Abstract

The use of photorefractive materials such as Bi12SiO20 as dynamic holographic media is becoming an interesting alternative to that of the current liquid-crystal-based modulators in real-time optical image processing. We present an experimental realization of optical correlation for pattern recognition by means of a photorefractive joint transform correlator. The correlator operates with a liquid-crystal television as the input and a photorefractive crystal at the recording plane. We consider two possible ways of registering the Fourier plane information: conventional detection of the joint power spectrum, and utilization of only phase information at the Fourier plane by suitable preprocessing of the scene and the reference at the object plane. We compare the latter case with the performance of a binary joint transform correlator. Analysis, simulations, and experimental results are presented.

© 1998 Optical Society of America

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References

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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 and J. W. Goodman, “A technique for optically convolving two functions,” Appl. Opt. 5, 1248–1249 (1966).
    [Crossref] [PubMed]
  3. S. Yu and X. J. Lu, “A real-time programmable joint transform correlator,” Opt. Commun. 52, 10–16 (1984).
    [Crossref]
  4. H-K. Liu, J. A. Davis, and R. A. Lilly, “Optical-data-processing properties of a liquid-crystal television spatial light modulator,” Opt. Lett. 10, 635–637 (1985).
    [Crossref] [PubMed]
  5. C. Kirsch, D. A. Gregory, M. W. Thie, and B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
    [Crossref]
  6. L. Pichon and J. P. Huignard, “Dynamic joint-Fourier transform correlator by Bragg diffraction in photorefractive Bi12SiO20 crystals,” Opt. Commun. 36, 277–280 (1981).
    [Crossref]
  7. C. Soutar, Z. Q. Wang, C. M. Cartwright, and W. A. Gillespie, “Real-time optical intensity correlator using photorefractive BSO and liquid crystal television,” J. Mod. Opt. 39, 761–769 (1992).
    [Crossref]
  8. B. Javidi, “Nonlinear correlation joint transform correlation,” Appl. Opt. 28, 2358–2367 (1989).
    [Crossref] [PubMed]
  9. S. Vallmitjana, A. Carnicer, E. Martı́n-Badosa, and I. Juvells, “Nonlinear filtering in object and Fourier space in a joint transform optical correlator: comparison and experimental realization,” Appl. Opt. 34, 3942–3949 (1995).
    [Crossref] [PubMed]
  10. C. Soutar, S. E. Monroe, and J. Knopp, “Complex characterisation of the Epson liquid crystal television,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 269–277 (1993).
    [Crossref]
  11. F. T. S. Yu, S. Jutamulia, T. W. Lin, and D. A. Gregory, “Adaptive real-time pattern recognition using a liquid crystal TV based joint transform correlator,” Appl. Opt. 26, 1370–1372 (1987).
    [Crossref] [PubMed]
  12. B. Javidi, J. Wang, and Q. Tang, “Multiple-object binary joint transform correlation using multiple level threshold crossing,” Appl. Opt. 30, 4234–4244 (1991).
    [Crossref] [PubMed]
  13. Q. Zhan and T. Minemoto, “Successful pattern matching with a large number of reference patterns using a joint Fourier-transform correlator,” Jpn. J. Appl. Phys. 32, 3471–3476 (1993).
    [Crossref]
  14. Y. Osugi, Q. Zhan, and T. Minemoto, “Hybrid binary subtracted joint transform correlator for a large number of reference patterns using a Bi12SiO20 (BSO) spatial light modulator and a laser scanner,” Opt. Rev. 1, 159–162 (1994).
    [Crossref]
  15. K. Chalasinska-Macukow and C. Gorecki, “Optoelectronic implementation of a quasi-phase correlator,” Opt. Commun. 93, 11–18 (1992).
    [Crossref]
  16. A. Carnicer, E. Martı́n-Badosa, I. Juvells, and S. Vallmitjana, “Spatial envelope-free nonlinear joint transform correlator,” Opt. Commun. 114, 336–343 (1995).
    [Crossref]
  17. D. Feng, H. Zhao, and S. Xia, “Amplitude modulated joint transform correlator for improving correlation discrimination,” Opt. Commun. 86, 260–264 (1991).
    [Crossref]
  18. F. Cheng, F. T. S. Yu, and D. A. Gregory, “Multitarget detection using spatial synthesis joint transform correlator,” Appl. Opt. 32, 6521–6526 (1993).
    [Crossref] [PubMed]
  19. H. Gunter and P. H. Higuard, Photorefractive Materials and Their Applications II, Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1989).
  20. T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect. A review,” Prog. Quantum Electron. 10, 77–146 (1985).
    [Crossref]
  21. M. G. Moharam, T. K. Gaylord, R. Magusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
    [Crossref]
  22. E. Ochoa, F. Vachss, and L. Hesselink, “Higher order analysis of the photorefractive effect for large modulation depths,” J. Opt. Soc. Am. A 3, 181–187 (1986).
    [Crossref]
  23. Y. Osugi, H. Mizukawa, and T. Minemoto, “Quantization and truncation conditions of Fourier power spectrum for good performance in a binary subtracted joint transform correlator,” Opt. Rev. 3, 161–170 (1996).
    [Crossref]
  24. B. Javidi, J. Ruiz, and C. Ruiz, “Performance of the binary nonlinear joint transform correlators in the presence of the Fourier plane quantization,” Opt. Commun. 80, 275–284 (1991).
    [Crossref]
  25. W. H. Lee, “Sampled Fourier transform hologram generated by computer,” Appl. Opt. 9, 639–643 (1970).
    [Crossref] [PubMed]
  26. H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms, Vol. 2 of Information Sciences (Springer-Verlag, Berlin, 1982).
  27. The number of flops per second can be obtained by means of a performance test. Specialized algorithms to deal with Fourier transforms are also available. The C code to test the marks of our computed was obtained from an anonymous ftp at ftp://ftp.nosc.mil/pub/aburto/tfftdp.c. Further details of compiler requirements for carrying out the test can be found at http://www.netlib.org/performance/html/PDSreports.html .
  28. B. V. K. Vijaya Kumar and L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
    [Crossref]
  29. C. Soutar, W. A. Gillespie, and C. M. Cartwright, “The effect of optical bias on grating formation dynamics in photorefractive BSO,” Opt. Commun. 90, 329–334 (1992).
    [Crossref]

1996 (1)

Y. Osugi, H. Mizukawa, and T. Minemoto, “Quantization and truncation conditions of Fourier power spectrum for good performance in a binary subtracted joint transform correlator,” Opt. Rev. 3, 161–170 (1996).
[Crossref]

1995 (2)

1994 (1)

Y. Osugi, Q. Zhan, and T. Minemoto, “Hybrid binary subtracted joint transform correlator for a large number of reference patterns using a Bi12SiO20 (BSO) spatial light modulator and a laser scanner,” Opt. Rev. 1, 159–162 (1994).
[Crossref]

1993 (2)

Q. Zhan and T. Minemoto, “Successful pattern matching with a large number of reference patterns using a joint Fourier-transform correlator,” Jpn. J. Appl. Phys. 32, 3471–3476 (1993).
[Crossref]

F. Cheng, F. T. S. Yu, and D. A. Gregory, “Multitarget detection using spatial synthesis joint transform correlator,” Appl. Opt. 32, 6521–6526 (1993).
[Crossref] [PubMed]

1992 (4)

C. Soutar, W. A. Gillespie, and C. M. Cartwright, “The effect of optical bias on grating formation dynamics in photorefractive BSO,” Opt. Commun. 90, 329–334 (1992).
[Crossref]

K. Chalasinska-Macukow and C. Gorecki, “Optoelectronic implementation of a quasi-phase correlator,” Opt. Commun. 93, 11–18 (1992).
[Crossref]

C. Kirsch, D. A. Gregory, M. W. Thie, and B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
[Crossref]

C. Soutar, Z. Q. Wang, C. M. Cartwright, and W. A. Gillespie, “Real-time optical intensity correlator using photorefractive BSO and liquid crystal television,” J. Mod. Opt. 39, 761–769 (1992).
[Crossref]

1991 (3)

D. Feng, H. Zhao, and S. Xia, “Amplitude modulated joint transform correlator for improving correlation discrimination,” Opt. Commun. 86, 260–264 (1991).
[Crossref]

B. Javidi, J. Wang, and Q. Tang, “Multiple-object binary joint transform correlation using multiple level threshold crossing,” Appl. Opt. 30, 4234–4244 (1991).
[Crossref] [PubMed]

B. Javidi, J. Ruiz, and C. Ruiz, “Performance of the binary nonlinear joint transform correlators in the presence of the Fourier plane quantization,” Opt. Commun. 80, 275–284 (1991).
[Crossref]

1990 (1)

1989 (1)

1987 (1)

1986 (1)

1985 (2)

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect. A review,” Prog. Quantum Electron. 10, 77–146 (1985).
[Crossref]

H-K. Liu, J. A. Davis, and R. A. Lilly, “Optical-data-processing properties of a liquid-crystal television spatial light modulator,” Opt. Lett. 10, 635–637 (1985).
[Crossref] [PubMed]

1984 (1)

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

1981 (1)

L. Pichon and J. P. Huignard, “Dynamic joint-Fourier transform correlator by Bragg diffraction in photorefractive Bi12SiO20 crystals,” Opt. Commun. 36, 277–280 (1981).
[Crossref]

1979 (1)

M. G. Moharam, T. K. Gaylord, R. Magusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

1970 (1)

1966 (1)

1964 (1)

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

Carnicer, A.

Cartwright, C. M.

C. Soutar, W. A. Gillespie, and C. M. Cartwright, “The effect of optical bias on grating formation dynamics in photorefractive BSO,” Opt. Commun. 90, 329–334 (1992).
[Crossref]

C. Soutar, Z. Q. Wang, C. M. Cartwright, and W. A. Gillespie, “Real-time optical intensity correlator using photorefractive BSO and liquid crystal television,” J. Mod. Opt. 39, 761–769 (1992).
[Crossref]

Chalasinska-Macukow, K.

K. Chalasinska-Macukow and C. Gorecki, “Optoelectronic implementation of a quasi-phase correlator,” Opt. Commun. 93, 11–18 (1992).
[Crossref]

Cheng, F.

Connors, L. M.

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect. A review,” Prog. Quantum Electron. 10, 77–146 (1985).
[Crossref]

Davis, J. A.

Feng, D.

D. Feng, H. Zhao, and S. Xia, “Amplitude modulated joint transform correlator for improving correlation discrimination,” Opt. Commun. 86, 260–264 (1991).
[Crossref]

Foote, P. D.

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect. A review,” Prog. Quantum Electron. 10, 77–146 (1985).
[Crossref]

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, R. Magusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

Gillespie, W. A.

C. Soutar, W. A. Gillespie, and C. M. Cartwright, “The effect of optical bias on grating formation dynamics in photorefractive BSO,” Opt. Commun. 90, 329–334 (1992).
[Crossref]

C. Soutar, Z. Q. Wang, C. M. Cartwright, and W. A. Gillespie, “Real-time optical intensity correlator using photorefractive BSO and liquid crystal television,” J. Mod. Opt. 39, 761–769 (1992).
[Crossref]

Goodman, J. W.

Gorecki, C.

K. Chalasinska-Macukow and C. Gorecki, “Optoelectronic implementation of a quasi-phase correlator,” Opt. Commun. 93, 11–18 (1992).
[Crossref]

Gregory, D. A.

Gunter, H.

H. Gunter and P. H. Higuard, Photorefractive Materials and Their Applications II, Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1989).

Hall, T. J.

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect. A review,” Prog. Quantum Electron. 10, 77–146 (1985).
[Crossref]

Hassebrook, L.

Hesselink, L.

Higuard, P. H.

H. Gunter and P. H. Higuard, Photorefractive Materials and Their Applications II, Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1989).

Huignard, J. P.

L. Pichon and J. P. Huignard, “Dynamic joint-Fourier transform correlator by Bragg diffraction in photorefractive Bi12SiO20 crystals,” Opt. Commun. 36, 277–280 (1981).
[Crossref]

Jaura, R.

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect. A review,” Prog. Quantum Electron. 10, 77–146 (1985).
[Crossref]

Javidi, B.

Jones, B. K.

C. Kirsch, D. A. Gregory, M. W. Thie, and B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
[Crossref]

Jutamulia, S.

Juvells, I.

Kirsch, C.

C. Kirsch, D. A. Gregory, M. W. Thie, and B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
[Crossref]

Knopp, J.

C. Soutar, S. E. Monroe, and J. Knopp, “Complex characterisation of the Epson liquid crystal television,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 269–277 (1993).
[Crossref]

Lee, W. H.

Lilly, R. A.

Lin, T. W.

Liu, H-K.

Lu, X. J.

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

Magusson, R.

M. G. Moharam, T. K. Gaylord, R. Magusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

Marti´n-Badosa, E.

Minemoto, T.

Y. Osugi, H. Mizukawa, and T. Minemoto, “Quantization and truncation conditions of Fourier power spectrum for good performance in a binary subtracted joint transform correlator,” Opt. Rev. 3, 161–170 (1996).
[Crossref]

Y. Osugi, Q. Zhan, and T. Minemoto, “Hybrid binary subtracted joint transform correlator for a large number of reference patterns using a Bi12SiO20 (BSO) spatial light modulator and a laser scanner,” Opt. Rev. 1, 159–162 (1994).
[Crossref]

Q. Zhan and T. Minemoto, “Successful pattern matching with a large number of reference patterns using a joint Fourier-transform correlator,” Jpn. J. Appl. Phys. 32, 3471–3476 (1993).
[Crossref]

Mizukawa, H.

Y. Osugi, H. Mizukawa, and T. Minemoto, “Quantization and truncation conditions of Fourier power spectrum for good performance in a binary subtracted joint transform correlator,” Opt. Rev. 3, 161–170 (1996).
[Crossref]

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, R. Magusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

Monroe, S. E.

C. Soutar, S. E. Monroe, and J. Knopp, “Complex characterisation of the Epson liquid crystal television,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 269–277 (1993).
[Crossref]

Nussbaumer, H. J.

H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms, Vol. 2 of Information Sciences (Springer-Verlag, Berlin, 1982).

Ochoa, E.

Osugi, Y.

Y. Osugi, H. Mizukawa, and T. Minemoto, “Quantization and truncation conditions of Fourier power spectrum for good performance in a binary subtracted joint transform correlator,” Opt. Rev. 3, 161–170 (1996).
[Crossref]

Y. Osugi, Q. Zhan, and T. Minemoto, “Hybrid binary subtracted joint transform correlator for a large number of reference patterns using a Bi12SiO20 (BSO) spatial light modulator and a laser scanner,” Opt. Rev. 1, 159–162 (1994).
[Crossref]

Pichon, L.

L. Pichon and J. P. Huignard, “Dynamic joint-Fourier transform correlator by Bragg diffraction in photorefractive Bi12SiO20 crystals,” Opt. Commun. 36, 277–280 (1981).
[Crossref]

Ruiz, C.

B. Javidi, J. Ruiz, and C. Ruiz, “Performance of the binary nonlinear joint transform correlators in the presence of the Fourier plane quantization,” Opt. Commun. 80, 275–284 (1991).
[Crossref]

Ruiz, J.

B. Javidi, J. Ruiz, and C. Ruiz, “Performance of the binary nonlinear joint transform correlators in the presence of the Fourier plane quantization,” Opt. Commun. 80, 275–284 (1991).
[Crossref]

Soutar, C.

C. Soutar, W. A. Gillespie, and C. M. Cartwright, “The effect of optical bias on grating formation dynamics in photorefractive BSO,” Opt. Commun. 90, 329–334 (1992).
[Crossref]

C. Soutar, Z. Q. Wang, C. M. Cartwright, and W. A. Gillespie, “Real-time optical intensity correlator using photorefractive BSO and liquid crystal television,” J. Mod. Opt. 39, 761–769 (1992).
[Crossref]

C. Soutar, S. E. Monroe, and J. Knopp, “Complex characterisation of the Epson liquid crystal television,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 269–277 (1993).
[Crossref]

Tang, Q.

Thie, M. W.

C. Kirsch, D. A. Gregory, M. W. Thie, and B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
[Crossref]

Vachss, F.

Vallmitjana, S.

VanderLugt, A.

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

Vijaya Kumar, B. V. K.

Wang, J.

Wang, Z. Q.

C. Soutar, Z. Q. Wang, C. M. Cartwright, and W. A. Gillespie, “Real-time optical intensity correlator using photorefractive BSO and liquid crystal television,” J. Mod. Opt. 39, 761–769 (1992).
[Crossref]

Weaver, C. S.

Xia, S.

D. Feng, H. Zhao, and S. Xia, “Amplitude modulated joint transform correlator for improving correlation discrimination,” Opt. Commun. 86, 260–264 (1991).
[Crossref]

Young, L.

M. G. Moharam, T. K. Gaylord, R. Magusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

Yu, F. T. S.

Yu, S.

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

Zhan, Q.

Y. Osugi, Q. Zhan, and T. Minemoto, “Hybrid binary subtracted joint transform correlator for a large number of reference patterns using a Bi12SiO20 (BSO) spatial light modulator and a laser scanner,” Opt. Rev. 1, 159–162 (1994).
[Crossref]

Q. Zhan and T. Minemoto, “Successful pattern matching with a large number of reference patterns using a joint Fourier-transform correlator,” Jpn. J. Appl. Phys. 32, 3471–3476 (1993).
[Crossref]

Zhao, H.

D. Feng, H. Zhao, and S. Xia, “Amplitude modulated joint transform correlator 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).

J. Appl. Phys. (1)

M. G. Moharam, T. K. Gaylord, R. Magusson, and L. Young, “Holographic grating formation in photorefractive crystals with arbitrary electron transport lengths,” J. Appl. Phys. 50, 5642–5651 (1979).
[Crossref]

J. Mod. Opt. (1)

C. Soutar, Z. Q. Wang, C. M. Cartwright, and W. A. Gillespie, “Real-time optical intensity correlator using photorefractive BSO and liquid crystal television,” J. Mod. Opt. 39, 761–769 (1992).
[Crossref]

J. Opt. Soc. Am. A (1)

Jpn. J. Appl. Phys. (1)

Q. Zhan and T. Minemoto, “Successful pattern matching with a large number of reference patterns using a joint Fourier-transform correlator,” Jpn. J. Appl. Phys. 32, 3471–3476 (1993).
[Crossref]

Opt. Commun. (7)

K. Chalasinska-Macukow and C. Gorecki, “Optoelectronic implementation of a quasi-phase correlator,” Opt. Commun. 93, 11–18 (1992).
[Crossref]

A. Carnicer, E. Martı́n-Badosa, I. Juvells, and S. Vallmitjana, “Spatial envelope-free nonlinear joint transform correlator,” Opt. Commun. 114, 336–343 (1995).
[Crossref]

D. Feng, H. Zhao, and S. Xia, “Amplitude modulated joint transform correlator for improving correlation discrimination,” Opt. Commun. 86, 260–264 (1991).
[Crossref]

L. Pichon and J. P. Huignard, “Dynamic joint-Fourier transform correlator by Bragg diffraction in photorefractive Bi12SiO20 crystals,” Opt. Commun. 36, 277–280 (1981).
[Crossref]

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

B. Javidi, J. Ruiz, and C. Ruiz, “Performance of the binary nonlinear joint transform correlators in the presence of the Fourier plane quantization,” Opt. Commun. 80, 275–284 (1991).
[Crossref]

C. Soutar, W. A. Gillespie, and C. M. Cartwright, “The effect of optical bias on grating formation dynamics in photorefractive BSO,” Opt. Commun. 90, 329–334 (1992).
[Crossref]

Opt. Eng. (1)

C. Kirsch, D. A. Gregory, M. W. Thie, and B. K. Jones, “Modulation characteristics of the Epson liquid crystal television,” Opt. Eng. 31, 963–969 (1992).
[Crossref]

Opt. Lett. (1)

Opt. Rev. (2)

Y. Osugi, Q. Zhan, and T. Minemoto, “Hybrid binary subtracted joint transform correlator for a large number of reference patterns using a Bi12SiO20 (BSO) spatial light modulator and a laser scanner,” Opt. Rev. 1, 159–162 (1994).
[Crossref]

Y. Osugi, H. Mizukawa, and T. Minemoto, “Quantization and truncation conditions of Fourier power spectrum for good performance in a binary subtracted joint transform correlator,” Opt. Rev. 3, 161–170 (1996).
[Crossref]

Prog. Quantum Electron. (1)

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect. A review,” Prog. Quantum Electron. 10, 77–146 (1985).
[Crossref]

Other (4)

H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms, Vol. 2 of Information Sciences (Springer-Verlag, Berlin, 1982).

The number of flops per second can be obtained by means of a performance test. Specialized algorithms to deal with Fourier transforms are also available. The C code to test the marks of our computed was obtained from an anonymous ftp at ftp://ftp.nosc.mil/pub/aburto/tfftdp.c. Further details of compiler requirements for carrying out the test can be found at http://www.netlib.org/performance/html/PDSreports.html .

H. Gunter and P. H. Higuard, Photorefractive Materials and Their Applications II, Vol. 62 of Topics in Applied Physics (Springer-Verlag, Berlin, 1989).

C. Soutar, S. E. Monroe, and J. Knopp, “Complex characterisation of the Epson liquid crystal television,” in Optical Pattern Recognition IV, D. P. Casasent, ed., Proc. SPIE1959, 269–277 (1993).
[Crossref]

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Figures (9)

Fig. 1
Fig. 1

Standard JTC experimental setup: L1, L2, lenses.

Fig. 2
Fig. 2

Variation of the square modulus of the space-charge field (proportional to the refractive index) with intensity modulation for a range of acceptor concentrations.

Fig. 3
Fig. 3

Matched joint scene with zero-mean Gaussian additive noise of standard deviation σ=70.

Fig. 4
Fig. 4

Simulated PTE results for the POPJTC and the PJTC with increasing noise.

Fig. 5
Fig. 5

BSO JTC experimental setup: P’s, polarizers; A, analyzer; other abbreviations as defined in text.

Fig. 6
Fig. 6

Experimental correlation of conventional input with a noisy scene (σ=70).

Fig. 7
Fig. 7

Experimental correlation of the encoded phase-only input with a noisy scene (σ=70).

Fig. 8
Fig. 8

Experimental PTE results for the POPJTC and the PJTC.

Fig. 9
Fig. 9

Measure of signal degradation owing to increasing noise.

Equations (26)

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

I(u, v)=|FR(u, v)|2+|FS(u, v)|2+2|FR(u, v)||FS(u, v)|cos[x0u+y0v+ϕS(u, v)-ϕR(u, v)],
Ib(u, v)=1I(u, v)IT(u, v)-1I(u, v)<IT(u, v),
Ib(u, v)=n=1An[u, v; IT(u, v)]cos{n[x0u+y0v+ϕS(u, v)-ϕR(u, v)]}.
IT(u, v)=|FR(u, v)|2+|FS(u, v)|2.
Ib(u, v)=n=0 12n+1 cos{(2n+1)[x0u+y0v+ϕS(u, v)-ϕR(u, v)]}=cos[x0u+y0v+ϕS(u, v)-ϕR(u, v)]+,
c(x, y)=δ(x-x0, y-y0)+δ(x+x0, y+y0).
m(u, v)=2[IS(u, v)IR(u, v)]1/2IS(u, v)+IR(u, v),
I(u, v)=[IR(u, v)+IS(u, v)]{1+m(u, v)×cos[x0u+y0v+ϕS(u, v)-ϕR(u, v)]}.
|Δn|=(n3r|E|)/2,
η=sin2πΔndλ2 cos θ2πΔndλ2 cos θ22,
|E|2 cos[x0u+y0v+ϕS(u, v)-ϕR(u, v)].
E=(1-m2)1/2-1m(Ea2+Ed2)1/2,
|E|2=(1-m2)1/2-1m2(Ea2+Ed2)+EdEq 2(1-m2)1/2-1m2(Ea2-Ed2)+2(1-m2)1/2-1(1-m2)1/2(Ea2+Ed2),
m=m1+(Ed/Eq)m.
fPO(x, y)=FT-1F(u, v)|F(u, v)|=FT-1FT[f(x, y)]|FT[f(x, y)]|,
h+(x, y)=h(x, y)h(x, y)00h(x, y)<0,
h-(x, y)=h(x, y)h(x, y)00h(x, y)>0.
r+(x, y)=1+nrn sin2πnxp,
r-(x, y)=1-nrn sin2πnxp.
hc(x, y)=h+(x, y)r+(x, y)+h-(x, y)r-(x, y)=[h+(x, y)+h-(x, y)]+[h+(x, y)-h-(x, y)]nrn sin2πnxp.
Hc(x, y)=[H+(u, v)+H-(u, v)]+[H+(u, v)-H-(u, v)]nrnδu-np=[H+(u, v)+H-(u, v)]+H(u, v)nrnδu-np.
flops=5N2(log2 N-2)+32N.
5N2(log2 N-2)+32N+5N2+5N2(log2 N-2)+32 N
=5N2(2 log2 N-3)+64N.
PTE=(fg)(0, 0)R2(fg)(x, y)dxdy.
SNR=correlationpeakmaximumvarianceofintensities<(max/2)

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