Abstract

We propose what we believe to be a novel and simple method for optical symmetry filtering, using anisotropic self-diffraction in BaTiO3 crystals. This method allows us to distinguish a centrosymmetric pattern from a noncentrosymmetric pattern easily with scale invariance. It is self-referential; no extra reference element is required. Both the theory and the experiment are demonstrated.

© 1999 Optical Society of America

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References

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  1. J.-P. Huignard, P. Gunter, Photorefractive Materials and Their Applications: I. Fundamental Phenomena; Photorefractive Materials and Their Applications: II. Applications (Springer-Verlag, New York, 1988, 1989).
  2. A. B. VanderLugt, “Signal detection by complex spatial filter,” IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  3. F. T. S. Yu, S. Jutamulia, Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992).
  4. F. T. S. Yu, S. Jutamulia, T. W. Lin, D. A. Gregory, “Adaptive real-time pattern recognition using a liquid crystal TV based on joint transform correlator,” Appl. Opt. 26, 1370–1372 (1987).
    [CrossRef] [PubMed]
  5. H. Rajbenbach, S. Bann, P. Réfrégier, P. Joffre, J.-P. Huignard, H.-S. Buchkremer, A. S. Jensen, E. Rasmussen, K.-H. Brenner, G. Lohman, “Compact photorefractive correlator for robotic applications,” Appl. Opt. 31, 5666–5674 (1992).
    [CrossRef] [PubMed]
  6. J. White, A. Yariv, “Real-time image processing via 4-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
    [CrossRef]
  7. E. T. Chiou, P. Yeh, “Symmetry filters using optical correlation and convolution,” Opt. Eng. 29, 1065–1072 (1990).
    [CrossRef]
  8. L. Pichon, J.-P. Huignard, “Dynamic joint-Fourier-transform by Bragg-diffraction in photorefractive Bi12SiO20 crystals,” Opt. Commun. 36, 277–280 (1981).
    [CrossRef]
  9. N. V. Kukhtarev, E. Krazig, H. C. Kulich, R. A. Rupp, “Anisotropic self-diffraction in BaTiO3,” Appl. Phys. B 35, 17–21 (1984).
    [CrossRef]
  10. C. C. Sun, M. W. Chang, K. Y. Hsu, “Matrix–matrix multiplication by using anisotropic self-diffraction in BaTiO3,” Appl. Opt. 33, 4501–4507 (1994).
    [CrossRef] [PubMed]
  11. C. C. Sun, M. W. Chang, K. Y. Hsu, “Anisotropic diffraction of strong volume hologram in BaTiO3,” Opt. Commun. 119, 597–603 (1995).
    [CrossRef]
  12. C. C. Sun, B. Wang, J. Y. Chang, “Photorefractive incoherent-to-coherent optical converter by using anisotropic self-diffraction in BaTiO3,” Appl. Opt. 37, 8247–8253 (1998).
    [CrossRef]
  13. C. C. Sun, M. W. Chang, K. Y. Hsu, “Optical information processing by using anisotropic diffraction in BaTiO3,” Intl. J. Optoelectron. 11, 413–424 (1997).
  14. H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  15. C. C. Sun, M. W. Chang, K. Y. Hsu, “Contrast-reversible photorefractive incoherent-to-coherent optical converter by using an anisotropic strong volume hologram,” Opt. Lett. 18, 655–657 (1993).
    [CrossRef] [PubMed]

1998

1997

C. C. Sun, M. W. Chang, K. Y. Hsu, “Optical information processing by using anisotropic diffraction in BaTiO3,” Intl. J. Optoelectron. 11, 413–424 (1997).

1995

C. C. Sun, M. W. Chang, K. Y. Hsu, “Anisotropic diffraction of strong volume hologram in BaTiO3,” Opt. Commun. 119, 597–603 (1995).
[CrossRef]

1994

1993

1992

1990

E. T. Chiou, P. Yeh, “Symmetry filters using optical correlation and convolution,” Opt. Eng. 29, 1065–1072 (1990).
[CrossRef]

1987

1984

N. V. Kukhtarev, E. Krazig, H. C. Kulich, R. A. Rupp, “Anisotropic self-diffraction in BaTiO3,” Appl. Phys. B 35, 17–21 (1984).
[CrossRef]

1981

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

1980

J. White, A. Yariv, “Real-time image processing via 4-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

1969

H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

1964

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

Bann, S.

Brenner, K.-H.

Buchkremer, H.-S.

Chang, J. Y.

Chang, M. W.

C. C. Sun, M. W. Chang, K. Y. Hsu, “Optical information processing by using anisotropic diffraction in BaTiO3,” Intl. J. Optoelectron. 11, 413–424 (1997).

C. C. Sun, M. W. Chang, K. Y. Hsu, “Anisotropic diffraction of strong volume hologram in BaTiO3,” Opt. Commun. 119, 597–603 (1995).
[CrossRef]

C. C. Sun, M. W. Chang, K. Y. Hsu, “Matrix–matrix multiplication by using anisotropic self-diffraction in BaTiO3,” Appl. Opt. 33, 4501–4507 (1994).
[CrossRef] [PubMed]

C. C. Sun, M. W. Chang, K. Y. Hsu, “Contrast-reversible photorefractive incoherent-to-coherent optical converter by using an anisotropic strong volume hologram,” Opt. Lett. 18, 655–657 (1993).
[CrossRef] [PubMed]

Chiou, E. T.

E. T. Chiou, P. Yeh, “Symmetry filters using optical correlation and convolution,” Opt. Eng. 29, 1065–1072 (1990).
[CrossRef]

Gregory, D. A.

Gunter, P.

J.-P. Huignard, P. Gunter, Photorefractive Materials and Their Applications: I. Fundamental Phenomena; Photorefractive Materials and Their Applications: II. Applications (Springer-Verlag, New York, 1988, 1989).

Hsu, K. Y.

C. C. Sun, M. W. Chang, K. Y. Hsu, “Optical information processing by using anisotropic diffraction in BaTiO3,” Intl. J. Optoelectron. 11, 413–424 (1997).

C. C. Sun, M. W. Chang, K. Y. Hsu, “Anisotropic diffraction of strong volume hologram in BaTiO3,” Opt. Commun. 119, 597–603 (1995).
[CrossRef]

C. C. Sun, M. W. Chang, K. Y. Hsu, “Matrix–matrix multiplication by using anisotropic self-diffraction in BaTiO3,” Appl. Opt. 33, 4501–4507 (1994).
[CrossRef] [PubMed]

C. C. Sun, M. W. Chang, K. Y. Hsu, “Contrast-reversible photorefractive incoherent-to-coherent optical converter by using an anisotropic strong volume hologram,” Opt. Lett. 18, 655–657 (1993).
[CrossRef] [PubMed]

Huignard, J.-P.

H. Rajbenbach, S. Bann, P. Réfrégier, P. Joffre, J.-P. Huignard, H.-S. Buchkremer, A. S. Jensen, E. Rasmussen, K.-H. Brenner, G. Lohman, “Compact photorefractive correlator for robotic applications,” Appl. Opt. 31, 5666–5674 (1992).
[CrossRef] [PubMed]

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

J.-P. Huignard, P. Gunter, Photorefractive Materials and Their Applications: I. Fundamental Phenomena; Photorefractive Materials and Their Applications: II. Applications (Springer-Verlag, New York, 1988, 1989).

Jensen, A. S.

Joffre, P.

Jutamulia, S.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Krazig, E.

N. V. Kukhtarev, E. Krazig, H. C. Kulich, R. A. Rupp, “Anisotropic self-diffraction in BaTiO3,” Appl. Phys. B 35, 17–21 (1984).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, E. Krazig, H. C. Kulich, R. A. Rupp, “Anisotropic self-diffraction in BaTiO3,” Appl. Phys. B 35, 17–21 (1984).
[CrossRef]

Kulich, H. C.

N. V. Kukhtarev, E. Krazig, H. C. Kulich, R. A. Rupp, “Anisotropic self-diffraction in BaTiO3,” Appl. Phys. B 35, 17–21 (1984).
[CrossRef]

Lin, T. W.

Lohman, G.

Pichon, L.

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

Rajbenbach, H.

Rasmussen, E.

Réfrégier, P.

Rupp, R. A.

N. V. Kukhtarev, E. Krazig, H. C. Kulich, R. A. Rupp, “Anisotropic self-diffraction in BaTiO3,” Appl. Phys. B 35, 17–21 (1984).
[CrossRef]

Sun, C. C.

VanderLugt, A. B.

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

Wang, B.

White, J.

J. White, A. Yariv, “Real-time image processing via 4-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Yariv, A.

J. White, A. Yariv, “Real-time image processing via 4-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Yeh, P.

E. T. Chiou, P. Yeh, “Symmetry filters using optical correlation and convolution,” Opt. Eng. 29, 1065–1072 (1990).
[CrossRef]

Yu, F. T. S.

Appl. Opt.

Appl. Phys. B

N. V. Kukhtarev, E. Krazig, H. C. Kulich, R. A. Rupp, “Anisotropic self-diffraction in BaTiO3,” Appl. Phys. B 35, 17–21 (1984).
[CrossRef]

Appl. Phys. Lett.

J. White, A. Yariv, “Real-time image processing via 4-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
[CrossRef]

Bell Syst. Tech. J.

H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

IEEE Trans. Inf. Theory

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

Intl. J. Optoelectron.

C. C. Sun, M. W. Chang, K. Y. Hsu, “Optical information processing by using anisotropic diffraction in BaTiO3,” Intl. J. Optoelectron. 11, 413–424 (1997).

Opt. Commun.

C. C. Sun, M. W. Chang, K. Y. Hsu, “Anisotropic diffraction of strong volume hologram in BaTiO3,” Opt. Commun. 119, 597–603 (1995).
[CrossRef]

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

Opt. Eng.

E. T. Chiou, P. Yeh, “Symmetry filters using optical correlation and convolution,” Opt. Eng. 29, 1065–1072 (1990).
[CrossRef]

Opt. Lett.

Other

J.-P. Huignard, P. Gunter, Photorefractive Materials and Their Applications: I. Fundamental Phenomena; Photorefractive Materials and Their Applications: II. Applications (Springer-Verlag, New York, 1988, 1989).

F. T. S. Yu, S. Jutamulia, Optical Signal Processing, Computing, and Neural Networks (Wiley, New York, 1992).

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram of ASD. K e and K o are the wave numbers of the extraordinary and the ordinary waves, respectively.

Fig. 2
Fig. 2

Theoretical calculation of diffraction efficiency as a function of interaction length. In the calculation, m = 1 and λ = 514.5 nm.

Fig. 3
Fig. 3

Experimental setup. M, mirror; L, lens; BS, beam splitter; P, input pattern.

Fig. 4
Fig. 4

Computer simulation. The upper patterns are the input ones, and the lower patterns are the autoconvolutions of the corresponding input patterns. P, central peak value.

Fig. 5
Fig. 5

Experimental results. Leftmost, input patterns; middle, output signals; rightmost, three-dimensional profiles of the output signals. P, central peak value.

Fig. 6
Fig. 6

Synthesis of the output patterns when the pump beams were incident on the crystal at different angles.

Fig. 7
Fig. 7

Normalized autoconvolution factor F ac with respect to pattern size.

Fig. 8
Fig. 8

Temporal behavior of output powers with different illumination intensities.

Equations (16)

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Kg=Ke2-Ke1.
Ko1=Ke1-Kg,
Ko2=Ke2+Kg.
Ke1,2 sin θw=Ko1,2 sin θd,
Ke1,2 cos θw=Ko1,2 cos θd,
θw=sin-11neno2-ne21/2,
θd=sin-13nono2-ne21/2,
12Io1Io1x+i Ψo1xIo11/2 expiΨo1=γ Ie1Ie21/2I0Ie11/2 expi2Ψe1-Ψe2,12Io2Io2x+i Ψo2xIo21/2 expiΨo2=-γ Ie1Ie21/2I0Ie21/2 expi2Ψe2-Ψe1,12Ie1Ie1x+i Ψe1xIe11/2 expiΨe1=-γ Ie1Ie21/2I0Io11/2 expiΨo1-Ψe1+Ψe2,12Ie2Ie2x+i Ψe2xIe21/2 expiΨe2=γ Ie1Ie21/2I0Io21/2 expiΨo2+Ψe1-Ψe2,
ηLIo1,2LIe1,20=11+mπΔnLλ-2,
Δn=12KbTqKg1+Kg/K02none2γ42,
K0=Nq2oKbT1/2,
Ψo1,2=2Ψe1,2-Ψe2,1,
Ao1,2  Ae1,22Ae2,1*,
Ao1  Fae1Fae1,
FAo1  ao1ao1,
Fac=Id/Ii.

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