Abstract

This paper describes a multichannel optical correlator that uses two spatial dimensions to achieve multichannel capability and operates in real time. Given I signals, ri(t), and J signals, sj(t), it can produce the I × J cross products, ri(t)sj(t), averaged over some interval. Multiplication is based on the fact that the square of the sum of two signals contains their cross product. Light fields modulated by the signals are added and their sum squared by measuring its intensity. An experimental correlator and its performance are described along with applications.

© 1971 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, IRE Trans. Information Theory IT-6, 386 (1960).
    [Crossref]
  2. L. Slobodin, Proc. IEEE 51, 1782 (1963).
    [Crossref]
  3. M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
    [Crossref]
  4. F. N. Izzo, Proc. IEEE 53, 1740 (1965).
    [Crossref]
  5. A. V. Bunker, in Optical and Electro-Optical Information Processing (MIT Press, Cambridge, 1965).
  6. E. B. Felstead, IEEE Trans. Aerospace Electron. Syst. AES-3, 907 (1967).
    [Crossref]
  7. E. B. Felstead, Appl. Opt. 7, 105 (1968).
    [Crossref] [PubMed]
  8. H. R. Carleton, W. T. Maloney, G. Metz, Proc. IEEE 57, 769 (1969).
    [Crossref]
  9. F. H. Lange, Correlation Technique (Iliffe, London, 1967), pp. 111–127).
  10. B. H. Billings, J. Opt. Soc. Am. 39, 797 (1949); J. Opt. Soc. Am. 42, 12 (1952).
    [Crossref]
  11. I. P. Kaminow, E. H. Turner, Proc. IEEE 54, 1374 (1966).
    [Crossref]
  12. K. Preston, J., IEEE Trans. Aerospace Electron. Syst. AES-6, 458 (1970).
    [Crossref]

1970 (1)

K. Preston, J., IEEE Trans. Aerospace Electron. Syst. AES-6, 458 (1970).
[Crossref]

1969 (1)

H. R. Carleton, W. T. Maloney, G. Metz, Proc. IEEE 57, 769 (1969).
[Crossref]

1968 (1)

1967 (1)

E. B. Felstead, IEEE Trans. Aerospace Electron. Syst. AES-3, 907 (1967).
[Crossref]

1966 (1)

I. P. Kaminow, E. H. Turner, Proc. IEEE 54, 1374 (1966).
[Crossref]

1965 (1)

F. N. Izzo, Proc. IEEE 53, 1740 (1965).
[Crossref]

1964 (1)

M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
[Crossref]

1963 (1)

L. Slobodin, Proc. IEEE 51, 1782 (1963).
[Crossref]

1960 (1)

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, IRE Trans. Information Theory IT-6, 386 (1960).
[Crossref]

1949 (1)

Arm, M.

M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
[Crossref]

Billings, B. H.

Bunker, A. V.

A. V. Bunker, in Optical and Electro-Optical Information Processing (MIT Press, Cambridge, 1965).

Carleton, H. R.

H. R. Carleton, W. T. Maloney, G. Metz, Proc. IEEE 57, 769 (1969).
[Crossref]

Cutrona, L. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, IRE Trans. Information Theory IT-6, 386 (1960).
[Crossref]

Felstead, E. B.

E. B. Felstead, Appl. Opt. 7, 105 (1968).
[Crossref] [PubMed]

E. B. Felstead, IEEE Trans. Aerospace Electron. Syst. AES-3, 907 (1967).
[Crossref]

Izzo, F. N.

F. N. Izzo, Proc. IEEE 53, 1740 (1965).
[Crossref]

Kaminow, I. P.

I. P. Kaminow, E. H. Turner, Proc. IEEE 54, 1374 (1966).
[Crossref]

Lambert, L.

M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
[Crossref]

Lange, F. H.

F. H. Lange, Correlation Technique (Iliffe, London, 1967), pp. 111–127).

Leith, E. N.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, IRE Trans. Information Theory IT-6, 386 (1960).
[Crossref]

Maloney, W. T.

H. R. Carleton, W. T. Maloney, G. Metz, Proc. IEEE 57, 769 (1969).
[Crossref]

Metz, G.

H. R. Carleton, W. T. Maloney, G. Metz, Proc. IEEE 57, 769 (1969).
[Crossref]

Palermo, C. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, IRE Trans. Information Theory IT-6, 386 (1960).
[Crossref]

Porcello, L. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, IRE Trans. Information Theory IT-6, 386 (1960).
[Crossref]

Preston, K.

K. Preston, J., IEEE Trans. Aerospace Electron. Syst. AES-6, 458 (1970).
[Crossref]

Slobodin, L.

L. Slobodin, Proc. IEEE 51, 1782 (1963).
[Crossref]

Turner, E. H.

I. P. Kaminow, E. H. Turner, Proc. IEEE 54, 1374 (1966).
[Crossref]

Weissman, I.

M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
[Crossref]

Appl. Opt. (1)

IEEE Trans. Aerospace Electron. Syst. (1)

E. B. Felstead, IEEE Trans. Aerospace Electron. Syst. AES-3, 907 (1967).
[Crossref]

IRE Trans. Information Theory (1)

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, IRE Trans. Information Theory IT-6, 386 (1960).
[Crossref]

J. Opt. Soc. Am. (1)

J., IEEE Trans. Aerospace Electron. Syst. (1)

K. Preston, J., IEEE Trans. Aerospace Electron. Syst. AES-6, 458 (1970).
[Crossref]

Proc. IEEE (5)

I. P. Kaminow, E. H. Turner, Proc. IEEE 54, 1374 (1966).
[Crossref]

H. R. Carleton, W. T. Maloney, G. Metz, Proc. IEEE 57, 769 (1969).
[Crossref]

L. Slobodin, Proc. IEEE 51, 1782 (1963).
[Crossref]

M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
[Crossref]

F. N. Izzo, Proc. IEEE 53, 1740 (1965).
[Crossref]

Other (2)

A. V. Bunker, in Optical and Electro-Optical Information Processing (MIT Press, Cambridge, 1965).

F. H. Lange, Correlation Technique (Iliffe, London, 1967), pp. 111–127).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic layout of the multi-channel correlator.

Fig. 2
Fig. 2

Output field of light at the plane of mask M3. Only the doubly shaded regions, which represent the sum of the two sets of modulated light fields, are passed by M3.

Fig. 3
Fig. 3

Block diagram of the experimental correlator.

Fig. 4
Fig. 4

Input-output characteristics of the correlator. Scattering is due to random fluctuations (see text). Uncorrelated noise refers to independent random waveforms added to each channel to simulate actual operating conditions.

Fig. 5
Fig. 5

Autocorrelation function of a random noise with an approximately guassian spectral density function 1 kHz wide centered at 4 kHz.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

R r s ( τ ) = l i m T 1 T - T / 2 + T / 2 r ( t ) s ( t + τ ) d t ,
R r i s j ( τ j ) = 1 T - T / 2 T / 2 r i ( t ) s j ( t + τ j ) d t
E 1 ( x , y , t ) = rect ( x A ) i = 1 I rect ( y - i l w ) [ 1 + κ r i ( t ) ] ,
E 2 ( x , y , t ) = rect ( y B ) j = 1 J rect ( x - j l w ) [ 1 + κ s j ( t ) ] ,
rect ( α / w ) = 1 ; α w = 0 ; > w ,
E ( x , y , t ) = i = 1 I j = 1 J rect ( y - i l w ) rect ( x - j l w ) × { [ 1 + κ r i ( t ) ] + [ 1 + κ s j ( t ) ] exp ( - j β d ) } ,
v i j ( t ) = K κ 2 [ r i 2 ( t ) - 2 r i ( t ) s j ( t ) + s j 2 ( t ) ] ,
v i j ( t ) = K κ 2 [ r i 2 ( t ) + 2 r i ( t ) s j ( t ) + s j 2 ( t ) ] .
v i j ( t ) = K κ 2 4 [ r i ( t ) s j ( t ) ] ,
R r i s j ( 0 ) = 4 K κ 2 T - T / 2 + T / 2 r i ( t ) s j ( t ) d t .
V i j ( t , T ) = K κ 2 T - T / 2 + T / 2 ( r i 2 ( t ) u ( t ) + 2 r i ( t ) s j ( t ) u 2 ( t ) + s j 2 ( t ) u 3 ( t ) d t K κ 2 T - T / 2 + T / 2 2 r i ( t ) s j ( t ) d t ,
R r s j ( τ i ) = K κ T - T / 2 + T / 2 r ( t + τ i ) s j ( t ) d t .
E ( j l , i l , t ) = { exp [ j κ r i ( l ) ] - exp [ j κ s j ( t ) ] } .
E ( j l , i l , t ) = [ 1 + j κ r i ( t ) - 1 - j κ s j ( t ) ] .
v i j ( t ) = K κ 2 [ r i 2 ( t ) - 2 r i ( t ) s j ( t ) + s j 2 ( t ) ] ,

Metrics