Abstract

A simple real-time coherent optical processor is investigated. The processor uses a filter mask upon which is recorded the Fresnel field of the signal replica. Target range-Doppler information is obtained by observing the time and position of the output. A distinguishing feature of the processor is that for the ordinary PCW pulse, these output quantities are correlated, albeit weakly, in much the same fashion as the range-Doppler estimates associated with the output of the linear FM correlator. This interesting property is shown to depend on a single optical parameter. A modified optical configuration that enables a greater practical exploitation of this property is suggested. To obtain unbiased target range estimates, two output terms must be observed, but the range estimate thus obtained has a lower variance than the estimate obtained from either output.

© 1971 Optical Society of America

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References

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  1. L. J. Cutrona et al., IRE Trans. Inform. Theory IT-6, 386 (1960).
    [CrossRef]
  2. A. B. Vander Lugt, IEEE Trans. Inform. Theory IT-10, 139 (1964).
    [CrossRef]
  3. E. B. Felstead, IEEE Trans. Aero and Electron. Syst. AES-3, 907 (1967).
    [CrossRef]
  4. G. Meltz, W. T. Maloney, Appl. Opt. 7, 10, 2091 (1968).
    [CrossRef]
  5. L. B. Lambert, Modern Radar Analysis, Valuation and Design, R. S. Berkowitz, Ed. (Wiley, New York, 1965), Chap. 3, p. 245–273.
  6. M. Arm et al., IEEE Proc. 52, 842 (1964).
    [CrossRef]
  7. L. Slobodin, IEEE Proc. 51, 1782 (1963).
    [CrossRef]
  8. As elsewhere in this paper, only relative magnitudes (or intensities) are of interest. Constants, unimportant phase factors, and the like are freely, and without warning to the reader, dropped.
  9. A. Kozma, D. L. Kelly, Appl. Opt. 4, 4, 387 (1965).
    [CrossRef]
  10. L. B. Lambert, Tech. Report T-1/321, Elec. Res. Labs. of Columbia University, New York (1965).
  11. T. H. Glisson, C. I. Black, A. P. Sage, IEEE Trans. Aero. and Electron. Syst. AES-6, 37 (1970).
    [CrossRef]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 59.
  13. D. Treves, H. Stark, M. Sayar, Israel J. Tech. 9, 289 (1971).

1971 (1)

D. Treves, H. Stark, M. Sayar, Israel J. Tech. 9, 289 (1971).

1970 (1)

T. H. Glisson, C. I. Black, A. P. Sage, IEEE Trans. Aero. and Electron. Syst. AES-6, 37 (1970).
[CrossRef]

1968 (1)

G. Meltz, W. T. Maloney, Appl. Opt. 7, 10, 2091 (1968).
[CrossRef]

1967 (1)

E. B. Felstead, IEEE Trans. Aero and Electron. Syst. AES-3, 907 (1967).
[CrossRef]

1965 (1)

A. Kozma, D. L. Kelly, Appl. Opt. 4, 4, 387 (1965).
[CrossRef]

1964 (2)

M. Arm et al., IEEE Proc. 52, 842 (1964).
[CrossRef]

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

1963 (1)

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

1960 (1)

L. J. Cutrona et al., IRE Trans. Inform. Theory IT-6, 386 (1960).
[CrossRef]

Arm, M.

M. Arm et al., IEEE Proc. 52, 842 (1964).
[CrossRef]

Black, C. I.

T. H. Glisson, C. I. Black, A. P. Sage, IEEE Trans. Aero. and Electron. Syst. AES-6, 37 (1970).
[CrossRef]

Cutrona, L. J.

L. J. Cutrona et al., IRE Trans. Inform. Theory IT-6, 386 (1960).
[CrossRef]

Felstead, E. B.

E. B. Felstead, IEEE Trans. Aero and Electron. Syst. AES-3, 907 (1967).
[CrossRef]

Glisson, T. H.

T. H. Glisson, C. I. Black, A. P. Sage, IEEE Trans. Aero. and Electron. Syst. AES-6, 37 (1970).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 59.

Kelly, D. L.

A. Kozma, D. L. Kelly, Appl. Opt. 4, 4, 387 (1965).
[CrossRef]

Kozma, A.

A. Kozma, D. L. Kelly, Appl. Opt. 4, 4, 387 (1965).
[CrossRef]

Lambert, L. B.

L. B. Lambert, Tech. Report T-1/321, Elec. Res. Labs. of Columbia University, New York (1965).

L. B. Lambert, Modern Radar Analysis, Valuation and Design, R. S. Berkowitz, Ed. (Wiley, New York, 1965), Chap. 3, p. 245–273.

Maloney, W. T.

G. Meltz, W. T. Maloney, Appl. Opt. 7, 10, 2091 (1968).
[CrossRef]

Meltz, G.

G. Meltz, W. T. Maloney, Appl. Opt. 7, 10, 2091 (1968).
[CrossRef]

Sage, A. P.

T. H. Glisson, C. I. Black, A. P. Sage, IEEE Trans. Aero. and Electron. Syst. AES-6, 37 (1970).
[CrossRef]

Sayar, M.

D. Treves, H. Stark, M. Sayar, Israel J. Tech. 9, 289 (1971).

Slobodin, L.

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

Stark, H.

D. Treves, H. Stark, M. Sayar, Israel J. Tech. 9, 289 (1971).

Treves, D.

D. Treves, H. Stark, M. Sayar, Israel J. Tech. 9, 289 (1971).

Vander Lugt, A. B.

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

Appl. Opt. (2)

G. Meltz, W. T. Maloney, Appl. Opt. 7, 10, 2091 (1968).
[CrossRef]

A. Kozma, D. L. Kelly, Appl. Opt. 4, 4, 387 (1965).
[CrossRef]

IEEE Proc. (2)

M. Arm et al., IEEE Proc. 52, 842 (1964).
[CrossRef]

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

IEEE Trans. Aero and Electron. Syst. (1)

E. B. Felstead, IEEE Trans. Aero and Electron. Syst. AES-3, 907 (1967).
[CrossRef]

IEEE Trans. Aero. and Electron. Syst. (1)

T. H. Glisson, C. I. Black, A. P. Sage, IEEE Trans. Aero. and Electron. Syst. AES-6, 37 (1970).
[CrossRef]

IEEE Trans. Inform. Theory (1)

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

IRE Trans. Inform. Theory (1)

L. J. Cutrona et al., IRE Trans. Inform. Theory IT-6, 386 (1960).
[CrossRef]

Israel J. Tech. (1)

D. Treves, H. Stark, M. Sayar, Israel J. Tech. 9, 289 (1971).

Other (4)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 59.

L. B. Lambert, Modern Radar Analysis, Valuation and Design, R. S. Berkowitz, Ed. (Wiley, New York, 1965), Chap. 3, p. 245–273.

As elsewhere in this paper, only relative magnitudes (or intensities) are of interest. Constants, unimportant phase factors, and the like are freely, and without warning to the reader, dropped.

L. B. Lambert, Tech. Report T-1/321, Elec. Res. Labs. of Columbia University, New York (1965).

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Figures (6)

Fig. 1
Fig. 1

Recording of filter mask.

Fig. 2
Fig. 2

Static filtering configuration.

Fig. 3
Fig. 3

Dynamical processing configuration.

Fig. 4
Fig. 4

A 3-dB contour of output.

Fig. 5
Fig. 5

Spot size variation with k when target range is known.

Fig. 6
Fig. 6

Modified signal processor.

Equations (32)

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A ( ξ ) = A 0 exp ( - j 2 π α ξ ) ,
I f ( ξ ) = A 0 exp ( - j 2 π α ξ ) + f ( ξ ) 2 = A 0 2 + f ( ξ ) 2 + A 0 * exp ( j 2 π α ξ ) f ( ξ ) + A 0 exp ( - j 2 π α ξ ) f * ( ξ ) ,
f ( ξ ) 1 λ z 0 - r ( x ) exp [ j π λ z 0 ( x - ξ ) 2 ] d x .
( z - f ) / ( f z - d z + d f ) = ( z 0 - z 0 ) / z 0 z 0
U ( ζ ) = | - r * ( x ) s ( x - k ζ ) exp ( - j 2 π λ f ζ x ) d x |
= | - R * ( u ) S ( u + ζ λ f ) exp ( - j 2 π u k ζ ) d u | U ( ζ ) ,
U ( ζ ) = | + r ( x - - k ζ ) r * ( x ) exp ( - j 2 π λ f x ζ ) d x | ,
U ( ζ , t ) | ζ = 0 t = t 0 = - + | r ( x ) | 2 d x .
U ( ζ , t ) = | s ( x - S t - k ζ ) r * ( x ) exp ( - j 2 π λ f x ζ ) d x | .
T ( x , t ) = [ 1 + K s ( x - S t ) ] rect ( x / D ) ,
r ( x , ν 0 ) = rect ( x / δ ) cos 2 π ( ν 0 / S ) x ,
s ( x , t ) = r ( x - S t , ν ) rect ( x / D ) = rect [ ( x - S t ) / δ ] cos ( 2 π ν / S ) ( x - S t ) rect ( x / D ) ,
U + 1 , - 1 ( ζ , t ) = | ( 1 - S t + k ζ δ ) sinc [ δ ( v d S ± ζ λ f ) × ( 1 - S t + k ζ δ ) ] |
U 2 , - 2 ( ζ , t ) = | ( 1 - S t + k ζ δ ) sinc [ δ ( 2 ν 0 + ν d S ± ζ λ f ) × ( 1 - S t + k ζ δ ) ] | S t + k ζ < δ ,             t < [ ( D - δ ) / 2 S ] , δ < D ,
U 1 ( ζ , t ) :             peak at ζ = ζ 1 λ f ν d / S and t = t 1 - λ f ν d k / S 2 ,
U - 1 ( ζ , t ) :             peak at ζ = ζ - 1 - λ f ν d / S and t = t - 1 λ f ν d k / S 2 ,
U 2 ( ζ , t ) :             peak at ζ = ζ 2 [ λ f ( 2 ν 0 + ν d ) / S ] and t = t 2 ( - λ f k / S 2 ) ( 2 ν 0 + ν d ) ,
U - 2 ( ζ , t ) :             peak at ζ = ζ - 2 [ - λ f ( 2 ν 0 + ν d ) / S ] and t = t - 2 ( λ f k / S 2 ) ( 2 ν 0 + ν d ) ,
ζ ˜ = ζ - ( λ f ν d / S ) , t ˜ = t + ( k λ f ν d / S 2 ) .
a t ˜ 2 + b t ˜ ζ ˜ + c ζ ˜ 2 = 1 ,
a = 11.1 S 2 / δ 2 , b = 22.2 ( S k / δ 2 ) , c = ( 11.1 / δ 2 ) k 2 + ( 5.16 δ 2 / ( λ f ) 2 ] .
Δ ν = ( S / λ f ) Δ ζ
Δ ζ = Δ ζ ˜ = 2 δ / { 11.1 k 2 + [ 5.16 δ 4 / ( λ f ) 2 ] } 1 2
Δ ( k , δ ) Δ ν Δ t = ( 1.2 / λ f ) δ 2 / { 11.1 k 2 + [ 5.16 δ 4 / ( λ f ) 2 ] } 1 2 ,
[ t ˜ 2 / ( 0.3 τ ) 2 ] + [ ν ˜ 2 / ( 0.44 / τ ) 2 ] = 1 ,
T = ( 1 / 2 ) ( T 1 + T - 1 ) ,
var T = ( 1 / 4 ) ( var T 1 + var T - 1 ) = ( 1 / 2 ) var T 1 ,
R ( β ) R * [ ( ζ / λ f ) - β ] exp ( - j 2 π k β ζ ) d β
U ( ζ , t ) = | - s ( x - S t - k ζ ) r * ( x ) exp [ - j ( 2 π / λ f 2 ) x ζ ] d x | ,
k = k 2 ( 1 - k 1 ) ,
ζ " = ( 1 - k 1 ) ζ ,
2.15 k 2 2 ( λ f 2 / δ 2 ) 2 + k 1 2 - 2 k 1 = 3 ,

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