Abstract

The use of coded waveforms in space-variant optical signal processors using coordinate transformations is considered. It is shown that nonlinear transmitted coded signals must be used with such a processor and that this results in novel waveform design and system approaches for radar and communications.

© 1979 Optical Society of America

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References

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  1. Optical Information Processing—Real-Time Devices and Novel Techniques, Vol. 83 of SPIE Seminar Proceedings (Society of Photo-Optical Instrumentation Engineers, Bellingham, Washington, 1976).
  2. G. M. Robbins, T. S. Huang, Proc. IEEE 60, 862 (1972).
    [CrossRef]
  3. A. Sawchuck, J. Opt. Soc. Am. 64, 138 (1974).
    [CrossRef]
  4. D. Casasent, D. Psaltis, in Proceedings of the Electro-Optical Systems Design Conference (Milton S. Kiver, Chicago, 1975), p. 38.
  5. D. Casasent, D. Psaltis, Opt. Commun. 17, 59 (1976).
    [CrossRef]
  6. D. Casasent, D. Psaltis, Proc. IEEE 65, 77 (1977).
    [CrossRef]
  7. D. Psaltis, D. Casasent, Appl. Opt. 16, 2288 (1977).
    [CrossRef] [PubMed]
  8. D. Casasent, D. Psaltis, Appl. Opt. 15, 2015 (1976).
    [CrossRef] [PubMed]
  9. D. Casasent, M. Kraus, Opt. Commun. 19, 212 (1976).
    [CrossRef]
  10. O. Bryngdahl, J. Opt. Soc. Am. 64, 1092 (1974).
    [CrossRef]
  11. D. Casasent, C. Szczutkowski, Proc. SPIE 83, 91 (1976).
  12. D. Casasent, C. Szczutkowski, Opt. Commun. 19, 217 (1976).
    [CrossRef]
  13. J. W. Goodman, Proc. IEEE 65, 29 (1977).
    [CrossRef]
  14. J. W. Goodman, P. Kellman, E. W. Hansen, Appl. Opt. 16, 733 (1977).
    [CrossRef] [PubMed]
  15. P. Kellman, J. W. Goodman, Appl. Opt. 16, 2609 (1977).
    [CrossRef] [PubMed]
  16. C. E. Cook, M. Bernfeld, Radar Signals (Academic, New York, 1967).
  17. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 753.

1977 (5)

1976 (5)

D. Casasent, M. Kraus, Opt. Commun. 19, 212 (1976).
[CrossRef]

D. Casasent, D. Psaltis, Appl. Opt. 15, 2015 (1976).
[CrossRef] [PubMed]

D. Casasent, C. Szczutkowski, Proc. SPIE 83, 91 (1976).

D. Casasent, C. Szczutkowski, Opt. Commun. 19, 217 (1976).
[CrossRef]

D. Casasent, D. Psaltis, Opt. Commun. 17, 59 (1976).
[CrossRef]

1974 (2)

1972 (1)

G. M. Robbins, T. S. Huang, Proc. IEEE 60, 862 (1972).
[CrossRef]

Bernfeld, M.

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

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 753.

Bryngdahl, O.

Casasent, D.

D. Casasent, D. Psaltis, Proc. IEEE 65, 77 (1977).
[CrossRef]

D. Psaltis, D. Casasent, Appl. Opt. 16, 2288 (1977).
[CrossRef] [PubMed]

D. Casasent, D. Psaltis, Opt. Commun. 17, 59 (1976).
[CrossRef]

D. Casasent, M. Kraus, Opt. Commun. 19, 212 (1976).
[CrossRef]

D. Casasent, C. Szczutkowski, Proc. SPIE 83, 91 (1976).

D. Casasent, C. Szczutkowski, Opt. Commun. 19, 217 (1976).
[CrossRef]

D. Casasent, D. Psaltis, Appl. Opt. 15, 2015 (1976).
[CrossRef] [PubMed]

D. Casasent, D. Psaltis, in Proceedings of the Electro-Optical Systems Design Conference (Milton S. Kiver, Chicago, 1975), p. 38.

Cook, C. E.

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

Goodman, J. W.

Hansen, E. W.

Huang, T. S.

G. M. Robbins, T. S. Huang, Proc. IEEE 60, 862 (1972).
[CrossRef]

Kellman, P.

Kraus, M.

D. Casasent, M. Kraus, Opt. Commun. 19, 212 (1976).
[CrossRef]

Psaltis, D.

D. Psaltis, D. Casasent, Appl. Opt. 16, 2288 (1977).
[CrossRef] [PubMed]

D. Casasent, D. Psaltis, Proc. IEEE 65, 77 (1977).
[CrossRef]

D. Casasent, D. Psaltis, Appl. Opt. 15, 2015 (1976).
[CrossRef] [PubMed]

D. Casasent, D. Psaltis, Opt. Commun. 17, 59 (1976).
[CrossRef]

D. Casasent, D. Psaltis, in Proceedings of the Electro-Optical Systems Design Conference (Milton S. Kiver, Chicago, 1975), p. 38.

Robbins, G. M.

G. M. Robbins, T. S. Huang, Proc. IEEE 60, 862 (1972).
[CrossRef]

Sawchuck, A.

Szczutkowski, C.

D. Casasent, C. Szczutkowski, Proc. SPIE 83, 91 (1976).

D. Casasent, C. Szczutkowski, Opt. Commun. 19, 217 (1976).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 753.

Appl. Opt. (4)

J. Opt. Soc. Am. (2)

Opt. Commun. (3)

D. Casasent, M. Kraus, Opt. Commun. 19, 212 (1976).
[CrossRef]

D. Casasent, D. Psaltis, Opt. Commun. 17, 59 (1976).
[CrossRef]

D. Casasent, C. Szczutkowski, Opt. Commun. 19, 217 (1976).
[CrossRef]

Proc. IEEE (3)

J. W. Goodman, Proc. IEEE 65, 29 (1977).
[CrossRef]

D. Casasent, D. Psaltis, Proc. IEEE 65, 77 (1977).
[CrossRef]

G. M. Robbins, T. S. Huang, Proc. IEEE 60, 862 (1972).
[CrossRef]

Proc. SPIE (1)

D. Casasent, C. Szczutkowski, Proc. SPIE 83, 91 (1976).

Other (4)

D. Casasent, D. Psaltis, in Proceedings of the Electro-Optical Systems Design Conference (Milton S. Kiver, Chicago, 1975), p. 38.

Optical Information Processing—Real-Time Devices and Novel Techniques, Vol. 83 of SPIE Seminar Proceedings (Society of Photo-Optical Instrumentation Engineers, Bellingham, Washington, 1976).

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

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 753.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of a space-variant, Doppler-invariant optical signal processor.

Fig. 2
Fig. 2

Cross-sectional scan of the optically produced correlation of a nonlinear coordinate-transformed Barker-coded waveform: (a) autocorrelation, (b) jammer.

Fig. 3
Fig. 3

Block diagram of space-variant optical-ambiguity-function processor for use with coded waveforms.

Fig. 4
Fig. 4

Schematic diagram of a single-channel space-variant optical processor to calculate the 2-D ambiguity function for coded waveforms.

Equations (12)

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

f ( x ) = f [ g ( x , a ) ] ,
t = h - 1 ( x ) = d t 0 d a - x g / x g / a d x
R ( t ^ ) = f 1 ( t ) f 1 ( t ) = f 1 ( t ) f 1 ( t ) * δ ( t ^ - t 0 ) ,
f ( t ) = cos [ ω 0 t + ϕ ( t ) ] = a ( t ) cos ( ω 0 t ) ,
a n ( t ) = exp [ j ϕ n ( t ) ] = + 1 , + 1 , + 1 , + 1 , + 1 , - 1 , - 1 , + 1 , + 1 , - 1 , + 1 , - 1 , + 1.
f ( exp t ) = f 1 ( t ) = cos [ ω 0 exp t + ϕ ( exp t ) ] .
R ( t ^ ) = f ( exp t ) f ( exp t ) .
f t ( t ) = cos [ ω 0 ln ( t + t 0 ) + ϕ [ ln ( t + t 0 ) ] }
t = ln ( t + t 0 )
t = exp x - t ^ ,
f t l ( t ) = f t ( e x - t ^ ) = f 1 ( t ^ , x ) .
R ( t ^ , x ^ ) = f 1 ( t ^ , x ) f ( x ) ,

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