Abstract

The optical cross correlation of an image with another image that was spatial-frequency shifted in one dimension was demonstrated in a photorefractive VanderLugt correlator. The first image was stored as a Fourier-transform hologram in a photorefractive Bi12SiO20 crystal (BSO) and was successively correlated with different spatial-frequency-shifted versions of a second image. We implemented the spatial-frequency shift by rotating a galvanometer mirror in an image plane, causing the Fourier transform to be shifted laterally in the BSO. We verified that the resulting operation in the BSO was an accurate complex multiplication of the shifted and the stored Fourier transforms. As many as 20 successive readouts were conducted without measurable erasure of the stored hologram. The dynamic range, saturation behavior, and other performance parameters were measured and are discussed.

© 2004 Optical Society of America

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References

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  1. J. White, A. Yariv, “Real-time image processing via four-wave mixing in a photorefractive medium,” Appl. Phys. Lett. 37, 5–7 (1980).
    [CrossRef]
  2. J. White, A. Yariv, “Spatial information processing and distortion correction via four-wave mixing,” Opt. Eng. 21, 224–230 (1982).
    [CrossRef]
  3. S. I. Stepanov, V. D. Gural’nik, “Correlation analysis of two-dimensional images with VanderLugt volume filters,” Sov. Tech. Phys. Lett. 8, 49–51 (1982).
  4. L. Pichon, J. P. Huignard, “Dynamic joint-Fourier-transform correlator by Bragg diffraction in photorefractive Bi12SiO20 crystals,” Opt. Commun. 36, 277–280 (1981).
    [CrossRef]
  5. B. Loiseaux, G. Illiaquer, J. P. Huignard, “Dynamic optical cross-correlation using a liquid crystal light valve and a bismuth silicon oxide crystal in the Fourier plane,” Opt. Eng. 24, 144–149 (1985).
    [CrossRef]
  6. X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B B51, 153–164 (1990).
    [CrossRef]
  7. F. T. S. Yu, S. Yin, “Bragg diffraction-limited photorefractive crystal-based correlators,” Opt. Eng. 34, 2224–2231 (1995).
    [CrossRef]
  8. C.-C. Sun, M.-S. Tsaur, W.-C. Su, B. Wang, A. E. T. Chiou, “Two-dimensional shifting tolerance of a volume-holographic correlator,” Appl. Opt. 38, 4316–4324 (1999).
    [CrossRef]

1999 (1)

1995 (1)

F. T. S. Yu, S. Yin, “Bragg diffraction-limited photorefractive crystal-based correlators,” Opt. Eng. 34, 2224–2231 (1995).
[CrossRef]

1990 (1)

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B B51, 153–164 (1990).
[CrossRef]

1985 (1)

B. Loiseaux, G. Illiaquer, J. P. Huignard, “Dynamic optical cross-correlation using a liquid crystal light valve and a bismuth silicon oxide crystal in the Fourier plane,” Opt. Eng. 24, 144–149 (1985).
[CrossRef]

1982 (2)

J. White, A. Yariv, “Spatial information processing and distortion correction via four-wave mixing,” Opt. Eng. 21, 224–230 (1982).
[CrossRef]

S. I. Stepanov, V. D. Gural’nik, “Correlation analysis of two-dimensional images with VanderLugt volume filters,” Sov. Tech. Phys. Lett. 8, 49–51 (1982).

1981 (1)

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

1980 (1)

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

Chiou, A. E. T.

Gregory, D. A.

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B B51, 153–164 (1990).
[CrossRef]

Gural’nik, V. D.

S. I. Stepanov, V. D. Gural’nik, “Correlation analysis of two-dimensional images with VanderLugt volume filters,” Sov. Tech. Phys. Lett. 8, 49–51 (1982).

Huignard, J. P.

B. Loiseaux, G. Illiaquer, J. P. Huignard, “Dynamic optical cross-correlation using a liquid crystal light valve and a bismuth silicon oxide crystal in the Fourier plane,” Opt. Eng. 24, 144–149 (1985).
[CrossRef]

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

Illiaquer, G.

B. Loiseaux, G. Illiaquer, J. P. Huignard, “Dynamic optical cross-correlation using a liquid crystal light valve and a bismuth silicon oxide crystal in the Fourier plane,” Opt. Eng. 24, 144–149 (1985).
[CrossRef]

Loiseaux, B.

B. Loiseaux, G. Illiaquer, J. P. Huignard, “Dynamic optical cross-correlation using a liquid crystal light valve and a bismuth silicon oxide crystal in the Fourier plane,” Opt. Eng. 24, 144–149 (1985).
[CrossRef]

Lu, X. J.

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B B51, 153–164 (1990).
[CrossRef]

Pichon, L.

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

Stepanov, S. I.

S. I. Stepanov, V. D. Gural’nik, “Correlation analysis of two-dimensional images with VanderLugt volume filters,” Sov. Tech. Phys. Lett. 8, 49–51 (1982).

Su, W.-C.

Sun, C.-C.

Tsaur, M.-S.

Wang, B.

White, J.

J. White, A. Yariv, “Spatial information processing and distortion correction via four-wave mixing,” Opt. Eng. 21, 224–230 (1982).
[CrossRef]

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

Yariv, A.

J. White, A. Yariv, “Spatial information processing and distortion correction via four-wave mixing,” Opt. Eng. 21, 224–230 (1982).
[CrossRef]

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

Yin, S.

F. T. S. Yu, S. Yin, “Bragg diffraction-limited photorefractive crystal-based correlators,” Opt. Eng. 34, 2224–2231 (1995).
[CrossRef]

Yu, F. T. S.

F. T. S. Yu, S. Yin, “Bragg diffraction-limited photorefractive crystal-based correlators,” Opt. Eng. 34, 2224–2231 (1995).
[CrossRef]

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B B51, 153–164 (1990).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

X. J. Lu, F. T. S. Yu, D. A. Gregory, “Comparison of VanderLugt and joint transform correlators,” Appl. Phys. B B51, 153–164 (1990).
[CrossRef]

Appl. Phys. Lett. (1)

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

Opt. Commun. (1)

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

Opt. Eng. (3)

B. Loiseaux, G. Illiaquer, J. P. Huignard, “Dynamic optical cross-correlation using a liquid crystal light valve and a bismuth silicon oxide crystal in the Fourier plane,” Opt. Eng. 24, 144–149 (1985).
[CrossRef]

J. White, A. Yariv, “Spatial information processing and distortion correction via four-wave mixing,” Opt. Eng. 21, 224–230 (1982).
[CrossRef]

F. T. S. Yu, S. Yin, “Bragg diffraction-limited photorefractive crystal-based correlators,” Opt. Eng. 34, 2224–2231 (1995).
[CrossRef]

Sov. Tech. Phys. Lett. (1)

S. I. Stepanov, V. D. Gural’nik, “Correlation analysis of two-dimensional images with VanderLugt volume filters,” Sov. Tech. Phys. Lett. 8, 49–51 (1982).

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Figures (9)

Fig. 1
Fig. 1

(a) Writing waves that store a hologram of the input, and (b) readout waves that reconstruct the output of the photorefractive BSO crystal in a VanderLugt optical correlator. EDC = dc bias electric field.

Fig. 2
Fig. 2

Block diagram that illustrates the process of a 1-D frequency shift and the multiplication of two 2-D images in a VanderLugt optical correlator (* denotes convolution and the star denotes correlation).

Fig. 3
Fig. 3

Optical setup of the photorefractive optical correlator. Collimated light is input from the power splitter and the beam expanding telescopes described in the text.

Fig. 4
Fig. 4

Input image used in the correlator tests. An appropriate mask was used so that only two of these spatial frequencies were used at a time for the actual tests.

Fig. 5
Fig. 5

Sample autocorrelation image (with zero frequency shift) for an input image containing 10 and 15 lp/mm frequency components. Top half, experimental image; bottom half, MATLAB simulation based on the 10 and 15 lp/mm portions of Fig. 4. The BSO crystal was 5 mm long with 16-dB attenuation of both the write and the read beams. The experimental image has been contrast enhanced and brightness adjusted to make the weaker features more visible.

Fig. 6
Fig. 6

(a) Auto-power spectrum of images containing frequencies of 15 and 20 lp/mm (negative image for enhanced visibility), (b) horizontal section through this auto-power spectrum, and (c) a horizontal section through a cross-power spectrum for the same input images with a frequency shift of +5 lp/mm. Horizontal (spatial frequency) scale is in camera pixel number, and the vertical scales in (b) and (c) are the digital numbers of the digitized video signal amplitudes. The BSO is 2.5 mm long.

Fig. 7
Fig. 7

Horizontal cross sections through the -15 lp/mm cross-power spectrum peak, with small variations in the frequency shift (galvo-mirror voltage) about the +5 lp/mm shift (-0.151 V).

Fig. 8
Fig. 8

Simulation of the cross sections shown in Fig. 7, derived from a numerical shift and multiplication of the -20 and -15 lp/mm peaks measured in Fig. 6(b).

Fig. 9
Fig. 9

Cross-power spectrum linearized signal power versus (write and readout) attenuation at each spatial frequency by use of images with 10 and 15 lp/mm components and a shift of +5 lp/mm. Vertical scale is normalized to a camera saturation of 0 dB. This frequency shift should generate strong outputs at -10 and +15 lp/mm.

Equations (5)

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Exposure Irradiance = | R + A | 2 = RA * + R * A + | A | 2 + | R | 2 .
B | R + A | 2 = B RA * + R * A + | A | 2 + | R | 2 ,
RA * B + R * AB + B | R | 2 + B | A | 2 .
| RA * B | 2 ,
| RA * μ ,   ν B μ ,   ν - Δ ν | 2 .

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