Abstract

The need for sensitive methods of detection and visualization of acoustic surface perturbations has grown with the increasing interest in such fields as acoustic holography, ultrasonic surface wave devices, and acoustic trapped energy resonators. One very sensitive detection method utilizes a coherent light beam as a probe for locally measuring phase and amplitude of the acoustic field. Several variants of this technique are possible, based on measuring phase, deflection, wave front curvature, and spatial frequency content of the reflected beam. Each one of these variants may be combined with a scanning motion of the beam in order to visualize the entire sound field. This paper will attempt to survey the present state of the art and compare the different techniques on the basis of their sensitivity and applicability to specific requirements.

© 1969 Optical Society of America

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References

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  1. A. Korpel, P. Desmares, J. Acoust. Soc. Amer. 45, 881 (1969).
    [CrossRef]
  2. R. Adler, A. Korpel, P. Desmares, IEEE Trans. Sonics Ultrasonic, SU-15, 157 (1968).
    [CrossRef]
  3. G. A. Massey, Proc. IEEE 56, 2157 (1968).
    [CrossRef]
  4. R. Whitman, L. Laub, W. Bates, IEEE Trans. Sonics Ultrasonics, SU-15, 186 (1968).
    [CrossRef]
  5. A. Korpel, L. J. Laub, H. C. Sievering, Appl. Phys. Lett., 10, 295 (1967).
    [CrossRef]
  6. P. Rabinowitz, S. Jacobs, R. Torg, G. Gould, Proc. IRE Lett. 50, 2365 (1962).
    [CrossRef]
  7. R. Adler, IEEE Spectrum 4, 42 (1967).
    [CrossRef]
  8. R. M. White, F. W. Voltmer, Appl. Phys. Lett. 7, 314 (1965).
    [CrossRef]

1969 (1)

A. Korpel, P. Desmares, J. Acoust. Soc. Amer. 45, 881 (1969).
[CrossRef]

1968 (3)

R. Adler, A. Korpel, P. Desmares, IEEE Trans. Sonics Ultrasonic, SU-15, 157 (1968).
[CrossRef]

G. A. Massey, Proc. IEEE 56, 2157 (1968).
[CrossRef]

R. Whitman, L. Laub, W. Bates, IEEE Trans. Sonics Ultrasonics, SU-15, 186 (1968).
[CrossRef]

1967 (2)

A. Korpel, L. J. Laub, H. C. Sievering, Appl. Phys. Lett., 10, 295 (1967).
[CrossRef]

R. Adler, IEEE Spectrum 4, 42 (1967).
[CrossRef]

1965 (1)

R. M. White, F. W. Voltmer, Appl. Phys. Lett. 7, 314 (1965).
[CrossRef]

1962 (1)

P. Rabinowitz, S. Jacobs, R. Torg, G. Gould, Proc. IRE Lett. 50, 2365 (1962).
[CrossRef]

Adler, R.

R. Adler, A. Korpel, P. Desmares, IEEE Trans. Sonics Ultrasonic, SU-15, 157 (1968).
[CrossRef]

R. Adler, IEEE Spectrum 4, 42 (1967).
[CrossRef]

Bates, W.

R. Whitman, L. Laub, W. Bates, IEEE Trans. Sonics Ultrasonics, SU-15, 186 (1968).
[CrossRef]

Desmares, P.

A. Korpel, P. Desmares, J. Acoust. Soc. Amer. 45, 881 (1969).
[CrossRef]

R. Adler, A. Korpel, P. Desmares, IEEE Trans. Sonics Ultrasonic, SU-15, 157 (1968).
[CrossRef]

Gould, G.

P. Rabinowitz, S. Jacobs, R. Torg, G. Gould, Proc. IRE Lett. 50, 2365 (1962).
[CrossRef]

Jacobs, S.

P. Rabinowitz, S. Jacobs, R. Torg, G. Gould, Proc. IRE Lett. 50, 2365 (1962).
[CrossRef]

Korpel, A.

A. Korpel, P. Desmares, J. Acoust. Soc. Amer. 45, 881 (1969).
[CrossRef]

R. Adler, A. Korpel, P. Desmares, IEEE Trans. Sonics Ultrasonic, SU-15, 157 (1968).
[CrossRef]

A. Korpel, L. J. Laub, H. C. Sievering, Appl. Phys. Lett., 10, 295 (1967).
[CrossRef]

Laub, L.

R. Whitman, L. Laub, W. Bates, IEEE Trans. Sonics Ultrasonics, SU-15, 186 (1968).
[CrossRef]

Laub, L. J.

A. Korpel, L. J. Laub, H. C. Sievering, Appl. Phys. Lett., 10, 295 (1967).
[CrossRef]

Massey, G. A.

G. A. Massey, Proc. IEEE 56, 2157 (1968).
[CrossRef]

Rabinowitz, P.

P. Rabinowitz, S. Jacobs, R. Torg, G. Gould, Proc. IRE Lett. 50, 2365 (1962).
[CrossRef]

Sievering, H. C.

A. Korpel, L. J. Laub, H. C. Sievering, Appl. Phys. Lett., 10, 295 (1967).
[CrossRef]

Torg, R.

P. Rabinowitz, S. Jacobs, R. Torg, G. Gould, Proc. IRE Lett. 50, 2365 (1962).
[CrossRef]

Voltmer, F. W.

R. M. White, F. W. Voltmer, Appl. Phys. Lett. 7, 314 (1965).
[CrossRef]

White, R. M.

R. M. White, F. W. Voltmer, Appl. Phys. Lett. 7, 314 (1965).
[CrossRef]

Whitman, R.

R. Whitman, L. Laub, W. Bates, IEEE Trans. Sonics Ultrasonics, SU-15, 186 (1968).
[CrossRef]

Appl. Phys. Lett. (2)

A. Korpel, L. J. Laub, H. C. Sievering, Appl. Phys. Lett., 10, 295 (1967).
[CrossRef]

R. M. White, F. W. Voltmer, Appl. Phys. Lett. 7, 314 (1965).
[CrossRef]

IEEE Spectrum (1)

R. Adler, IEEE Spectrum 4, 42 (1967).
[CrossRef]

IEEE Trans. Sonics Ultrasonic (1)

R. Adler, A. Korpel, P. Desmares, IEEE Trans. Sonics Ultrasonic, SU-15, 157 (1968).
[CrossRef]

IEEE Trans. Sonics Ultrasonics (1)

R. Whitman, L. Laub, W. Bates, IEEE Trans. Sonics Ultrasonics, SU-15, 186 (1968).
[CrossRef]

J. Acoust. Soc. Amer. (1)

A. Korpel, P. Desmares, J. Acoust. Soc. Amer. 45, 881 (1969).
[CrossRef]

Proc. IEEE (1)

G. A. Massey, Proc. IEEE 56, 2157 (1968).
[CrossRef]

Proc. IRE Lett. (1)

P. Rabinowitz, S. Jacobs, R. Torg, G. Gould, Proc. IRE Lett. 50, 2365 (1962).
[CrossRef]

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Figures (17)

Fig. 1
Fig. 1

An optical set-up for the knife edge technique.

Fig. 2
Fig. 2

Acoustic surface wave deflecting probing beam.

Fig. 3
Fig. 3

Spot apertured by knife edge in focal plane of lens L2 before (solid) and after (dashed) tilting of surface.

Fig. 4
Fig. 4

Diffracted orders of probing beam in focal plane of L2.

Fig. 5
Fig. 5

Block diagram of knife edge system (omitting optics) after R. Adler et al.

Fig. 6
Fig. 6

After R. Adler el al. (a) A plane surface wave is reflected from the straight edge of a steel plate. Angles of incidence and of reflection are 45°. The intercepting edge in front of the photocell, which serves to detect the 8-MHz component, is oriented so as to respond to both waves, (b) Intercepting edge, rotated 45° from position (a) to suppress reflected wave, favors incident wave. (c) Intercepting edge, rotated 90° from position (b) to reject incident wave, shows only reflected wave.

Fig. 7
Fig. 7

After R. Adler et al. Plane wave coming from the right is reflected from curved edge (beyond left boundary of picture) of a round steel disk. Reflected wave, which goes through focus, is enhanced by choice of Doppler frequency while incident plane wave is rejected. This picture was taken with 7-mm horizontal scan.

Fig. 8
Fig. 8

After R. Adler et al. Two deep grooves in a steel plate, lined up with direction of sound travel. 7-mm horizontal scan. Note retardation of portion of wave which adheres to edges of each groove. Along center line of pair of grooves, phase velocity appears to be even a little higher than in unperturbed region.

Fig. 9
Fig. 9

After Massey. Experimental configuration for 2.6 MHz ultrasound image conversion.

Fig. 10
Fig. 10

After Massey. Heterodyne signal along scan path shown by arrow. Obstructions shown as shaded areas: (a) Half-plane, (b) 6-mm tube, (c) Two 6-mm. tubes spaced 12 mm apart. Upper trace is signal without obstruction; lower trace is signal with obstruction in place.

Fig. 11
Fig. 11

After Whitman et al. Block diagram of optical heterodyne system II(B).

Fig. 12
Fig. 12

Quartz wedge. After Whitman et al.

Fig. 13
Fig. 13

Square of surface displacement vs position on wedge.

Fig. 14
Fig. 14

(Upper) schematic outline of geometry of grating technique. (Lower) Phasor diagram showing relative phase of zero and first orders of diffracted probing beam as they propagate away from surface.

Fig. 15
Fig. 15

(Upper) Diagram demonstrating variation of overlap of diffracted orders with increasing distance (z) from surface. (Lower) Plot of photodiode signal current vs position of grating placement relative to the surface.

Fig. 16
Fig. 16

After Korpel et al. Block diagram of grating technique.

Fig. 17
Fig. 17

After Korpel et al. Patterns of acoustic surface wave on substrate, (a) Standing wave; (b) Traveling wave.

Equations (49)

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ϴ m = ( 2 π / Λ ) δ cos ( ω m t + ϕ ) *
2 ϴ m f 2 = 4 ( π / Λ ) δ f 2 cos ( ω m t + ϕ )
P sig = P 0 2 ϴ m f 2 D ( f 2 / f 1 ) = P 0 ( f 1 / D ) ( 4 π / Λ ) δ cos ( ω m t + ϕ ) ,
P sig = P 0 4 π ( d / Λ ) ( δ / λ ) cos ω m t .
I s = α P sig
P sig max = P 0 2 π ( δ / λ ) cos ω m t .
A ( x , t ) = A ( x ) cos { ω 0 t + m p cos [ ω m t + ϕ ( x ) ] }
A ( x , t ) = A ( x ) ( cos ω 0 t cos { m p cos [ ω m t + ϕ ( x ) ] } sin ω 0 t sin { m p cos [ ω m t + ϕ ( x ) ] } )
A ( x , t ) = A ( x ) { cos ω 0 t m p cos [ ω m t + ϕ ( x ) ] sin ω 0 t } = A ( x ) { cos ω 0 t ( m p / 2 ) sin [ ( ω 0 ω m ) t ϕ ( x ) ] ( m p / 2 ) sin [ ( ω 0 + ω m ) t + ϕ ( x ) ] } .
P sig = λ / Λ λ / d 2 ( 2 P 0 ) m p 2 sin ( ω 0 + ω m ) t cos ω 0 t = m p P 0 ( d / Λ ) sin ω m t
P sig = 4 π ( d / Λ ) ( δ / λ ) P 0 sin ω m t
[ ( λ / d ) ( λ / Λ ) ] λ / d = [ 1 ( d / Λ ) ]
I n = [ 2 e B α ( P 0 / 2 ) ] 1 2
S N 0 = 1 2 Î sig 2 R L I n 2 R L = 1 2 [ 4 π α ( d / Λ ) ( δ / λ ) P 0 ] e B α P 0 2 = ( 4 π ) 2 [ ( d / Λ ) ( δ / λ ) ] 2 α ( P 0 / 2 e B ) ,
δ min = ( 2 e B / α P 0 ) 1 2 ( λ / 2 π )
P 0 = 10 m W
B = 1 MHz .
δ = ( 2 e B / α P 0 ) 1 2 ( λ / 2 π ) = [ 2 ( 1.6 ) ( 10 19 ) 10 6 / ( 0.22 ) 10 2 ] 1 2 [ ( 0.63 / 2 π ) 10 6 ] = 1.3 10 12 m
A p ( t ) = ( 2 P p ) 1 2 cos ( ω 0 t + ω s t + m p cos ω m t ) ( 2 P p ) 1 2 [ cos ( ω 0 + ω s ) t ( m p / 2 ) sin ( ω 0 + ω s ω m ) t ( m p / 2 ) sin ( ω 0 + ω s + ω m ) t ] for m p 1 ,
A r ( t ) = ( 2 P r ) 1 2 cos ( ω 0 ω s ) t .
P = [ A p ( t ) + A r ( t ) ] 2 = P p + P r ( P p P r ) 1 2 m p sin ( 2 ω s ω m ) t ( P p P r ) 1 2 m p sin ( 2 ω s + ω m ) t + 2 ( P p P r ) 1 2 cos 2 ω s t .
P sig = m p ( P p P r ) 1 2 sin ( 2 ω s ± ω m ) t
P r = r P 0 , P p = p P 0 , r + p 1 ,
P sig = ( r p ) 1 2 m p P 0 sin ( 2 ω s ± ω m ) t
P sig = ( r p ) 1 2 4 π ( δ / λ ) P 0 sin ( 2 ω s ± ω m ) t ,
i n = [ 2 e B α ( P r + P p ) ] 1 2
S / N 0 = 1 2 [ α ( r p ) 1 2 m p P 0 ] 2 / 2 e B α P 0 ( r + p ) = ( 2 π ) 2 ( δ / λ ) 2 [ r p / ( r + p ) ] ( α P 0 / e B ) .
( S / N 0 ) opt = ( 2 π ) 2 ( δ / λ ) 2 ( 1 / 8 ) ( α P 0 / e B ) .
δ min = ( 2 e B / α P 0 ) 1 2 ( λ / π ) ,
c cos ( λ / Λ )
Δ ϕ = ( 2 π / λ ) Z ( 2 π / λ ) [ cos ( λ / Λ ) ] Z ( 2 π / λ ) Z [ 1 2 ( λ 2 / Λ 2 ) ] for λ / Λ 1 ( which is always fulfilled in practice )
Δ ϕ Z ( λ / Λ 2 ) π .
Z n = ( n + 1 2 ) ( Λ 2 / λ )
A ( t , x , z n ) = [ 2 ( P 0 / d ) ] 1 2 cos ω 0 t { 1 + m p sin [ ω m t ( 2 π / Λ ) x ] } ,
A 0 = ( 2 P 0 / d ) 1 2 cos ω 0 t A ± 1 = ± ( 2 P 0 / d ) 1 2 ( m p / 2 ) cos [ ( ω 0 ± ω m ) ( 2 π / Λ ) x + ( π / 2 ) ]
I = ( 2 P 0 / d ) cos 2 ω 0 t { 1 + 2 m p sin [ ω m t ( 2 π / Λ ) x ] + m p 2 sin 2 [ ω m t ( 2 π / Λ ) x ] } .
P = 0 Λ / 2 Idx = 2 P 0 d cos 2 ω 0 t 0 Λ / 2 × d x { 1 + 2 m p sin ( ω m t 2 π Λ x ) ) } = 2 P 0 d cos 2 ω 0 t { x | x = 0 Λ / 2 + 2 m p 2 π / Λ cos ( ω m t 2 π Λ x ) | x = 0 Λ / 2 P = [ P 0 ( Λ / d ) + P 0 ( Λ / d ) ( 4 m p / π ) cos ( ω m t ) ] cos 2 ω 0 t .
P = ( P 0 / 2 ) ( Λ / d ) + 2 ( m p / π ) ( Λ / d ) P 0 cos ω m t .
( P t ) = N P = ( P 0 / 2 ) + V ( d , n ) [ ( 2 m p / π ) P 0 cos ω m t ] .
V ( d , n ) = 1 ( n + 1 2 ) ( Λ 2 / λ ) tan ( λ / Λ ) d = 1 ( n + 1 2 ) Λ d for λ Λ 1
V ( N , n ) = [ N ( n + 1 2 ) ] / N .
P sig = [ ( N 1 2 ) / N ] 2 ( m p / π ) P 0 cos ω m t .
S N 0 = 1 2 ( α P sig ) 2 2 e B α ( P 0 / 2 ) = { [ ( N 1 2 ) / N ] 8 ( δ / λ ) } 2 α P 0 2 e B
δ min = ( 2 e B / α P 0 ) 1 2 ( λ / 8 ) [ N / ( N 1 2 ) ] .
ϕ l = ( 2 π / c ) f l ( L r L p ) ,
ϕ l ϕ 1 = ( 2 π / c ) f l ( L r L p ) ( 2 π / c ) f 1 ( L r L p ) 2 π
[ ( f l f 1 ) / c ] ( L r L p ) 1 ,
( l 1 ) ( c / 2 L ) c ( L r L p ) 1
( l 1 ) ( L r L p ) 2 L

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