Abstract

Two-beam coupling in photorefractive BaTiO3 is used to perform time differentiation of time-varying coherent phase and amplitude images. Differentiation of one-dimensional signals and two-dimensional images is performed.

© 1987 Optical Society of America

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References

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  1. T. Kohonen, Self Organization and Associative Memory (Springer-Verlag, New York, 1984), Chap. 4.
  2. D. H. Ballard, C. M. Brown, Computer Vision (Prentice-Hall, Englewood Cliffs, N.J., 1982).
  3. D. Z. Anderson, D. M. Lininger, J. Feinberg, Opt. Lett. 12, 123 (1987).
    [CrossRef] [PubMed]
  4. M. Cronin-Golomb, in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), p. 142.
  5. M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
    [CrossRef]

1987 (1)

1985 (1)

M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
[CrossRef]

Anderson, D. Z.

Ballard, D. H.

D. H. Ballard, C. M. Brown, Computer Vision (Prentice-Hall, Englewood Cliffs, N.J., 1982).

Brown, C. M.

D. H. Ballard, C. M. Brown, Computer Vision (Prentice-Hall, Englewood Cliffs, N.J., 1982).

Cronin-Golomb, M.

M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
[CrossRef]

M. Cronin-Golomb, in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), p. 142.

Feinberg, J.

Kohonen, T.

T. Kohonen, Self Organization and Associative Memory (Springer-Verlag, New York, 1984), Chap. 4.

Lininger, D. M.

Yariv, A.

M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
[CrossRef]

J. Appl. Phys. (1)

M. Cronin-Golomb, A. Yariv, J. Appl. Phys. 57, 4906 (1985).
[CrossRef]

Opt. Lett. (1)

Other (3)

T. Kohonen, Self Organization and Associative Memory (Springer-Verlag, New York, 1984), Chap. 4.

D. H. Ballard, C. M. Brown, Computer Vision (Prentice-Hall, Englewood Cliffs, N.J., 1982).

M. Cronin-Golomb, in Digest of Topical Meeting on Photorefractive Materials, Effects, and Devices (Optical Society of America, Washington, D.C., 1987), p. 142.

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Figures (7)

Fig. 1
Fig. 1

Time differentiation by photorefractive two-beam coupling.

Fig. 2
Fig. 2

The fanning optical limiter. A time-varying input signal is input, resulting in a deamplified output signal and amplified scattering in the crystal.

Fig. 3
Fig. 3

The experimental setup of the differentiator.

Fig. 4
Fig. 4

Experimental plots of the time differentiator's input and output intensity patterns. The input signal is the top plot, showing a sinusoidal input, and the output intensity is shown in the lower plot. One block along the horizontal (time) axis represents 2.4 sec.

Fig. 5
Fig. 5

Theoretical plots of the time differentiator's input and output intensity patterns. The solid line indicates a sinusoidal input signal, and the dotted line indicates the theoretical output of the device. It is approximately the time derivative of the input.

Fig. 6
Fig. 6

Two-dimensional input signal of the hand that was waved in-front of the video camera.

Fig. 7
Fig. 7

Two-dimensional time-differentiated output of the hand.

Equations (3)

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A 2 ( x , t ) out A 2 ( x , t ) in A 2 ( x , t T ) in T ( d A 2 / d t )
A 2 * ( z , t ) = A 2 * ( 0 , t ) K ( t ) + 0 t [ A 2 * ( 0 , T ) τ + d A 2 * ( 0 , T ) d T ] K ( t T ) d T ,
K ( t ) = exp ( t / τ ) J 0 ( 2 γ z t / τ )

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