrossRef]

Betz, D.

B. Sorazu, G. Thursby, B. Culshaw, F. Dong, S. G. Pierce, Y. Yang, and D. Betz, “Optical generation and detection of ultrasound,” Strain 39, 111-114 (2003).
[CrossRef]

Chow, J. H.

Culshaw, B.

B. Sorazu, G. Thursby, B. Culshaw, F. Dong, S. G. Pierce, Y. Yang, and D. Betz, “Optical generation and detection of ultrasound,” Strain 39, 111-114 (2003).
[CrossRef]

De Natale, P.

G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Interrogation of FBG-based strain sensors by means of laser radio-frequency modulation techniques,” J. Opt. A Pure Appl. Opt. 8, S507-S513 (2006).
[CrossRef]

G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Fiber Bragg-grating strain sensor interrogation using laser radio-frequency modulation,” Opt. Express 13, 2377-2384 (2005).
[CrossRef] [PubMed]

Dong, F.

B. Sorazu, G. Thursby, B. Culshaw, F. Dong, S. G. Pierce, Y. Yang, and D. Betz, “Optical generation and detection of ultrasound,” Strain 39, 111-114 (2003).
[CrossRef]

Ferraro, P.

G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Interrogation of FBG-based strain sensors by means of laser radio-frequency modulation techniques,” J. Opt. A Pure Appl. Opt. 8, S507-S513 (2006).
[CrossRef]

G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Fiber Bragg-grating strain sensor interrogation using laser radio-frequency modulation,” Opt. Express 13, 2377-2384 (2005).
[CrossRef] [PubMed]

Fisher, N. E.

M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
[CrossRef]

N. E. Fisher, J. Surowiec, D. J. Webb, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “In-fibre Bragg gratings for ultrasonic medical applications,” Meas. Sci. Technol. 8, 1050-1054 (1997).
[CrossRef]

Gagliardi, G.

G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Interrogation of FBG-based strain sensors by means of laser radio-frequency modulation techniques,” J. Opt. A Pure Appl. Opt. 8, S507-S513 (2006).
[CrossRef]

G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Fiber Bragg-grating strain sensor interrogation using laser radio-frequency modulation,” Opt. Express 13, 2377-2384 (2005).
[CrossRef] [PubMed]

Gavrilov, L. R.

M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
[CrossRef]

N. E. Fisher, J. Surowiec, D. J. Webb, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “In-fibre Bragg gratings for ultrasonic medical applications,” Meas. Sci. Technol. 8, 1050-1054 (1997).
[CrossRef]

Gray, M. B.

Hand, J. W.

M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
[CrossRef]

N. E. Fisher, J. Surowiec, D. J. Webb, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “In-fibre Bragg gratings for ultrasonic medical applications,” Meas. Sci. Technol. 8, 1050-1054 (1997).
[CrossRef]

Hathaway, M. W.

M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
[CrossRef]

Hirose, A.

N. Takahashi, A. Hirose, and S. Takahashi, “Underwater acoustic sensor with fiber Bragg grating,” Opt. Rev. 4, 691-694(1997).
[CrossRef]

Hopkins, W. S.

Imamura, K.

N. Takahashi, K. Yoshimura, S. Takahashi, and K. Imamura, “Development of an optical fiber hydrophone with fiber Bragg grating,” Ultrasonics 38, 581-585 (2000).
[CrossRef] [PubMed]

Jackson, D. A.

M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
[CrossRef]

N. E. Fisher, J. Surowiec, D. J. Webb, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “In-fibre Bragg gratings for ultrasonic medical applications,” Meas. Sci. Technol. 8, 1050-1054 (1997).
[CrossRef]

Kozin, I.

Q. X. Yang, H. P. Loock, I. Kozin, and D. Pedersen, “Fiber Bragg grating photoacoustic detector for liquid chromatography,” Analyst (Amsterdam) 133, 1567-1572 (2008).

Lissak, B.

Littler, I. C. M.

Loock, H. P.

H. P. Loock, W. S. Hopkins, C. Morris-Blair, R. Resendes, J. Saari, and N. R. Trefiak, “Recording the sound of musical instruments with FBGs: the photonic pickup,” Appl. Opt. 48, 2735-2741 (2009).
[CrossRef] [PubMed]

Q. X. Yang, H. P. Loock, I. Kozin, and D. Pedersen, “Fiber Bragg grating photoacoustic detector for liquid chromatography,” Analyst (Amsterdam) 133, 1567-1572 (2008).

Q. X. Yang, J. Barnes, H. P. Loock, and D. Pedersen, “Time-resolved photoacoustic spectroscopy using fiber Bragg grating acoustic transducers,” Opt. Commun. 276, 97-106(2007).
[CrossRef]

McClelland, D. E.

Morris-Blair, C.

Pannell, C. N.

M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
[CrossRef]

Pedersen, D.

Q. X. Yang, H. P. Loock, I. Kozin, and D. Pedersen, “Fiber Bragg grating photoacoustic detector for liquid chromatography,” Analyst (Amsterdam) 133, 1567-1572 (2008).

Q. X. Yang, J. Barnes, H. P. Loock, and D. Pedersen, “Time-resolved photoacoustic spectroscopy using fiber Bragg grating acoustic transducers,” Opt. Commun. 276, 97-106(2007).
[CrossRef]

Pierce, S. G.

B. Sorazu, G. Thursby, B. Culshaw, F. Dong, S. G. Pierce, Y. Yang, and D. Betz, “Optical generation and detection of ultrasound,” Strain 39, 111-114 (2003).
[CrossRef]

Resendes, R.

Saari, J.

Salza, M.

G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Interrogation of FBG-based strain sensors by means of laser radio-frequency modulation techniques,” J. Opt. A Pure Appl. Opt. 8, S507-S513 (2006).
[CrossRef]

G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Fiber Bragg-grating strain sensor interrogation using laser radio-frequency modulation,” Opt. Express 13, 2377-2384 (2005).
[CrossRef] [PubMed]

Sorazu, B.

B. Sorazu, G. Thursby, B. Culshaw, F. Dong, S. G. Pierce, Y. Yang, and D. Betz, “Optical generation and detection of ultrasound,” Strain 39, 111-114 (2003).
[CrossRef]

Surowiec, J.

N. E. Fisher, J. Surowiec, D. J. Webb, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “In-fibre Bragg gratings for ultrasonic medical applications,” Meas. Sci. Technol. 8, 1050-1054 (1997).
[CrossRef]

Takahashi, N.

N. Takahashi, K. Yoshimura, S. Takahashi, and K. Imamura, “Development of an optical fiber hydrophone with fiber Bragg grating,” Ultrasonics 38, 581-585 (2000).
[CrossRef] [PubMed]

N. Takahashi, K. Tetsumura, and S. Takahashi, “Underwater acoustic sensor using optical fiber Bragg grating as detecting element,” Jpn. J. Appl. Phys. 38, 1 (1999).
[CrossRef]

N. Takahashi, A. Hirose, and S. Takahashi, “Underwater acoustic sensor with fiber Bragg grating,” Opt. Rev. 4, 691-694(1997).
[CrossRef]

Takahashi, S.

N. Takahashi, K. Yoshimura, S. Takahashi, and K. Imamura, “Development of an optical fiber hydrophone with fiber Bragg grating,” Ultrasonics 38, 581-585 (2000).
[CrossRef] [PubMed]

N. Takahashi, K. Tetsumura, and S. Takahashi, “Underwater acoustic sensor using optical fiber Bragg grating as detecting element,” Jpn. J. Appl. Phys. 38, 1 (1999).
[CrossRef]

N. Takahashi, A. Hirose, and S. Takahashi, “Underwater acoustic sensor with fiber Bragg grating,” Opt. Rev. 4, 691-694(1997).
[CrossRef]

Tetsumura, K.

N. Takahashi, K. Tetsumura, and S. Takahashi, “Underwater acoustic sensor using optical fiber Bragg grating as detecting element,” Jpn. J. Appl. Phys. 38, 1 (1999).
[CrossRef]

Thursby, G.

B. Sorazu, G. Thursby, B. Culshaw, F. Dong, S. G. Pierce, Y. Yang, and D. Betz, “Optical generation and detection of ultrasound,” Strain 39, 111-114 (2003).
[CrossRef]

Trefiak, N. R.

Tur, M.

Webb, D. J.

M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
[CrossRef]

N. E. Fisher, J. Surowiec, D. J. Webb, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “In-fibre Bragg gratings for ultrasonic medical applications,” Meas. Sci. Technol. 8, 1050-1054 (1997).
[CrossRef]

Yang, Q. X.

Q. X. Yang, H. P. Loock, I. Kozin, and D. Pedersen, “Fiber Bragg grating photoacoustic detector for liquid chromatography,” Analyst (Amsterdam) 133, 1567-1572 (2008).

Q. X. Yang, J. Barnes, H. P. Loock, and D. Pedersen, “Time-resolved photoacoustic spectroscopy using fiber Bragg grating acoustic transducers,” Opt. Commun. 276, 97-106(2007).
[CrossRef]

Yang, Y.

B. Sorazu, G. Thursby, B. Culshaw, F. Dong, S. G. Pierce, Y. Yang, and D. Betz, “Optical generation and detection of ultrasound,” Strain 39, 111-114 (2003).
[CrossRef]

Yoshimura, K.

N. Takahashi, K. Yoshimura, S. Takahashi, and K. Imamura, “Development of an optical fiber hydrophone with fiber Bragg grating,” Ultrasonics 38, 581-585 (2000).
[CrossRef] [PubMed]

Zhang, L.

M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
[CrossRef]

N. E. Fisher, J. Surowiec, D. J. Webb, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “In-fibre Bragg gratings for ultrasonic medical applications,” Meas. Sci. Technol. 8, 1050-1054 (1997).
[CrossRef]

Analyst (Amsterdam) (1)

Q. X. Yang, H. P. Loock, I. Kozin, and D. Pedersen, “Fiber Bragg grating photoacoustic detector for liquid chromatography,” Analyst (Amsterdam) 133, 1567-1572 (2008).

Appl. Opt. (1)

J. Opt. A Pure Appl. Opt. (1)

G. Gagliardi, M. Salza, P. Ferraro, and P. De Natale, “Interrogation of FBG-based strain sensors by means of laser radio-frequency modulation techniques,” J. Opt. A Pure Appl. Opt. 8, S507-S513 (2006).
[CrossRef]

Jpn. J. Appl. Phys. (1)

N. Takahashi, K. Tetsumura, and S. Takahashi, “Underwater acoustic sensor using optical fiber Bragg grating as detecting element,” Jpn. J. Appl. Phys. 38, 1 (1999).
[CrossRef]

Meas. Sci. Technol. (1)

N. E. Fisher, J. Surowiec, D. J. Webb, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “In-fibre Bragg gratings for ultrasonic medical applications,” Meas. Sci. Technol. 8, 1050-1054 (1997).
[CrossRef]

Opt. Commun. (2)

M. W. Hathaway, N. E. Fisher, D. J. Webb, C. N. Pannell, D. A. Jackson, L. R. Gavrilov, J. W. Hand, L. Zhang, and I. Bennion, “Combined ultrasound and temperature sensor using a fibre Brag grating,” Opt. Commun. 171, 225-231 (1999).
[CrossRef]

Q. X. Yang, J. Barnes, H. P. Loock, and D. Pedersen, “Time-resolved photoacoustic spectroscopy using fiber Bragg grating acoustic transducers,” Opt. Commun. 276, 97-106(2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Rev. (1)

N. Takahashi, A. Hirose, and S. Takahashi, “Underwater acoustic sensor with fiber Bragg grating,” Opt. Rev. 4, 691-694(1997).
[CrossRef]

Strain (1)

B. Sorazu, G. Thursby, B. Culshaw, F. Dong, S. G. Pierce, Y. Yang, and D. Betz, “Optical generation and detection of ultrasound,” Strain 39, 111-114 (2003).
[CrossRef]

Ultrasonics (1)

N. Takahashi, K. Yoshimura, S. Takahashi, and K. Imamura, “Development of an optical fiber hydrophone with fiber Bragg grating,” Ultrasonics 38, 581-585 (2000).
[CrossRef] [PubMed]

Other (1)

http://www.chem.queensu.ca/people/faculty/loock/.

Supplementary Material (9)

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» Media 6: MP3 (632 KB)     
» Media 7: MP3 (1154 KB)     
» Media 8: MP3 (411 KB)     
» Media 9: MP3 (421 KB)     

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Figures (5)

Fig. 1
Fig. 1

Fabry–Perot cavity made of two FBGs (a) in resonance and (b) not in resonance with incoming light. (c) Reflection spectrum of 10 mm long fiber cavity, (d) shift of one cavity fringe in the wavelength window indicated by the red line in (c) in response to the indentation of the sound board onto which the fiber cavity is affixed.

Fig. 2
Fig. 2

Photograph of the acoustic guitar (©2006 Godin Guitars). The approximate positions of the FBG-FP cavity sensor head and the accelerometer are indicated.

Fig. 3
Fig. 3

Strain on the FBG-FP cavity measured from the spectral shift in Fig. 1d (squares) and calculated from model 1, in which the strain on the FBG-FP cavity is ( d 2 + 1850 cm 2 ) 1 / 2 / 4 mm 1 (triangles). The empty circles are the result of model 2, in which the bending radius is constant but the length of the deformed plate changes. The inset shows a cross section through the soundboard according to model 1 [straight (blue online) lines] and according to the more realistic model 2 [curved (red online) lines]; see text and supplementary material [14].

Fig. 4
Fig. 4

Vibration of the soundboard measured with (a) the FBG-FP cavity and (b) an accelerometer. The raw data from the accelerometer were integrated twice to obtain the displacement amplitude (c). The strain on the FBG-FP cavity was calculated assuming the linear relation of Fig. 3.

Fig. 5
Fig. 5

(a) FBG reflection signal recorded when playing C 6 ( 1046.5 Hz ) on a violin. A 5 Hz vibrato is apparent as a modulation of the envelope (b) enlarged portion of the time trace (c) Fourier transform of the trace in panel (a). The split peaks (see the inset for the 5th overtone) are also likely due to vibrato.

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