Abstract

A novel technique of processing optical images that we call spatial amplification is proposed and demonstrated. The basic idea is to amplify coherently a set of selected spatial frequency components of an image. Unlike in the usual spatial filtering techniques, in which the components are selectively blocked out at the Fourier plane of a coherent processor, spatial amplification does not discard any of the incident image information. The advantages of the proposed technique over spatial filtering include high energy efficiency and the possibility for cascading several stages. In the demonstrated experiments, the required amplification is provided by two-beam energy coupling in a photorefractive BaTiO3 crystal with a nonuniform pump beam.

© 1990 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).
  2. J. Tsujiuchi, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. II, Chap. IV.
  3. V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
    [Crossref]
  4. Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).
  5. P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989).
    [Crossref]
  6. A. E. T. Chiou, P. Yeh, Opt. Lett. 10, 621 (1985).
    [Crossref] [PubMed]
  7. J. Feinberg, Opt. Lett. 5, 330 (1980).
    [Crossref] [PubMed]
  8. B. Fischer, S. Weiss, S. Sternklar, Appl. Phys. Lett. 50, 483 (1987).
    [Crossref]

1989 (1)

P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989).
[Crossref]

1987 (1)

B. Fischer, S. Weiss, S. Sternklar, Appl. Phys. Lett. 50, 483 (1987).
[Crossref]

1986 (1)

Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

1985 (1)

1980 (1)

1979 (1)

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[Crossref]

Chiou, A. E. T.

Fainman, Y.

Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

Feinberg, J.

Fischer, B.

B. Fischer, S. Weiss, S. Sternklar, Appl. Phys. Lett. 50, 483 (1987).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

Klancnik, E.

Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

Kukhtarev, N. V.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[Crossref]

Lee, S. H.

Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

Odulov, S. G.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[Crossref]

Soskin, M. S.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[Crossref]

Sternklar, S.

B. Fischer, S. Weiss, S. Sternklar, Appl. Phys. Lett. 50, 483 (1987).
[Crossref]

Tsujiuchi, J.

J. Tsujiuchi, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. II, Chap. IV.

Vinetskii, V. L.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[Crossref]

Weiss, S.

B. Fischer, S. Weiss, S. Sternklar, Appl. Phys. Lett. 50, 483 (1987).
[Crossref]

Yeh, P.

Appl. Phys. Lett. (1)

B. Fischer, S. Weiss, S. Sternklar, Appl. Phys. Lett. 50, 483 (1987).
[Crossref]

IEEE J. Quantum Electron. (1)

P. Yeh, IEEE J. Quantum Electron. 25, 484 (1989).
[Crossref]

Opt. Eng. (1)

Y. Fainman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

Opt. Lett. (2)

Sov. Phys. Usp. (1)

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[Crossref]

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

J. Tsujiuchi, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1963), Vol. II, Chap. IV.

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Figures (5)

Fig. 1
Fig. 1

Concept of spatial amplification: an input image is Fourier transformed into an amplifying medium, where spatial frequencies are selectively amplified, then it is reimaged by another Fourier transformation. Since no spatial frequency component is removed, this process can be cascaded for further processing. IP, input plane; OP, output plane.

Fig. 2
Fig. 2

Example of spatial amplification using numerical simulation, (a) Input intensity pattern, (b) after high-frequency-pass spatial filtering (the intensity is magnified 30 times to accentuate features otherwise not clearly visible), and (c) after amplification of higher-order spatial frequencies. The energy efficiency and the preservation of the original image aspects of spatial amplification compared with spatial filtering are illustrated well.

Fig. 3
Fig. 3

Experimental arrangement to demonstrate spatial amplification. M1–M3, mirrors.

Fig. 4
Fig. 4

Experimental result of spatial amplification, (a) The original image, (b) the processed image after amplifying only the spatial frequencies corresponding to horizontal lines, (c) the processed image after amplifying only the spatial frequencies corresponding to the vertical lines. The characteristic double line for each original bar is clearly seen in (b) and (c). The exposure time of (b) and (c) was snorter than that of (a) since the overall intensity of the enhanced image is much higher owing to the gain of 100 in higher-order spatial frequency components. Even though it is not apparent, (b) and (c) contain the image of (a).

Fig. 5
Fig. 5

Edge-enhancement result of a three-bar image using spatial amplification, (a) The scanned original image beam profile, (b) the scanned processed image beam profile. The result shown in (b) agrees well with the numerical simulation result given in Fig. 2(c).

Equations (3)

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d d z I 1 = Γ I 1 I 2 I 1 + I 2 α I 1 ,
d d z I 2 = Γ I 1 I 2 I 1 + I 2 α I 2 ,
d d z ψ 1 = β I 2 I 1 + I 2 , d d z ψ 2 = β I 2 I 1 + I 2 ,

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