Abstract

In photography, information is stored in a medium which is essentially two-dimensional. Three-dimensional optical storage is possible in semitransparent colored materials, like alkali halides with color centers. With the use of coherent light sources, like lasers, large amounts of information can be stored in the volume, and retrieved with little interference. The storage of information is accomplished by the formation of interference patterns between each two plane parallel waves. This paper develops the theory of this form of storage. It turns out that the information storage capacity is as if every little cube with sides equal to the wavelength of light acts as an independent information storage cell, and the essential noise in recovering this information is only the statistical fluctuation in the number of color centers in such a cube. The storage capacity is therefore of the order of 1012–1013 bits per cm3. The main property of this way of information storage is the appearance of a “ghost image,” partly but not completely analogous to the one described previously. This property makes three-dimensional storage very suitable for associative memories. The theory lends support to Beurle’s proposed mechanism of information storage in the brain.

© 1963 Optical Society of America

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References

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  1. R. W. Pohl, Physik. Z. 39, 36 (1938); F. Seitz, Rev. Modern Phys. 26, 7 (1954).
    [CrossRef]
  2. Encyclopædia Britannica, Photography, Colour (U. of Chicago Press, Chicago, 1947), Vol. 17, p. 816.
  3. P. J. van Heerden, Appl. Opt. 2, 387 (1963).
    [CrossRef]
  4. R. L. Beurle, Phil. Trans. Roy. Soc. London, Ser. B, 240, 55 (1956).
    [CrossRef]
  5. D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. A197, 454 (1949); Proc. Phys. Soc. B64, 449 (1951).
    [CrossRef] [PubMed]

1963

1956

R. L. Beurle, Phil. Trans. Roy. Soc. London, Ser. B, 240, 55 (1956).
[CrossRef]

1948

D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. A197, 454 (1949); Proc. Phys. Soc. B64, 449 (1951).
[CrossRef] [PubMed]

1938

R. W. Pohl, Physik. Z. 39, 36 (1938); F. Seitz, Rev. Modern Phys. 26, 7 (1954).
[CrossRef]

Beurle, R. L.

R. L. Beurle, Phil. Trans. Roy. Soc. London, Ser. B, 240, 55 (1956).
[CrossRef]

Gabor, D.

D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. A197, 454 (1949); Proc. Phys. Soc. B64, 449 (1951).
[CrossRef] [PubMed]

Pohl, R. W.

R. W. Pohl, Physik. Z. 39, 36 (1938); F. Seitz, Rev. Modern Phys. 26, 7 (1954).
[CrossRef]

van Heerden, P. J.

Appl. Opt.

Nature

D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. A197, 454 (1949); Proc. Phys. Soc. B64, 449 (1951).
[CrossRef] [PubMed]

Phil. Trans. Roy. Soc. London

R. L. Beurle, Phil. Trans. Roy. Soc. London, Ser. B, 240, 55 (1956).
[CrossRef]

Physik. Z.

R. W. Pohl, Physik. Z. 39, 36 (1938); F. Seitz, Rev. Modern Phys. 26, 7 (1954).
[CrossRef]

Other

Encyclopædia Britannica, Photography, Colour (U. of Chicago Press, Chicago, 1947), Vol. 17, p. 816.

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Figures (9)

Fig. 1
Fig. 1

Bleached interference pattern of two waves A0 and A1. The pattern consists of planes such that the reflection of the direction of propagation of A0 is that of A1, and vice versa.

Fig. 2
Fig. 2

Storage in the crystal, by bleaching, of the image of a picture in O. It can be reproduced by illuminating with A0.

Fig. 3
Fig. 3

Diffraction of A0 by a volume element ΔV.

Fig. 4
Fig. 4

Illuminating vectors A0 and A0′ of different frequencies and directions. For different frequencies, A0′ is not diffracted by the bleaching plane (k,λ,μ). For different directions A0′ is diffracted by (k,λ,μ) only in a special case.

Fig. 5
Fig. 5

Reproduction of time dependent signals. Amplitude modulating of L with a pulse of a specific shape will reproduce the movie.

Fig. 6
Fig. 6

Storage of an image in the crystal with the center beam A0 cut off.

Fig. 7
Fig. 7

Three-dimensional storage as an associative memory. Exposure of Sj in O after bleaching will reproduce a ghost image of Lj, which in turn will illuminate Ij.

Fig. 8
Fig. 8

A simplified associative memory Subject to noise.

Fig. 9
Fig. 9

Simple neuron network obeying Huygens principle.

Equations (11)

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Δ B ( x 2 y 2 z 2 ) = - A 0 ( x y z ) 2 α λ 0 r cos φ 01 Δ V exp [ i ( k x + l y + m z - ω 0 t ) ] .
Δ B = 2 b t 1 λ 0 r cos φ 01 cos θ 01 A 0 A 0 * A 1 Δ V exp × [ i ( k x + l y + m z - ω 0 t ) ] .
Δ B = 2 b t 1 λ 0 r 2 cos φ 01 cos θ 01 A 00 A 00 * A 10 × exp [ i ( k 2 x 2 + l 2 y 2 + m 2 z 2 - ω 0 t ) ] × exp { i [ ( k 1 - k 2 ) x + ( l 1 - l 2 ) y + ( m 1 - m 2 ) z ] } Δ x Δ y Δ z .
I = v exp [ i { ( k 1 - k 2 ) x + ( l 1 - l 2 ) y + ( m 1 - m 2 ) z } ] d x d y d z = i ( k 1 - k 2 ) ( l 1 - l 2 ) ( m 1 - m 2 ) { exp [ i ( k 1 - k 2 ) a ] - 1 } × { exp [ i ( l 1 - l 2 ) a ] - 1 } × { exp [ i ( m 1 - m 2 ) d ] - 1 } .
B 1 ( x 2 y 2 z 2 ) = 2 b t 1 a 2 d λ 0 r 2 cos φ 01 cos θ 01 A 00 A 00 * A 10 × exp [ i ( k 1 x 2 + l 1 y 2 + m 1 z 2 - ω 0 t ) ] .
B 1 ( k 1 l 1 m 1 ) = 2 b t 1 d cos φ 01 cos θ 01 A 00 A 00 * A 10 × exp [ i ( k 1 x 2 + l 1 y 2 + m 1 z 2 - ω 0 t ) ] .
D i ( t ) = - n + n C i n exp [ i n ω t ) .
1 n i j [ A i A j * + A i * A j ] .
j A i [ A j A j * ] .
Δ E 1 = ( A 0 a 2 λ 0 r - Δ B r ) 2 λ 0 2 a 2 r 2 = - 2 A 0 Δ B λ 0 .
Δ B = A 0 2 α λ 0 Δ V .

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