Abstract

Edge enhancement, a type of optical image processing, is performed in a photorefractive material in real time and with low incident-light intensities (10−3 W/cm2). We calculate the expected images using two different four-wave mixing geometries, which show good agreement with the images that we experimentally observe using a single-domain crystal of BaTiO3 as the photorefractive material.

© 1980 Optical Society of America

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References

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  1. J. P. Huignard, J. P. Herriau, Appl. Opt. 17, 2671 (1978).
    [CrossRef] [PubMed]
  2. J. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
    [CrossRef]
  3. F. S. Cheng, J. T. La Macchia, D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).
    [CrossRef]
  4. For a discussion of grating formation by Gaussian beams, seeM. G. Moharam, L. Young, J. Appl. Phys. 47, 4048 (1976). The plane-wave approximation is sufficient to describe grating formation in our experiments because in both imaging geometries used here the width of the focused object beam (~0.2 mm) is much less than the width (2 mm FWHM) of the reference beam. The plane-wave approximation is sufficient for image reconstruction whenever g = d sin θ/w ≲ 1. Here d is the grating width (d = 2 mm), θ is the Bragg angle in the medium (θ ~ 7.5°), and w is the Gaussian reading beam 1/e2 radius (~1 mm). This gives g = 0.3. See M. G. Moharam, T. K. Gaylord, R. Magnusson, J. Opt. Soc. Am. 70, 300 (1980).
    [CrossRef]
  5. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
    [CrossRef]

1980 (2)

J. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

1978 (1)

1976 (1)

For a discussion of grating formation by Gaussian beams, seeM. G. Moharam, L. Young, J. Appl. Phys. 47, 4048 (1976). The plane-wave approximation is sufficient to describe grating formation in our experiments because in both imaging geometries used here the width of the focused object beam (~0.2 mm) is much less than the width (2 mm FWHM) of the reference beam. The plane-wave approximation is sufficient for image reconstruction whenever g = d sin θ/w ≲ 1. Here d is the grating width (d = 2 mm), θ is the Bragg angle in the medium (θ ~ 7.5°), and w is the Gaussian reading beam 1/e2 radius (~1 mm). This gives g = 0.3. See M. G. Moharam, T. K. Gaylord, R. Magnusson, J. Opt. Soc. Am. 70, 300 (1980).
[CrossRef]

1968 (1)

F. S. Cheng, J. T. La Macchia, D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).
[CrossRef]

Cheng, F. S.

F. S. Cheng, J. T. La Macchia, D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).
[CrossRef]

Feinberg, J.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Fraser, D. B.

F. S. Cheng, J. T. La Macchia, D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).
[CrossRef]

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Hellwarth, R. W.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Herriau, J. P.

Huignard, J. P.

La Macchia, J. T.

F. S. Cheng, J. T. La Macchia, D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).
[CrossRef]

Moharam, M. G.

For a discussion of grating formation by Gaussian beams, seeM. G. Moharam, L. Young, J. Appl. Phys. 47, 4048 (1976). The plane-wave approximation is sufficient to describe grating formation in our experiments because in both imaging geometries used here the width of the focused object beam (~0.2 mm) is much less than the width (2 mm FWHM) of the reference beam. The plane-wave approximation is sufficient for image reconstruction whenever g = d sin θ/w ≲ 1. Here d is the grating width (d = 2 mm), θ is the Bragg angle in the medium (θ ~ 7.5°), and w is the Gaussian reading beam 1/e2 radius (~1 mm). This gives g = 0.3. See M. G. Moharam, T. K. Gaylord, R. Magnusson, J. Opt. Soc. Am. 70, 300 (1980).
[CrossRef]

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

White, J.

J. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

Yariv, A.

J. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

Young, L.

For a discussion of grating formation by Gaussian beams, seeM. G. Moharam, L. Young, J. Appl. Phys. 47, 4048 (1976). The plane-wave approximation is sufficient to describe grating formation in our experiments because in both imaging geometries used here the width of the focused object beam (~0.2 mm) is much less than the width (2 mm FWHM) of the reference beam. The plane-wave approximation is sufficient for image reconstruction whenever g = d sin θ/w ≲ 1. Here d is the grating width (d = 2 mm), θ is the Bragg angle in the medium (θ ~ 7.5°), and w is the Gaussian reading beam 1/e2 radius (~1 mm). This gives g = 0.3. See M. G. Moharam, T. K. Gaylord, R. Magnusson, J. Opt. Soc. Am. 70, 300 (1980).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

J. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

F. S. Cheng, J. T. La Macchia, D. B. Fraser, Appl. Phys. Lett. 13, 223 (1968).
[CrossRef]

J. Appl. Phys. (2)

For a discussion of grating formation by Gaussian beams, seeM. G. Moharam, L. Young, J. Appl. Phys. 47, 4048 (1976). The plane-wave approximation is sufficient to describe grating formation in our experiments because in both imaging geometries used here the width of the focused object beam (~0.2 mm) is much less than the width (2 mm FWHM) of the reference beam. The plane-wave approximation is sufficient for image reconstruction whenever g = d sin θ/w ≲ 1. Here d is the grating width (d = 2 mm), θ is the Bragg angle in the medium (θ ~ 7.5°), and w is the Gaussian reading beam 1/e2 radius (~1 mm). This gives g = 0.3. See M. G. Moharam, T. K. Gaylord, R. Magnusson, J. Opt. Soc. Am. 70, 300 (1980).
[CrossRef]

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Experimental setup showing writing beams with intensities I1 and I2 (ordinary polarization) and reading beam with intensity I3 (extraordinary polarization). The angle θ measured outside the BaTiO3 crystal is 18°. The direction of the c axis of the crystal is as shown. Adjustable neutral-density filters (F) are used to vary the intensities of the three incident beams. M are mirrors, and BS1 and BS2 are 50% reflecting beam splitters. BS3 is a 4% reflecting beam splitter. The lens (L3) and the pinhole (H) spatially filter the object beam, which is recollimated by lens L2 and focused in the crystal by lens L1. The polarizer (P) passes the signal beam but prevents scattered light from the writing beams from reaching the camera (C) or the optical multichannel array (not shown). The two unfocused optical beams measure approximately 2 mm in diameter at the crystal, which has a thickness l = 2.2 mm.

Fig. 2
Fig. 2

Images of a moustache comb showing the second type (Fourier) of edge enhancement described in the text. In the photograph on the left, the intensity of the object beam is 1/100 the intensity of the reference beam. In the photograph on the right, the intensity of the object beam is 100 times the intensity of the reference beam. The teeth of the comb are separated by 0.8 mm. The intensity doublets described in the text and shown in Fig. 4 are barely resolvable here at the edges of the teeth of the edge-enhanced comb.

Fig. 3
Fig. 3

Theoretical and experimentally observed plots of the intensity of the observed image of a single slit 0.8 mm wide when a real image (demagnification, 1/6) of this object is focused in the sample by a 100-mm focal-length lens. The theoretical plots have been smoothed to take into account the finite resolution of the optical detection system. The ratio of the intensity of the object beam to the intensity of the reference beam (I1/I2) is (a) 0.5, (b) 5, (c) 50.

Fig. 4
Fig. 4

Theoretical plots of the electric field and intensity in the image plane and the experimentally measured intensity using the Fourier geometry described in the text. The ratio of the intensity of the object beam to the intensity of the reference beam (I1I2) is (a) 0.06, (b) 6, (c) 60.

Fig. 5
Fig. 5

Images of a resolution chart showing enhancement of only horizontal edges as a result of misaligning the object beam vertically by about 1 mm. The radial pattern is 1 cm in diameter. The ratio of intensities of the object and reference beams is 1/1000 in the photograph on the left and 1000/1 in the photograph on the right.

Equations (8)

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E j ( x ) = Re [ E j ( x ) e ˆ j exp ( i k j · x iωt ) ] ,
R = | BLCm | 2
m 2 E 1 E 2 * e ˆ 1 · e 2 * / ( | E 1 | 2 + | E 2 | 2 + | E 3 | 2 ) .
m = 2 ( I 1 I 2 ) 1 / 2 / ( I 1 + I 2 ) ,
m ( x ) = 2 ( I 1 ( x ) I 2 ) 1 / 2 / ( I 1 ( x ) + I 2 ) .
I 1 ( x ) = I 1 rect ( x / Md ) ,
E 1 ( x ) = E 1 sin πx d / ( πx / d ) ,
I observed ( x ) α | 40 / d 40 / d E 1 ( x ) · E 2 / ( | E 1 ( x ) | 2 + | E 2 | 2 ) cos 2 π x x d x | 2 ,

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