Abstract

Pulsed TV holography combined with computerized tomography (CT) are used to evaluate the three-dimensional distribution of transient acoustic fields in air. Experiments are performed with an electrical discharge between two electrodes as the sound source. Holograms from several directions of the acoustic field are recorded directly onto a CCD detector by use of a double-pulsed ruby laser as the light source. Phase maps, representing projections of the acoustic field, are evaluated quantitatively from the recorded holograms. The projections are used for the CT reconstruction to evaluate the pressure-field distribution in any cross section of the measured volume of air.

© 1998 Optical Society of America

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References

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  1. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  2. S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
    [CrossRef]
  3. S. Schedin, P. O. Gren, A. O. Wåhlin , “Shock waves in an elliptical cavity with varying height,” Shock Wave J. (to be published).
    [PubMed]
  4. K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
    [CrossRef]
  5. N.-E. Molin, A. O. Wåhlin, E. V. Jansson, “Transient wave response of the violin body revisited,” J. Acoust. Soc. Am. 90, 2192–2195 (1991).
    [CrossRef]
  6. S. Schedin, P. Gren, “Phase evaluation and speckle averaging in pulsed television holography,” Appl. Opt. 36, 3941–3947 (1997).
    [CrossRef] [PubMed]
  7. K. Iizuka, Engineering Optics, 2nd ed. (Springer-Verlag, Berlin, 1983).
  8. R. Cusak, J. M. Huntley, H. T. Goldrein, “Improved noise-immune phase-unwrapping algorithm,” Appl. Opt. 34, 781–789 (1995).
    [CrossRef]
  9. D. W. Sweeny, C. M. Vest, “Reconstruction of three-dimensional refractive index fields from multidirectional interferometric data,” Appl. Opt. 12, 2649–2664 (1973).
    [CrossRef]
  10. H. M. Hertz, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131–136 (1985).
    [CrossRef]
  11. D. Vukičević, H. Jäger, T. Neger, H. Philipp, J. Woisetschläger, “Tomographic reconstruction of the temperature distribution in a convective heat flow using multidirectional holographic interferometry,” Appl. Opt. 28, 1508–1515 (1989).
    [CrossRef]
  12. T. C. Liu, W. Merzkirch, K. Oberste-Lehn, “Optical tomography applied to speckle photographic measurement of asymmetric flows with variable density,” Exp. Fluids 7, 151–163 (1989).
  13. O. J. Løkberg, M. Espeland, H. M. Pedersen, “Tomographic reconstruction of sound fields using TV holography,” Appl. Opt. 34, 1640–1645 (1995).
    [CrossRef] [PubMed]
  14. H. O. Saldner, N.-E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
    [CrossRef] [PubMed]
  15. G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
    [CrossRef]

1997 (2)

S. Schedin, P. Gren, “Phase evaluation and speckle averaging in pulsed television holography,” Appl. Opt. 36, 3941–3947 (1997).
[CrossRef] [PubMed]

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
[CrossRef]

1996 (2)

H. O. Saldner, N.-E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
[CrossRef] [PubMed]

S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
[CrossRef]

1995 (2)

1991 (1)

N.-E. Molin, A. O. Wåhlin, E. V. Jansson, “Transient wave response of the violin body revisited,” J. Acoust. Soc. Am. 90, 2192–2195 (1991).
[CrossRef]

1989 (3)

D. Vukičević, H. Jäger, T. Neger, H. Philipp, J. Woisetschläger, “Tomographic reconstruction of the temperature distribution in a convective heat flow using multidirectional holographic interferometry,” Appl. Opt. 28, 1508–1515 (1989).
[CrossRef]

T. C. Liu, W. Merzkirch, K. Oberste-Lehn, “Optical tomography applied to speckle photographic measurement of asymmetric flows with variable density,” Exp. Fluids 7, 151–163 (1989).

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

1985 (1)

H. M. Hertz, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131–136 (1985).
[CrossRef]

1973 (1)

Cusak, R.

Espeland, M.

Fällström, K.-E.

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

Goldrein, H. T.

Gren, P.

Gren, P. O.

S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
[CrossRef]

S. Schedin, P. O. Gren, A. O. Wåhlin , “Shock waves in an elliptical cavity with varying height,” Shock Wave J. (to be published).
[PubMed]

Gustavsson, H.

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

Hertz, H. M.

H. M. Hertz, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131–136 (1985).
[CrossRef]

Huntley, J. M.

Iizuka, K.

K. Iizuka, Engineering Optics, 2nd ed. (Springer-Verlag, Berlin, 1983).

Jäger, H.

Jansson, E. V.

N.-E. Molin, A. O. Wåhlin, E. V. Jansson, “Transient wave response of the violin body revisited,” J. Acoust. Soc. Am. 90, 2192–2195 (1991).
[CrossRef]

Liu, T. C.

T. C. Liu, W. Merzkirch, K. Oberste-Lehn, “Optical tomography applied to speckle photographic measurement of asymmetric flows with variable density,” Exp. Fluids 7, 151–163 (1989).

Løkberg, O. J.

Merzkirch, W.

T. C. Liu, W. Merzkirch, K. Oberste-Lehn, “Optical tomography applied to speckle photographic measurement of asymmetric flows with variable density,” Exp. Fluids 7, 151–163 (1989).

Molin, N.-E.

H. O. Saldner, N.-E. Molin, K. A. Stetson, “Fourier-transform evaluation of phase data in spatially phase-biased TV holograms,” Appl. Opt. 35, 332–336 (1996).
[CrossRef] [PubMed]

N.-E. Molin, A. O. Wåhlin, E. V. Jansson, “Transient wave response of the violin body revisited,” J. Acoust. Soc. Am. 90, 2192–2195 (1991).
[CrossRef]

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

Neger, T.

Oberste-Lehn, K.

T. C. Liu, W. Merzkirch, K. Oberste-Lehn, “Optical tomography applied to speckle photographic measurement of asymmetric flows with variable density,” Exp. Fluids 7, 151–163 (1989).

Pedersen, H. M.

Pedrini, G.

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
[CrossRef]

Philipp, H.

Saldner, H. O.

Schedin, S.

S. Schedin, P. Gren, “Phase evaluation and speckle averaging in pulsed television holography,” Appl. Opt. 36, 3941–3947 (1997).
[CrossRef] [PubMed]

S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
[CrossRef]

S. Schedin, P. O. Gren, A. O. Wåhlin , “Shock waves in an elliptical cavity with varying height,” Shock Wave J. (to be published).
[PubMed]

Stetson, K. A.

Sweeny, D. W.

Tiziani, H. J.

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
[CrossRef]

Vest, C. M.

Vukicevic, D.

Wåhlin, A.

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

Wåhlin, A. O.

S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
[CrossRef]

N.-E. Molin, A. O. Wåhlin, E. V. Jansson, “Transient wave response of the violin body revisited,” J. Acoust. Soc. Am. 90, 2192–2195 (1991).
[CrossRef]

S. Schedin, P. O. Gren, A. O. Wåhlin , “Shock waves in an elliptical cavity with varying height,” Shock Wave J. (to be published).
[PubMed]

Woisetschläger, J.

Zou, Y.

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
[CrossRef]

Appl. Opt. (6)

Exp. Fluids (1)

T. C. Liu, W. Merzkirch, K. Oberste-Lehn, “Optical tomography applied to speckle photographic measurement of asymmetric flows with variable density,” Exp. Fluids 7, 151–163 (1989).

Exp. Mech. (1)

K.-E. Fällström, H. Gustavsson, N.-E. Molin, A. Wåhlin, “Transient bending waves in plates studied by hologram interferometry,” Exp. Mech. 29, 378–387 (1989).
[CrossRef]

J. Acoust. Soc. Am. (2)

N.-E. Molin, A. O. Wåhlin, E. V. Jansson, “Transient wave response of the violin body revisited,” J. Acoust. Soc. Am. 90, 2192–2195 (1991).
[CrossRef]

S. Schedin, P. O. Gren, A. O. Wåhlin, “Transient acoustic near field in air generated by impacted plates,” J. Acoust. Soc. Am. 99, 700–705 (1996).
[CrossRef]

Opt. Commun. (1)

H. M. Hertz, “Experimental determination of 2-D flame temperature fields by interferometric tomography,” Opt. Commun. 54, 131–136 (1985).
[CrossRef]

Opt. Lasers Eng. (1)

G. Pedrini, H. J. Tiziani, Y. Zou, “Digital double pulse-TV-holography,” Opt. Lasers Eng. 26, 199–219 (1997).
[CrossRef]

Other (3)

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

K. Iizuka, Engineering Optics, 2nd ed. (Springer-Verlag, Berlin, 1983).

S. Schedin, P. O. Gren, A. O. Wåhlin , “Shock waves in an elliptical cavity with varying height,” Shock Wave J. (to be published).
[PubMed]

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Figures (9)

Fig. 1
Fig. 1

Coordinate system for a cross section and its projection. Each projection value is a line integral of n(x, y, z), where the line of integration is specified by the parameters x r and θ.

Fig. 2
Fig. 2

Experimental device for producing the acoustic wave (AW). E, electrode.

Fig. 3
Fig. 3

RAD’s used in the experiment. (a) The circular aperture. (b) The double-slit aperture.

Fig. 4
Fig. 4

(a) Experimental setup. M, mirror; RL, ruby laser. (b) Optical unit in detail. M, mirror.

Fig. 5
Fig. 5

Fourier spectrum of the recorded hologram resulting from a single-slit aperture and an off-axis reference beam. The outer bright bands represent the spatial frequencies of the interference pattern.

Fig. 6
Fig. 6

Two-dimensional projections of the acoustic wave at 235 μs after discharge. (a) Diffraction through the circular aperture. (b) Diffraction through the double-slit aperture. The aperture is in both cases situated at the upper edge of the image.

Fig. 7
Fig. 7

Reconstructed cross sections of the acoustic field diffracted through the circular aperture at vertical distances of (a) 14 mm, (b) 19 mm, and (c) 26 mm from the RAD.

Fig. 8
Fig. 8

Reconstructed cross sections of the acoustic field diffracted through the double-slit aperture at vertical distances of (a) 14 mm, (b) 19 mm, and (c) 29 mm from the RAD.

Fig. 9
Fig. 9

Pressure profiles across the reconstructed cross sections at 26 mm from the circular aperture (solid curve) and 29 mm from the double-slit aperture (dashed curve).

Equations (9)

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Δ Φ x ,   y ,   z = k     n x ,   y ,   z - n 0 d s ,
n - 1 = K ρ ,
P P 0 = ρ ρ 0 γ ,
P P 0 = 1 + n - n 0 n 0 - 1 γ .
x r = x   cos   θ + y   sin   θ .
Δ Φ x r ,   θ = k   - - n x ,   y ,   z - n 0 × δ x   cos   θ + y   sin   θ - x r d x d y ,
k n x ,   y ,   z - n 0 = 0 π   Q x r ,   θ d θ = 0 π   Q x   cos   θ + y   sin   θ d θ ,
Q x r ,   θ = -   Δ Φ s ,   θ h x r - s d s = Δ Φ x r ,   θ   *   h x r ,
h x r = - w w   | f | exp j 2 π fx r d f ,

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