Abstract

The focusing properties of traveling acoustic waves can be employed in line-scan systems to convert a low-resolution optical beam into a high-resolution beam, both beams scanning linearly in synchronism with the acoustic wave velocity. Used in conjunction with any low-resolution scanner, for example a simple Bragg deflection cell, the scanning lens can yield at least an order of magnitude improvement in resolution, without the need for mechanical elements such as spinning mirrors. The device is inherently achromatic, and can be used just as effectively with white light as with monochromatic laser light. Experiments with dilational acoustic waves in water, and flexural waves on thin elastic strips, have confirmed the effectiveness of this novel approach, and indicate that systems with resolution capabilities up to a few thousand spots per line can be expected. Thus, immediate applications should be found in the fields of recording and reproduction of photographic images, analog and digital data recording and display, and high-speed printing.

© 1970 Optical Society of America

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References

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  1. A. Korpel, R. Adler, P. Desmares, W. H. Watson, Proc. IEEE 54, 1429 (1966).
    [CrossRef]
  2. A. Yariv, J. P. Gordon, Proc. IEEE 51, 4 (1963). See also: R. L. Fork, D. R. Herriott, A. Kogelnik, Appl. Opt. 3, 1471 (1964).
    [CrossRef]
  3. R. Lipnik, A. Reich, G. A. Schoen, Proc. IEEE 52, 853 (1964).
    [CrossRef]
  4. H. G. Aas, R. K. Erf, J. Acoust. Soc. Amer. 36, 1906 (1964).
    [CrossRef]
  5. A. J. De Maria, G. E. Danielson, IEEE J. Quantum Electron. QE-2, 157 (1966).
    [CrossRef]
  6. T. M. Smith, A. Korpel, IEEE J. Quantum Electron. QE-1, 283 (1965).
    [CrossRef]
  7. T. R. Meeker, A. H. Mietzler, Physical Acoustics, W. P. Mason, Ed. (Academic, New York, 1964), Vol. I, Chap. 2, p. 123.
  8. M. R. Redwood, Mechanical Waveguides (Pergamon, New York, 1960), p. 120.

1966

A. Korpel, R. Adler, P. Desmares, W. H. Watson, Proc. IEEE 54, 1429 (1966).
[CrossRef]

A. J. De Maria, G. E. Danielson, IEEE J. Quantum Electron. QE-2, 157 (1966).
[CrossRef]

1965

T. M. Smith, A. Korpel, IEEE J. Quantum Electron. QE-1, 283 (1965).
[CrossRef]

1964

R. Lipnik, A. Reich, G. A. Schoen, Proc. IEEE 52, 853 (1964).
[CrossRef]

H. G. Aas, R. K. Erf, J. Acoust. Soc. Amer. 36, 1906 (1964).
[CrossRef]

1963

A. Yariv, J. P. Gordon, Proc. IEEE 51, 4 (1963). See also: R. L. Fork, D. R. Herriott, A. Kogelnik, Appl. Opt. 3, 1471 (1964).
[CrossRef]

Aas, H. G.

H. G. Aas, R. K. Erf, J. Acoust. Soc. Amer. 36, 1906 (1964).
[CrossRef]

Adler, R.

A. Korpel, R. Adler, P. Desmares, W. H. Watson, Proc. IEEE 54, 1429 (1966).
[CrossRef]

Danielson, G. E.

A. J. De Maria, G. E. Danielson, IEEE J. Quantum Electron. QE-2, 157 (1966).
[CrossRef]

De Maria, A. J.

A. J. De Maria, G. E. Danielson, IEEE J. Quantum Electron. QE-2, 157 (1966).
[CrossRef]

Desmares, P.

A. Korpel, R. Adler, P. Desmares, W. H. Watson, Proc. IEEE 54, 1429 (1966).
[CrossRef]

Erf, R. K.

H. G. Aas, R. K. Erf, J. Acoust. Soc. Amer. 36, 1906 (1964).
[CrossRef]

Gordon, J. P.

A. Yariv, J. P. Gordon, Proc. IEEE 51, 4 (1963). See also: R. L. Fork, D. R. Herriott, A. Kogelnik, Appl. Opt. 3, 1471 (1964).
[CrossRef]

Korpel, A.

A. Korpel, R. Adler, P. Desmares, W. H. Watson, Proc. IEEE 54, 1429 (1966).
[CrossRef]

T. M. Smith, A. Korpel, IEEE J. Quantum Electron. QE-1, 283 (1965).
[CrossRef]

Lipnik, R.

R. Lipnik, A. Reich, G. A. Schoen, Proc. IEEE 52, 853 (1964).
[CrossRef]

Meeker, T. R.

T. R. Meeker, A. H. Mietzler, Physical Acoustics, W. P. Mason, Ed. (Academic, New York, 1964), Vol. I, Chap. 2, p. 123.

Mietzler, A. H.

T. R. Meeker, A. H. Mietzler, Physical Acoustics, W. P. Mason, Ed. (Academic, New York, 1964), Vol. I, Chap. 2, p. 123.

Redwood, M. R.

M. R. Redwood, Mechanical Waveguides (Pergamon, New York, 1960), p. 120.

Reich, A.

R. Lipnik, A. Reich, G. A. Schoen, Proc. IEEE 52, 853 (1964).
[CrossRef]

Schoen, G. A.

R. Lipnik, A. Reich, G. A. Schoen, Proc. IEEE 52, 853 (1964).
[CrossRef]

Smith, T. M.

T. M. Smith, A. Korpel, IEEE J. Quantum Electron. QE-1, 283 (1965).
[CrossRef]

Watson, W. H.

A. Korpel, R. Adler, P. Desmares, W. H. Watson, Proc. IEEE 54, 1429 (1966).
[CrossRef]

Yariv, A.

A. Yariv, J. P. Gordon, Proc. IEEE 51, 4 (1963). See also: R. L. Fork, D. R. Herriott, A. Kogelnik, Appl. Opt. 3, 1471 (1964).
[CrossRef]

IEEE J. Quantum Electron.

A. J. De Maria, G. E. Danielson, IEEE J. Quantum Electron. QE-2, 157 (1966).
[CrossRef]

T. M. Smith, A. Korpel, IEEE J. Quantum Electron. QE-1, 283 (1965).
[CrossRef]

J. Acoust. Soc. Amer.

H. G. Aas, R. K. Erf, J. Acoust. Soc. Amer. 36, 1906 (1964).
[CrossRef]

Proc. IEEE

A. Korpel, R. Adler, P. Desmares, W. H. Watson, Proc. IEEE 54, 1429 (1966).
[CrossRef]

A. Yariv, J. P. Gordon, Proc. IEEE 51, 4 (1963). See also: R. L. Fork, D. R. Herriott, A. Kogelnik, Appl. Opt. 3, 1471 (1964).
[CrossRef]

R. Lipnik, A. Reich, G. A. Schoen, Proc. IEEE 52, 853 (1964).
[CrossRef]

Other

T. R. Meeker, A. H. Mietzler, Physical Acoustics, W. P. Mason, Ed. (Academic, New York, 1964), Vol. I, Chap. 2, p. 123.

M. R. Redwood, Mechanical Waveguides (Pergamon, New York, 1960), p. 120.

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Figures (11)

Fig. 1
Fig. 1

General optical system.

Fig. 2
Fig. 2

Gaussian beam focusing parameters.

Fig. 3
Fig. 3

Resolution improvement of a moving lens.

Fig. 4
Fig. 4

Optical input arrangement for traveling lens.

Fig. 5
Fig. 5

Dilational-wave acoustic lens.

Fig. 6
Fig. 6

Flexural-wave mirror.

Fig. 7
Fig. 7

Re-entrant flex-wave resonator.

Fig. 8
Fig. 8

Flexural-wave recorder.

Fig. 9
Fig. 9

Burst pattern comparison, dilational-wave lens.

Fig. 10
Fig. 10

1-MHz, 2-MHz, 8-MHz video, dilational-wave lens.

Fig. 11
Fig. 11

Burst pattern comparison, flexural-wave mirror.

Equations (37)

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w 1 = λ f 1 / π w 0 [ 1 + ( λ f 1 / π w 0 2 ) 2 ] 1 2 λ f 1 / π w 0 ,
Z 1 = f 1 / [ 1 + ( λ f 1 / π w 0 2 ) 2 ] f 1 .
N 1 = N 0 ( w 0 / w 1 ) .
N 1 / N 0 = ( π w 0 2 / λ f 1 ) [ 1 + ( λ f 1 / π w 0 2 ) 2 ] 1 2 π w 0 2 / λ f 1 .
F # = f 1 / 2 w 0 ,
N 1 / N 0 = π w 0 / 2 λ F # .
2 w 0 = Λ / 4 = V s / 4 f a ,
n ( x , t ) = n 0 + Δ n cos [ ( 2 π x / Λ ) ω a t ] ,
Δ n = ( k P 0 / 6 n 0 ) ( n 0 2 1 ) ( n 0 2 + 2 ) .
f 1 = ( Λ / 4 ) ( n 0 / Δ n ) 1 2 .
f 1 = 2 w 0 ( n 0 / Δ n ) .
F # = f 1 / π w 0 = ( 2 / π ) ( n 0 / Δ n ) 1 2 ,
w 1 2 π λ F # = 2 λ f 1 π 2 w 0 = 4 λ π 2 ( n 0 Δ n ) 1 2 .
N 1 N 0 = 2 w 0 2 w 1 = Λ 8 w 1 = π Λ 16 λ F # = π 2 Λ 32 λ ( Δ n n 0 ) 1 2 .
M = n 0 6 p 0 2 / ρ 0 V s 3 ( MKS : sec 3 / kg ) ,
Δ n = 1 2 n 0 3 p 0 k P 0 .
p 0 = ( 3 n 0 4 ) 1 ( n 0 2 1 ) ( n 0 2 + 2 ) .
P 0 = ( 2 ρ 0 V s I s ) 1 2 .
Δ n = ( k ρ 0 V s 2 ) ( M I s / 2 ) 1 2 .
Δ n = ( 1 2 M I s ) 1 2 ,
I s = ( 2 / M ) ( Δ n ) 2 .
W s = I s 4 w 0 f 1 = I s Λ f 1 / 2 = 2 M ( Δ n 2 ) Λ 2 · Λ 4 ( n 0 Δ n ) 1 2 / 2 W s = Λ 2 4 M ( n 0 ) 1 2 ( Δ n ) 3 2 .
L s = V s τ = 9.53 cm .
D 0 = L s N 0 = 2 w 0 = 9.53 cm 95 = 1.0 mm .
4 ( γ b ) 2 ( β b ) ( α b ) tan ( β b ) = [ ( γ b ) 2 ( β b ) 2 ] 2 tan ( α b ) ,
α 2 + γ 2 = ( ω / V D ) 2 ,
β 2 + γ 2 = ( ω / V T ) 2 ,
( V D / V T ) 2 = 2 ( 1 σ ) / ( 1 2 σ ) ,
γ = ω / V p ,
V p = { ω T V T / [ 6 ( 1 σ ) ] 1 2 } 1 2 .
x ( z , t ) = x 0 cos [ ( 2 π z / Λ ) ω a t ] .
R = Λ 2 / 4 π 2 x 0 ,
f 1 = R / 2 = Λ 2 / 8 π 2 x 0 .
x 0 = Λ 2 π 2 F # = V p 2 π 2 F # f a .
W s = 1 2 ( ω x 0 ) 2 ρ 0 W T V g ,
W s = 4 π 2 ( f a x 0 ) 2 ρ 0 W T V p .
W s = ρ 0 W T V p 3 / π 2 F # 2 .

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