Abstract

Based on results of diffraction theory, it is shown that the proportions of storage plate and detector matrix, respectively, page-composer, of a fast holographic mass memory are strongly coupled. A high capacity fast data store needs a large detector array. Optimized geometry results if storage plate and detector matrix have the same size. A square detector matrix, able to read about 1010 bits in an optimum designed memory, should have a diagonal extension of about 1 m.

© 1972 Optical Society of America

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References

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  1. See, for instance, F. M. Smits, L. E. Gallaher, Bell Syst. Tech. J. 46, 1267 (1967); V. A. Vitols, IBM Tech. Disclosure Bull. 8, 1581 (1966); L. K. Anderson, Bell Lab. Rec. 46, 319 (1968); A. H. Eschenfelder, J. Appl. Phys. 41, 1372 (1971); J. A. Rajchman, J. Appl. Phys. 41, 1376 (1970).
    [CrossRef]
  2. See, for instance, U. Schmidt, in Optical Processing of InformationD. K. Pollock, C. J. Koester, J. T. Tippett, Eds. (Spartan Books, Baltimore, 1963), pp. 98–103; W. Kulcke, T. J. Harris, K. Kosanke, E. Max, IBM J. Res. Dev. 8, 64 (1964); W. Kulcke et al., Appl. Opt. 5, 1657 (1966); U. Schmidt, W. Thust, J. Opto Electron. 1, 21 (1969).
    [CrossRef] [PubMed]
  3. L. K. Anderson et al., Sixth Internat. Quantum Electronics Conference Kyoto, Japan, (7–10 Sept. 1970).
  4. J. T. LaMacchia, Laser Focus, 35 (Feb.1970).
  5. P. Graf, Proc. 1970 IEEE Computer Group Conference, Washington D.C., pp. 83–87.
  6. In practical applications this criterion can be improved in the sense of tolerating overlappings as long as one light spot does not activate two or more neighboring detectors.
  7. G. B. Airy, Trans. Camb. Philos. Soc. 5, 283 (1835); M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965); A. Sommerfeld, Vorlesungen über theoretische Physik, Band IV, Optik (Akad. Verlagsgesellschaft Geest und Portig K.G., Leipzig, 1964).

1970 (1)

J. T. LaMacchia, Laser Focus, 35 (Feb.1970).

1967 (1)

See, for instance, F. M. Smits, L. E. Gallaher, Bell Syst. Tech. J. 46, 1267 (1967); V. A. Vitols, IBM Tech. Disclosure Bull. 8, 1581 (1966); L. K. Anderson, Bell Lab. Rec. 46, 319 (1968); A. H. Eschenfelder, J. Appl. Phys. 41, 1372 (1971); J. A. Rajchman, J. Appl. Phys. 41, 1376 (1970).
[CrossRef]

1835 (1)

G. B. Airy, Trans. Camb. Philos. Soc. 5, 283 (1835); M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965); A. Sommerfeld, Vorlesungen über theoretische Physik, Band IV, Optik (Akad. Verlagsgesellschaft Geest und Portig K.G., Leipzig, 1964).

Airy, G. B.

G. B. Airy, Trans. Camb. Philos. Soc. 5, 283 (1835); M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965); A. Sommerfeld, Vorlesungen über theoretische Physik, Band IV, Optik (Akad. Verlagsgesellschaft Geest und Portig K.G., Leipzig, 1964).

Anderson, L. K.

L. K. Anderson et al., Sixth Internat. Quantum Electronics Conference Kyoto, Japan, (7–10 Sept. 1970).

Gallaher, L. E.

See, for instance, F. M. Smits, L. E. Gallaher, Bell Syst. Tech. J. 46, 1267 (1967); V. A. Vitols, IBM Tech. Disclosure Bull. 8, 1581 (1966); L. K. Anderson, Bell Lab. Rec. 46, 319 (1968); A. H. Eschenfelder, J. Appl. Phys. 41, 1372 (1971); J. A. Rajchman, J. Appl. Phys. 41, 1376 (1970).
[CrossRef]

Graf, P.

P. Graf, Proc. 1970 IEEE Computer Group Conference, Washington D.C., pp. 83–87.

LaMacchia, J. T.

J. T. LaMacchia, Laser Focus, 35 (Feb.1970).

Schmidt, U.

See, for instance, U. Schmidt, in Optical Processing of InformationD. K. Pollock, C. J. Koester, J. T. Tippett, Eds. (Spartan Books, Baltimore, 1963), pp. 98–103; W. Kulcke, T. J. Harris, K. Kosanke, E. Max, IBM J. Res. Dev. 8, 64 (1964); W. Kulcke et al., Appl. Opt. 5, 1657 (1966); U. Schmidt, W. Thust, J. Opto Electron. 1, 21 (1969).
[CrossRef] [PubMed]

Smits, F. M.

See, for instance, F. M. Smits, L. E. Gallaher, Bell Syst. Tech. J. 46, 1267 (1967); V. A. Vitols, IBM Tech. Disclosure Bull. 8, 1581 (1966); L. K. Anderson, Bell Lab. Rec. 46, 319 (1968); A. H. Eschenfelder, J. Appl. Phys. 41, 1372 (1971); J. A. Rajchman, J. Appl. Phys. 41, 1376 (1970).
[CrossRef]

Bell Syst. Tech. J. (1)

See, for instance, F. M. Smits, L. E. Gallaher, Bell Syst. Tech. J. 46, 1267 (1967); V. A. Vitols, IBM Tech. Disclosure Bull. 8, 1581 (1966); L. K. Anderson, Bell Lab. Rec. 46, 319 (1968); A. H. Eschenfelder, J. Appl. Phys. 41, 1372 (1971); J. A. Rajchman, J. Appl. Phys. 41, 1376 (1970).
[CrossRef]

Laser Focus (1)

J. T. LaMacchia, Laser Focus, 35 (Feb.1970).

Trans. Camb. Philos. Soc. (1)

G. B. Airy, Trans. Camb. Philos. Soc. 5, 283 (1835); M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1965); A. Sommerfeld, Vorlesungen über theoretische Physik, Band IV, Optik (Akad. Verlagsgesellschaft Geest und Portig K.G., Leipzig, 1964).

Other (4)

P. Graf, Proc. 1970 IEEE Computer Group Conference, Washington D.C., pp. 83–87.

In practical applications this criterion can be improved in the sense of tolerating overlappings as long as one light spot does not activate two or more neighboring detectors.

See, for instance, U. Schmidt, in Optical Processing of InformationD. K. Pollock, C. J. Koester, J. T. Tippett, Eds. (Spartan Books, Baltimore, 1963), pp. 98–103; W. Kulcke, T. J. Harris, K. Kosanke, E. Max, IBM J. Res. Dev. 8, 64 (1964); W. Kulcke et al., Appl. Opt. 5, 1657 (1966); U. Schmidt, W. Thust, J. Opto Electron. 1, 21 (1969).
[CrossRef] [PubMed]

L. K. Anderson et al., Sixth Internat. Quantum Electronics Conference Kyoto, Japan, (7–10 Sept. 1970).

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Figures (6)

Fig. 1
Fig. 1

Hexagonal arrangement of subholograms.

Fig. 2
Fig. 2

Storage plate with circular subholograms.

Fig. 3
Fig. 3

Matrix with m × m light-sensitive detectors.

Fig. 4
Fig. 4

Arrangement of storage plate and detector matrix.

Fig. 5
Fig. 5

Coordinate system used to calculate the intensity distribution near a detector position.

Fig. 6
Fig. 6

Extension in x2-direction of a light spot in the detector plane.

Tables (4)

Tables Icon

Table I Lower Limits for the Diagonal M of the Detector Matrix for λ = 6.33 × 10−5 cm, β = 2, γ 2 = 1 2

Tables Icon

Table II Examples of Optimum Design for λ = 6.33 × 10−5 cm, β = 2, γ 2 = 1 2

Tables Icon

Table III Out-of-Optimum Design with M = 4.5 cm, λ = 6.33 × 10−5 cm, β = 2, γ 2 = 1 2

Tables Icon

Table IV Out-of-Optimum Design for 1010 Bits for λ = 6.33 × 10−5 cm, β = 2, γ 2 = 1 2

Equations (47)

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H = γ 2 H eff , where 0 γ 2 1.
a = ϰ a ˆ , where 0 ϰ 1 ,
square arrangement , γ s q 2 = π ϰ 2 / 4 ,
hexagonal arrangement , γ hex 2 = ( 2 / 3 ) γ s q 2 .
γ 2 = 1 2 .
M = 2 m q .
n = N / H = m 2 / π a 2 ,
n eff = N / H eff = γ 2 n .
N = γ 2 ( n D 2 / 2 ) = γ 2 ( m 2 D 2 / 2 π a 2 ) .
| u P | 2 = ( 2 π C a ) 2 | J 1 ( k a σ ) σ | 2 ,
σ 2 = | sin ψ 0 + exp { i [ ( π / 2 ) + φ ] } sin ψ | 2 .
σ 0.61 ( λ / a ) .
2 σ = 1.22 ( λ / a ) = 2 sin ϑ 0 2 ϑ 0 .
b 0 = 2 L 0 tan ϑ 0 1.22 ( λ / a ) L 0
q = β b 0 with 1 β .
2 ϑ ˜ 0 2 β ϑ 0 .
tan θ 0 = M / 2 L 0 2 m ϑ ˜ 0 .
N = ( α γ / β ) ( M D / λ L 0 ) ,
α = 1 / ( 2.44 π ) 0.23.
sin ψ = sin ψ max ± 0.61 ( λ / a ) .
ψ = ψ max + ϑ ,
| sin ϑ | 0.61 [ λ / ( a cos ψ max ) ] .
b = b 1 + b 2 .
r 1 = R max cos ψ max cos ( ψ max + ϑ ) and r 2 = R max cos ψ max cos ( ψ max ϑ ) ,
b 1 L 0 = tan ϑ cos 2 ψ max tan ϑ cos ψ max sin ψ max ( b 0 / 2 L 0 ) cos ψ max [ cos 2 ψ max ( b 0 / 2 L 0 ) sin ψ max ]
b 2 L 0 = tan ϑ cos 2 ψ max + tan ϑ cos ψ max sin ψ max ( b 0 / 2 L 0 ) cos ψ max [ cos 2 ψ max + ( b 0 / 2 L 0 ) sin ψ max ] .
b L 0 = 2 tan ϑ cos 2 ψ max tan 2 ϑ sin 2 ψ max ( b 0 / L 0 ) cos ψ max [ cos 2 ψ max ( b 0 / 2 L 0 ) 2 tan 2 ψ max ] ,
Δ b b 0 = b b 0 b 0 1 cos ψ max [ cos 2 ψ max ( b 0 / 2 L 0 ) 2 tan 2 ψ max ] 1.
1 cos ψ max [ cos 2 ψ max ( b 0 / 2 L 0 ) 2 tan 2 ψ max ] β .
1 / ( cos 3 ψ max ) β .
ψ max 38 ° .
z = tan ψ max = ( D + M ) / 2 L 0 ,
N = α γ β M λ [ 2 z ( M L 0 ) ] ,
L 0 = M 2 z ( β λ N / α γ M ) ,
D = β λ N α γ 1 2 z ( β λ N / α γ M ) ,
n = [ 2 α β λ ( 2 z β λ N α γ M ) ] 2 ,
q = ( M / 2 m ) ,
a = 1.22 2 β λ m 2 z β λ N / α γ M .
( β λ N / 2 α γ z ) < M < 2 z L 0 .
β = 2 , γ 2 = 1 2 , λ = 6.33 × 10 5 cm .
z = ( M / L 0 ) or M = D .
N = α γ z M / β λ ,
L 0 = β λ N / α γ z 2 ,
D = M = β λ N / α γ z ,
n = ( 2 α z / β λ ) 2 ,
q = β λ N / ( 2 α γ z m ) ,
a = 1.22 2 ( β λ m / z ) .

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