Abstract

A Bi12SiO20 crystal, cut in the transverse orientation as for holographic applications, is used as a spatial filtering device in the Fourier plane of a coherent single-beam optical processor with λ = 633 nm. Frequency selection is obtained by adjusting a polarizing compensator to suppress or to select some part of the spectrum, which is characterized by a certain ellipticity of polarization, depending on its intensity.

© 1990 Optical Society of America

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References

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  1. J. P. Huignard and F. Micheron, “High-sensitivity read-write volume holographic storage in BSO and BGO crystals,” Appl. Phys. Lett. 29, 591–593 (1976).
    [Crossref]
  2. P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
    [Crossref]
  3. R. A. Sprague and P. Nisenson, “The PROM–a status report,” Opt. Eng. 17, 256–266 (1978).
    [Crossref]
  4. F. Höller and H. J. Tiziani, “A spatial light modulator using BSO crystals,” Opt. Commun. 58, 20–24 (1986).
    [Crossref]
  5. L. Pugliese and G. M. Morris, “Bandpass filtering in BaTiO3,” Appl. Opt. 27, 4535–4539 (1988).
    [Crossref] [PubMed]
  6. J. Ma, L. Liu, Z. Wang, and L. Xu, “Controllable real-time simple spatial filter based on selectivity erasing in photorefractive two-beam coupling,” Opt. Commun. 74, 15–18 (1989).
    [Crossref]
  7. J. A. Khoury, G. Hussian, and R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70, 272–276 (1989).
    [Crossref]
  8. N. A. Vainos and R. W. Eason, “Real time edge enhancement by active spatial filtering via five wave mixing in photorefractive BSO,” Opt. Commun. 59, 167–172 (1986).
    [Crossref]
  9. J. P. Huignard and J. P. Herriau, “Real-time coherent object edge reconstruction with BSO crystals,” Appl. Opt. 17, 2671–2672 (1978).
    [Crossref] [PubMed]
  10. E. Ochoa, J. W. Goodman, and L. Hesselink, “Real-time enhancement of defects in a periodic mask using photorefractive BSO,” Opt. Lett. 10, 430–432 (1985).
    [Crossref] [PubMed]
  11. R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. A 38, 671 (1948).
    [Crossref]
  12. G. N. Ramachandran and S. Ramaseshan, “Crystal optics,” in Encyclopaedia of Physics, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. 25, p. 1.
  13. P. Pellat-Finet, “Measurement of the electro-optical coefficient in BSO,” Opt. Commun. 50, 275–280 (1984).
    [Crossref]
  14. D. Joyeux and S. Lowenthal, “Optical Fourier transform: what is the optimal setup?”Appl. Opt. 21, 4368–4372 (1982).
    [Crossref] [PubMed]
  15. H. Bayer, Theorie und Praxis des Phasenkontrastverfahrens (Akademische Verlagsgesellschaft, Frankfurt, 1965).
  16. M. Pluta, “Simplified polanret system for microscopy,” Appl. Opt. 28, 1453–1466 (1989).
    [Crossref] [PubMed]
  17. H. Wolter, “Phasen-und Amplitudenmessung durch Elliptizitätsanalyse an Phasenkontrastbildern,” Z. Phys. 140, 57–74 (1955).
    [Crossref]
  18. K. G. Birch, “A spatial frequency filter to remove zero frequency,” Opt. Acta 15, 113–127 (1968).
  19. M. Young, “Spatial filtering for linewidth measurement,” Appl. Opt. 28, 1467–1473 (1989).
    [Crossref] [PubMed]

1989 (4)

J. Ma, L. Liu, Z. Wang, and L. Xu, “Controllable real-time simple spatial filter based on selectivity erasing in photorefractive two-beam coupling,” Opt. Commun. 74, 15–18 (1989).
[Crossref]

J. A. Khoury, G. Hussian, and R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70, 272–276 (1989).
[Crossref]

M. Pluta, “Simplified polanret system for microscopy,” Appl. Opt. 28, 1453–1466 (1989).
[Crossref] [PubMed]

M. Young, “Spatial filtering for linewidth measurement,” Appl. Opt. 28, 1467–1473 (1989).
[Crossref] [PubMed]

1988 (1)

1986 (2)

N. A. Vainos and R. W. Eason, “Real time edge enhancement by active spatial filtering via five wave mixing in photorefractive BSO,” Opt. Commun. 59, 167–172 (1986).
[Crossref]

F. Höller and H. J. Tiziani, “A spatial light modulator using BSO crystals,” Opt. Commun. 58, 20–24 (1986).
[Crossref]

1985 (1)

1984 (1)

P. Pellat-Finet, “Measurement of the electro-optical coefficient in BSO,” Opt. Commun. 50, 275–280 (1984).
[Crossref]

1982 (2)

D. Joyeux and S. Lowenthal, “Optical Fourier transform: what is the optimal setup?”Appl. Opt. 21, 4368–4372 (1982).
[Crossref] [PubMed]

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

1978 (2)

1976 (1)

J. P. Huignard and F. Micheron, “High-sensitivity read-write volume holographic storage in BSO and BGO crystals,” Appl. Phys. Lett. 29, 591–593 (1976).
[Crossref]

1968 (1)

K. G. Birch, “A spatial frequency filter to remove zero frequency,” Opt. Acta 15, 113–127 (1968).

1955 (1)

H. Wolter, “Phasen-und Amplitudenmessung durch Elliptizitätsanalyse an Phasenkontrastbildern,” Z. Phys. 140, 57–74 (1955).
[Crossref]

1948 (1)

R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. A 38, 671 (1948).
[Crossref]

Bayer, H.

H. Bayer, Theorie und Praxis des Phasenkontrastverfahrens (Akademische Verlagsgesellschaft, Frankfurt, 1965).

Birch, K. G.

K. G. Birch, “A spatial frequency filter to remove zero frequency,” Opt. Acta 15, 113–127 (1968).

Eason, R. W.

J. A. Khoury, G. Hussian, and R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70, 272–276 (1989).
[Crossref]

N. A. Vainos and R. W. Eason, “Real time edge enhancement by active spatial filtering via five wave mixing in photorefractive BSO,” Opt. Commun. 59, 167–172 (1986).
[Crossref]

Goodman, J. W.

Günter, P.

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

Herriau, J. P.

Hesselink, L.

Höller, F.

F. Höller and H. J. Tiziani, “A spatial light modulator using BSO crystals,” Opt. Commun. 58, 20–24 (1986).
[Crossref]

Huignard, J. P.

J. P. Huignard and J. P. Herriau, “Real-time coherent object edge reconstruction with BSO crystals,” Appl. Opt. 17, 2671–2672 (1978).
[Crossref] [PubMed]

J. P. Huignard and F. Micheron, “High-sensitivity read-write volume holographic storage in BSO and BGO crystals,” Appl. Phys. Lett. 29, 591–593 (1976).
[Crossref]

Hussian, G.

J. A. Khoury, G. Hussian, and R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70, 272–276 (1989).
[Crossref]

Jones, R. C.

R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. A 38, 671 (1948).
[Crossref]

Joyeux, D.

Khoury, J. A.

J. A. Khoury, G. Hussian, and R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70, 272–276 (1989).
[Crossref]

Liu, L.

J. Ma, L. Liu, Z. Wang, and L. Xu, “Controllable real-time simple spatial filter based on selectivity erasing in photorefractive two-beam coupling,” Opt. Commun. 74, 15–18 (1989).
[Crossref]

Lowenthal, S.

Ma, J.

J. Ma, L. Liu, Z. Wang, and L. Xu, “Controllable real-time simple spatial filter based on selectivity erasing in photorefractive two-beam coupling,” Opt. Commun. 74, 15–18 (1989).
[Crossref]

Micheron, F.

J. P. Huignard and F. Micheron, “High-sensitivity read-write volume holographic storage in BSO and BGO crystals,” Appl. Phys. Lett. 29, 591–593 (1976).
[Crossref]

Morris, G. M.

Nisenson, P.

R. A. Sprague and P. Nisenson, “The PROM–a status report,” Opt. Eng. 17, 256–266 (1978).
[Crossref]

Ochoa, E.

Pellat-Finet, P.

P. Pellat-Finet, “Measurement of the electro-optical coefficient in BSO,” Opt. Commun. 50, 275–280 (1984).
[Crossref]

Pluta, M.

Pugliese, L.

Ramachandran, G. N.

G. N. Ramachandran and S. Ramaseshan, “Crystal optics,” in Encyclopaedia of Physics, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. 25, p. 1.

Ramaseshan, S.

G. N. Ramachandran and S. Ramaseshan, “Crystal optics,” in Encyclopaedia of Physics, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. 25, p. 1.

Sprague, R. A.

R. A. Sprague and P. Nisenson, “The PROM–a status report,” Opt. Eng. 17, 256–266 (1978).
[Crossref]

Tiziani, H. J.

F. Höller and H. J. Tiziani, “A spatial light modulator using BSO crystals,” Opt. Commun. 58, 20–24 (1986).
[Crossref]

Vainos, N. A.

N. A. Vainos and R. W. Eason, “Real time edge enhancement by active spatial filtering via five wave mixing in photorefractive BSO,” Opt. Commun. 59, 167–172 (1986).
[Crossref]

Wang, Z.

J. Ma, L. Liu, Z. Wang, and L. Xu, “Controllable real-time simple spatial filter based on selectivity erasing in photorefractive two-beam coupling,” Opt. Commun. 74, 15–18 (1989).
[Crossref]

Wolter, H.

H. Wolter, “Phasen-und Amplitudenmessung durch Elliptizitätsanalyse an Phasenkontrastbildern,” Z. Phys. 140, 57–74 (1955).
[Crossref]

Xu, L.

J. Ma, L. Liu, Z. Wang, and L. Xu, “Controllable real-time simple spatial filter based on selectivity erasing in photorefractive two-beam coupling,” Opt. Commun. 74, 15–18 (1989).
[Crossref]

Young, M.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

J. P. Huignard and F. Micheron, “High-sensitivity read-write volume holographic storage in BSO and BGO crystals,” Appl. Phys. Lett. 29, 591–593 (1976).
[Crossref]

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

R. C. Jones, “A new calculus for the treatment of optical systems,” J. Opt. Soc. Am. A 38, 671 (1948).
[Crossref]

Opt. Acta (1)

K. G. Birch, “A spatial frequency filter to remove zero frequency,” Opt. Acta 15, 113–127 (1968).

Opt. Commun. (5)

P. Pellat-Finet, “Measurement of the electro-optical coefficient in BSO,” Opt. Commun. 50, 275–280 (1984).
[Crossref]

F. Höller and H. J. Tiziani, “A spatial light modulator using BSO crystals,” Opt. Commun. 58, 20–24 (1986).
[Crossref]

J. Ma, L. Liu, Z. Wang, and L. Xu, “Controllable real-time simple spatial filter based on selectivity erasing in photorefractive two-beam coupling,” Opt. Commun. 74, 15–18 (1989).
[Crossref]

J. A. Khoury, G. Hussian, and R. W. Eason, “Contrast manipulation and controllable spatial filtering via photorefractive two-beam coupling,” Opt. Commun. 70, 272–276 (1989).
[Crossref]

N. A. Vainos and R. W. Eason, “Real time edge enhancement by active spatial filtering via five wave mixing in photorefractive BSO,” Opt. Commun. 59, 167–172 (1986).
[Crossref]

Opt. Eng. (1)

R. A. Sprague and P. Nisenson, “The PROM–a status report,” Opt. Eng. 17, 256–266 (1978).
[Crossref]

Opt. Lett. (1)

Phys. Rep. (1)

P. Günter, “Holography, coherent light amplification and optical phase conjugation with photorefractive materials,” Phys. Rep. 93, 199–299 (1982).
[Crossref]

Z. Phys. (1)

H. Wolter, “Phasen-und Amplitudenmessung durch Elliptizitätsanalyse an Phasenkontrastbildern,” Z. Phys. 140, 57–74 (1955).
[Crossref]

Other (2)

H. Bayer, Theorie und Praxis des Phasenkontrastverfahrens (Akademische Verlagsgesellschaft, Frankfurt, 1965).

G. N. Ramachandran and S. Ramaseshan, “Crystal optics,” in Encyclopaedia of Physics, S. Flügge, ed. (Springer-Verlag, Berlin, 1961), Vol. 25, p. 1.

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Figures (9)

Fig. 1
Fig. 1

Orientation and indicatrix of the BSO crystal with and without applied electrical field.

Fig. 2
Fig. 2

Optical setup.

Fig. 3
Fig. 3

Dependence of amplitude and phase transmission function of the BSO filter on the analyzer orientation.

Fig. 4
Fig. 4

Phase contrast: (a) positive, (b) negative.

Fig. 5
Fig. 5

Edge enhancement: (a) input image of a wire; (b) edge-enhanced and (c) contrast-inverted images.

Fig. 6
Fig. 6

Defect enhancement: (a) input image with disturbance in periodicity, (b) defect-enhanced image.

Fig. 7
Fig. 7

Edge-enhanced periodic image of Fig. 6(a).

Fig. 8
Fig. 8

Defect suppression applied to Fig. 6.

Fig. 9
Fig. 9

Example of noise suppression: (a) noisy input, (b) restorated grating.

Equations (5)

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E = j / σ .
σ = σ d + σ p = σ d / η I ,
σ d = 1.6 × 10 15 Ω 1 cm 1 , η = 3.7 × 10 10 cm Ω 1 W 1 .
n ± = n 0 ± 1 2 n 0 3 r 41 E .
M BSO = [ cos ( d r g ) ( ρ + i g 45 ) sin ( d r g ) r g ( ρ + i g 45 ) sin ( d r g ) r g cos ( d r g ) ] ,

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