Abstract

A multichannel coherent optical processor for radar signals is described in which pulse compression is achieved by matched spatial filtering. The optical system can be used for phased array, linear frequency modulated pulse burst, or other radar systems. However, only its application to linear phased array signal processing is discussed in depth. From the output optical pattern, one can obtain data on the target's fine range and azimuth (for a phased array) or fine range and Doppler (for a pulse burst radar) etc.

© 1978 Optical Society of America

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References

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  1. R. Scudder, W. Sheppard, Microwave J. 17, 51 (1974).
  2. L. Stark, Proc. IEEE 62, 1661 (1974).
  3. T. Cheston, J. Frank, in Radar Handbook, M. I. Skolnik, Ed. (McGraw-Hill, New York, 1970).
  4. W. S. Burdic, Radar Signal Analysis (Prentice-Hall, Englewood Cliffs, N. J., 1968).
  5. C. Tsao, R. Cease, W. Bickford, H. Rowland, IEEE Trans. Aerosp. Electron. Syst. AES-6, 771 (1970).
    [CrossRef]
  6. W. Delany, Microwave J. 18, 10 (1975).
  7. W. T. Maloney, IEEE Spectrum 6, 40 (1969).
    [CrossRef]
  8. J. Collins, E. Lean, H. Shaw, Appl. Phys. Lett. 11, 240 (1967).
    [CrossRef]
  9. L. Lambert, M. Arm, A. Aimette, in Optical and Electro-Optical Information Processing, J. T. Tippet et al., Eds. (MIT Press, Cambridge, Mass., 1965), pp. 715–747.
  10. R. A. Meyer, D. G. Grant, in Proceedings, Electro-Optical Systems Design Conference (1972), pp. 259–264.
  11. D. Casasent, F. Casasayas, IEEE Trans. Aerosp. Electron. Syste. AES-11, 65 (1975).
    [CrossRef]
  12. W. G. Hoefer, IRE Trans. Mil. Electron. MIL-6, 174 (1962).
    [CrossRef]
  13. D. Casasent, F. Casasayas, Appl. Opt. 14, 1364 (1975).
    [CrossRef] [PubMed]
  14. D. Beste, E. Leith, IEEE Trans. Aerosp. Electron. Syst. AES-2, 376 (1966).
    [CrossRef]
  15. R. E. Williams, K. von Bieren, Appl. Opt. 10, 1386 (1971).
    [CrossRef] [PubMed]
  16. E. Leith, IEEE Trans. Aerosp. Electron. Syst. AES-4, 879 (1968).
    [CrossRef]
  17. W. Cutrona, E. Leith, L. Porcello, W. Vivian, Proc. IEEE 54, 1026 (1966).
    [CrossRef]
  18. J. Gerig, H. Montague, Proc. IEEE 52, 1753 (1964).
    [CrossRef]
  19. L. Slobodin, Proc. IEEE 51, 1782 (1963).
    [CrossRef]
  20. M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
    [CrossRef]
  21. B. Felsted, IEEE Trans. Aerosp. Electron. Syst. AES-3, 907 (1967).
    [CrossRef]
  22. A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]
  23. P. M. Woodward, Probability and Information Theory (McGraw-Hill, New York, 1953).
  24. K. Preston, “Use of the Fourier Transformable Properties of Lenses for Signal Spectrum Analysis,” in Optical and Electro-Optical Information Processing, J. T. Tippet et al., Eds. (MIT Press, Cambridge, Mass., 1965).
  25. D. Casasent, Proc. IEEE 65, 143 (1977).
    [CrossRef]
  26. C. Weaver, J. Goodman, Appl. Opt. 5, 1248 (1966).
    [CrossRef] [PubMed]

1977

D. Casasent, Proc. IEEE 65, 143 (1977).
[CrossRef]

1975

W. Delany, Microwave J. 18, 10 (1975).

D. Casasent, F. Casasayas, IEEE Trans. Aerosp. Electron. Syste. AES-11, 65 (1975).
[CrossRef]

D. Casasent, F. Casasayas, Appl. Opt. 14, 1364 (1975).
[CrossRef] [PubMed]

1974

R. Scudder, W. Sheppard, Microwave J. 17, 51 (1974).

L. Stark, Proc. IEEE 62, 1661 (1974).

1972

R. A. Meyer, D. G. Grant, in Proceedings, Electro-Optical Systems Design Conference (1972), pp. 259–264.

1971

1970

C. Tsao, R. Cease, W. Bickford, H. Rowland, IEEE Trans. Aerosp. Electron. Syst. AES-6, 771 (1970).
[CrossRef]

1969

W. T. Maloney, IEEE Spectrum 6, 40 (1969).
[CrossRef]

1968

E. Leith, IEEE Trans. Aerosp. Electron. Syst. AES-4, 879 (1968).
[CrossRef]

1967

B. Felsted, IEEE Trans. Aerosp. Electron. Syst. AES-3, 907 (1967).
[CrossRef]

J. Collins, E. Lean, H. Shaw, Appl. Phys. Lett. 11, 240 (1967).
[CrossRef]

1966

D. Beste, E. Leith, IEEE Trans. Aerosp. Electron. Syst. AES-2, 376 (1966).
[CrossRef]

W. Cutrona, E. Leith, L. Porcello, W. Vivian, Proc. IEEE 54, 1026 (1966).
[CrossRef]

C. Weaver, J. Goodman, Appl. Opt. 5, 1248 (1966).
[CrossRef] [PubMed]

1964

J. Gerig, H. Montague, Proc. IEEE 52, 1753 (1964).
[CrossRef]

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

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

1963

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

1962

W. G. Hoefer, IRE Trans. Mil. Electron. MIL-6, 174 (1962).
[CrossRef]

Aimette, A.

L. Lambert, M. Arm, A. Aimette, in Optical and Electro-Optical Information Processing, J. T. Tippet et al., Eds. (MIT Press, Cambridge, Mass., 1965), pp. 715–747.

Arm, M.

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

L. Lambert, M. Arm, A. Aimette, in Optical and Electro-Optical Information Processing, J. T. Tippet et al., Eds. (MIT Press, Cambridge, Mass., 1965), pp. 715–747.

Beste, D.

D. Beste, E. Leith, IEEE Trans. Aerosp. Electron. Syst. AES-2, 376 (1966).
[CrossRef]

Bickford, W.

C. Tsao, R. Cease, W. Bickford, H. Rowland, IEEE Trans. Aerosp. Electron. Syst. AES-6, 771 (1970).
[CrossRef]

Burdic, W. S.

W. S. Burdic, Radar Signal Analysis (Prentice-Hall, Englewood Cliffs, N. J., 1968).

Casasayas, F.

D. Casasent, F. Casasayas, IEEE Trans. Aerosp. Electron. Syste. AES-11, 65 (1975).
[CrossRef]

D. Casasent, F. Casasayas, Appl. Opt. 14, 1364 (1975).
[CrossRef] [PubMed]

Casasent, D.

D. Casasent, Proc. IEEE 65, 143 (1977).
[CrossRef]

D. Casasent, F. Casasayas, IEEE Trans. Aerosp. Electron. Syste. AES-11, 65 (1975).
[CrossRef]

D. Casasent, F. Casasayas, Appl. Opt. 14, 1364 (1975).
[CrossRef] [PubMed]

Cease, R.

C. Tsao, R. Cease, W. Bickford, H. Rowland, IEEE Trans. Aerosp. Electron. Syst. AES-6, 771 (1970).
[CrossRef]

Cheston, T.

T. Cheston, J. Frank, in Radar Handbook, M. I. Skolnik, Ed. (McGraw-Hill, New York, 1970).

Collins, J.

J. Collins, E. Lean, H. Shaw, Appl. Phys. Lett. 11, 240 (1967).
[CrossRef]

Cutrona, W.

W. Cutrona, E. Leith, L. Porcello, W. Vivian, Proc. IEEE 54, 1026 (1966).
[CrossRef]

Delany, W.

W. Delany, Microwave J. 18, 10 (1975).

Felsted, B.

B. Felsted, IEEE Trans. Aerosp. Electron. Syst. AES-3, 907 (1967).
[CrossRef]

Frank, J.

T. Cheston, J. Frank, in Radar Handbook, M. I. Skolnik, Ed. (McGraw-Hill, New York, 1970).

Gerig, J.

J. Gerig, H. Montague, Proc. IEEE 52, 1753 (1964).
[CrossRef]

Goodman, J.

Grant, D. G.

R. A. Meyer, D. G. Grant, in Proceedings, Electro-Optical Systems Design Conference (1972), pp. 259–264.

Hoefer, W. G.

W. G. Hoefer, IRE Trans. Mil. Electron. MIL-6, 174 (1962).
[CrossRef]

Lambert, L.

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

L. Lambert, M. Arm, A. Aimette, in Optical and Electro-Optical Information Processing, J. T. Tippet et al., Eds. (MIT Press, Cambridge, Mass., 1965), pp. 715–747.

Lean, E.

J. Collins, E. Lean, H. Shaw, Appl. Phys. Lett. 11, 240 (1967).
[CrossRef]

Leith, E.

E. Leith, IEEE Trans. Aerosp. Electron. Syst. AES-4, 879 (1968).
[CrossRef]

D. Beste, E. Leith, IEEE Trans. Aerosp. Electron. Syst. AES-2, 376 (1966).
[CrossRef]

W. Cutrona, E. Leith, L. Porcello, W. Vivian, Proc. IEEE 54, 1026 (1966).
[CrossRef]

Maloney, W. T.

W. T. Maloney, IEEE Spectrum 6, 40 (1969).
[CrossRef]

Meyer, R. A.

R. A. Meyer, D. G. Grant, in Proceedings, Electro-Optical Systems Design Conference (1972), pp. 259–264.

Montague, H.

J. Gerig, H. Montague, Proc. IEEE 52, 1753 (1964).
[CrossRef]

Porcello, L.

W. Cutrona, E. Leith, L. Porcello, W. Vivian, Proc. IEEE 54, 1026 (1966).
[CrossRef]

Preston, K.

K. Preston, “Use of the Fourier Transformable Properties of Lenses for Signal Spectrum Analysis,” in Optical and Electro-Optical Information Processing, J. T. Tippet et al., Eds. (MIT Press, Cambridge, Mass., 1965).

Rowland, H.

C. Tsao, R. Cease, W. Bickford, H. Rowland, IEEE Trans. Aerosp. Electron. Syst. AES-6, 771 (1970).
[CrossRef]

Scudder, R.

R. Scudder, W. Sheppard, Microwave J. 17, 51 (1974).

Shaw, H.

J. Collins, E. Lean, H. Shaw, Appl. Phys. Lett. 11, 240 (1967).
[CrossRef]

Sheppard, W.

R. Scudder, W. Sheppard, Microwave J. 17, 51 (1974).

Slobodin, L.

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

Stark, L.

L. Stark, Proc. IEEE 62, 1661 (1974).

Tsao, C.

C. Tsao, R. Cease, W. Bickford, H. Rowland, IEEE Trans. Aerosp. Electron. Syst. AES-6, 771 (1970).
[CrossRef]

Vander Lugt, A.

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

Vivian, W.

W. Cutrona, E. Leith, L. Porcello, W. Vivian, Proc. IEEE 54, 1026 (1966).
[CrossRef]

von Bieren, K.

Weaver, C.

Weissman, I.

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

Williams, R. E.

Woodward, P. M.

P. M. Woodward, Probability and Information Theory (McGraw-Hill, New York, 1953).

Appl. Opt.

Appl. Phys. Lett.

J. Collins, E. Lean, H. Shaw, Appl. Phys. Lett. 11, 240 (1967).
[CrossRef]

IEEE Spectrum

W. T. Maloney, IEEE Spectrum 6, 40 (1969).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst.

E. Leith, IEEE Trans. Aerosp. Electron. Syst. AES-4, 879 (1968).
[CrossRef]

C. Tsao, R. Cease, W. Bickford, H. Rowland, IEEE Trans. Aerosp. Electron. Syst. AES-6, 771 (1970).
[CrossRef]

D. Beste, E. Leith, IEEE Trans. Aerosp. Electron. Syst. AES-2, 376 (1966).
[CrossRef]

B. Felsted, IEEE Trans. Aerosp. Electron. Syst. AES-3, 907 (1967).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syste.

D. Casasent, F. Casasayas, IEEE Trans. Aerosp. Electron. Syste. AES-11, 65 (1975).
[CrossRef]

IEEE Trans. Inf. Theory

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

IRE Trans. Mil. Electron.

W. G. Hoefer, IRE Trans. Mil. Electron. MIL-6, 174 (1962).
[CrossRef]

Microwave J.

W. Delany, Microwave J. 18, 10 (1975).

R. Scudder, W. Sheppard, Microwave J. 17, 51 (1974).

Proc. IEEE

L. Stark, Proc. IEEE 62, 1661 (1974).

W. Cutrona, E. Leith, L. Porcello, W. Vivian, Proc. IEEE 54, 1026 (1966).
[CrossRef]

J. Gerig, H. Montague, Proc. IEEE 52, 1753 (1964).
[CrossRef]

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

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

D. Casasent, Proc. IEEE 65, 143 (1977).
[CrossRef]

Proceedings, Electro-Optical Systems Design Conference

R. A. Meyer, D. G. Grant, in Proceedings, Electro-Optical Systems Design Conference (1972), pp. 259–264.

Other

T. Cheston, J. Frank, in Radar Handbook, M. I. Skolnik, Ed. (McGraw-Hill, New York, 1970).

W. S. Burdic, Radar Signal Analysis (Prentice-Hall, Englewood Cliffs, N. J., 1968).

L. Lambert, M. Arm, A. Aimette, in Optical and Electro-Optical Information Processing, J. T. Tippet et al., Eds. (MIT Press, Cambridge, Mass., 1965), pp. 715–747.

P. M. Woodward, Probability and Information Theory (McGraw-Hill, New York, 1953).

K. Preston, “Use of the Fourier Transformable Properties of Lenses for Signal Spectrum Analysis,” in Optical and Electro-Optical Information Processing, J. T. Tippet et al., Eds. (MIT Press, Cambridge, Mass., 1965).

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Figures (5)

Fig. 1
Fig. 1

Multichannel optical correlator schematic. P0 is the input plane, P1 the Fourier transform plane, and P2 the output corelation plane. Lenses L1 and L2 form the 1-D transform of the contents of P0 at P1. The coordinates of P2 are proportional to the target's azimuth (or Doppler) and fine range.

Fig. 2
Fig. 2

Schematic representations of the contents of the (a) input plane P0, and (b) the output correlation plane in the optical system of Fig. 1.

Fig. 3
Fig. 3

One-dimensional transform (power spectrum) for a boresight target for a 100-element linear phased array with a 13-bit Barker code.

Fig. 4
Fig. 4

Real-time multichannel correlation for the linear phased array described in Table I for a boresight target and various fine ranges RF in the range bin RB. (a) RF = 0.45RB, (b) RF = 0.50RB, and (c) RB = 0.55RB.

Fig. 5
Fig. 5

Real-time multichannel correlation for the linear phased array described in Table I for various target azimuth angles θ and fine ranges RF in the range bin RB. (a) θ = 5°, RF = 0.55RB; and (b) θ = 30°, RF = 0.45RB.

Tables (2)

Tables Icon

Table I Linear Phased Array Parameters

Tables Icon

Table II Comparison of Theoretical and Experimental Values In mm of the Displacements Δx2 and Δy2 of the Correlation Peak In Plane P2 of Fig. 1 from RF = 0.5RB and θ = 0° Reference Point In Plane P2

Equations (13)

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υ n ( x 0 ) = s x p ( x 0 T i / D ) cos 2 π ( f i f x 0 T i / D n α β ) ,
t ( x 0 , y 0 ) = n = ( N 1 ) / 2 ( N 1 ) / 2 δ ( y 0 n l 0 ) * [ 1 + μ υ n ( x 0 ) ] ,
T ( x 1 / λ f 2 , y 1 ) n = ( N 1 ) / 2 ( n 1 ) / 2 δ ( y 1 n l 1 ) * δ ( x 1 / λ f 2 ± f i f ) * S ( x 1 / λ f 2 ) exp [ j 2 π ( x 1 / λ f 2 ) ( n α + β ) ] ,
n = ( N 1 ) / 2 ( N 1 ) / 2 δ ( y 1 n l 1 ) * δ ( u 1 ± f i f ) * S * ( u 1 ) exp { j 2 π x 1 [ γ + ( n α 0 + β 0 ) / λ f 2 ) ] } ,
f ( x 2 , y 2 ) + n = ( N 1 ) / 2 ( N 1 ) / 2 δ ( y 1 n l 1 ) * δ ( u 1 ± f i f ) * S ( u 1 ) S * ( u 1 ) exp { j 2 π x 1 [ γ + ( n Δ α + Δ β ) / λ f 2 ] } exp [ j 2 π ( x 1 x 2 + y 1 y 2 ) / λ f 3 ] d x 1 d y 1 ,
x 2 = λ f 3 [ γ + ( n Δ α + Δ β ) / λ f 2 ] ,
w H = ( N f 3 l 0 tan θ ) / f 2 .
n = ( N 1 ) / 2 ( N 1 ) / 2 exp [ j 2 π n ( Δ α υ 2 l 1 ) ] ,
y 2 = ( λ f 1 f 3 p d sin θ ) / l 0 f 2 λ c ,
w V = 2 λ f 1 f 3 [ Δ α + 2 / ( N 1 ) ] / l 0 f 2 .
δ ( y 2 λ f 1 f 3 Δ α / l 0 f 2 ) * δ [ x 2 γ λ f 3 f 3 ( n Δ α + Δ β ) / f 2 ] * [ s s ] .
x 2 = γ λ f 3 + f 3 Δ β / f 2 ,
y 2 = λ f 1 f 3 Δ α / l 0 f 2 .

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