Abstract

In some applications, the performance of multichannel Bragg cells is compromised by the spreading of the acoustic waves as they propagate; the spreading causes the signals in the channels to overlap. The overlapping can be significantly reduced by a spatial filter in a Fourier–image plane. The spatial filter is shown to be a cylindrical lens whose power is a function of the distance from the transducer. The effects of changes in the drive frequency as well as those of displacements of the filter are calculated. The reduction in the modulation transfer function as a function of propagation distance is calculated, and some bounds on the time–bandwidth product and the number of channels are dserived. In general, the overall performance can be improved by increasing the center frequency of the Bragg cell while keeping the bandwidth fixed.

© 1983 Optical Society of America

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References

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  1. L. B. Lambert, IRE Nat. Conv. Rec. 10, Part 6 (1962).
  2. L. B. Lambert, M. Arm, A. Aimette, Optical and Electro-Optical Information Processing, J. T. Tippett et al., Ed. (MIT Press, Cambridge, 1965).
  3. A. Bardos, Appl. Opt. 13, 832 (1974).
    [CrossRef] [PubMed]
  4. A. VanderLugt, Appl. Opt. 21, 1092 (1982).
    [CrossRef] [PubMed]
  5. P. C. Waterman, Phys. Rev. 113, 1240 (1959).
    [CrossRef]
  6. M. G. Cohen, J. Appl. Phys. 35, 3821 (1967).
    [CrossRef]
  7. I. A. Vodovatov, N. A. Esepkina, V. Yu Petrunkin, S. A. Rogov, Pis'ma Zh. Tekh. Fiz. 7, 369 (1981) [ Sov. Tech. Phys. Lett. 7, 159 (1981)] p. 159.
  8. J. B. Thomas, Statistical Communication Theory (Wiley, New York, 1969), p. 388.

1982

1981

I. A. Vodovatov, N. A. Esepkina, V. Yu Petrunkin, S. A. Rogov, Pis'ma Zh. Tekh. Fiz. 7, 369 (1981) [ Sov. Tech. Phys. Lett. 7, 159 (1981)] p. 159.

1974

1967

M. G. Cohen, J. Appl. Phys. 35, 3821 (1967).
[CrossRef]

1962

L. B. Lambert, IRE Nat. Conv. Rec. 10, Part 6 (1962).

1959

P. C. Waterman, Phys. Rev. 113, 1240 (1959).
[CrossRef]

Aimette, A.

L. B. Lambert, M. Arm, A. Aimette, Optical and Electro-Optical Information Processing, J. T. Tippett et al., Ed. (MIT Press, Cambridge, 1965).

Arm, M.

L. B. Lambert, M. Arm, A. Aimette, Optical and Electro-Optical Information Processing, J. T. Tippett et al., Ed. (MIT Press, Cambridge, 1965).

Bardos, A.

Cohen, M. G.

M. G. Cohen, J. Appl. Phys. 35, 3821 (1967).
[CrossRef]

Esepkina, N. A.

I. A. Vodovatov, N. A. Esepkina, V. Yu Petrunkin, S. A. Rogov, Pis'ma Zh. Tekh. Fiz. 7, 369 (1981) [ Sov. Tech. Phys. Lett. 7, 159 (1981)] p. 159.

Lambert, L. B.

L. B. Lambert, IRE Nat. Conv. Rec. 10, Part 6 (1962).

L. B. Lambert, M. Arm, A. Aimette, Optical and Electro-Optical Information Processing, J. T. Tippett et al., Ed. (MIT Press, Cambridge, 1965).

Rogov, S. A.

I. A. Vodovatov, N. A. Esepkina, V. Yu Petrunkin, S. A. Rogov, Pis'ma Zh. Tekh. Fiz. 7, 369 (1981) [ Sov. Tech. Phys. Lett. 7, 159 (1981)] p. 159.

Thomas, J. B.

J. B. Thomas, Statistical Communication Theory (Wiley, New York, 1969), p. 388.

VanderLugt, A.

Vodovatov, I. A.

I. A. Vodovatov, N. A. Esepkina, V. Yu Petrunkin, S. A. Rogov, Pis'ma Zh. Tekh. Fiz. 7, 369 (1981) [ Sov. Tech. Phys. Lett. 7, 159 (1981)] p. 159.

Waterman, P. C.

P. C. Waterman, Phys. Rev. 113, 1240 (1959).
[CrossRef]

Yu Petrunkin, V.

I. A. Vodovatov, N. A. Esepkina, V. Yu Petrunkin, S. A. Rogov, Pis'ma Zh. Tekh. Fiz. 7, 369 (1981) [ Sov. Tech. Phys. Lett. 7, 159 (1981)] p. 159.

Appl. Opt.

IRE Nat. Conv. Rec.

L. B. Lambert, IRE Nat. Conv. Rec. 10, Part 6 (1962).

J. Appl. Phys.

M. G. Cohen, J. Appl. Phys. 35, 3821 (1967).
[CrossRef]

Phys. Rev.

P. C. Waterman, Phys. Rev. 113, 1240 (1959).
[CrossRef]

Pis'ma Zh. Tekh. Fiz.

I. A. Vodovatov, N. A. Esepkina, V. Yu Petrunkin, S. A. Rogov, Pis'ma Zh. Tekh. Fiz. 7, 369 (1981) [ Sov. Tech. Phys. Lett. 7, 159 (1981)] p. 159.

Other

J. B. Thomas, Statistical Communication Theory (Wiley, New York, 1969), p. 388.

L. B. Lambert, M. Arm, A. Aimette, Optical and Electro-Optical Information Processing, J. T. Tippett et al., Ed. (MIT Press, Cambridge, 1965).

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Figures (5)

Fig. 1
Fig. 1

Model for acoustic spreading in a Bragg cell.

Fig. 2
Fig. 2

Optical system for constructing the holographic element and correcting the acoustic spreading.

Fig. 3
Fig. 3

Multichannel Bragg cell diffraction beams: (a) uncorrected case showing beam overlap; (b) corrected beams at optimum acoustic wavelength (123 MHz).

Fig. 4
Fig. 4

Corrected beams showing energy confinement: (a) result for 175 MHz; (b) result for 95 MHz.

Fig. 5
Fig. 5

Diagram showing the surface of acoustic energy and the transducer geometry.

Equations (26)

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G ( x , β ) = 1 j Λ x ϕ 0 x ϕ 0 x exp [ j 2 π y 2 / 2 Λ x ( 1 2 s ) ] × exp ( j 2 π β y / λ ) d y ,
ϕ 0 = Λ ( 1 2 s ) / H .
c = π / Λ x ( 1 2 s ) , d = π β / λ
G ( x , β ) = 1 j Λ x ϕ 0 x ϕ 0 x exp [ j ( c y 2 + 2 d y ) ] d y .
G ( x , β ) = 1 j Λ x exp ( j d 2 / c ) sinc ( β H / λ ) a b exp ( j u 2 ) d u ,
| β | ϕ 0 λ / Λ ( 1 2 s ) .
| β | λ / H ,
G ( x , β ) = f ( x , β ) exp [ j π x Λ ( 1 2 s ) β 2 / λ 2 ] .
A ( x , β ) = R exp ( j 2 π β D / λ ) + G ( x , β ) ,
H ( x , β ) = R G * ( x , β ) exp ( j 2 π β D / λ ) .
θ ( x , β ) = a β 2 x ( a + a 0 ) ( β + β 0 ) 2 ( x + x 0 ) ,
θ ( x , β ) = a 0 β 2 + a β 2 x 0 + a 0 β 2 x 0 + 2 ( a + a 0 ) β 0 β x + 2 ( a + a 0 ) β 0 β x 0 + ( a + a 0 ) β 0 2 x + ( a + a 0 ) β 0 2 x 0 .
θ ( x , β ) a 0 = 0 = a β 2 x 0 + 2 a β 0 β x + 2 a β 0 β x 0 + a β 0 2 x + a β 0 2 x 0 .
θ ( x , β ) = a β 2 x 1 + a 0 β 2 x .
θ ( x , β ) = a 0 β 2 ( x L / 2 ) ,
Λ 0 = V ( f 2 + f 1 ) / 2 f 2 f 1 .
h = Λ ( 1 2 s ) L / 2 H .
V ϕ = V [ 1 s ϕ 2 / ( 1 2 s ) ] .
x 3 V t [ 1 ϕ 2 / 2 ( 1 2 s ) ,
d 1 = V t ϕ 2 / 2 ( 1 2 s ) .
d 1 x Λ 2 ( 1 2 s ) / 2 H 2 .
d 2 = V Δ F + x Λ 2 ( 1 2 s ) 60 H 2 .
Z = ( f f c ) Δ f [ 1 + x Λ 2 ( 1 2 s ) N 60 H 2 ] ,
N c H / Λ 1 ( 1 2 s ) ,
Λ e = V Δ f / 2 f 1 f 2 ,
N c 2 f 1 f 2 H V Δ f ( 1 2 s ) .

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