Abstract

An all-optical nonlinear joint-transform correlator that is based on a square-law receiver has been implemented for the first time to our knowledge without the use of a spatial light modulator and digital processing in the Fourier plane. The correlator uses energy transfer from two-beam coupling in the Fourier plane. We implement compressional nonlinearity in the hard-clipped regime by pumping a weak plane wave with the intense joint spectrum of the reference and the signal images. Operation of this device rivals or exceeds that of the phase-only filter for detecting objects in cluttered noise. Experimental results are compared with both plane-wave and beam-propagation simulations.

© 1994 Optical Society of America

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References

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  1. J. O. White and A. Yariv, "Real time image processing via four-wave mixing," Appl. Phys. Lett. 37, 5–7 (1980).
    [CrossRef]
  2. M. G. Nicholson, I. R. Cooper, M. W. McCall, and C. R. Petts, "Simple computational model of image correlation by four-wave mixing in photorefractive media," Appl. Opt. 26, 278–286 (1987).
    [CrossRef] [PubMed]
  3. J. L. Horner and P. D. Gianino, "Phase-only matched filtering," Appl. Opt. 23, 812–816 (1984).
    [CrossRef]
  4. J. L. Horner and P. D. Gianino, "Pattern recognition with binary phase-only filters," Appl. Opt. 24, 609–611 (1985).
    [CrossRef] [PubMed]
  5. B. V. K. V. Kumar and L. Hassebrook, "Performance measurement of correlation filters," Appl. Opt. 29, 2997–3006 (1990).
    [CrossRef] [PubMed]
  6. J. L. Horner, "Metrics for assessing pattern recognition performance," Appl. Opt. 31, 165–166 (1992).
    [CrossRef] [PubMed]
  7. J. Khoury, J. C. Fu, M. Cronin-Golomb and C. Woods, "Quadratic processing and nonlinear optical phase rectification in noise reduction," J. Opt. Soc. Am. B 11, 1960–1971 (1994).
    [CrossRef]
  8. B. Javidi, "Nonlinear joint power spectrum based optical correlation," Appl. Opt. 28, 2358–2367 (1989).
    [CrossRef] [PubMed]
  9. C. S. Weaver and J. W. Goodman, "Technique for optically convolving two functions," Appl. Opt. 5, 1248–1249 (1966).
    [CrossRef] [PubMed]
  10. J. Khoury, A. M. Biernaki, C. Woods, and M. Cronin-Golomb, "Photorefractive quadratic processor for signal recovery from multiplicative complex noise," Opt. Eng. 32, 2872–2876 (1993).
    [CrossRef]
  11. J. Khoury, A. M. Biernaki, and M. Cronin-Golomb, "Photorefractive phase conjugate techniques for measuring surface granularity," Appl. Opt. (to be published).
  12. K. H. Fielding and J. L. Horner, "Clutter effects on optical correlators," in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. In-strum. Eng. 1151, 130–137 (1989); D. L. Flannery and J. L. Horner, "Fourier optics signal processing," Proc. IEEE 77, 1511–1527 (1989).
    [CrossRef]
  13. P. Yeh, "Photorefractive phase conjugators," Proc. IEEE 80, 436–450 (1992).
    [CrossRef]
  14. G. C. Valley and M. B. Klein, "Optimal properties of photorefractive material for optical data processing," Opt. Eng. 22, 704–711 (1983).
    [CrossRef]
  15. J. A. Khoury and R. W. Eason, "Photorefractive deconvolu-tion techniques for optical differentiation of images," J. Mod. Opt. 36, 369–379 (1989).
    [CrossRef]
  16. M. Cronin-Golomb, "Whole beam method for photorefractive nonlinear optics," Opt. Commun. 89, 276–282 (1992).
    [CrossRef]
  17. M. Cronin-Golomb, H. Kong, and W. Krolikowski, "Photorefractive two-beam coupling with light of partial spatiotem-poral coherence," J. Opt. Soc. Am. B 9, 1698–1703 (1992).
    [CrossRef]
  18. 18. V. A. D'yakov, S. A. Korol'kov, A. V. Mamaev, V. V. Shkunov, and A. A. Zozulya, "Reflection-grating photorefractive self-pumped ring mirror," Opt. Lett. 16, 1614–1616 (1991).
    [CrossRef]
  19. P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).
  20. RCA, Electro-optics Handbook, Technical Series EOH-11 (Pan Americard Copyright, RCA Corporation, Lancaster, Pa., 1974); S. O. Rice, "Mathematical analysis of random noise," Bell Syst. Tech. J. 23, 232–332 (1944).
  21. H. L. Van Trees, Detection, Estimation and Modulation Theory, Part 1 (Wiley, New York, 1968), Chap. 2, pp. 39, 100; Chap. 4, p. 251.
  22. B. Javidi, University of Connecticut, Storrs, Mansfield, Conn. 06268 (personal communication).
  23. T. Grycewicz, J. L. Horner, and B. Javidi, "Fourier plane binarization processing for the optical joint transform correlator," presented at OSA Annual Meeting, Toronto, October 3–8, 1993.
  24. B. V. K. V. Kumar and Z. Bahri, "Phase only filter with improved signal to noise ratio," Appl. Opt. 28, 250–257 (1989).
    [CrossRef] [PubMed]
  25. B. Javidi, Ph. Réfrégier, and P. Willet, "Optimal receiver design for pattern recognition with nonoverlapping target and scene noise," Opt. Lett. 18, 1660–1662 (1993).
    [CrossRef] [PubMed]
  26. B. Javidi and J. L. Horner, "Single spatial light modulator joint transform correlator," Appl. Opt. 28, 1027–1032 (1989).
    [CrossRef] [PubMed]
  27. L. Pichon and J.-P. Huignard, "Dynamic joint-Fourier transform correlator by Bragg diffraction in BSO crystal," Opt. Commun. 36, 277–280 (1981).
    [CrossRef]
  28. B. Loiseaux, G. Illiaquer, and J.-P. Huignard, "Dynamic optical cross correlation using a liquid crystal valve and BSO crystal in the Fourier plane," Opt. Eng. 24, 144–149 (1985).
    [CrossRef]
  29. I. R. Cooper, M. G. Nicholson, and C. R. Petts, "Dynamic frequency plane correlator," Proc. IEEE Pt. J. 133, 70–76 (1986).
  30. J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (McGraw-Hill, New York, 1968), Chap. 7, p. 146.

1994 (1)

1993 (2)

J. Khoury, A. M. Biernaki, C. Woods, and M. Cronin-Golomb, "Photorefractive quadratic processor for signal recovery from multiplicative complex noise," Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

B. Javidi, Ph. Réfrégier, and P. Willet, "Optimal receiver design for pattern recognition with nonoverlapping target and scene noise," Opt. Lett. 18, 1660–1662 (1993).
[CrossRef] [PubMed]

1992 (3)

1991 (1)

1990 (1)

1989 (4)

1987 (1)

1985 (2)

B. Loiseaux, G. Illiaquer, and J.-P. Huignard, "Dynamic optical cross correlation using a liquid crystal valve and BSO crystal in the Fourier plane," Opt. Eng. 24, 144–149 (1985).
[CrossRef]

J. L. Horner and P. D. Gianino, "Pattern recognition with binary phase-only filters," Appl. Opt. 24, 609–611 (1985).
[CrossRef] [PubMed]

1984 (1)

1983 (1)

G. C. Valley and M. B. Klein, "Optimal properties of photorefractive material for optical data processing," Opt. Eng. 22, 704–711 (1983).
[CrossRef]

1981 (1)

L. Pichon and J.-P. Huignard, "Dynamic joint-Fourier transform correlator by Bragg diffraction in BSO crystal," Opt. Commun. 36, 277–280 (1981).
[CrossRef]

1980 (1)

J. O. White and A. Yariv, "Real time image processing via four-wave mixing," Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

1966 (1)

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation and Modulation Theory, Part 1 (Wiley, New York, 1968), Chap. 2, pp. 39, 100; Chap. 4, p. 251.

Bahri, Z.

Biernaki, A. M.

J. Khoury, A. M. Biernaki, C. Woods, and M. Cronin-Golomb, "Photorefractive quadratic processor for signal recovery from multiplicative complex noise," Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

J. Khoury, A. M. Biernaki, and M. Cronin-Golomb, "Photorefractive phase conjugate techniques for measuring surface granularity," Appl. Opt. (to be published).

Cooper, I. R.

Cronin-Golomb, M.

J. Khoury, J. C. Fu, M. Cronin-Golomb and C. Woods, "Quadratic processing and nonlinear optical phase rectification in noise reduction," J. Opt. Soc. Am. B 11, 1960–1971 (1994).
[CrossRef]

J. Khoury, A. M. Biernaki, C. Woods, and M. Cronin-Golomb, "Photorefractive quadratic processor for signal recovery from multiplicative complex noise," Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

M. Cronin-Golomb, H. Kong, and W. Krolikowski, "Photorefractive two-beam coupling with light of partial spatiotem-poral coherence," J. Opt. Soc. Am. B 9, 1698–1703 (1992).
[CrossRef]

M. Cronin-Golomb, "Whole beam method for photorefractive nonlinear optics," Opt. Commun. 89, 276–282 (1992).
[CrossRef]

J. Khoury, A. M. Biernaki, and M. Cronin-Golomb, "Photorefractive phase conjugate techniques for measuring surface granularity," Appl. Opt. (to be published).

D’yakov, V. A.

Eason, R. W.

J. A. Khoury and R. W. Eason, "Photorefractive deconvolu-tion techniques for optical differentiation of images," J. Mod. Opt. 36, 369–379 (1989).
[CrossRef]

Fielding, K. H.

K. H. Fielding and J. L. Horner, "Clutter effects on optical correlators," in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. In-strum. Eng. 1151, 130–137 (1989); D. L. Flannery and J. L. Horner, "Fourier optics signal processing," Proc. IEEE 77, 1511–1527 (1989).
[CrossRef]

Fu, J. C.

Gianino, P. D.

Goodman, J. W.

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

J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (McGraw-Hill, New York, 1968), Chap. 7, p. 146.

Grycewicz, T.

T. Grycewicz, J. L. Horner, and B. Javidi, "Fourier plane binarization processing for the optical joint transform correlator," presented at OSA Annual Meeting, Toronto, October 3–8, 1993.

Hassebrook, L.

Horner, J. L.

J. L. Horner, "Metrics for assessing pattern recognition performance," Appl. Opt. 31, 165–166 (1992).
[CrossRef] [PubMed]

B. Javidi and J. L. Horner, "Single spatial light modulator joint transform correlator," Appl. Opt. 28, 1027–1032 (1989).
[CrossRef] [PubMed]

J. L. Horner and P. D. Gianino, "Pattern recognition with binary phase-only filters," Appl. Opt. 24, 609–611 (1985).
[CrossRef] [PubMed]

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

T. Grycewicz, J. L. Horner, and B. Javidi, "Fourier plane binarization processing for the optical joint transform correlator," presented at OSA Annual Meeting, Toronto, October 3–8, 1993.

K. H. Fielding and J. L. Horner, "Clutter effects on optical correlators," in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. In-strum. Eng. 1151, 130–137 (1989); D. L. Flannery and J. L. Horner, "Fourier optics signal processing," Proc. IEEE 77, 1511–1527 (1989).
[CrossRef]

Huignard, J.-P.

B. Loiseaux, G. Illiaquer, and J.-P. Huignard, "Dynamic optical cross correlation using a liquid crystal valve and BSO crystal in the Fourier plane," Opt. Eng. 24, 144–149 (1985).
[CrossRef]

L. Pichon and J.-P. Huignard, "Dynamic joint-Fourier transform correlator by Bragg diffraction in BSO crystal," Opt. Commun. 36, 277–280 (1981).
[CrossRef]

Illiaquer, G.

B. Loiseaux, G. Illiaquer, and J.-P. Huignard, "Dynamic optical cross correlation using a liquid crystal valve and BSO crystal in the Fourier plane," Opt. Eng. 24, 144–149 (1985).
[CrossRef]

Javidi, B.

Khoury, J.

J. Khoury, J. C. Fu, M. Cronin-Golomb and C. Woods, "Quadratic processing and nonlinear optical phase rectification in noise reduction," J. Opt. Soc. Am. B 11, 1960–1971 (1994).
[CrossRef]

J. Khoury, A. M. Biernaki, C. Woods, and M. Cronin-Golomb, "Photorefractive quadratic processor for signal recovery from multiplicative complex noise," Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

J. Khoury, A. M. Biernaki, and M. Cronin-Golomb, "Photorefractive phase conjugate techniques for measuring surface granularity," Appl. Opt. (to be published).

Khoury, J. A.

J. A. Khoury and R. W. Eason, "Photorefractive deconvolu-tion techniques for optical differentiation of images," J. Mod. Opt. 36, 369–379 (1989).
[CrossRef]

Klein, M. B.

G. C. Valley and M. B. Klein, "Optimal properties of photorefractive material for optical data processing," Opt. Eng. 22, 704–711 (1983).
[CrossRef]

Kong, H.

Korol’kov, S. A.

Krolikowski, W.

Kumar, B. V. K. V.

Loiseaux, B.

B. Loiseaux, G. Illiaquer, and J.-P. Huignard, "Dynamic optical cross correlation using a liquid crystal valve and BSO crystal in the Fourier plane," Opt. Eng. 24, 144–149 (1985).
[CrossRef]

Mamaev, A. V.

McCall, M. W.

Nicholson, M. G.

Petts, C. R.

Pichon, L.

L. Pichon and J.-P. Huignard, "Dynamic joint-Fourier transform correlator by Bragg diffraction in BSO crystal," Opt. Commun. 36, 277–280 (1981).
[CrossRef]

Réfrégier, Ph.

Shkunov, V. V.

Valley, G. C.

G. C. Valley and M. B. Klein, "Optimal properties of photorefractive material for optical data processing," Opt. Eng. 22, 704–711 (1983).
[CrossRef]

Weaver, C. S.

White, J. O.

J. O. White and A. Yariv, "Real time image processing via four-wave mixing," Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Willet, P.

Woods, C.

J. Khoury, J. C. Fu, M. Cronin-Golomb and C. Woods, "Quadratic processing and nonlinear optical phase rectification in noise reduction," J. Opt. Soc. Am. B 11, 1960–1971 (1994).
[CrossRef]

J. Khoury, A. M. Biernaki, C. Woods, and M. Cronin-Golomb, "Photorefractive quadratic processor for signal recovery from multiplicative complex noise," Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

Yariv, A.

J. O. White and A. Yariv, "Real time image processing via four-wave mixing," Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

P. Yeh, "Photorefractive phase conjugators," Proc. IEEE 80, 436–450 (1992).
[CrossRef]

Zozulya, A. A.

Appl. Opt. (9)

Appl. Phys. Lett. (1)

J. O. White and A. Yariv, "Real time image processing via four-wave mixing," Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

J. Mod. Opt. (1)

J. A. Khoury and R. W. Eason, "Photorefractive deconvolu-tion techniques for optical differentiation of images," J. Mod. Opt. 36, 369–379 (1989).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

L. Pichon and J.-P. Huignard, "Dynamic joint-Fourier transform correlator by Bragg diffraction in BSO crystal," Opt. Commun. 36, 277–280 (1981).
[CrossRef]

M. Cronin-Golomb, "Whole beam method for photorefractive nonlinear optics," Opt. Commun. 89, 276–282 (1992).
[CrossRef]

Opt. Eng. (3)

J. Khoury, A. M. Biernaki, C. Woods, and M. Cronin-Golomb, "Photorefractive quadratic processor for signal recovery from multiplicative complex noise," Opt. Eng. 32, 2872–2876 (1993).
[CrossRef]

B. Loiseaux, G. Illiaquer, and J.-P. Huignard, "Dynamic optical cross correlation using a liquid crystal valve and BSO crystal in the Fourier plane," Opt. Eng. 24, 144–149 (1985).
[CrossRef]

G. C. Valley and M. B. Klein, "Optimal properties of photorefractive material for optical data processing," Opt. Eng. 22, 704–711 (1983).
[CrossRef]

Opt. Lett. (2)

Other (10)

J. Khoury, A. M. Biernaki, and M. Cronin-Golomb, "Photorefractive phase conjugate techniques for measuring surface granularity," Appl. Opt. (to be published).

K. H. Fielding and J. L. Horner, "Clutter effects on optical correlators," in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. Soc. Photo-Opt. In-strum. Eng. 1151, 130–137 (1989); D. L. Flannery and J. L. Horner, "Fourier optics signal processing," Proc. IEEE 77, 1511–1527 (1989).
[CrossRef]

P. Yeh, "Photorefractive phase conjugators," Proc. IEEE 80, 436–450 (1992).
[CrossRef]

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

RCA, Electro-optics Handbook, Technical Series EOH-11 (Pan Americard Copyright, RCA Corporation, Lancaster, Pa., 1974); S. O. Rice, "Mathematical analysis of random noise," Bell Syst. Tech. J. 23, 232–332 (1944).

H. L. Van Trees, Detection, Estimation and Modulation Theory, Part 1 (Wiley, New York, 1968), Chap. 2, pp. 39, 100; Chap. 4, p. 251.

B. Javidi, University of Connecticut, Storrs, Mansfield, Conn. 06268 (personal communication).

T. Grycewicz, J. L. Horner, and B. Javidi, "Fourier plane binarization processing for the optical joint transform correlator," presented at OSA Annual Meeting, Toronto, October 3–8, 1993.

I. R. Cooper, M. G. Nicholson, and C. R. Petts, "Dynamic frequency plane correlator," Proc. IEEE Pt. J. 133, 70–76 (1986).

J. W. Goodman, Introduction to Fourier Optics, McGraw-Hill Physical and Quantum Electronics Series (McGraw-Hill, New York, 1968), Chap. 7, p. 146.

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Figures (6)

Fig. 1
Fig. 1

Two circles representing the signal and references: (A) two dissimilar and (B) two identical circles.

Fig. 2
Fig. 2

Correlation results for two different-sized circles: (A) the TBJTC modeled by plane-wave theory, (B) the TBJTC modeled by the beam-propagating technique, (C) the CJTC. Results for two identical circles: (D) the TBJTC modeled by plane-wave theory, (E) the TBJTC modeled by the beam-propagating technique, (F) the CJTC.

Fig. 3
Fig. 3

Schematic diagram of the experimental arrangement. L’s, lenses; M, mirror.

Fig. 4
Fig. 4

TBJTC experimental correlation results for A, two identical circles and B, two different-sized circles.

Fig. 5
Fig. 5

Top, reference (tank) and, bottom, input signal (tank in clutter noise).

Fig. 6
Fig. 6

Cross section in the correlation plane, showing first- and second-order correlation peaks.

Equations (15)

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

d A 1 d z = - γ I 0 A 1 A 2 2 - α 2 A 1 ,
d A 2 * d z = γ I 0 A 2 * A 1 2 - α 2 A 2 * .
A 1 ( x , z ) = A 1 ( x , 0 ) [ 1 + m ( x ) 1 + m ( x ) exp ( Γ z ) ] 1 / 2 × exp ( - α 2 z ) ,
A 2 ( x , z ) = A 2 ( x , 0 ) [ 1 + m ( x ) 1 + m ( x ) exp ( - Γ z ) ] 1 / 2 × exp ( - α 2 z ) ,
m = | A 1 ( 0 ) A 2 ( 0 ) | 2 .
A 2 ( z ) = A 2 ( 0 ) f ( g ) .
f ( g ) = ( 1 + m g 2 1 + m b g 2 ) 1 / 2 ,
A ( ν x , ν y ) = A ( 0 ) [ 1 + m / ( λ f ) 2 R ( ν x , ν y ) + S ( ν x , ν y ) 2 1 + m / ( λ f ) 2 R ( ν x , ν y ) + S ( ν x , ν y ) 2 exp ( - Γ L ) ] 1 / 2 ,
A ( ν x , ν y ) = Z clip ( R ( ν x , ν y ) + S ( ν x , ν y ) 2 ) 0 .
Z clip = A ( 0 ) exp ( Γ L / 2 ) .
A ( ν x , ν y ) = Z clip k = 1 k cos [ 2 k x 0 ν x + k ϕ r ( ν x , ν y ) - k ϕ s ( ν x , ν y ) ] Γ m ( 1 - k / 2 ) Γ m ( 1 + k / 2 ) ,
k = { 1 k = 0 2 k > 0 .
H ( ν x , ν y ) = exp { i 2 π d z λ [ 1 - λ 2 ( ν x 2 + ν y 2 ) ] 1 / 2 } ,
W ( x , y , z = d z ) = exp ( i k Δ n d z ) ,
E u = F - 1 { - F [ d d u ln ( I + 1 ) ] k u k v 1 + k u 2 + k v 2 } , E v = F - 1 { - F [ d d v ln ( I + 1 ) ] k u k v 1 + k u 2 + k v 2 } ,

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