Abstract

The signal model used and the output SNR0 measure chosen are shown to affect the performance of an acoustooptic time-integrating correlator. Nonuniform acoustic fields are also shown to affect the results, but these error sources can be overcome with a new hybrid time- and space-integrating acoustooptic matched filter correlator that we describe and for which initial simulation data are provided.

© 1982 Optical Society of America

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References

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  1. R. A. Sprague, C. L. Kolopoulos, Appl. Opt. 15, 89 (1976).
    [CrossRef] [PubMed]
  2. I. C. Chang, D. L. Hecht, Proc. Soc. Photo-Opt. Instrum. Eng. 241, 129 (1980).
  3. D. Casasent, G. Silbershatz, Appl. Opt. 21, 2076 (1982).
    [CrossRef] [PubMed]
  4. R. Denaro, IEEE Spectrum 18, 35 (May1981).
  5. J. Spilker, Inst. J.Navig. 25, 121 (1978).
  6. H. Mostafavi, F. Smith, IEEE Trans. Aerosp. Electron. Syst. 14, 487 (1978).
    [CrossRef]
  7. H. Mostafavi, IEEE Trans. Acoust. Speech Signal Process. 27, 163 (1979).
    [CrossRef]
  8. J. M. Wozencraft, I. M. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965), pp. 186–188,see also Ref. 14, pp. 145–170.
  9. J. W. R. Griffiths, J. E. Hudson, in Aspects of Signal Processing with Emphasis on Underwater Acoustics, Part I, G. Tacconi, Ed. (Reidel, Boston, 1977), pp. 299–300.
    [CrossRef]
  10. I. S. Reed, J. D. Mallet, L. E. Brennan, IEEE Trans. Aerosp. Electron. Syst. 10, 853 (1974).
    [CrossRef]
  11. J. P. Y. Lee, Appl. Opt. 20, 595 (1981).
    [CrossRef] [PubMed]
  12. Isomet Corp. note on “Series 250 Electronic Devices for Acousto-Optic Modulators” (May1977).
  13. P. Kellman, “Time Integration Optical Signal Processing,” Ph.D. Thesis, Stanford U. (1979).
  14. W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), p. 250.
  15. A. VanderLugt, IEEE Trans. Inf. Theory, IT-10139 (1964).

1982 (1)

1981 (2)

R. Denaro, IEEE Spectrum 18, 35 (May1981).

J. P. Y. Lee, Appl. Opt. 20, 595 (1981).
[CrossRef] [PubMed]

1980 (1)

I. C. Chang, D. L. Hecht, Proc. Soc. Photo-Opt. Instrum. Eng. 241, 129 (1980).

1979 (1)

H. Mostafavi, IEEE Trans. Acoust. Speech Signal Process. 27, 163 (1979).
[CrossRef]

1978 (2)

J. Spilker, Inst. J.Navig. 25, 121 (1978).

H. Mostafavi, F. Smith, IEEE Trans. Aerosp. Electron. Syst. 14, 487 (1978).
[CrossRef]

1976 (1)

1974 (1)

I. S. Reed, J. D. Mallet, L. E. Brennan, IEEE Trans. Aerosp. Electron. Syst. 10, 853 (1974).
[CrossRef]

1964 (1)

A. VanderLugt, IEEE Trans. Inf. Theory, IT-10139 (1964).

Brennan, L. E.

I. S. Reed, J. D. Mallet, L. E. Brennan, IEEE Trans. Aerosp. Electron. Syst. 10, 853 (1974).
[CrossRef]

Casasent, D.

Chang, I. C.

I. C. Chang, D. L. Hecht, Proc. Soc. Photo-Opt. Instrum. Eng. 241, 129 (1980).

Davenport, W. B.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), p. 250.

Denaro, R.

R. Denaro, IEEE Spectrum 18, 35 (May1981).

Griffiths, J. W. R.

J. W. R. Griffiths, J. E. Hudson, in Aspects of Signal Processing with Emphasis on Underwater Acoustics, Part I, G. Tacconi, Ed. (Reidel, Boston, 1977), pp. 299–300.
[CrossRef]

Hecht, D. L.

I. C. Chang, D. L. Hecht, Proc. Soc. Photo-Opt. Instrum. Eng. 241, 129 (1980).

Hudson, J. E.

J. W. R. Griffiths, J. E. Hudson, in Aspects of Signal Processing with Emphasis on Underwater Acoustics, Part I, G. Tacconi, Ed. (Reidel, Boston, 1977), pp. 299–300.
[CrossRef]

Jacobs, I. M.

J. M. Wozencraft, I. M. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965), pp. 186–188,see also Ref. 14, pp. 145–170.

Kellman, P.

P. Kellman, “Time Integration Optical Signal Processing,” Ph.D. Thesis, Stanford U. (1979).

Kolopoulos, C. L.

Lee, J. P. Y.

Mallet, J. D.

I. S. Reed, J. D. Mallet, L. E. Brennan, IEEE Trans. Aerosp. Electron. Syst. 10, 853 (1974).
[CrossRef]

Mostafavi, H.

H. Mostafavi, IEEE Trans. Acoust. Speech Signal Process. 27, 163 (1979).
[CrossRef]

H. Mostafavi, F. Smith, IEEE Trans. Aerosp. Electron. Syst. 14, 487 (1978).
[CrossRef]

Reed, I. S.

I. S. Reed, J. D. Mallet, L. E. Brennan, IEEE Trans. Aerosp. Electron. Syst. 10, 853 (1974).
[CrossRef]

Root, W. L.

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), p. 250.

Silbershatz, G.

Smith, F.

H. Mostafavi, F. Smith, IEEE Trans. Aerosp. Electron. Syst. 14, 487 (1978).
[CrossRef]

Spilker, J.

J. Spilker, Inst. J.Navig. 25, 121 (1978).

Sprague, R. A.

VanderLugt, A.

A. VanderLugt, IEEE Trans. Inf. Theory, IT-10139 (1964).

Wozencraft, J. M.

J. M. Wozencraft, I. M. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965), pp. 186–188,see also Ref. 14, pp. 145–170.

Appl. Opt. (3)

IEEE Spectrum (1)

R. Denaro, IEEE Spectrum 18, 35 (May1981).

IEEE Trans. Acoust. Speech Signal Process. (1)

H. Mostafavi, IEEE Trans. Acoust. Speech Signal Process. 27, 163 (1979).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (2)

I. S. Reed, J. D. Mallet, L. E. Brennan, IEEE Trans. Aerosp. Electron. Syst. 10, 853 (1974).
[CrossRef]

H. Mostafavi, F. Smith, IEEE Trans. Aerosp. Electron. Syst. 14, 487 (1978).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, IEEE Trans. Inf. Theory, IT-10139 (1964).

Inst. J.Navig. (1)

J. Spilker, Inst. J.Navig. 25, 121 (1978).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

I. C. Chang, D. L. Hecht, Proc. Soc. Photo-Opt. Instrum. Eng. 241, 129 (1980).

Other (5)

J. M. Wozencraft, I. M. Jacobs, Principles of Communication Engineering (Wiley, New York, 1965), pp. 186–188,see also Ref. 14, pp. 145–170.

J. W. R. Griffiths, J. E. Hudson, in Aspects of Signal Processing with Emphasis on Underwater Acoustics, Part I, G. Tacconi, Ed. (Reidel, Boston, 1977), pp. 299–300.
[CrossRef]

Isomet Corp. note on “Series 250 Electronic Devices for Acousto-Optic Modulators” (May1977).

P. Kellman, “Time Integration Optical Signal Processing,” Ph.D. Thesis, Stanford U. (1979).

W. B. Davenport, W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958), p. 250.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of a time-integrating acoustooptic correlator.

Fig. 2
Fig. 2

Output voltage from the system of Fig. 1 for various input signal-to-jammer ratios: (a) SNRi = + ∞; (b) SNRi = −20 dB; (c) SNRi = −25 dB; (d) SNRi = − ∞.

Fig. 3
Fig. 3

Schematic diagram of a hybrid time- and space-integrating acoustooptic matched spatial filter correlator.

Fig. 4
Fig. 4

Nonuniform acoustooptic cell response assumed for the experiments in Figs. 5 and 6.

Fig. 5
Fig. 5

Simulated output data from the conventional time-integrating correlator of Fig. 1 (for different delays td) with the assumed nonuniform acoustooptic coll response in Fig. 4.

Fig. 6
Fig. 6

Simulated output data (for different delays td) from the acoustooptic matched spatial filter correlator of Fig. 3 with the nonuniform cell response in Fig. 4.

Equations (31)

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C ( τ ) = ( 1 / T I ) 0 T I s 1 ( t ) s 2 ( t + τ ) d t ,
R ( τ ) = E [ s 1 ( t ) s 2 ( t + τ ) ] ,
R s ( τ ) = P s m = + Λ ( τ m T s T p ) ,
PG = SNR 0 SNR i = P s / Var { C ( τ ) } P s / P n 0 ,
Var { C ( τ ) } = P s P n m = + Λ ( ζ ) Λ [ ( ITBW ) ζ ( STBW ) m ] × exp [ ζ 2 γ 2 ( ITBW ) 2 / 2 ] d ζ .
SNR 1 = E 2 { C ( 0 ) } Var { C ( 0 ) } .
SNR 2 = E 2 { C ( τ ) } Var { C ( τ ) } τ 0 τ = 0 .
SNR 3 = E 2 { C ( 0 ) } ( 1 / T C ) T C / 2 T C / 2 var { C ( τ ) } d τ .
E 2 { C ( 0 ) } = ( 1 / T I ) 2 { T I / 2 T I / 2 E [ s 2 ( t ) + s ( t ) n ( t ) ] d t } 2 = R s 2 ( 0 ) ,
E { C 2 ( 0 ) } = ( 1 / T I ) 2 [ T I / 2 T I / 2 E { s ( ζ ) s ( η ) [ s ( ζ ) + n ( ζ ) ] × [ s ( η ) + n ( η ) ] } d ζ d η = R s 2 ( 0 ) + ( 1 / T I ) T I T I ( 1 | τ | / T I ) R s ( τ ) × [ 2 R s ( τ ) + R n ( τ ) ] d τ ,
var { C ( 0 ) } = ( 1 / T I ) T I + T I ( 1 | τ | / T I ) R s ( τ ) [ 2 R s ( τ ) + R n ( τ ) ] d τ .
var { C ( τ ) } = E { C 2 ( τ ) } = ( 1 / T I ) 2 T I / 2 T I / 2 [ R s 2 ( ζ η ) + R s ( ζ η ) R n ( ζ η ) ] d ζ d η = ( 1 / T I ) T I T I R s ( τ ) ( 1 | τ | / T I ) [ R s ( τ ) + R n ( τ ) ] d τ .
var { C ( 0 ) } = ( 2 + 1 / SNR i ) [ ( 1 / T I ) T I T I × ( 1 | τ | / T I ) R s 2 ( τ ) d τ ] ,
var { C ( τ ) } τ 0 = ( 1 + 1 / SNR i ) [ ( 1 / T I ) T I T I × ( 1 | τ | / T I ) R s 2 ( τ ) d τ ] .
var { C ( 0 ) } = 2 var { C ( τ ) } τ 0
SNR 1 ( dB ) = SNR 2 ( dB ) 3.0 dB .
var { C ( 0 ) } = var { C ( τ ) } τ 0
SNR 1 = SNR 2 .
var { C ( 0 ) } = ( 3 / 2 ) var { C ( τ ) } τ 0
SNR 1 ( dB ) = SNR 2 ( dB ) 1.76 dB .
SNR 2 SNR 1 = 10 log 10 ( 1 + 2 SNR i 1 + SNR i ) .
I PT ( t ) = s 1 ( t ) + B 1 = s 1 ( t ) .
I AO ( x , t ) = s 2 ( t τ ) + B 2 = s 2 ( t τ ) .
I PT ( t ) I AO ( τ , t ) d t ,
T I / 2 T I / 2 s 1 ( t ) s 2 ( t τ ) d t + T I B 1 B 2 + T I / 2 T I / 2 B 1 s 2 ( t τ ) d t + T I / 2 T I / 2 B 2 s 1 ( t ) d t .
C ( τ ) = s ( t ) s ( t τ ) a ( τ ) d t = a ( τ ) s ( t ) s ( t τ ) d t .
u 3 ( t , x ) = T A a ( τ ) s ( t t d τ ) s ( x τ ) d τ ,
s 0 ( t d ) = m = 0 N A 1 u 3 ( t d + m T p , m T p ) , s 0 ( t d ) = m = 0 N A 1 T A a ( τ ) s 2 ( m T p τ ) d τ .
s 0 ( t d ) = T A a ( τ ) [ m = 0 N A 1 s 2 ( m T p τ ) ] d t = E s T A a ( τ ) d τ ,
u 3 ( t d ) = T A s ( τ ) s ( τ ) a ( τ ) d τ .
u 3 ( t d ) = K a ( τ ) d τ ,

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