Abstract

Theory and practice of an optical ambiguity processor based on space-variant joint Fourier transform holography are presented. The approach evolves from the joint Fourier transform optical correlator concept, which represents a different technique of implementing the matched filter correlator concept advanced by Vander Lugt. Experimental demonstration using photographic film for signal recording and the thermoplastic device for hologram recording will be reported.

© 1980 Optical Society of America

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References

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  1. L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, IRE Trans. Inf. Theory IT-6, 386 (1960).
    [Crossref]
  2. K. Preston, Coherent Optical Computers (McGraw-Hill, New York, 1972).
  3. R. Said, D. Cooper, Inst. Electr. Eng. Proc. 120, 423 (1973).
    [Crossref]
  4. R. J. Marks, J. F. Walkup, T. F. Krile, Appl. Opt. 16, 746 (1977).
    [Crossref]
  5. C. S. Weaver, J. W. Goodman, Appl. Opt. 5, 1248 (1966).
    [Crossref] [PubMed]
  6. D. Casasent, Electro Opt. Syst. Des. 10, 26 (1978).
  7. T. C. Lee, J. Rebholz, P. Tamura, Opt. Lett. 4, 121 (1979).
    [Crossref] [PubMed]
  8. J. C. Urbach, R. W. Meier, Appl. Opt. 5, 666 (1966).
    [Crossref] [PubMed]
  9. T. C. Lee, Appl. Opt. 13, 888 (1974).
    [Crossref] [PubMed]
  10. C. E. Cook, M. Bernfield, Radar Signals (Academic, New York, 1967).
  11. C. E. Curie, F. G. Gebhardt, G. C. Orbits, Proc. Soc. Photo Opt. Instrum. Eng. 128, 217 (1977).
  12. W. S. Colburn, B. J. Chang, Opt. Eng. 17, 334 (1978).
  13. W. P. Bleha et al., Opt. Eng. 17, 371 (1978).
  14. J. Grinberg et al., IEEE Trans. Electron Devices ED-22, 775 (1975).
    [Crossref]
  15. J. P. Huignard, J. P. Herriau, Appl. Opt. 16, 1807 (1977).
    [Crossref] [PubMed]
  16. J. P. Huignard et al., Opt. Lett. 4, 21 (1979).
    [Crossref] [PubMed]

1979 (2)

1978 (3)

D. Casasent, Electro Opt. Syst. Des. 10, 26 (1978).

W. S. Colburn, B. J. Chang, Opt. Eng. 17, 334 (1978).

W. P. Bleha et al., Opt. Eng. 17, 371 (1978).

1977 (3)

1975 (1)

J. Grinberg et al., IEEE Trans. Electron Devices ED-22, 775 (1975).
[Crossref]

1974 (1)

1973 (1)

R. Said, D. Cooper, Inst. Electr. Eng. Proc. 120, 423 (1973).
[Crossref]

1966 (2)

1960 (1)

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

Bernfield, M.

C. E. Cook, M. Bernfield, Radar Signals (Academic, New York, 1967).

Bleha, W. P.

W. P. Bleha et al., Opt. Eng. 17, 371 (1978).

Casasent, D.

D. Casasent, Electro Opt. Syst. Des. 10, 26 (1978).

Chang, B. J.

W. S. Colburn, B. J. Chang, Opt. Eng. 17, 334 (1978).

Colburn, W. S.

W. S. Colburn, B. J. Chang, Opt. Eng. 17, 334 (1978).

Cook, C. E.

C. E. Cook, M. Bernfield, Radar Signals (Academic, New York, 1967).

Cooper, D.

R. Said, D. Cooper, Inst. Electr. Eng. Proc. 120, 423 (1973).
[Crossref]

Curie, C. E.

C. E. Curie, F. G. Gebhardt, G. C. Orbits, Proc. Soc. Photo Opt. Instrum. Eng. 128, 217 (1977).

Cutrona, L. J.

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

Gebhardt, F. G.

C. E. Curie, F. G. Gebhardt, G. C. Orbits, Proc. Soc. Photo Opt. Instrum. Eng. 128, 217 (1977).

Goodman, J. W.

Grinberg, J.

J. Grinberg et al., IEEE Trans. Electron Devices ED-22, 775 (1975).
[Crossref]

Herriau, J. P.

Huignard, J. P.

Krile, T. F.

Lee, T. C.

Leith, E. N.

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

Marks, R. J.

Meier, R. W.

Orbits, G. C.

C. E. Curie, F. G. Gebhardt, G. C. Orbits, Proc. Soc. Photo Opt. Instrum. Eng. 128, 217 (1977).

Palermo, C. J.

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

Porcello, L. J.

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

Preston, K.

K. Preston, Coherent Optical Computers (McGraw-Hill, New York, 1972).

Rebholz, J.

Said, R.

R. Said, D. Cooper, Inst. Electr. Eng. Proc. 120, 423 (1973).
[Crossref]

Tamura, P.

Urbach, J. C.

Walkup, J. F.

Weaver, C. S.

Appl. Opt. (5)

Electro Opt. Syst. Des. (1)

D. Casasent, Electro Opt. Syst. Des. 10, 26 (1978).

IEEE Trans. Electron Devices (1)

J. Grinberg et al., IEEE Trans. Electron Devices ED-22, 775 (1975).
[Crossref]

Inst. Electr. Eng. Proc. (1)

R. Said, D. Cooper, Inst. Electr. Eng. Proc. 120, 423 (1973).
[Crossref]

IRE Trans. Inf. Theory (1)

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

Opt. Eng. (2)

W. S. Colburn, B. J. Chang, Opt. Eng. 17, 334 (1978).

W. P. Bleha et al., Opt. Eng. 17, 371 (1978).

Opt. Lett. (2)

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

C. E. Curie, F. G. Gebhardt, G. C. Orbits, Proc. Soc. Photo Opt. Instrum. Eng. 128, 217 (1977).

Other (2)

K. Preston, Coherent Optical Computers (McGraw-Hill, New York, 1972).

C. E. Cook, M. Bernfield, Radar Signals (Academic, New York, 1967).

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Figures (6)

Fig. 1
Fig. 1

Two approaches to optical ambiguity processing.

Fig. 2
Fig. 2

Joint Fourier transform processor: (A) recording optics; (B) readout optics.

Fig. 3
Fig. 3

Frequency plot of V-FM signal on carrier.

Fig. 4
Fig. 4

Ambiguity map for a V-FM signal with a time–bandwidth product of 30.

Fig. 5
Fig. 5

Profile of a diagonal line of the map in Fig. 4 compared with a calculated profile.

Fig. 6
Fig. 6

Joint Fourier transform ambiguity processor using 1-D SLMs.

Tables (1)

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Table I Input SLM Comparison

Equations (8)

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χ ( τ , ν ) = - f 1 ( t ) f 2 * ( t - τ ) exp ( i 2 π ν t ) d t .
g 1 ( t , ν D ) = f 1 ( t ) exp ( - i 2 π ν D t ) , g 2 ( t , ν D ) = f 2 ( t ) ,
χ ( τ , ν D ) = - g 1 ( t , ν D ) g 2 * ( t - τ , ν D ) d t .
G 1 ( ν , ν D ) G 2 * ( ν , ν D ) + c . c . ,
Re { exp [ i 2 π ( ν c + α t ) t ] } .
Re { exp [ i 2 π ( ν c + α t ) t ] } + B .
Re { exp [ i 2 π ( ν c + α t + n Δ ν ) t ] } + B ,
SBW 4 F / tan θ ,

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