Abstract

We analyze the influence of the phase or amplitude coding of the input information in an optical correlator. For binary images, we show that the ratio between the signal-to-noise ratios of both codings is independent of the images when the matched filter is modified in order to have a zero mean value. Moreover these signal-to-noise ratios can be equivalent, but the price is a decrease in the amplitude of the correlation peak in the phase-coding case. With the nonmodified matched filter, characteristics of the phase coding appear to be unattractive.

© 1992 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  11. For the determination of 〈CP(0)〉 and σP2 one needs the following relations:〈exp[ikn(x)]〉=exp(−k2σ2/2),〈exp{ik[n(x1)−n(x2)]}〉=exp(−k2σ2)+δx1,x2[1−exp(−k2σ2)].

1991 (1)

1989 (1)

1988 (3)

1987 (1)

1984 (1)

D. Psaltis, E. G. Paek, S. S. Wenkatesh, Opt. Eng. 23, 668 (1984).

1982 (2)

1964 (1)

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Caulfield, H. J.

Dickey, F. M.

Farn, M. W.

Flannery, D. L.

Gianino, P. D.

Goodman, J. W.

Horner, J. L.

Loomis, J. S.

Milkovich, M. E.

Paek, E. G.

D. Psaltis, E. G. Paek, S. S. Wenkatesh, Opt. Eng. 23, 668 (1984).

Psaltis, D.

D. Psaltis, E. G. Paek, S. S. Wenkatesh, Opt. Eng. 23, 668 (1984).

Refregier, Ph.

Romero, L. A.

Soref, R. A.

J. L. Horner, R. A. Soref, Electron. Lett. 24, 626 (1988).
[CrossRef]

Vander Lugt, A.

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Wenkatesh, S. S.

D. Psaltis, E. G. Paek, S. S. Wenkatesh, Opt. Eng. 23, 668 (1984).

Appl. Opt. (5)

Electron. Lett. (1)

J. L. Horner, R. A. Soref, Electron. Lett. 24, 626 (1988).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Opt. Eng. (1)

D. Psaltis, E. G. Paek, S. S. Wenkatesh, Opt. Eng. 23, 668 (1984).

Opt. Lett. (2)

Other (1)

For the determination of 〈CP(0)〉 and σP2 one needs the following relations:〈exp[ikn(x)]〉=exp(−k2σ2/2),〈exp{ik[n(x1)−n(x2)]}〉=exp(−k2σ2)+δx1,x2[1−exp(−k2σ2)].

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Figures (1)

Fig. 1
Fig. 1

Evolution of the ratio ρ1 between the SNR’s of the phase- and the amplitude-coding schemes as a function of k and for different values of the noise power σ2.

Tables (2)

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Table 1 Comparisons of the SNR for the Different Codings for Centered Filters

Tables Icon

Table 2 Comparisons of the SNR for the Different Codings for Noncentered Filters

Equations (18)

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h ( x ) = Ψ ( x ) α [ x Ψ ( x ) ] / N ,
h ( x ) = f ( x ) exp ( i k ) + [ 1 f ( x ) ] α [ m N exp ( i k ) + ( 1 m N ) ] .
P x 1 , x 2 ( n 1 , n 2 ) = ( 1 δ x 1 , x 2 ) P ( n 1 ) P ( n 2 ) + δ x 1 , x 2 P ( n 1 ) ,
P ( n ) = 1 2 Π σ exp ( n 2 2 σ 2 ) ,
C A ( 0 ) = m ( 1 α m / N ) ,
σ A 2 = σ 2 m ( 1 α m / N ) ,
SNR A = m ( 1 α m / N ) σ 2 .
C P ( 0 ) = exp ( k 2 σ 2 / 2 ) × [ N α N + 2 α m N ( N m ) ( 1 cos k ) ] ,
σ P 2 = [ 1 exp ( k 2 σ 2 ) ] × [ N α N + 2 α m N ( N m ) ( 1 cos k ) ] ,
SNR P = 1 exp ( k 2 σ 2 ) 1 × [ N α N + 2 α m N ( N m ) ( 1 cos k ) ] .
ρ 1 = g ( k ) G ( k 2 σ 2 ) ,
η 1 = 2 [ 1 cos ( k ) ] exp ( k 2 σ 2 / 2 ) ,
C A ( 0 ) = m , σ A 2 = m σ 2 ,
C P ( 0 ) = N exp ( k 2 σ 2 / 2 ) , σ P 2 = N [ 1 exp ( k 2 σ 2 ) ] .
SNR P = | C P ( 0 ) C min | 2 / | C P ( 0 ) C P ( 0 ) | 2 ,
SNR P = 4 m 2 [ 1 cos ( k ) ] 2 N [ exp ( k 2 σ 2 ) 1 ] .
ρ 0 = 2 m N [ 1 cos ( k ) ] g ( k ) G ( k 2 σ 2 ) .
exp[ikn(x)]=exp(k2σ2/2),exp{ik[n(x1)n(x2)]}=exp(k2σ2)+δx1,x2[1exp(k2σ2)].

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