Abstract

We introduce a new, to our knowledge, design for a Wiener-like correlation filter, which consists of cascading a phase-only filter (POF) with a photorefractive Wiener-like filter. Its performance is compared with that of the POF and the Wiener correlation filter (WCF). Correlation results show that for intermediate and higher levels of noise this correlation filter has a peak-to-noise ratio that is larger than that of either the POF or the WCF while still preserving a correlation peak that is almost as high as that of the POF.

© 2000 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (McGraw-Hill, New York, 1968), Chap. 7, p. 180.
  2. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  3. J. L. Horner, J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609–611 (1985).
    [CrossRef] [PubMed]
  4. D. L. Flannery, “Optimal trade-off distortion-tolerant constrained-modulator correlation filter,” J. Opt. Soc. Am. A 12, 66–72 (1995).
    [CrossRef]
  5. Ph. Réfrégier, B. V. K. Vijaya Kumar, C. Hendrix, “Multicriteria optimal binary amplitude phase-only filter,” J. Opt. Soc. Am. A 9, 2118–2125 (1992).
    [CrossRef]
  6. J. Figue, Ph. Réfrégier, “Optimality of trade-off filters,” Appl. Opt. 32, 1933–1935 (1993).
    [CrossRef] [PubMed]
  7. B. V. K. Vijaya Kumar, D. W. Carlson, A. Mahalanobis, “Optimal trade-off synthetic discriminant function filter for arbitrary devices,” Opt. Lett. 19, 1556–1558 (1994).
    [CrossRef]
  8. L. P. Yaroslavsky, “Is the phase-only filter and its modification optimal in terms of the discrimination capability in pattern recognition?” Appl. Opt. 31, 1677–1679 (1992).
    [CrossRef] [PubMed]
  9. R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993).
    [CrossRef] [PubMed]
  10. J. D. Downie, J. F. Walkup, “Optimal correlation filter for images with signal-dependent noise,” J. Opt. Soc. Am. A 11, 1599–1609 (1994).
    [CrossRef]
  11. H. J. Caulfield, W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969).
    [CrossRef] [PubMed]
  12. L. Laude, Ph. Réfrégier, “Multicriteria characterization of coding domains with optimal Fourier spatial light modulator filters,” Appl. Opt. 33, 4465–4471 (1994).
    [CrossRef] [PubMed]
  13. Ph. Réfrégier, “Optimal trade-off filters for noise robustness, sharpness of the correlation peak, and Horner efficiency,” Opt. Lett. 16, 829–831 (1991).
    [CrossRef] [PubMed]
  14. Ph. Réfrégier, “Application of the stabilization functional approach to pattern-recognition filters,” J. Opt. Soc. Am. A 11, 1234–1252 (1994).
  15. B. V. K Vijaya Kumar, Z. Bahri, “Phase-only filters with improved signal-to-noise ratio,” Appl. Opt. 28, 250–257 (1989).
    [CrossRef]
  16. B. V. K. Vijaya Kumar, Z. Bahri, “Efficient algorithm for designing a ternary value filter yielding maximum signal-to-noise ratio,” Appl. Opt. 28, 1919–1925 (1989).
    [CrossRef]
  17. S. Yin, M. Lu, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Design of a bipolar composite filter by a simulated annealing algorithm,” Opt. Lett. 20, 1409–1411 (1995).
    [CrossRef] [PubMed]
  18. M. Lu, S. Yin, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Optimum synthesis of a bipolar composite reference function with a simulated annealing algorithm,” Opt. Eng. 35, 2710–2720 (1996).
    [CrossRef]
  19. G. Mu, X. Wang, Z. Wang, “Amplitude-compensated matched filtering,” Appl. Opt. 27, 3461–3463 (1988).
    [CrossRef] [PubMed]
  20. A. Awwal, M. Karim, S. Jahan, “Improved correlation discrimination using an amplitude-modulated phase-only filter,” Appl. Opt. 29, 233–236 (1990).
    [CrossRef] [PubMed]
  21. J. Fu, J. Khoury, M. Cronin-Golomb, C. Woods, “Photorefractive two-beam coupling optimal thresholding filter for additive signal dependent noise,” Appl. Opt. 34, 346–351 (1995).
    [CrossRef] [PubMed]
  22. J. Khoury, J. Fu, M. Cronin-Golomb, C. Woods, “Photorefractive deamplification of additive signal dependent noise,” Opt. Eng. 32, 2877–2883 (1993).
    [CrossRef]
  23. J. Khoury, M. Cronin-Golomb, C. L. Woods, “Noise reduction using adaptive spatial filtering in photorefractive two-beam coupling,” Opt. Lett. 16, 747–749 (1990).
    [CrossRef]
  24. J. Khoury, G. Asimellis, C. Woods, “Incoherent-erasure joint-transform correlator,” Opt. Lett. 20, 2321–2323 (1995);G. Asimellis, J. Khoury, C. Woods, “Effects of saturation on the nonlinear incoherent-erasure joint transform correlator,” J. Opt. Soc. Am. A 13, 1345–1356 (1996).
    [CrossRef] [PubMed]
  25. G. Asimellis, M. Cronin-Golomb, J. Khoury, J. Kane, C. Woods, “Analysis of the dual discrimination ability of the two-port joint transform correlator,” Appl. Opt. 34, 8154–8166 (1995);G. Asimellis, J. Khoury, J. Kane, C. Woods, “Two-port photorefractive joint transform correlator,” Opt. Lett. 20, 2517–2519 (1995).
    [CrossRef] [PubMed]
  26. J. Khoury, M. Cronin-Golomb, P. D. Gianino, C. L. Woods, “Photorefractive two-beam coupling nonlinear joint transform correlator,” J. Opt. Soc. Am. B11, 2167–2174 (1994); J. Khoury, M. Cronin-Golomb, J. Kane, C. L. Woods, “Two-port photorefractive correlator,” in OSA Annual Meeting Digest, Volume 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993).
  27. J. Khoury, G. Asimellis, P. D. Gianino, C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66–73 (1998);J. Khoury, J. S. Kane, G. Asimellis, M. Cronin-Golomb, C. L. Woods, “All-optical nonlinear joint transform correlator,” Appl. Opt. 33, 8216–8225 (1994).
    [CrossRef] [PubMed]
  28. K. Lizuka, Engineering Optics, Vol. 36 of Springer Series on Applied Sciences (Springer-Verlag, Berlin, 1985).
  29. J. Horner, “Optical spatial filtering with the least mean-square-error filter,” J. Opt. Soc. Am. 59, 553–558 (1969).
    [CrossRef]
  30. A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filter,” Appl. Opt. 26, 3633–3640 (1987).
    [CrossRef] [PubMed]
  31. M. S. Alam, M. A. Karim, “Multiple target detection using modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
    [CrossRef]
  32. M. S. Alam, M. A. Karim, “Fringe-adjusted joint transform correlator,” Appl. Opt. 32, 4344–4350 (1993).
    [CrossRef] [PubMed]
  33. F. Cheng, P. Andres, F. T. S. Yu, D. Gregory, “Intensity compensation filter for joint transform correlation peak enhancement,” Appl. Opt. 32, 4357–4364 (1993).
    [CrossRef] [PubMed]

1998 (1)

J. Khoury, G. Asimellis, P. D. Gianino, C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66–73 (1998);J. Khoury, J. S. Kane, G. Asimellis, M. Cronin-Golomb, C. L. Woods, “All-optical nonlinear joint transform correlator,” Appl. Opt. 33, 8216–8225 (1994).
[CrossRef] [PubMed]

1996 (1)

M. Lu, S. Yin, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Optimum synthesis of a bipolar composite reference function with a simulated annealing algorithm,” Opt. Eng. 35, 2710–2720 (1996).
[CrossRef]

1995 (5)

1994 (5)

1993 (5)

1992 (2)

1991 (1)

1990 (2)

1989 (2)

1988 (1)

1987 (1)

1985 (1)

1984 (1)

1969 (2)

Alam, M. S.

M. S. Alam, M. A. Karim, “Multiple target detection using 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]

Andres, P.

Asimellis, G.

Awwal, A.

Bahri, Z.

Carlson, D. W.

Casasent, D.

Caulfield, H. J.

Chen, C.

M. Lu, S. Yin, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Optimum synthesis of a bipolar composite reference function with a simulated annealing algorithm,” Opt. Eng. 35, 2710–2720 (1996).
[CrossRef]

S. Yin, M. Lu, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Design of a bipolar composite filter by a simulated annealing algorithm,” Opt. Lett. 20, 1409–1411 (1995).
[CrossRef] [PubMed]

Cheng, F.

Cronin-Golomb, M.

G. Asimellis, M. Cronin-Golomb, J. Khoury, J. Kane, C. Woods, “Analysis of the dual discrimination ability of the two-port joint transform correlator,” Appl. Opt. 34, 8154–8166 (1995);G. Asimellis, J. Khoury, J. Kane, C. Woods, “Two-port photorefractive joint transform correlator,” Opt. Lett. 20, 2517–2519 (1995).
[CrossRef] [PubMed]

J. Fu, J. Khoury, M. Cronin-Golomb, C. Woods, “Photorefractive two-beam coupling optimal thresholding filter for additive signal dependent noise,” Appl. Opt. 34, 346–351 (1995).
[CrossRef] [PubMed]

J. Khoury, J. Fu, M. Cronin-Golomb, C. Woods, “Photorefractive deamplification of additive signal dependent noise,” Opt. Eng. 32, 2877–2883 (1993).
[CrossRef]

J. Khoury, M. Cronin-Golomb, C. L. Woods, “Noise reduction using adaptive spatial filtering in photorefractive two-beam coupling,” Opt. Lett. 16, 747–749 (1990).
[CrossRef]

J. Khoury, M. Cronin-Golomb, P. D. Gianino, C. L. Woods, “Photorefractive two-beam coupling nonlinear joint transform correlator,” J. Opt. Soc. Am. B11, 2167–2174 (1994); J. Khoury, M. Cronin-Golomb, J. Kane, C. L. Woods, “Two-port photorefractive correlator,” in OSA Annual Meeting Digest, Volume 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993).

Downie, J. D.

Figue, J.

Flannery, D. L.

Fu, J.

J. Fu, J. Khoury, M. Cronin-Golomb, C. Woods, “Photorefractive two-beam coupling optimal thresholding filter for additive signal dependent noise,” Appl. Opt. 34, 346–351 (1995).
[CrossRef] [PubMed]

J. Khoury, J. Fu, M. Cronin-Golomb, C. Woods, “Photorefractive deamplification of additive signal dependent noise,” Opt. Eng. 32, 2877–2883 (1993).
[CrossRef]

Gianino, P. D.

J. Khoury, G. Asimellis, P. D. Gianino, C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66–73 (1998);J. Khoury, J. S. Kane, G. Asimellis, M. Cronin-Golomb, C. L. Woods, “All-optical nonlinear joint transform correlator,” Appl. Opt. 33, 8216–8225 (1994).
[CrossRef] [PubMed]

J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

J. Khoury, M. Cronin-Golomb, P. D. Gianino, C. L. Woods, “Photorefractive two-beam coupling nonlinear joint transform correlator,” J. Opt. Soc. Am. B11, 2167–2174 (1994); J. Khoury, M. Cronin-Golomb, J. Kane, C. L. Woods, “Two-port photorefractive correlator,” in OSA Annual Meeting Digest, Volume 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (McGraw-Hill, New York, 1968), Chap. 7, p. 180.

Gregory, D.

Hendrix, C.

Horner, J.

Horner, J. L.

Hudson, T. D.

M. Lu, S. Yin, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Optimum synthesis of a bipolar composite reference function with a simulated annealing algorithm,” Opt. Eng. 35, 2710–2720 (1996).
[CrossRef]

S. Yin, M. Lu, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Design of a bipolar composite filter by a simulated annealing algorithm,” Opt. Lett. 20, 1409–1411 (1995).
[CrossRef] [PubMed]

Jahan, S.

Juday, R. D.

Kane, J.

Karim, M.

Karim, M. A.

M. S. Alam, M. A. Karim, “Multiple target detection using 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]

Khoury, J.

J. Khoury, G. Asimellis, P. D. Gianino, C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66–73 (1998);J. Khoury, J. S. Kane, G. Asimellis, M. Cronin-Golomb, C. L. Woods, “All-optical nonlinear joint transform correlator,” Appl. Opt. 33, 8216–8225 (1994).
[CrossRef] [PubMed]

G. Asimellis, M. Cronin-Golomb, J. Khoury, J. Kane, C. Woods, “Analysis of the dual discrimination ability of the two-port joint transform correlator,” Appl. Opt. 34, 8154–8166 (1995);G. Asimellis, J. Khoury, J. Kane, C. Woods, “Two-port photorefractive joint transform correlator,” Opt. Lett. 20, 2517–2519 (1995).
[CrossRef] [PubMed]

J. Fu, J. Khoury, M. Cronin-Golomb, C. Woods, “Photorefractive two-beam coupling optimal thresholding filter for additive signal dependent noise,” Appl. Opt. 34, 346–351 (1995).
[CrossRef] [PubMed]

J. Khoury, G. Asimellis, C. Woods, “Incoherent-erasure joint-transform correlator,” Opt. Lett. 20, 2321–2323 (1995);G. Asimellis, J. Khoury, C. Woods, “Effects of saturation on the nonlinear incoherent-erasure joint transform correlator,” J. Opt. Soc. Am. A 13, 1345–1356 (1996).
[CrossRef] [PubMed]

J. Khoury, J. Fu, M. Cronin-Golomb, C. Woods, “Photorefractive deamplification of additive signal dependent noise,” Opt. Eng. 32, 2877–2883 (1993).
[CrossRef]

J. Khoury, M. Cronin-Golomb, C. L. Woods, “Noise reduction using adaptive spatial filtering in photorefractive two-beam coupling,” Opt. Lett. 16, 747–749 (1990).
[CrossRef]

J. Khoury, M. Cronin-Golomb, P. D. Gianino, C. L. Woods, “Photorefractive two-beam coupling nonlinear joint transform correlator,” J. Opt. Soc. Am. B11, 2167–2174 (1994); J. Khoury, M. Cronin-Golomb, J. Kane, C. L. Woods, “Two-port photorefractive correlator,” in OSA Annual Meeting Digest, Volume 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993).

Laude, L.

Leger, J. R.

Lizuka, K.

K. Lizuka, Engineering Optics, Vol. 36 of Springer Series on Applied Sciences (Springer-Verlag, Berlin, 1985).

Lu, M.

M. Lu, S. Yin, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Optimum synthesis of a bipolar composite reference function with a simulated annealing algorithm,” Opt. Eng. 35, 2710–2720 (1996).
[CrossRef]

S. Yin, M. Lu, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Design of a bipolar composite filter by a simulated annealing algorithm,” Opt. Lett. 20, 1409–1411 (1995).
[CrossRef] [PubMed]

Mahalanobis, A.

Maloney, W. T.

McMillen, D. K.

M. Lu, S. Yin, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Optimum synthesis of a bipolar composite reference function with a simulated annealing algorithm,” Opt. Eng. 35, 2710–2720 (1996).
[CrossRef]

S. Yin, M. Lu, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Design of a bipolar composite filter by a simulated annealing algorithm,” Opt. Lett. 20, 1409–1411 (1995).
[CrossRef] [PubMed]

Mu, G.

Réfrégier, Ph.

Vijaya Kumar, B. V. K

Vijaya Kumar, B. V. K.

Walkup, J. F.

Wang, X.

Wang, Z.

Woods, C.

Woods, C. L.

J. Khoury, G. Asimellis, P. D. Gianino, C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66–73 (1998);J. Khoury, J. S. Kane, G. Asimellis, M. Cronin-Golomb, C. L. Woods, “All-optical nonlinear joint transform correlator,” Appl. Opt. 33, 8216–8225 (1994).
[CrossRef] [PubMed]

J. Khoury, M. Cronin-Golomb, C. L. Woods, “Noise reduction using adaptive spatial filtering in photorefractive two-beam coupling,” Opt. Lett. 16, 747–749 (1990).
[CrossRef]

J. Khoury, M. Cronin-Golomb, P. D. Gianino, C. L. Woods, “Photorefractive two-beam coupling nonlinear joint transform correlator,” J. Opt. Soc. Am. B11, 2167–2174 (1994); J. Khoury, M. Cronin-Golomb, J. Kane, C. L. Woods, “Two-port photorefractive correlator,” in OSA Annual Meeting Digest, Volume 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993).

Yaroslavsky, L. P.

Yin, S.

M. Lu, S. Yin, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Optimum synthesis of a bipolar composite reference function with a simulated annealing algorithm,” Opt. Eng. 35, 2710–2720 (1996).
[CrossRef]

S. Yin, M. Lu, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Design of a bipolar composite filter by a simulated annealing algorithm,” Opt. Lett. 20, 1409–1411 (1995).
[CrossRef] [PubMed]

Yu, F. T. S.

Appl. Opt. (16)

J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
[CrossRef] [PubMed]

A. Mahalanobis, B. V. K. Vijaya Kumar, D. Casasent, “Minimum average correlation energy filter,” Appl. Opt. 26, 3633–3640 (1987).
[CrossRef] [PubMed]

G. Mu, X. Wang, Z. Wang, “Amplitude-compensated matched filtering,” Appl. Opt. 27, 3461–3463 (1988).
[CrossRef] [PubMed]

B. V. K Vijaya Kumar, Z. Bahri, “Phase-only filters with improved signal-to-noise ratio,” Appl. Opt. 28, 250–257 (1989).
[CrossRef]

B. V. K. Vijaya Kumar, Z. Bahri, “Efficient algorithm for designing a ternary value filter yielding maximum signal-to-noise ratio,” Appl. Opt. 28, 1919–1925 (1989).
[CrossRef]

A. Awwal, M. Karim, S. Jahan, “Improved correlation discrimination using an amplitude-modulated phase-only filter,” Appl. Opt. 29, 233–236 (1990).
[CrossRef] [PubMed]

L. P. Yaroslavsky, “Is the phase-only filter and its modification optimal in terms of the discrimination capability in pattern recognition?” Appl. Opt. 31, 1677–1679 (1992).
[CrossRef] [PubMed]

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

F. Cheng, P. Andres, F. T. S. Yu, D. Gregory, “Intensity compensation filter for joint transform correlation peak enhancement,” Appl. Opt. 32, 4357–4364 (1993).
[CrossRef] [PubMed]

R. D. Juday, “Optimal realizable filters and the minimum Euclidean distance principle,” Appl. Opt. 32, 5100–5111 (1993).
[CrossRef] [PubMed]

L. Laude, Ph. Réfrégier, “Multicriteria characterization of coding domains with optimal Fourier spatial light modulator filters,” Appl. Opt. 33, 4465–4471 (1994).
[CrossRef] [PubMed]

J. Fu, J. Khoury, M. Cronin-Golomb, C. Woods, “Photorefractive two-beam coupling optimal thresholding filter for additive signal dependent noise,” Appl. Opt. 34, 346–351 (1995).
[CrossRef] [PubMed]

G. Asimellis, M. Cronin-Golomb, J. Khoury, J. Kane, C. Woods, “Analysis of the dual discrimination ability of the two-port joint transform correlator,” Appl. Opt. 34, 8154–8166 (1995);G. Asimellis, J. Khoury, J. Kane, C. Woods, “Two-port photorefractive joint transform correlator,” Opt. Lett. 20, 2517–2519 (1995).
[CrossRef] [PubMed]

J. Figue, Ph. Réfrégier, “Optimality of trade-off filters,” Appl. Opt. 32, 1933–1935 (1993).
[CrossRef] [PubMed]

H. J. Caulfield, W. T. Maloney, “Improved discrimination in optical character recognition,” Appl. Opt. 8, 2354–2356 (1969).
[CrossRef] [PubMed]

J. L. Horner, J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609–611 (1985).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Opt. Eng. (4)

M. Lu, S. Yin, C. Chen, F. T. S. Yu, T. D. Hudson, D. K. McMillen, “Optimum synthesis of a bipolar composite reference function with a simulated annealing algorithm,” Opt. Eng. 35, 2710–2720 (1996).
[CrossRef]

J. Khoury, J. Fu, M. Cronin-Golomb, C. Woods, “Photorefractive deamplification of additive signal dependent noise,” Opt. Eng. 32, 2877–2883 (1993).
[CrossRef]

J. Khoury, G. Asimellis, P. D. Gianino, C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66–73 (1998);J. Khoury, J. S. Kane, G. Asimellis, M. Cronin-Golomb, C. L. Woods, “All-optical nonlinear joint transform correlator,” Appl. Opt. 33, 8216–8225 (1994).
[CrossRef] [PubMed]

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

Opt. Lett. (5)

Other (3)

J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (McGraw-Hill, New York, 1968), Chap. 7, p. 180.

K. Lizuka, Engineering Optics, Vol. 36 of Springer Series on Applied Sciences (Springer-Verlag, Berlin, 1985).

J. Khoury, M. Cronin-Golomb, P. D. Gianino, C. L. Woods, “Photorefractive two-beam coupling nonlinear joint transform correlator,” J. Opt. Soc. Am. B11, 2167–2174 (1994); J. Khoury, M. Cronin-Golomb, J. Kane, C. L. Woods, “Two-port photorefractive correlator,” in OSA Annual Meeting Digest, Volume 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993).

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Figures (6)

Fig. 1
Fig. 1

Experimental arrangement for both the PWLF and WLCF. With no POF present, the system constitutes a PWLF. With the POF installed either before or after the crystal, the system becomes a WLCF. L1 and L2, lenses; RB, reference beam; f, focal length; PR, photoreactive crystal.

Fig. 2
Fig. 2

Input used in our computer simulation. The signal consists of a 64-pixel square rect function of unit height embedded in a 128-pixel square array with additive Gaussian noise. In (a) the rms value of the noise in the input plane relative to the unit signal is 0.3; in (b) the rms value is 0.6. Gray-scale intensities are shown in the upper right-hand corners.

Fig. 3
Fig. 3

Bar charts representing the simulation results of (a) peak intensity and (b) PNR for POF and WCF. The numbers under the bar charts represent the rms values of the noise in the input plane relative to the unit rect signal.

Fig. 4
Fig. 4

Same as in Fig. 3 except that two variations of the WLCF were added, one with a beam ratio m = 0.001 and one with m = 1.

Fig. 5
Fig. 5

Three-dimensional correlation patterns of the simulation results for (a) POF, (b) WCF, (c) WLCF with m = 0.001, and (d) WLCF with m = 1. The rms noise level was 0.03. Gray-scale intensities for each pattern are shown in the upper right-hand corners.

Fig. 6
Fig. 6

Same as in Fig. 5 except that the rms noise level was 0.6.

Equations (8)

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

Sout=S+N|S|2|S|2+|N|2,
Sout=mS+NmS+N2+|N|2mS+N2+|N|2expΓL1/2,
Sout=SS  N0S  N,
Sout=mSS  NmS+Nexp-ΓL/20S  N.
Cout=S+NS*|S|2+|N|2,
for WCF:  Cout=|S|2/|S|2=1S  NS+NS*/|N|20S  N.
Cout=mS+Nexp-jϕνx, νy×mS+N2+|N|2mS+N2+|N|2expΓL1/2,
for WLCF: Cout=mS  exp-jϕνx, νyS  NmN exp-jϕνx, νyexp-ΓL/20S  N.

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