Abstract

An optimization technique for the optical correlation detection process is proposed. The noise correlation output is suppressed by prewhitening its spectrum. Since the optimization operates on the noise instead of the signal spectrum, the system tolerance for size and orientation variation is not severely affected. Experimental illustrations are also presented.

© 1980 Optical Society of America

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References

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  1. A. Vander Lugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]
  2. A Vander Lugt, Opt. Acta 15, 1 (1968).
    [CrossRef]
  3. F. T. S. Yu, IEEE Trans. Inf. Theory IT-17, 524 (1971).
    [CrossRef]
  4. J. Thomas, Introduction to Statistical Communication Theory (Wiley, New York, 1969), Chap. 5.
  5. F. T. S. Yu, Introduction to Diffraction, Information Processing and Holography (MIT Press, Cambridge, Mass., 1973), Chap. 8.
  6. J. W. Goodman, Laser Speckle and Related Phenomena, Vol. 9, in Topics in Applied Physics, J. C. Dainty, Ed. (Springer, New York, 1975).
    [CrossRef]
  7. A. Tai, T. Cheng, F. T. S. Yu, Appl. Opt. 16, 2559 (1977).
    [CrossRef] [PubMed]
  8. M. Dymek, A. Tai, T. H. Chao, F. T. S. Yu, Appl. Opt. 19, 829 (1980).
    [CrossRef] [PubMed]
  9. H. Kato, J. W. Goodman, Appl. Opt. 14, 1813 (1975).
    [CrossRef] [PubMed]
  10. M. Schwartz, Information, Transmission, Modulation and Noise (McGraw-Hill, New York, 1970), Chap. 6-2.

1980 (1)

1977 (1)

1975 (1)

1971 (1)

F. T. S. Yu, IEEE Trans. Inf. Theory IT-17, 524 (1971).
[CrossRef]

1968 (1)

A Vander Lugt, Opt. Acta 15, 1 (1968).
[CrossRef]

1964 (1)

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

Chao, T. H.

Cheng, T.

Dymek, M.

Goodman, J. W.

H. Kato, J. W. Goodman, Appl. Opt. 14, 1813 (1975).
[CrossRef] [PubMed]

J. W. Goodman, Laser Speckle and Related Phenomena, Vol. 9, in Topics in Applied Physics, J. C. Dainty, Ed. (Springer, New York, 1975).
[CrossRef]

Kato, H.

Schwartz, M.

M. Schwartz, Information, Transmission, Modulation and Noise (McGraw-Hill, New York, 1970), Chap. 6-2.

Tai, A.

Thomas, J.

J. Thomas, Introduction to Statistical Communication Theory (Wiley, New York, 1969), Chap. 5.

Vander Lugt, A

A Vander Lugt, Opt. Acta 15, 1 (1968).
[CrossRef]

Vander Lugt, A.

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

Yu, F. T. S.

M. Dymek, A. Tai, T. H. Chao, F. T. S. Yu, Appl. Opt. 19, 829 (1980).
[CrossRef] [PubMed]

A. Tai, T. Cheng, F. T. S. Yu, Appl. Opt. 16, 2559 (1977).
[CrossRef] [PubMed]

F. T. S. Yu, IEEE Trans. Inf. Theory IT-17, 524 (1971).
[CrossRef]

F. T. S. Yu, Introduction to Diffraction, Information Processing and Holography (MIT Press, Cambridge, Mass., 1973), Chap. 8.

Appl. Opt. (3)

IEEE Trans. Inf. Theory (2)

F. T. S. Yu, IEEE Trans. Inf. Theory IT-17, 524 (1971).
[CrossRef]

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

Opt. Acta (1)

A Vander Lugt, Opt. Acta 15, 1 (1968).
[CrossRef]

Other (4)

J. Thomas, Introduction to Statistical Communication Theory (Wiley, New York, 1969), Chap. 5.

F. T. S. Yu, Introduction to Diffraction, Information Processing and Holography (MIT Press, Cambridge, Mass., 1973), Chap. 8.

J. W. Goodman, Laser Speckle and Related Phenomena, Vol. 9, in Topics in Applied Physics, J. C. Dainty, Ed. (Springer, New York, 1975).
[CrossRef]

M. Schwartz, Information, Transmission, Modulation and Noise (McGraw-Hill, New York, 1970), Chap. 6-2.

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Figures (7)

Fig. 1
Fig. 1

Optimum filtering process for colored noise.

Fig. 2
Fig. 2

Coherent optical system for generation of a whitening spatial filter: S, monochromatic point source; FD, film drive; L, transform lens; Ph, photographic plate.

Fig. 3
Fig. 3

Generation of a complex matched filter: S, monochromatic point source; L1 and L2 transform lenses; S(x,y), input signal; W(p,q), whitening filter; Ph, photographic plate; R, reference beam.

Fig. 4
Fig. 4

Optimized correlation detection system: S, monochromatic point source; L1, L2, and L3, transform lenses; W(p,q), whitening filter; H(p,q), matched filter.

Fig. 5
Fig. 5

Input Chinese character embedded in additive speckle noise.

Fig. 6
Fig. 6

Output correlation detection without use of whitening filter: (a) autocorrelation of input signal; (b) output correlation of the signal embedded in additive speckle noise.

Fig. 7
Fig. 7

Output correlation detection with use of whitening filter: (a) autocorrelation of input signal; (b) output correlation of the signal embedded in additive speckle noise.

Equations (13)

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S 0 ( x , y ) = S ( p , q ) H ( p , q ) exp [ i ( p x + q y ) ] dpdq ,
N 0 ( p , q ) = N ( p , q ) | H ( p , q ) | 2 .
| S 0 ( x , y ) | 2 = | S ( p , q ) H ( p , q ) exp i ( p x + q y ) dpdq | 2 ,
N ̅ 0 = N 0 ( p , q ) dpdq = | H ( p , q ) | 2 N ( p , q ) dpdq .
| S 0 ( x , y ) | 2 N ̅ 0 = | S ( p , q ) | 2 N ( p , q ) dpdq .
H ( p , q ) = K S * ( p , q ) N ( p , q ) ,
H ( p , q ) = [ K S * ( p , q ) ] / N = K S * ( p , q ) ,
N ( p , q ) 1 M m = 1 m = M | X / 2 X / 2 Y / 2 Y / 2 n ( x , y ) × exp [ i ( p x + q y ) ] dxdy | 2 .
T A = E γ / 2 ,
W ( p , q ) = K [ 0 T | n ( p , q ; t ) | 2 d t ] γ / 2 K N ( p , q ) , for γ = 1 ,
E ( p , q ) = K S ( p , q ) N ( p , q ) + exp ( ikp sin θ ) .
H ( p , q ) = K 1 + | K S ( p , q ) N ( p , q ) | 2 + K S ( p , q ) N ( p , q ) exp ( ikp sin θ ) + K S * ( p , q ) N ( p , q ) exp ( ikp sin θ ) ,
Ω ( x , y ) = F 1 [ | K S ( p , q ) | 2 N ( p , q ) ] + F 1 [ K S * ( p , q ) N ( p , q ) N ( p , q ) ] .

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