Abstract

A joint transform correlator may suffer from overlapping of the zero diffraction order of the output, which does not contain relevant information, and the correlation peaks that appear in the first diffraction orders if objects are not sufficiently separated. Such overlapping significantly reduces the signal-to-noise ratio of the identification process. We propose a novel approach based on code division multiplexing technique in which the contrast of the identification peaks is significantly enhanced. The approach does not include placing the two objects side by side but rather includes code multiplexing them. Moreover, the code division multiplexing technique allows the space–bandwidth product to be improved. Optical implementation results are given.

© 2006 Optical Society of America

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References

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  2. B. G. Boone, Signal Processing Using Optics: Fundamentals, Devices, Architectures, and Applications (Oxford U. Press, 1998).
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    [CrossRef]
  6. M. S. Alam, A. A. S Awwal, and M. A. Karim, "Improved correlation discrimination using joint Fourier transform optical correlator," Microwave Opt. Technol. Lett. 4, 103-106 (1991).
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    [CrossRef]
  10. M. S. Alam and M. A. Karim, "Fringe-adjusted joint transform correlator," Appl. Opt. 32, 4344-4350 (1993).
    [CrossRef] [PubMed]
  11. F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, Opt. Eng. 30, 1947-1957 (1991).
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2005 (1)

2003 (2)

1997 (1)

P. Purswosumarto and F. T. S. Yu, "Robustness of joint transform correlator versus VanderLugt correlator," Opt. Eng. 36, 2775-2780 (1997).
[CrossRef]

1996 (2)

1995 (1)

1993 (1)

1991 (4)

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

M. S. Alam, A. A. S Awwal, and M. A. Karim, "Improved correlation discrimination using joint Fourier transform optical correlator," Microwave Opt. Technol. Lett. 4, 103-106 (1991).
[CrossRef]

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, "Analysis of a joint transform correlator using a phse-only spatial light modulator," Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

D. Feng, H. Zhao, and S. Xia, "Amplitude-modulated JTC for improving correlation discrimination," Opt. Commun. 86, 260-264 (1991).
[CrossRef]

1988 (1)

1966 (1)

1964 (1)

A. VanderLugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).
[CrossRef]

Alam, M. S.

M. S. Alam and M. A. Karim, "Fringe-adjusted joint transform correlator," Appl. Opt. 32, 4344-4350 (1993).
[CrossRef] [PubMed]

M. S. Alam, A. A. S Awwal, and M. A. Karim, "Improved correlation discrimination using joint Fourier transform optical correlator," Microwave Opt. Technol. Lett. 4, 103-106 (1991).
[CrossRef]

Awwal, A. A. S

M. S. Alam, A. A. S Awwal, and M. A. Karim, "Improved correlation discrimination using joint Fourier transform optical correlator," Microwave Opt. Technol. Lett. 4, 103-106 (1991).
[CrossRef]

Barnes, T. H.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, "Analysis of a joint transform correlator using a phse-only spatial light modulator," Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

Boone, B. G.

B. G. Boone, Signal Processing Using Optics: Fundamentals, Devices, Architectures, and Applications (Oxford U. Press, 1998).

Eiju, T.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, "Analysis of a joint transform correlator using a phse-only spatial light modulator," Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

Erbach, P. S.

Feng, D.

D. Feng, H. Zhao, and S. Xia, "Amplitude-modulated JTC for improving correlation discrimination," Opt. Commun. 86, 260-264 (1991).
[CrossRef]

García, J.

Goodman, J. W.

Gregory, D. A.

Hammock, J. B.

Haskell, T. G.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, "Analysis of a joint transform correlator using a phse-only spatial light modulator," Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

Javidi, B.

Johnson, F. T. J.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, "Analysis of a joint transform correlator using a phse-only spatial light modulator," Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

Karim, M. A.

M. S. Alam and M. A. Karim, "Fringe-adjusted joint transform correlator," Appl. Opt. 32, 4344-4350 (1993).
[CrossRef] [PubMed]

M. S. Alam, A. A. S Awwal, and M. A. Karim, "Improved correlation discrimination using joint Fourier transform optical correlator," Microwave Opt. Technol. Lett. 4, 103-106 (1991).
[CrossRef]

Kuo, C.

Lu, G.

Matsuda, K.

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, "Analysis of a joint transform correlator using a phse-only spatial light modulator," Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

Mendlovic, D.

Purswosumarto, P.

P. Purswosumarto and F. T. S. Yu, "Robustness of joint transform correlator versus VanderLugt correlator," Opt. Eng. 36, 2775-2780 (1997).
[CrossRef]

Solomon, J.

VanderLugt, A.

A. VanderLugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).
[CrossRef]

Viterbi, A. J.

A. J. Viterbi, CDMA, Principles of Spread Spectrum Communication (Addison-Wesley, 1996).

Weaver, C. S.

Xia, S.

D. Feng, H. Zhao, and S. Xia, "Amplitude-modulated JTC for improving correlation discrimination," Opt. Commun. 86, 260-264 (1991).
[CrossRef]

Yu, F. T. S.

Zalevsky, Z.

Zhang, Z.

Zhao, H.

D. Feng, H. Zhao, and S. Xia, "Amplitude-modulated JTC for improving correlation discrimination," Opt. Commun. 86, 260-264 (1991).
[CrossRef]

Appl. Opt. (8)

IEEE Trans. Inf. Theory (1)

A. VanderLugt, "Signal detection by complex spatial filtering," IEEE Trans. Inf. Theory IT-10, 139-145 (1964).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

M. S. Alam, A. A. S Awwal, and M. A. Karim, "Improved correlation discrimination using joint Fourier transform optical correlator," Microwave Opt. Technol. Lett. 4, 103-106 (1991).
[CrossRef]

Opt. Commun. (1)

D. Feng, H. Zhao, and S. Xia, "Amplitude-modulated JTC for improving correlation discrimination," Opt. Commun. 86, 260-264 (1991).
[CrossRef]

Opt. Eng. (3)

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, "Analysis of a joint transform correlator using a phse-only spatial light modulator," Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

P. Purswosumarto and F. T. S. Yu, "Robustness of joint transform correlator versus VanderLugt correlator," Opt. Eng. 36, 2775-2780 (1997).
[CrossRef]

F. T. J. Johnson, T. H. Barnes, T. Eiju, T. G. Haskell, and K. Matsuda, Opt. Eng. 30, 1947-1957 (1991).
[CrossRef]

Opt. Lett. (1)

Other (3)

A. J. Viterbi, CDMA, Principles of Spread Spectrum Communication (Addison-Wesley, 1996).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

B. G. Boone, Signal Processing Using Optics: Fundamentals, Devices, Architectures, and Applications (Oxford U. Press, 1998).

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Figures (19)

Fig. 1
Fig. 1

(Color online) JTC system.

Fig. 2
Fig. 2

Masks that block right and left pixels, respectively.

Fig. 3
Fig. 3

(Color online) JTC-CDMA system.

Fig. 4
Fig. 4

(Color online) Cross section of the output.

Fig. 5
Fig. 5

(a) Airplane and (b) car input images for the simulation. (c) Joint multiplexed image.

Fig. 6
Fig. 6

(Color online) Correlation and its cross-section (airplane and car).

Fig. 7
Fig. 7

(Color online) Simulation results. (a) Autocorrelation and its cross section (even pixels, airplane and car). (b) Cross correlation and its cross section (odd pixels, airplane and car).

Fig. 8
Fig. 8

(a), (b) Two identical objects; (c) joint multiplexed image.

Fig. 9
Fig. 9

(Color online) Simulation results. (a) Autocorrelation and its cross section (even pixels, two airplanes). (b) Cross correlation and its cross section (odd pixels, two airplanes).

Fig. 10
Fig. 10

Input pattern for the regular JTC arrangement.

Fig. 11
Fig. 11

(Color online) Correlation ratio with half optics and digitally realized IFFT of regular JTC. The ratio between the autocorrelation and the cross correlation was 1:18.

Fig. 12
Fig. 12

All-optical experiment; correlation plane of regular JTC.

Fig. 13
Fig. 13

Input for JTC-CDMA.

Fig. 14
Fig. 14

Joint power spectrum of JTC-CDMA.

Fig. 15
Fig. 15

(Color online) (a) Cross-correlation output (odd pixels) with the 1D profile and (b) autocorrelation output (even pixels) with the 1D profile, both results with digital IFFT. (c) Autocorrelation output (even pixels) with the IFFT performed optically.

Fig. 16
Fig. 16

Input object with a small shift.

Fig. 17
Fig. 17

Joint spectrum of input object with a small shift.

Fig. 18
Fig. 18

(Color online) Correlation after digital IFFT and its cross section of the autocorrelation and cross-correlation peaks of the input object with a small shift.

Fig. 19
Fig. 19

Correlation plane after optical IFFT of the joint spectrum. The presented region corresponds to the spatial region around the diffraction order of −1, where the autocorrelation and cross-correlation peaks should appear.

Equations (11)

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JPS ( u , v ) = | F ( u , v ) exp ( 2 π i u x 0 λ f ) + G ( u , v ) × exp ( 2 π i u x 0 λ f ) | 2
= | F ( u , v ) | 2 + | G ( u , v ) | 2 + F * ( u , v ) × G ( u , v ) exp ( 2 π i u 2 x 0 λ f ) + F ( u , v ) × G ( u , v ) * exp ( 2 π i u 2 x 0 λ f ) ,
C JTC ( x , y ) = f ( x , y ) f ( x , y ) + g ( x , y ) g ( x , y ) + g ( x , y ) f ( x , y ) δ ( x 2 x 0 , y ) + f ( x , y ) g ( x , y ) δ ( x + 2 x 0 , y ) ,
t 1 ( x ) = n δ ( x n Δ x ) , t 2 ( x ) = n δ ( x n Δ x + Δ x 2 ) ,
s ( x ) = f ( x ) t 1 ( x ) + g ( x ) t 2 ( x ) .
C JTC - CDMA ( x ) = [ f ( x ) t 1 ( x ) ] [ f ( x ) t 1 ( x ) ]
+ [ g ( x ) t 2 ( x ) ] [ g ( x ) t 2 ( x ) ] + [ g ( x ) t 2 ( x ) ] [ f ( x ) t 1 ( x ) ] + [ f ( x ) t 1 ( x ) ] [ g ( x ) t 2 ( x ) ] .
[ f ( x ) t 1 ( x ) ] [ f ( x ) t 1 ( x ) ] = [ f ( x ) n δ ( x n Δ x ) ] [ f ( x ) n δ ( x n Δ x ) ]
= [ f ( x ) f ( x ) ] n δ ( x n Δ x ) ,
[ g ( x ) t 2 ( x ) ] [ g ( x ) t 2 ( x ) ] = [ g ( x ) n δ ( x n Δ x + Δ x 2 ) ] [ g ( x ) n δ ( x n Δ x + Δ x 2 ) ] = [ g ( x ) g ( x ) ] n δ ( x n Δ x ) .
[ g ( x ) t 2 ( x ) ] [ f ( x ) t 1 ( x ) ] = [ g ( x ) n δ ( x n Δ x + Δ x 2 ) ] [ f ( x ) n δ ( x n Δ x ) ] = [ g ( x ) f ( x ) ] × n δ ( x n Δ x + Δ x 2 ) .

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