Abstract

We propose a new technique to improve the performance of the joint transform correlator (JTC). In this technique we have applied the phase-iterative algorithm to a phase-shifting JTC (PSJTC). By doing so, we restrain the noise that is contained in the recovered phase of the joint transform power spectra for the input images with background and additive noise. In the case in which the input image is embedded in the input noise, we find that, by using the phase-iterative techniques with the PSJTC, one can get a higher cross-correlation peak and signal-to-noise ratio than with a PSJTC alone. From the computer-simulation results, one can conclude that the proposed algorithm successfully enhances PSJTC performance, especially for an input image with large noise.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. S. Weaver and J. W. Goodman, “Technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  2. A. VanderLugt, “Signal detection by complex spatial filtering,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  3. M. S. Alam and M. A. Karim, “Improved correlation discrimination in multiobject bipolar joint transform correlator,” Opt. Laser Technol. 24, 45–50 (1992).
    [CrossRef]
  4. B. Javidi and C. Kuo, “Joint transform image correlation using a binary spatial light modulator at the Fourier plane,” Appl. Opt. 27, 663–665 (1988).
    [CrossRef] [PubMed]
  5. F. T. S. Yu, F. Cheng, T. Nagate, and D. A. Gregory, “Effect of fringe binarization of multiobject joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
    [CrossRef] [PubMed]
  6. M. S. Alam, O. Perez, and M. A. Karim, “Preprocessed multiobject joint transform correlator,” Appl. Opt. 32, 3102–3107 (1993).
    [CrossRef] [PubMed]
  7. M. S. Alam and M. A. Karim, “Fringe-adjusted joint transform correlation,” Appl. Opt. 32, 4344–4350 (1993).
    [CrossRef] [PubMed]
  8. M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3215 (1995).
    [CrossRef]
  9. G. Lu, Z. Zhang, S. Wu, and 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]
  10. K. Creath, “Phase-measurement interfermetry techniques,” Prog. Opt. 26, 349–398 (1988).
    [CrossRef]
  11. H. J. Su, J. L. Li, and X. Y. Su, “Phase algorithm without the influence of carrier frequency,” Opt. Eng. 36, 1799–1805 (1997).
    [CrossRef]
  12. J. L. Li, H. J. Su, and X. Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36, 277–280 (1997).
    [CrossRef] [PubMed]
  13. Jie Gu, Y. Y. Hung, and Fang Chen, “Iteration algorithm for computer-aided speckle interferometry,” Appl. Opt. 33, 5308–5317 (1994).
    [CrossRef] [PubMed]
  14. B. V. K. Kumar and L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
    [CrossRef] [PubMed]
  15. J. L. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 32, 165–166 (1992).
    [CrossRef]

1997 (3)

1995 (1)

M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3215 (1995).
[CrossRef]

1994 (1)

1993 (2)

1992 (2)

J. L. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 32, 165–166 (1992).
[CrossRef]

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

1990 (1)

1989 (1)

1988 (2)

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, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3215 (1995).
[CrossRef]

M. S. Alam, O. Perez, and M. A. Karim, “Preprocessed multiobject joint transform correlator,” Appl. Opt. 32, 3102–3107 (1993).
[CrossRef] [PubMed]

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

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

Chen, Fang

Cheng, F.

Creath, K.

K. Creath, “Phase-measurement interfermetry techniques,” Prog. Opt. 26, 349–398 (1988).
[CrossRef]

Goodman, J. W.

Gregory, D. A.

Gu, Jie

Hassebrook, L.

Horner, J. L.

J. L. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 32, 165–166 (1992).
[CrossRef]

Hung, Y. Y.

Javidi, B.

Karim, M. A.

Kumar, B. V. K.

Kuo, C.

Li, J. L.

H. J. Su, J. L. Li, and X. Y. Su, “Phase algorithm without the influence of carrier frequency,” Opt. Eng. 36, 1799–1805 (1997).
[CrossRef]

J. L. Li, H. J. Su, and X. Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36, 277–280 (1997).
[CrossRef] [PubMed]

Lu, G.

Nagate, T.

Perez, O.

Su, H. J.

J. L. Li, H. J. Su, and X. Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36, 277–280 (1997).
[CrossRef] [PubMed]

H. J. Su, J. L. Li, and X. Y. Su, “Phase algorithm without the influence of carrier frequency,” Opt. Eng. 36, 1799–1805 (1997).
[CrossRef]

Su, X. Y.

H. J. Su, J. L. Li, and X. Y. Su, “Phase algorithm without the influence of carrier frequency,” Opt. Eng. 36, 1799–1805 (1997).
[CrossRef]

J. L. Li, H. J. Su, and X. Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36, 277–280 (1997).
[CrossRef] [PubMed]

VanderLugt, A.

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

Weaver, C. S.

Wu, S.

Yu, F. T. S.

Zhang, Z.

Appl. Opt. (10)

J. L. Horner, “Metrics for assessing pattern-recognition performance,” Appl. Opt. 32, 165–166 (1992).
[CrossRef]

B. V. K. Kumar and L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
[CrossRef] [PubMed]

M. S. Alam, O. Perez, and M. A. Karim, “Preprocessed multiobject joint transform correlator,” Appl. Opt. 32, 3102–3107 (1993).
[CrossRef] [PubMed]

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

Jie Gu, Y. Y. Hung, and Fang Chen, “Iteration algorithm for computer-aided speckle interferometry,” Appl. Opt. 33, 5308–5317 (1994).
[CrossRef] [PubMed]

G. Lu, Z. Zhang, S. Wu, and 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]

J. L. Li, H. J. Su, and X. Y. Su, “Two-frequency grating used in phase-measuring profilometry,” Appl. Opt. 36, 277–280 (1997).
[CrossRef] [PubMed]

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

F. T. S. Yu, F. Cheng, T. Nagate, and D. A. Gregory, “Effect of fringe binarization of multiobject joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
[CrossRef] [PubMed]

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

IEEE Trans. Inf. Theory (1)

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

Opt. Eng. (2)

M. S. Alam, “Fractional power fringe-adjusted joint transform correlation,” Opt. Eng. 34, 3208–3215 (1995).
[CrossRef]

H. J. Su, J. L. Li, and X. Y. Su, “Phase algorithm without the influence of carrier frequency,” Opt. Eng. 36, 1799–1805 (1997).
[CrossRef]

Opt. Laser Technol. (1)

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

Prog. Opt. (1)

K. Creath, “Phase-measurement interfermetry techniques,” Prog. Opt. 26, 349–398 (1988).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Architecture for the phase-shifting JTC. AMSLM, amplitude-modulated SLM; PMSLM, phase-modulated SLM.

Fig. 2
Fig. 2

Input scene with reference for the computer simulation.

Fig. 3
Fig. 3

Output correlation distribution (a) for the PSJTC and (b) for the phase-iterative PSJTC.

Fig. 4
Fig. 4

PCE versus the rms of the input additive noise. The solid curve corresponds to the PSJTC method, and the dashed curve corresponds to the proposed method. Results were obtained in six iterations.

Fig. 5
Fig. 5

SNR versus the rms of the input additive noise. The solid curve corresponds to the PSJTC method, and the dashed curve corresponds to the proposed method. Results were obtained in six iterations.

Equations (7)

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

J i u ,   v = | F u ,   v | 2 + | R u ,   v | 2 + 2 | F u ,   v R u ,   v | cos [ 2 bu + ϕ F u ,   v - ϕ R u ,   v + δ i ] .
ϕ JTPS = 2 bu + ϕ F u ,   v - ϕ R u ,   v = arctan n = 0 N - 1   J i u ,   v sin 2 π n / N n = 0 N - 1   J i u ,   v cos 2 π n / N .
ϕ JTPS = 2 bu + ϕ F u ,   v - ϕ R u ,   v = 3 J 1 - J 2 2 J 0 - J 1 - J 2 .
PJ = exp j ϕ JTPS = exp j 2 bu + ϕ F u ,   v - ϕ R u ,   v
I i u ,   v = 1 + cos ϕ JTPS + 2 π N i ,
PCE = I x ,   y Max x , y = 1 N   I x ,   y ,
SNR = I x ,   y Max 1 / 2 1 n x , y R   I x ,   y 1 / 2 ,

Metrics