Abstract

The integrated amplitude and phase distribution of the sound field propagating from sinusoidally vibrating objects in air have been recorded by time-averaged TV holography. The behavior of the sound field is observed in real time by use of dynamic phase modulation. The magnitude and direction of the field are found by acoustic phase stepping and image processing. The field is three dimensional, and recordings of several cross sections are necessary for a complete description, but in many cases valuable information can be obtained by two-dimensional projections. The technique has been used to study sound propagation and details in the sound emission from extended sources.

© 1994 Optical Society of America

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References

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  1. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), Chaps. 5 and 6.
  2. K. Høgmoen, O. J. Løkberg, “Detection and measurement of small vibrations using electronic speckle pattern interferometry,” Appl. Opt. 16, 1869–1875 (1977).
    [CrossRef] [PubMed]
  3. S. Ellingsrud, G. O. Rosvold, “Analysis of a data-based TV-holography system used to measure small vibration amplitudes,” J. Opt. Soc. Am. A 9, 237–251 (1992).
    [CrossRef]
  4. S. Ellingsrud, O. J. Løkberg, “Full field amplitude and phase measurement of loudspeakers using TV holography and digital image processing,” J. Sound Vib. 168, 193–208 (1993).
    [CrossRef]
  5. R. Jones, C. Wykeds, Holographic and Speckle Interferometry (Cambridge U. Press, London, 1983).
  6. O. J. Løkberg, G. Å. Slettemoen, “Basic electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, J. C. Wyant, R. Shannon, eds. (Academic, San Diego, Calif., 1987), Vol. 10, pp. 455–504.
  7. G. O. Rosvold, “Fast measurements of phase using a PC-based frame grabber and phase stepping technique,” Appl. Opt. 29, 237–241 (1990).
    [CrossRef] [PubMed]
  8. G. Å. Slettemoen, “Electronic speckle pattern interferometric system based on a speckle reference beam,” Appl. Opt. 19, 616–623 (1980).
    [CrossRef] [PubMed]

1993

S. Ellingsrud, O. J. Løkberg, “Full field amplitude and phase measurement of loudspeakers using TV holography and digital image processing,” J. Sound Vib. 168, 193–208 (1993).
[CrossRef]

1992

1990

1980

1977

Ellingsrud, S.

S. Ellingsrud, O. J. Løkberg, “Full field amplitude and phase measurement of loudspeakers using TV holography and digital image processing,” J. Sound Vib. 168, 193–208 (1993).
[CrossRef]

S. Ellingsrud, G. O. Rosvold, “Analysis of a data-based TV-holography system used to measure small vibration amplitudes,” J. Opt. Soc. Am. A 9, 237–251 (1992).
[CrossRef]

Høgmoen, K.

Jones, R.

R. Jones, C. Wykeds, Holographic and Speckle Interferometry (Cambridge U. Press, London, 1983).

Løkberg, O. J.

S. Ellingsrud, O. J. Løkberg, “Full field amplitude and phase measurement of loudspeakers using TV holography and digital image processing,” J. Sound Vib. 168, 193–208 (1993).
[CrossRef]

K. Høgmoen, O. J. Løkberg, “Detection and measurement of small vibrations using electronic speckle pattern interferometry,” Appl. Opt. 16, 1869–1875 (1977).
[CrossRef] [PubMed]

O. J. Løkberg, G. Å. Slettemoen, “Basic electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, J. C. Wyant, R. Shannon, eds. (Academic, San Diego, Calif., 1987), Vol. 10, pp. 455–504.

Rosvold, G. O.

Slettemoen, G. Å.

G. Å. Slettemoen, “Electronic speckle pattern interferometric system based on a speckle reference beam,” Appl. Opt. 19, 616–623 (1980).
[CrossRef] [PubMed]

O. J. Løkberg, G. Å. Slettemoen, “Basic electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, J. C. Wyant, R. Shannon, eds. (Academic, San Diego, Calif., 1987), Vol. 10, pp. 455–504.

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), Chaps. 5 and 6.

Wykeds, C.

R. Jones, C. Wykeds, Holographic and Speckle Interferometry (Cambridge U. Press, London, 1983).

Appl. Opt.

J. Opt. Soc. Am. A

J. Sound Vib.

S. Ellingsrud, O. J. Løkberg, “Full field amplitude and phase measurement of loudspeakers using TV holography and digital image processing,” J. Sound Vib. 168, 193–208 (1993).
[CrossRef]

Other

R. Jones, C. Wykeds, Holographic and Speckle Interferometry (Cambridge U. Press, London, 1983).

O. J. Løkberg, G. Å. Slettemoen, “Basic electronic speckle pattern interferometry,” in Applied Optics and Optical Engineering, J. C. Wyant, R. Shannon, eds. (Academic, San Diego, Calif., 1987), Vol. 10, pp. 455–504.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), Chaps. 5 and 6.

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Figures (10)

Fig. 1
Fig. 1

Setups for recording the sound field: (a) single-pass transmission, (b) double-pass reflection.

Fig. 2
Fig. 2

Integration of ray paths through the wave fronts of a point sound source.

Fig. 3
Fig. 3

Intensity of time-average fringe function J02 at low vibration amplitudes. Amplitude ar represents the working point when sinusoidal PM is used.

Fig. 4
Fig. 4

Flow diagram of the TV holographic setup used for recording sound fields. SA, speckle averaging.

Fig. 5
Fig. 5

Recording of the sound field from the acoustical point source (dome tweeter) at 5000 Hz placed in the left part of the field: (a) real-time presentation of the TV monitor, (b) computed amplitude and phase values.

Fig. 6
Fig. 6

Two identical sound sources in the left part of the field at frequencies that provide an acoustical Young's fringe pattern: (a) 2500 Hz, (b) 5000 Hz, (c) 8000 Hz, (d) same sources as above but placed in the extreme left and right parts of the field facing each other; the frequency is 5000 Hz.

Fig. 7
Fig. 7

Amplitude and phase of the sound field generated by a midtone speaker at a frequency of 5000 Hz. The field is interrupted (diffracted) by (a) the acoustical edge (a brick), (b), (c) the acoustical slits made of two bricks separated by (b) 2.5 cm and (c) 8 cm, (d) the acoustical mirror at an angle (two bricks at an angle slanted to the field).

Fig. 8
Fig. 8

Steel plate (9 cm × 12 cm) vibrating at 2660 Hz: (a) the ordinary time-average vibration pattern of the plate surface showing two antinodes separated by a central nodal line, (b) the sound field in a direction parallel to the nodal line.

Fig. 9
Fig. 9

Same object as in Fig. 8 but vibrating at 6474 Hz: (a) time-averaging vibration pattern, (b) sound field along nodal lines.

Fig. 10
Fig. 10

Wave fronts emitted from a violin excited by piezoelectric transducers fastened on the back plate. The front plate faces left. The figures cover the entire body of the violin and half of the neck: (a) 1250 Hz, (b) 2200 Hz, (c) 3500 Hz.

Equations (10)

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n 1 ρ = const . ,
Δ m = d λ ( n 0 1 ) ( p υ p 0 1 ) ,
I TA ( x , y ) J 0 2 [ 2 π λ g ( ϕ ) a 0 ( x , y ) ] ,
I TA / PM ( x , y ) J 0 2 ( 2 π λ { [ g ( ϕ ) a 0 ( x , y ) ] 2 + a r 2 2 g ( ϕ ) a 0 ( x , y ) a r × cos [ φ 0 ( x , y ) φ r ] } 1 / 2 ) .
I 0 ( x , y ) = I b ( x , y ) k ( x , y ) a 0 ( x , y ) cos φ 0 ( x , y ) ,
I 90 ( x , y ) = I b ( x , y ) + k ( x , y ) a 0 ( x , y ) sin φ 0 ( x , y ) ,
I 180 ( x , y ) = I b ( x , y ) + k ( x , y ) a 0 ( x , y ) cos φ 0 ( x , y ) ,
I 270 ( x , y ) = I b ( x , y ) k ( x , y ) a 0 ( x , y ) sin φ 0 ( x , y ) ,
φ 0 ( x , y ) = arctan [ I 90 ( x , y ) I 270 ( x , y ) I 180 ( x , y ) I 0 ( x , y ) ] .
a 0 ( x , y ) = { [ I 180 ( x , y ) I 0 ( x , y ) ] 2 + [ I 90 ( x , y ) I 270 ( x , y ) ] 2 } 1 / 2 2 k ( x , y ) .

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