Abstract

Holographic interferometry with a phase-modulated reference beam is used to visualize a progressive ultrasonic wave in the interior of a transparent medium. The medium is illuminated with sheetlike light, and the light scattered from the plane of the light sheet is recorded in the hologram. The ultrasonic field on the plane is obtained from the reconstructed image, which provides the equiphase positions of the wave, i.e., wave fronts. Experiments were performed at 200-kHz frequency. The effect of flow in the medium is estimated. An analysis of the optical system suggests that this method is applicable to ultrasonic waves with frequencies up to ~6 MHz.

© 1980 Optical Society of America

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References

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  1. C. C. Aleksoff, Appl. Phys. Lett. 14, 23 (1969).
    [CrossRef]
  2. D. B. Neumann, C. F. Jacobson, G. M. Brown, Appl. Opt. 9, 1357 (1970).
    [CrossRef] [PubMed]
  3. A. F. Metherell, in Acoustical Holography, P. S. Green, Ed. (Plenum, New York, 1974), Vol. 5, pp. 41–58.
  4. M. Ueda, S. Okuno, Y. Oshida, K. Iwata, R. Nagata, Optik (Stuttgart) 52, 71 (1978–79).
  5. K. Iwata, T. Hakoshima, R. Nagata, J. Opt. Soc. Am. 67, 1117 (1977).
    [CrossRef]
  6. W. E. Moore, J. A. Bucaro, J. Acoust. Soc. Am. 63, 60 (1978).
    [CrossRef]

1978

W. E. Moore, J. A. Bucaro, J. Acoust. Soc. Am. 63, 60 (1978).
[CrossRef]

1977

1970

1969

C. C. Aleksoff, Appl. Phys. Lett. 14, 23 (1969).
[CrossRef]

Aleksoff, C. C.

C. C. Aleksoff, Appl. Phys. Lett. 14, 23 (1969).
[CrossRef]

Brown, G. M.

Bucaro, J. A.

W. E. Moore, J. A. Bucaro, J. Acoust. Soc. Am. 63, 60 (1978).
[CrossRef]

Hakoshima, T.

Iwata, K.

M. Ueda, S. Okuno, Y. Oshida, K. Iwata, R. Nagata, Optik (Stuttgart) 52, 71 (1978–79).

K. Iwata, T. Hakoshima, R. Nagata, J. Opt. Soc. Am. 67, 1117 (1977).
[CrossRef]

Jacobson, C. F.

Metherell, A. F.

A. F. Metherell, in Acoustical Holography, P. S. Green, Ed. (Plenum, New York, 1974), Vol. 5, pp. 41–58.

Moore, W. E.

W. E. Moore, J. A. Bucaro, J. Acoust. Soc. Am. 63, 60 (1978).
[CrossRef]

Nagata, R.

M. Ueda, S. Okuno, Y. Oshida, K. Iwata, R. Nagata, Optik (Stuttgart) 52, 71 (1978–79).

K. Iwata, T. Hakoshima, R. Nagata, J. Opt. Soc. Am. 67, 1117 (1977).
[CrossRef]

Neumann, D. B.

Okuno, S.

M. Ueda, S. Okuno, Y. Oshida, K. Iwata, R. Nagata, Optik (Stuttgart) 52, 71 (1978–79).

Oshida, Y.

M. Ueda, S. Okuno, Y. Oshida, K. Iwata, R. Nagata, Optik (Stuttgart) 52, 71 (1978–79).

Ueda, M.

M. Ueda, S. Okuno, Y. Oshida, K. Iwata, R. Nagata, Optik (Stuttgart) 52, 71 (1978–79).

Appl. Opt.

Appl. Phys. Lett.

C. C. Aleksoff, Appl. Phys. Lett. 14, 23 (1969).
[CrossRef]

J. Acoust. Soc. Am.

W. E. Moore, J. A. Bucaro, J. Acoust. Soc. Am. 63, 60 (1978).
[CrossRef]

J. Opt. Soc. Am.

Optik (Stuttgart)

M. Ueda, S. Okuno, Y. Oshida, K. Iwata, R. Nagata, Optik (Stuttgart) 52, 71 (1978–79).

Other

A. F. Metherell, in Acoustical Holography, P. S. Green, Ed. (Plenum, New York, 1974), Vol. 5, pp. 41–58.

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Figures (8)

Fig. 1
Fig. 1

Schematic illustration of the progressive wave: (a) spatial variation; (b) temporal variation at P1; (c) temporal variation at P2; (d) temporal variation at P3.

Fig. 2
Fig. 2

Schematic description for phase-modulating holographic interferometry.

Fig. 3
Fig. 3

Working point by reference phase modulation.

Fig. 4
Fig. 4

Intersections of the ultrasonic wave fronts with the plane of the light sheet.

Fig. 5
Fig. 5

Experimental setup: L, lens; M, mirror; BS, beam splitter; Hm, hologram; Td, transducer.

Fig. 6
Fig. 6

Reconstructed image in water.

Fig. 7
Fig. 7

Reconstructed images in gelatin: (a) illuminating directions of the light sheet; (b) image on S1; (c) image on S2; (d) image on S3; (e) image on S4.

Fig. 8
Fig. 8

Schematic diagram of top view of sheetlike light: S, slit of width d; L, cylindrical lens of focal length f.

Equations (25)

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d ( r , t ) = a ( r ) cos [ Ω t + μ ( r ) ] ,
d ( t ) = b cos ( Ω t + ϕ ) ,
I ( r ) = I s t ( r ) = J 0 2 [ 2 π λ c ( r ) ] ,
c 2 ( r ) = p 2 ( r ) + q 2 - 2 p ( r ) q cos [ μ ( r ) - ϕ ] p ( r ) = [ s o ( r ) - s i ( r ) ] · a ( r ) , q = ( s o - s i ) · b
I ( r ) = I s t ( r ) { J 0 2 ( 2 π λ q ) - 4 π p ( r ) λ cos [ μ ( r ) - ϕ ] × J o ( 2 π λ q ) J 1 ( 2 π λ q ) } ,
J 0 2 ( 2 π λ q ) = 1 2 ,             J 1 ( 2 π λ q ) = 0.477.
I ( r ) = 1 2 I s t ( r ) { 1 - 8.47 λ p ( r ) cos [ μ ( r ) - ϕ ] } .
V = | J 0 ( 2 π λ q ) | .
J 0 2 ( 2 π λ q ) 1 2 .
d v ( r , t ) = a ( r ) cos [ Ω t + μ ( r ) ] + v ( r ) t .
I ( r ) = I s t ( r ) 1 T - T 2 T 2 exp i 2 π λ { c ( r ) cos [ Ω t + ψ ( r ) ] + v ( r ) t } d t ,
ψ ( r ) = μ ( r ) - sin - 1 { q c ( r ) sin [ μ ( r ) - ϕ ] } v ( r ) = [ s o ( r ) - s i ( r ) ] · v ( r ) } ,
T 2 π Ω ,             2 π v ( r ) Ω λ ,
I ( r ) = I s t ( r ) J 0 2 [ 2 π λ c ( r ) ] [ sin u ( r ) u ( r ) ] 2 ,
u ( r ) = π λ v ( r ) T .
[ sin u ( r ) u ( r ) ] 2
π λ v ( r ) T < 0.74.
2 π 2 λ Ω v ( r ) 0.74
D 0 = 2 f λ / d .
D ( z ) = ( d / f ) z ,
D ( z ) D 0 .
Λ = α D ( ± z 0 / 2 ) ,
f / d = Λ / ( 2 α λ ) .
z 0 = Λ 2 / ( λ α 2 ) .
N = ( 1 / α 2 ) / ( Λ / λ ) .

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