Abstract

A simple model has been developed to explain the loss of correlation intensity in a joint transform architecture when the reference and test scenes have unequal illumination.

© 1989 Optical Society of America

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References

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  1. C. S. Weaver, J. W. Goodman, “A Technique for Optically Convolving Two Functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  2. F. T. S. Yu, J. E. Ludman, “Microcomputer Based Programmable Optical Correlator for Automatic Pattern Recognition and Identification,” Opt. Lett. 11, 395–397 (1986).
    [CrossRef] [PubMed]
  3. X. J. Lu, “Real-Time Optical VanderLugt and Joint Transform Correlation Systems,” Ph.D. Dissertation, Pennsylvania State University (Aug.1988).
  4. S. H. Lee, “Coherent Optical Processing,” in Optical Information Processing, S. H. Lee, Ed. (Springer-Verlag, New York, 1981), pp. 61–62.

1986 (1)

1966 (1)

Appl. Opt. (1)

Opt. Lett. (1)

Other (2)

X. J. Lu, “Real-Time Optical VanderLugt and Joint Transform Correlation Systems,” Ph.D. Dissertation, Pennsylvania State University (Aug.1988).

S. H. Lee, “Coherent Optical Processing,” in Optical Information Processing, S. H. Lee, Ed. (Springer-Verlag, New York, 1981), pp. 61–62.

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Figures (4)

Fig. 1
Fig. 1

Standard joint transform architecture. The input modulator is SLM1, and the filter modulator is SLM2.

Fig. 2
Fig. 2

Plot of Eq. (13) for a broad range of intensity ratios. This represents how the detected joint transform correlation signal should vary as the ratio of the intensity of the reference scene to the intensity of the test scene changes.

Fig. 3
Fig. 3

Reference and test scenes used in the experiment.

Fig. 4
Fig. 4

Plot of Eq. (13) for the intensity ratios used in the experiments. Points represent experimental data.

Equations (13)

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t ( x , y ) = A T h ( x , y + b ) + A R h ( x , y b ) ,
F { t ( x , y ) } = A T H exp ( j 2 π Ω y b ) + A R H exp ( j 2 π Ω y b ) .
U ( X f , Y f ) | F { t ( x , y ) } | 2
U ( X f , Y f ) A T 2 | H | 2 + A R 2 | H | 2 + A R A T | H | 2 [ exp ( j 4 π Ω y b ) + exp ( j 4 π Ω y b ) ]
| H | 2 { A T 2 + A R 2 + 2 A R A T cos ( 4 π Ω y b ) } .
U N ( X f , y f ) = | H | 2 | H M | 2 ( A R + A T ) 2 × { A T 2 + A R 2 + 2 A R A T cos ( 4 π Ω y b ) } ,
C J = 2 A R A T | H M | 2 ( A R + A T ) 2 F { | H | 2 cos ( 4 π Ω y b ) } .
R = A R A T ( A R + A T ) 2 .
R = ( A R A T ) ( A R A T + 1 ) 2 .
I J ( A R A T ) 2 ( A R A T + 1 ) 4 .
I R A R 2 ,
I T A T 2 .
I J ( I R I T ) ( I R I T + 1 ) 4 .

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