Abstract

The readout of a page of binary data from a holographic memory utilizing a thick recording material is treated for arbitrary angular positioning of the reference beam. The diffraction efficiency associated with each bit in the data page is calculated. Histograms showing the distribution of the diffracted powers and thus the fidelity of reconstruction for example cases are presented.

© 1981 Optical Society of America

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References

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  1. For example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).
  2. For example, H. J. Caulfield, Ed., Handbook of Optical Holography (Academic, New York, 1979).
  3. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).
  4. M. R. B. Forshaw, Opt. Laser Technol. 6, 28 (1974).
    [CrossRef]
  5. M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 14 (1980).
    [CrossRef]
  6. For example, D. H. Close, G. E. Moss, J. Opt. Soc. Am. 63, 1324 (1973).
  7. S. K. Case, J. Opt. Soc. Am. 64, 724 (1975).
    [CrossRef]

1980 (1)

M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 14 (1980).
[CrossRef]

1975 (1)

S. K. Case, J. Opt. Soc. Am. 64, 724 (1975).
[CrossRef]

1974 (1)

M. R. B. Forshaw, Opt. Laser Technol. 6, 28 (1974).
[CrossRef]

1973 (1)

For example, D. H. Close, G. E. Moss, J. Opt. Soc. Am. 63, 1324 (1973).

1969 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Burckhardt, C. B.

For example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Case, S. K.

S. K. Case, J. Opt. Soc. Am. 64, 724 (1975).
[CrossRef]

Close, D. H.

For example, D. H. Close, G. E. Moss, J. Opt. Soc. Am. 63, 1324 (1973).

Collier, R. J.

For example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Forshaw, M. R. B.

M. R. B. Forshaw, Opt. Laser Technol. 6, 28 (1974).
[CrossRef]

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 14 (1980).
[CrossRef]

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Lin, L. H.

For example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

Magnusson, R.

M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 14 (1980).
[CrossRef]

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 14 (1980).
[CrossRef]

Moss, G. E.

For example, D. H. Close, G. E. Moss, J. Opt. Soc. Am. 63, 1324 (1973).

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

J. Opt. Soc. Am. (2)

For example, D. H. Close, G. E. Moss, J. Opt. Soc. Am. 63, 1324 (1973).

S. K. Case, J. Opt. Soc. Am. 64, 724 (1975).
[CrossRef]

Opt. Commun. (1)

M. G. Moharam, T. K. Gaylord, R. Magnusson, Opt. Commun. 32, 14 (1980).
[CrossRef]

Opt. Laser Technol. (1)

M. R. B. Forshaw, Opt. Laser Technol. 6, 28 (1974).
[CrossRef]

Other (2)

For example, R. J. Collier, C. B. Burckhardt, L. H. Lin, Optical Holography (Academic, New York, 1971).

For example, H. J. Caulfield, Ed., Handbook of Optical Holography (Academic, New York, 1979).

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Figures (5)

Fig. 1
Fig. 1

Geometrical configuration of binary data page holographic system. Recording is accomplished with the simultaneous use of both the S beam and the R beam (with Δθ0 = Δϕ0 = 0). Reading is accomplished with the R beam, which may be dephased from the data page Bragg angle by Δθ0 and Δϕ0.

Fig. 2
Fig. 2

Plane of incidence and orthogonal transformation vectors for the reconstructed ijth data bit. The Floquet theorem (σij = ρKij) is satisfied inside the grating medium.

Fig. 3
Fig. 3

Diffraction efficiencies of two representative data bits as a function of reference beam angular dephasing from the data page Bragg angle (Δθ0 = Δϕ0 = 0) for (a) the central data bit and for (b) the corner data bit in the +x′, −y′ quadrant of the data page in Fig. 1.

Fig. 4
Fig. 4

Schematic representation of the orientation of several data bit Bragg cones about the data page Bragg angle (Δθ0 = Δϕ0 = 0). Data bits are located (a) above, (b) in, and (c) below the x-z plane.

Fig. 5
Fig. 5

Histograms of the data bit diffraction efficiencies for a 33 × 33 page of random binary data. The diffraction efficiency is divided into fifty linear intervals in each histogram.

Equations (22)

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ρ 0 = k 0 ( sin θ x ^ + cos θ z ^ ) ,
σ 0 i j = k 0 [ - cos ψ j sin ( θ + α i ) x ^ - sin ψ j y ^ + cos ψ j cos ( θ + α i ) z ^ ] .
K i j = ρ 0 - σ 0 i j .
2 E - ( · E ) + k 2 n 2 ( r ) E = 0 ,
E = R ( z ) exp ( - j ρ · r ) + S ( z ) exp ( - j σ · r ) ,
- 2 j ρ z R + j ρ R z + ρ ( ρ · R ) + j z ^ ( ρ · R ) + 2 κ k 0 S = 0 , - 2 j σ z S + j σ S z + S ( k 2 2 - σ 2 )
+ σ ( σ · S ) + j z ^ ( σ · S ) + 2 κ k 0 R = 0 ,
R ( z ) = R ( z ) r ^ + R ( z ) r ^ + R ρ ( z ) r ^ ρ , S ( z ) = S ( z ) s ^ + S ( z ) s ^ + S σ ( z ) s ^ σ ,
( ρ z / k 0 ) R ( z ) = - j κ ( r ^ · s ^ ) S ( z ) ,
( ρ z / k 0 ) R ( z ) = - j κ S ( z ) ,
( σ z / k 0 ) S ( z ) + j [ ( k 0 2 - σ 2 ) / 2 k 0 ] S ( z ) = - j κ ( r ^ · s ^ ) R ( z ) ,
( σ z / k 0 ) S ( z ) + j [ ( k 0 2 - σ 2 ) / 2 k 0 ] S ( z ) = - j κ R ( z ) .
R ( z ) = r 1 exp ( γ 1 z ) + r 2 exp ( γ 2 z ) , S ( z ) = s 1 exp ( γ 1 z ) + s 2 exp ( γ 2 z ) ,
γ 1 , 2 = j [ - ( ϑ / 2 c S ) ± ( ϑ 2 / 4 c S 2 + κ 2 / c R c S ) 1 / 2 ] ,
S ( z ) = j [ κ R ( 0 ) / c S ( γ 1 - γ 2 ) ] [ exp ( γ 1 z ) - exp ( γ 2 z ) ] .
S ( z ) = j [ κ R ( 0 ) / c S ( γ 3 - γ 4 ) ] [ exp ( γ 3 z ) - exp ( γ 4 z ) ] ,
γ 3 , 4 = j [ - ( ϑ / 2 c S ) ± ( ϑ 2 4 c S 2 + κ 2 / c R c S ) 1 / 2 ] .
D E = ( S S * + S S * ) c S / c R .
S S * = [ ( κ R ( 0 ) / c S ) 2 / ( ϑ 2 / 4 c S 2 + κ 2 / c R c S ) ] × sin 2 [ ( ϑ 2 / 4 c S 2 + κ 2 / c R c S ) 1 / 2 d ] ,
S S * = [ ( κ R ( 0 ) / c S ) 2 / ( ϑ 2 / 4 c S 2 + κ 2 / c R c S ) ] × sin 2 [ ( ϑ 2 / 4 c S 2 + κ 2 / c R c S ) 1 / 2 d ] ,
ρ = k 0 [ cos ( Δ ϕ ) sin ( θ + Δ θ ) x ^ - sin ( Δ ϕ ) y ^ + cos ( Δ ϕ ) cos ( θ + Δ θ ) z ^ ] ,
R ^ = [ sin ( Δ ϕ ) sin ( θ + Δ θ ) x ^ + cos ( Δ ϕ ) y ^ + sin ( Δ ϕ ) cos ( θ + Δ θ ) z ^ ] .

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