Abstract

A novel reference phase-encoded joint transform correlation technique is proposed for efficient multiple-target detection. The proposed method employs phase encoding for the reference image and nonlinear Fourier plane apodization to optimize the detection performance. Existing joint transform correlators (JTC’s) require multistep on-line processing to eliminate the false alarms. The proposed reference phase-encoded JTC overcomes false-target detection by eliminating the false correlation peaks while alleviating the effects of noise and other artifacts in just one step, thus ensuring higher processing speed. This technique yields only one peak per target instead of a pair of peaks produced by alternate JTC’s. An all-optical implementation for the reference phase-encoded JTC technique is proposed, and computer simulation results are presented.

© 2001 Optical Society of America

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  1. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  2. C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  3. F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
    [CrossRef]
  4. F. T. S. Yu, Q. W. Song, Y. S. Cheng, D. A. Gregory, “Comparison of detection efficiencies for VanderLugt and joint transform correlators,” Appl. Opt. 29, 225–232 (1990).
    [CrossRef] [PubMed]
  5. B. Javidi, C. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
    [CrossRef] [PubMed]
  6. B. Javidi, S. F. Odeh, “Multiple object identification by bipolar joint transform correlation,” Opt. Eng. 27, 295–300 (1988).
  7. B. Javidi, J. Li, A. H. Fazlollahi, J. Horner, “Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination,” Appl. Opt. 24, 886–896 (1995).
    [CrossRef]
  8. M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint transform correlator,” Opt. Laser Technol. 24, 45–50 (1992).
    [CrossRef]
  9. W. B. Hahn, D. L. Flannery, “Design elements of a binary joint transform correlator and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
    [CrossRef]
  10. F. T. S. Yu, F. Cheng, T. Nagata, D. A. Gregory, “Effects of fringe binarization of multi-object joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
    [CrossRef] [PubMed]
  11. M. S. Alam, M. A. Karim, “Fringe-adjusted joint transform correlator,” Appl. Opt. 32, 4344–4350 (1993).
    [CrossRef] [PubMed]
  12. M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3216 (1995).
    [CrossRef]
  13. M. S. Alam, M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
    [CrossRef]
  14. M. Schönleber, G. Cedilnik, H. J. Tisiani, “Joint transform correlator subtracting a modified Fourier spectrum,” Appl. Opt. 34, 7532–7537 (1995).
    [CrossRef] [PubMed]
  15. R. K. Wang, L. Shang, C. R. Chatwin, “Modified fringe-adjusted joint transform correlation subtracting to accommodate noise in the input scene,” Appl. Opt. 35, 286–296 (1996).
    [CrossRef] [PubMed]
  16. F. T. S. Yu, C. Li, S. Yin, “Comparison of detection efficiency for nonzero-order and conventional joint transform correlation,” Opt. Eng. 28, 52–57 (1998).
    [CrossRef]
  17. M. S. Alam, M. A. Karim, “Joint transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
    [CrossRef] [PubMed]
  18. M. S. Alam, “Multi-target photorefractive fringe-adjusted joint transform correlation,” J. Opt. Mem. Neural Networks 6, 287–294 (1998).
  19. T. Nomura, “Phase-encoded joint transform correlator to reduce the influence of extraneous signals,” Appl. Opt. 37, 3651–3657 (1998).
    [CrossRef]
  20. G. Lu, F. T. S. Yu, “Performance of a phase-transformed input joint transform correlator,” Appl. Opt. 35, 304–313 (1996).
    [CrossRef] [PubMed]
  21. G. Lu, Z. Zhang, S. Wu, F. T. S. Yu, “Implementation of a non-zero-order joint-transform correlator by use of phase-shifting techniques,” Appl. Opt. 36, 470–483 (1997).
    [CrossRef] [PubMed]
  22. H. E. Michel, A. A. S. Awwal, “Joint Fourier transform correlation with phase thresholding in the Fourier plane,” Opt. Eng. 27, 33–37 (1998).
    [CrossRef]

1998 (4)

F. T. S. Yu, C. Li, S. Yin, “Comparison of detection efficiency for nonzero-order and conventional joint transform correlation,” Opt. Eng. 28, 52–57 (1998).
[CrossRef]

M. S. Alam, “Multi-target photorefractive fringe-adjusted joint transform correlation,” J. Opt. Mem. Neural Networks 6, 287–294 (1998).

T. Nomura, “Phase-encoded joint transform correlator to reduce the influence of extraneous signals,” Appl. Opt. 37, 3651–3657 (1998).
[CrossRef]

H. E. Michel, A. A. S. Awwal, “Joint Fourier transform correlation with phase thresholding in the Fourier plane,” Opt. Eng. 27, 33–37 (1998).
[CrossRef]

1997 (1)

1996 (2)

1995 (3)

M. Schönleber, G. Cedilnik, H. J. Tisiani, “Joint transform correlator subtracting a modified Fourier spectrum,” Appl. Opt. 34, 7532–7537 (1995).
[CrossRef] [PubMed]

M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3216 (1995).
[CrossRef]

B. Javidi, J. Li, A. H. Fazlollahi, J. Horner, “Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination,” Appl. Opt. 24, 886–896 (1995).
[CrossRef]

1994 (1)

M. S. Alam, M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[CrossRef]

1993 (2)

1992 (2)

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint transform correlator,” Opt. Laser Technol. 24, 45–50 (1992).
[CrossRef]

W. B. Hahn, D. L. Flannery, “Design elements of a binary joint transform correlator and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

1990 (1)

1989 (1)

1988 (2)

B. Javidi, C. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
[CrossRef] [PubMed]

B. Javidi, S. F. Odeh, “Multiple object identification by bipolar joint transform correlation,” Opt. Eng. 27, 295–300 (1988).

1984 (1)

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

1966 (1)

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Alam, M. S.

M. S. Alam, “Multi-target photorefractive fringe-adjusted joint transform correlation,” J. Opt. Mem. Neural Networks 6, 287–294 (1998).

M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3216 (1995).
[CrossRef]

M. S. Alam, M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[CrossRef]

M. S. Alam, M. A. Karim, “Joint transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
[CrossRef] [PubMed]

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

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint transform correlator,” Opt. Laser Technol. 24, 45–50 (1992).
[CrossRef]

Awwal, A. A. S.

H. E. Michel, A. A. S. Awwal, “Joint Fourier transform correlation with phase thresholding in the Fourier plane,” Opt. Eng. 27, 33–37 (1998).
[CrossRef]

Cedilnik, G.

Chatwin, C. R.

Cheng, F.

Cheng, Y. S.

Fazlollahi, A. H.

B. Javidi, J. Li, A. H. Fazlollahi, J. Horner, “Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination,” Appl. Opt. 24, 886–896 (1995).
[CrossRef]

Flannery, D. L.

W. B. Hahn, D. L. Flannery, “Design elements of a binary joint transform correlator and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

Goodman, J. W.

Gregory, D. A.

Hahn, W. B.

W. B. Hahn, D. L. Flannery, “Design elements of a binary joint transform correlator and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

Horner, J.

B. Javidi, J. Li, A. H. Fazlollahi, J. Horner, “Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination,” Appl. Opt. 24, 886–896 (1995).
[CrossRef]

Javidi, B.

B. Javidi, J. Li, A. H. Fazlollahi, J. Horner, “Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination,” Appl. Opt. 24, 886–896 (1995).
[CrossRef]

B. Javidi, S. F. Odeh, “Multiple object identification by bipolar joint transform correlation,” Opt. Eng. 27, 295–300 (1988).

B. Javidi, C. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
[CrossRef] [PubMed]

Karim, M. A.

M. S. Alam, M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[CrossRef]

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

M. S. Alam, M. A. Karim, “Joint transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
[CrossRef] [PubMed]

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint transform correlator,” Opt. Laser Technol. 24, 45–50 (1992).
[CrossRef]

Kuo, C.

Li, C.

F. T. S. Yu, C. Li, S. Yin, “Comparison of detection efficiency for nonzero-order and conventional joint transform correlation,” Opt. Eng. 28, 52–57 (1998).
[CrossRef]

Li, J.

B. Javidi, J. Li, A. H. Fazlollahi, J. Horner, “Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination,” Appl. Opt. 24, 886–896 (1995).
[CrossRef]

Lu, G.

Lu, X. J.

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Michel, H. E.

H. E. Michel, A. A. S. Awwal, “Joint Fourier transform correlation with phase thresholding in the Fourier plane,” Opt. Eng. 27, 33–37 (1998).
[CrossRef]

Nagata, T.

Nomura, T.

Odeh, S. F.

B. Javidi, S. F. Odeh, “Multiple object identification by bipolar joint transform correlation,” Opt. Eng. 27, 295–300 (1988).

Schönleber, M.

Shang, L.

Song, Q. W.

Tisiani, H. J.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Wang, R. K.

Weaver, C. S.

Wu, S.

Yin, S.

F. T. S. Yu, C. Li, S. Yin, “Comparison of detection efficiency for nonzero-order and conventional joint transform correlation,” Opt. Eng. 28, 52–57 (1998).
[CrossRef]

Yu, F. T. S.

Zhang, Z.

Appl. Opt. (12)

C. S. Weaver, J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
[CrossRef] [PubMed]

F. T. S. Yu, Q. W. Song, Y. S. Cheng, D. A. Gregory, “Comparison of detection efficiencies for VanderLugt and joint transform correlators,” Appl. Opt. 29, 225–232 (1990).
[CrossRef] [PubMed]

B. Javidi, C. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
[CrossRef] [PubMed]

B. Javidi, J. Li, A. H. Fazlollahi, J. Horner, “Binary nonlinear joint transform correlator performance with different thresholding methods under unknown illumination,” Appl. Opt. 24, 886–896 (1995).
[CrossRef]

F. T. S. Yu, F. Cheng, T. Nagata, D. A. Gregory, “Effects of fringe binarization of multi-object joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
[CrossRef] [PubMed]

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

M. Schönleber, G. Cedilnik, H. J. Tisiani, “Joint transform correlator subtracting a modified Fourier spectrum,” Appl. Opt. 34, 7532–7537 (1995).
[CrossRef] [PubMed]

R. K. Wang, L. Shang, C. R. Chatwin, “Modified fringe-adjusted joint transform correlation subtracting to accommodate noise in the input scene,” Appl. Opt. 35, 286–296 (1996).
[CrossRef] [PubMed]

M. S. Alam, M. A. Karim, “Joint transform correlation under varying illumination,” Appl. Opt. 32, 4351–4356 (1993).
[CrossRef] [PubMed]

T. Nomura, “Phase-encoded joint transform correlator to reduce the influence of extraneous signals,” Appl. Opt. 37, 3651–3657 (1998).
[CrossRef]

G. Lu, F. T. S. Yu, “Performance of a phase-transformed input joint transform correlator,” Appl. Opt. 35, 304–313 (1996).
[CrossRef] [PubMed]

G. Lu, Z. Zhang, S. Wu, F. T. S. Yu, “Implementation of a non-zero-order joint-transform correlator by use of phase-shifting techniques,” Appl. Opt. 36, 470–483 (1997).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

J. Opt. Mem. Neural Networks (1)

M. S. Alam, “Multi-target photorefractive fringe-adjusted joint transform correlation,” J. Opt. Mem. Neural Networks 6, 287–294 (1998).

Opt. Commun. (1)

F. T. S. Yu, X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
[CrossRef]

Opt. Eng. (6)

B. Javidi, S. F. Odeh, “Multiple object identification by bipolar joint transform correlation,” Opt. Eng. 27, 295–300 (1988).

W. B. Hahn, D. L. Flannery, “Design elements of a binary joint transform correlator and selected optimization techniques,” Opt. Eng. 31, 896–905 (1992).
[CrossRef]

F. T. S. Yu, C. Li, S. Yin, “Comparison of detection efficiency for nonzero-order and conventional joint transform correlation,” Opt. Eng. 28, 52–57 (1998).
[CrossRef]

M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3216 (1995).
[CrossRef]

M. S. Alam, M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[CrossRef]

H. E. Michel, A. A. S. Awwal, “Joint Fourier transform correlation with phase thresholding in the Fourier plane,” Opt. Eng. 27, 33–37 (1998).
[CrossRef]

Opt. Laser Technol. (1)

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint transform correlator,” Opt. Laser Technol. 24, 45–50 (1992).
[CrossRef]

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Figures (18)

Fig. 1
Fig. 1

Classical JTC architecture. BS, beam splitter.

Fig. 2
Fig. 2

(a) Input joint image and (b) classical JTC-based correlation output.

Fig. 3
Fig. 3

Binary JTC-based correlation output.

Fig. 4
Fig. 4

FJTC-based correlation output.

Fig. 5
Fig. 5

Classical JTC-based correlation output by use of Fourier plane image subtraction.

Fig. 6
Fig. 6

FJTC-based correlation output by use of Fourier plane image subtraction.

Fig. 7
Fig. 7

RJTC-based correlation output.

Fig. 8
Fig. 8

RJTC correlation output when the letter T is the target.

Fig. 9
Fig. 9

Input joint images with (a) tank as the reference image and (b) truck as the reference image.

Fig. 10
Fig. 10

Classical JTC outputs for the input joint images of Figs. 9(a) and 9(b).

Fig. 11
Fig. 11

Binary JTC outputs by use of the input joint images of Figs. 9(a) and 9(b).

Fig. 12
Fig. 12

FJTC outputs by use of the input joint images of Figs. 9(a) and 9(b).

Fig. 13
Fig. 13

Classical JTC-based correlation output by use of the Fourier plane image subtraction for the input joint images of Figs. 9(a) and 9(b).

Fig. 14
Fig. 14

FJTC output by use of Fourier plane image subtraction for the input joint images of Figs. 9(a) and 9(b).

Fig. 15
Fig. 15

RJTC output for the input joint images of Figs. 9(a) and 9(b).

Fig. 16
Fig. 16

Input joint images by use of the noisy input scenes with the (a) tank as a target and (b) truck as a target.

Fig. 17
Fig. 17

RJTC-based correlation output for the input for (a) Fig. 16(a) and (b) Fig. 16(b).

Fig. 18
Fig. 18

All-optical implementation for the proposed RJTC. BS, beam splitter.

Equations (16)

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

fy=ry+y0+sy-y0,
sy-y0=by-y0+i=1n tiy-yi+i=1n niy-yi+i=1n oiy-yi,
Fν=|Rν|exp jϕrν+νy0+|Sν|×exp jϕSν-νy0,
Sνexp-jνy0=|Sν|exp jϕSν-νy0=|Bν|×exp jϕbν-νy0+i=1n |Tiν|exp jϕtiν-νyi+i=1n |Niν|exp jϕniν-νyi+i=1n |Oiν|exp jϕoiν-νyi,
|Fν|2=FνF*ν=|Rν|2+|Sν|2+2|RνSν|cosϕrν-ϕsν+2νy0,
|Sν|2=SνS*ν=|Bν|2+i=1n |Tiν|2+i=1n |Niν|2+i=1n |Oiν|2+2 i=1nk=1kin |TiνTkν|cosϕtiν-ϕtkν-νyi+νyk+2 i=1nk=1kin |NiνNkν|cosϕniν-ϕnkν-νyi+νyk+2 i=1nk=1kin |OiνOkν|cosϕoiν-ϕokν-νyi+νyk+2 i=1nk=1n |TiνNkν|cosϕtiν-ϕnkν-νyi+νyk+2 i=1nk=1n |TiνOkν|cosϕtiν-ϕokν-νyi+νyk+2 i=1nk=1n |NiνOkν|cosϕniν-ϕokν-νyi+νyk+2 i=1n |BνTiν|cosϕniν-ϕbν-νyi-νy0+2 i=1n |BνNiν|cosϕniν-ϕbν-νyi-νy0+2 i=1n |BνOiν|cosϕoiν-ϕbν-νyi-νy0.
Hν=CνDν+|Rν|2-1,
Gν=Hν|Fν|2|Rν|-2|Fν|2.
Pν=|Fν|2-|Rν|2-|Sν|2=2|RνSν|cosϕrν-ϕsν+2νy0.
Φu, ν=expjψu, ν,
fy=ry+y0ϕy+sy-y0,
|Fν|2=Rν|exp jϕrν+νy0Φν+|Sν|exp jϕSν-νy02|=|Rν|2+|Sν|2+|RνSν|×exp jϕrν-ϕSν+2νy0Φν+|RνSν|×exp-jϕrν-ϕSν+2νy0Φ*ν.
|Fν|2Φν=|Rν|2+|Sν|2Φν+|RνSν|exp jϕrν-ϕSν+2νy0ΦνΦν+|RνSν|exp-jϕr-ϕSν+2νy0.
|Fν|2Φν|RνSν|exp-jϕrν-ϕSν+2νy0.
|Fν|2Φν|Rν|exp-jϕrν+νy0|Bν|exp jϕbν-νy0+i=1n |Tiν|exp jϕtiν-νyi+i=1n |Niν|exp jϕniν-νyi+i=1n |Oiν|exp jϕoiν-νyi=|RνBν|exp-jϕrν-ϕbν+2νy0+i=1n |RνTiν|exp-jϕrν-ϕtiν+νyi+νy0+i=1n |RνNiν|exp-jϕrν-ϕniν+νyi+νy0+i=1n |RνOiν|exp-jϕrν-ϕoiν+νyi+νy0.
|Fν|2Φν|Rν|-2exp-jνy0+y1+exp-jνy0+y2+i=3n|Tiν||Rν|exp-jϕtiν-νyi+|Bν||Rν|exp-jϕrν-ϕbν+2νy0+i=1n|Niν||Rν|exp-jϕrν-ϕniν+νy0+yi+i=1n|Oiν||Rν|exp-jϕrν-ϕoiν+νy0+yi.

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