Abstract

Method for tracking vibrations with high amplitude of several hundreds of micrometers is presented. It is demonstrated that it is possible to reconstruct a synthetic high amplitude deformation of auto-oscillations encoded with digital Fresnel holograms. The setup is applied to the auto-oscillation of a clarinet reed in a synthetic mouth. Tracking of the vibration is performed by using the pressure signal delivered by the mouth. Experimental results show the four steps of the reed movement and especially emphasize the shocks of the reed on the mouthpiece.

© 2007 Optical Society of America

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References

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2007 (1)

2006 (2)

2005 (4)

2004 (1)

P. Picart, B. Diouf, E. Lolive, J.-M. Berthelot, "Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms," Opt. Eng. 43, 1169-1176 (2004).
[CrossRef]

2003 (3)

2001 (1)

I. Yamaguchi, J. Kato, S. Ohta, "Surface shape measurement by phase shifting digital holography,’’Opt. Rev. 8, 85-89 (2001).
[CrossRef]

1997 (1)

I.M. Lindevald, J. Gower, "Vibrational modes of clarinet reeds," J. Acoust. Soc. Am. 102, 3085 (1997).
[CrossRef]

1996 (1)

P. Hoekje, G. Roberts, "Observed vibration patterns of clarinet reeds," J. Acoust. Soc. Am. 99, 2462 (1996).
[CrossRef]

1994 (1)

U. Schnars, W. Jüptner, "Direct recording of holograms by a CCD target and numerical reconstruction,’’App. Opt. 33, 179-181 (1994).
[CrossRef]

1979 (1)

S. C. Thompson, "The effect of the reed resonance on woodwind tone production,’’ J. Acoust. Soc. Am. 66, 1299-1307 (1979).
[CrossRef]

App. Opt. (2)

U. Schnars, W. Jüptner, "Direct recording of holograms by a CCD target and numerical reconstruction,’’App. Opt. 33, 179-181 (1994).
[CrossRef]

A. Asundi, V.R. Singh, "Time-averaged in-line digital holographic interferometry for vibration analysis," App. Opt. 45, 2391-2395 (2006).
[CrossRef]

Appl. Opt. (1)

J. Acoust. Soc. Am. (5)

S. C. Thompson, "The effect of the reed resonance on woodwind tone production,’’ J. Acoust. Soc. Am. 66, 1299-1307 (1979).
[CrossRef]

P. Hoekje, G. Roberts, "Observed vibration patterns of clarinet reeds," J. Acoust. Soc. Am. 99, 2462 (1996).
[CrossRef]

I.M. Lindevald, J. Gower, "Vibrational modes of clarinet reeds," J. Acoust. Soc. Am. 102, 3085 (1997).
[CrossRef]

F. Pinard, B. Laine, H. Vach, "Musical quality assessment of clarinet reeds using optical holography," J. Acoust. Soc. Am. 113, 1736-1742 (2003).
[CrossRef] [PubMed]

J.P. Dalmont, J. Gilbert, J. Kergomard, S. Ollivier, "An analytical prediction of the oscillation and extinction thresholds of a clarinet," J. Acoust. Soc. Am. 118, 3294-3305 (2005).
[CrossRef] [PubMed]

Opt. Eng. (1)

P. Picart, B. Diouf, E. Lolive, J.-M. Berthelot, "Investigation of fracture mechanisms in resin concrete using spatially multiplexed digital Fresnel holograms," Opt. Eng. 43, 1169-1176 (2004).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Opt. Rev. (1)

I. Yamaguchi, J. Kato, S. Ohta, "Surface shape measurement by phase shifting digital holography,’’Opt. Rev. 8, 85-89 (2001).
[CrossRef]

Other (1)

J.W. Goodman, Introduction to Fourier Optics (Mc Graw Hill Editions, New York, 2nd Edition, 1996).

Supplementary Material (4)

» Media 1: MPG (2505 KB)     
» Media 2: MPG (913 KB)     
» Media 3: MPG (2987 KB)     
» Media 4: MPG (844 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Artificial mouth

Fig. 2.
Fig. 2.

Pressure signal issued form the artificial mouth

Fig. 3.
Fig. 3.

Different phases of the movement of the reed

Fig. 4.
Fig. 4.

Optical set-up

Fig. 5.
Fig. 5.

Full field reconstruction of diffracted field

Fig. 6.
Fig. 6.

2506 Ko Movie 1 - Dynamic deformation for the opened reed [Media 1]

Fig. 7.
Fig. 7.

914 Ko Movie 2 - Dynamic deformation for the closing reed [Media 2]

Fig. 8.
Fig. 8.

2988 Ko Movie 3 - Dynamic deformation for the closed reed [Media 3]

Fig. 9.
Fig. 9.

844 Ko Movie 4 - Dynamic deformation for the opening reed [Media 4]

Equations (10)

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A x y t = A 0 x y exp [ i ψ 0 x y ] exp [ i Δ φ x y t ]
O x y d 0 t = i exp ( i 2 π d 0 λ ) λ d 0 exp [ i π λ d 0 ( x 2 + y 2 ) ]
× + + A x y t exp [ i π λ d 0 ( x 2 + y 2 ) ] exp [ 2 i π λ d 0 ( x x + y y ) ] dxdy
H ( x , y , d 0 , t ) = O ( x , y , d 0 , t ) 2 + R ( x , y ) 2
+ R * ( x , y ) O ( x , y , d 0 , t ) + R ( x , y ) O * ( x , y , d 0 , t )
A R ( x , y , d 0 , t n ) = i exp ( 2 i π d 0 λ ) λ d 0 exp [ i π λ d 0 ( x 2 + y 2 ) ]
× k = 0 k = K 1 l = 0 l = L 1 H l p x k p y d 0 t n exp [ i π λ d 0 ( l 2 p x 2 + k 2 p y 2 ) ] exp [ 2 i π λ d 0 ( l x p x + k y p y ) ]
A + 1 R ( x , y , d 0 , t n ) M N λ 4 d 0 4 R * x y exp [ i π λ d 0 ( u 0 2 + v 0 2 ) ]
× A 0 x y exp [ i ψ 0 x y ] exp [ i Δ φ x y t n ] * δ ( x λ u 0 d 0 , y λ v 0 d 0 ) .
ψ n x y = 2 π ( u 0 x + v 0 y ) π λ d 0 ( u 0 2 + v 0 2 ) + ψ 0 x y + Δ φ x y t n .

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