Abstract

Specifications of a holographic memory suitable for a capacity of 108 bit are presented. Mathematical calculations show the influence of various system parameters. The storage density is derived as a function of the maximum spatial frequency in the storage material, the aspect ratio of the data input mask, and the crosstalk. In addition, optimizations of the storage density and the optical efficiency of the system are discussed.

© 1972 Optical Society of America

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References

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  1. F. M. Smits, L. E. Gallaher, Bell Syst. Tech. J. 46, 1267 (1967).
  2. L. K. Anderson, Bell Lab. Rec. 46, 319 (1968).
  3. R. M. Langdon, Rad. Electron. Eng. 38, 369 (1969).
    [CrossRef]
  4. A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, L. Z. Sokolava, J. Quantum Electron. QE-6, 193 (1970).
    [CrossRef]
  5. A. H. Eschenfelder, J. Appl. Phys. 41, 1372 (1970).
    [CrossRef]
  6. J. A. Rajchman, J. Appl. Phys. 41, 1376 (1970).
    [CrossRef]
  7. J. T. LaMacchia, Laser Focus, February, 35 (1970).
  8. L. K. Anderson, Laser-Tech. Sect. 62 (1970).
  9. J. A. Rajchman, Appl. Opt. 9, 2269 (1970).
    [CrossRef] [PubMed]
  10. W. C. Stewart, L. S. Cosentino, Appl. Opt. 9, 2271 (1970).
    [CrossRef] [PubMed]
  11. R. D. Lohman, R. S. Mezrich, W. C. Stewart, Electronics, 18January, 61 (1971).
  12. U. Schmidt, in Optical Processing of Information, D. K. Pollack, C. J. Koester, J. T. Tippett, Eds. (Spartan Books, Washington, D.C., 1963), pp. 98–103.
  13. U. Schmidt, W. Thust, IEEE J. Quantum Electron. QE-5, 351 (1969).
    [CrossRef]
  14. K. Biedermann, N.-E. Molin, J. Phys. E Sci. Instrum. 3, 669 (1970).
    [CrossRef]
  15. G. Marie, Philips Res. Repts. 22, 110 (1967).
  16. G. Groh, G. Marie, Opt. Comm. 2, 133 (1970).
    [CrossRef]
  17. G. H. Heartling, C. E. Land, J. Am. Ceramic Bull. 49, 6 (1970).
  18. S. A. Keneman, G. W. Taylor, A. Miller, W. H. Fonger, Appl. Phys. Lett. 17, 173 (1970).
    [CrossRef]
  19. A. H. Meitzler, J. R. Maldonado, Electronics, February, 34 (1971).
  20. R. W. Meier, J. Opt. Soc. Am. 55, 987 (1965).
    [CrossRef]
  21. B. Hill, J. Opt. Soc. Am. 61, 386 (1971).
    [CrossRef]
  22. C. B. Burckhardt, Appl. Opt. 9, 695 (1970).
    [CrossRef] [PubMed]
  23. H. Schlitt, Systemtheorie für regellose Vorgänge (Springer, Berlin, 1960).
  24. W. Martienssen, E. Spiller, Phys. Rev. 145, 285 (1966).
    [CrossRef]

1971 (3)

R. D. Lohman, R. S. Mezrich, W. C. Stewart, Electronics, 18January, 61 (1971).

A. H. Meitzler, J. R. Maldonado, Electronics, February, 34 (1971).

B. Hill, J. Opt. Soc. Am. 61, 386 (1971).
[CrossRef]

1970 (12)

A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, L. Z. Sokolava, J. Quantum Electron. QE-6, 193 (1970).
[CrossRef]

A. H. Eschenfelder, J. Appl. Phys. 41, 1372 (1970).
[CrossRef]

J. A. Rajchman, J. Appl. Phys. 41, 1376 (1970).
[CrossRef]

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

L. K. Anderson, Laser-Tech. Sect. 62 (1970).

K. Biedermann, N.-E. Molin, J. Phys. E Sci. Instrum. 3, 669 (1970).
[CrossRef]

G. Groh, G. Marie, Opt. Comm. 2, 133 (1970).
[CrossRef]

G. H. Heartling, C. E. Land, J. Am. Ceramic Bull. 49, 6 (1970).

S. A. Keneman, G. W. Taylor, A. Miller, W. H. Fonger, Appl. Phys. Lett. 17, 173 (1970).
[CrossRef]

C. B. Burckhardt, Appl. Opt. 9, 695 (1970).
[CrossRef] [PubMed]

J. A. Rajchman, Appl. Opt. 9, 2269 (1970).
[CrossRef] [PubMed]

W. C. Stewart, L. S. Cosentino, Appl. Opt. 9, 2271 (1970).
[CrossRef] [PubMed]

1969 (2)

U. Schmidt, W. Thust, IEEE J. Quantum Electron. QE-5, 351 (1969).
[CrossRef]

R. M. Langdon, Rad. Electron. Eng. 38, 369 (1969).
[CrossRef]

1968 (1)

L. K. Anderson, Bell Lab. Rec. 46, 319 (1968).

1967 (2)

F. M. Smits, L. E. Gallaher, Bell Syst. Tech. J. 46, 1267 (1967).

G. Marie, Philips Res. Repts. 22, 110 (1967).

1966 (1)

W. Martienssen, E. Spiller, Phys. Rev. 145, 285 (1966).
[CrossRef]

1965 (1)

Anderson, L. K.

L. K. Anderson, Laser-Tech. Sect. 62 (1970).

L. K. Anderson, Bell Lab. Rec. 46, 319 (1968).

Biedermann, K.

K. Biedermann, N.-E. Molin, J. Phys. E Sci. Instrum. 3, 669 (1970).
[CrossRef]

Bobrinev, V. I.

A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, L. Z. Sokolava, J. Quantum Electron. QE-6, 193 (1970).
[CrossRef]

Burckhardt, C. B.

Cosentino, L. S.

Eschenfelder, A. H.

A. H. Eschenfelder, J. Appl. Phys. 41, 1372 (1970).
[CrossRef]

Fonger, W. H.

S. A. Keneman, G. W. Taylor, A. Miller, W. H. Fonger, Appl. Phys. Lett. 17, 173 (1970).
[CrossRef]

Gallaher, L. E.

F. M. Smits, L. E. Gallaher, Bell Syst. Tech. J. 46, 1267 (1967).

Groh, G.

G. Groh, G. Marie, Opt. Comm. 2, 133 (1970).
[CrossRef]

Heartling, G. H.

G. H. Heartling, C. E. Land, J. Am. Ceramic Bull. 49, 6 (1970).

Hill, B.

Keneman, S. A.

S. A. Keneman, G. W. Taylor, A. Miller, W. H. Fonger, Appl. Phys. Lett. 17, 173 (1970).
[CrossRef]

LaMacchia, J. T.

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

Land, C. E.

G. H. Heartling, C. E. Land, J. Am. Ceramic Bull. 49, 6 (1970).

Langdon, R. M.

R. M. Langdon, Rad. Electron. Eng. 38, 369 (1969).
[CrossRef]

Lohman, R. D.

R. D. Lohman, R. S. Mezrich, W. C. Stewart, Electronics, 18January, 61 (1971).

Maldonado, J. R.

A. H. Meitzler, J. R. Maldonado, Electronics, February, 34 (1971).

Marie, G.

G. Groh, G. Marie, Opt. Comm. 2, 133 (1970).
[CrossRef]

G. Marie, Philips Res. Repts. 22, 110 (1967).

Martienssen, W.

W. Martienssen, E. Spiller, Phys. Rev. 145, 285 (1966).
[CrossRef]

Meier, R. W.

Meitzler, A. H.

A. H. Meitzler, J. R. Maldonado, Electronics, February, 34 (1971).

Mezrich, R. S.

R. D. Lohman, R. S. Mezrich, W. C. Stewart, Electronics, 18January, 61 (1971).

Mikaeliane, A. L.

A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, L. Z. Sokolava, J. Quantum Electron. QE-6, 193 (1970).
[CrossRef]

Miller, A.

S. A. Keneman, G. W. Taylor, A. Miller, W. H. Fonger, Appl. Phys. Lett. 17, 173 (1970).
[CrossRef]

Molin, N.-E.

K. Biedermann, N.-E. Molin, J. Phys. E Sci. Instrum. 3, 669 (1970).
[CrossRef]

Naumov, S. M.

A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, L. Z. Sokolava, J. Quantum Electron. QE-6, 193 (1970).
[CrossRef]

Rajchman, J. A.

J. A. Rajchman, J. Appl. Phys. 41, 1376 (1970).
[CrossRef]

J. A. Rajchman, Appl. Opt. 9, 2269 (1970).
[CrossRef] [PubMed]

Schlitt, H.

H. Schlitt, Systemtheorie für regellose Vorgänge (Springer, Berlin, 1960).

Schmidt, U.

U. Schmidt, W. Thust, IEEE J. Quantum Electron. QE-5, 351 (1969).
[CrossRef]

U. Schmidt, in Optical Processing of Information, D. K. Pollack, C. J. Koester, J. T. Tippett, Eds. (Spartan Books, Washington, D.C., 1963), pp. 98–103.

Smits, F. M.

F. M. Smits, L. E. Gallaher, Bell Syst. Tech. J. 46, 1267 (1967).

Sokolava, L. Z.

A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, L. Z. Sokolava, J. Quantum Electron. QE-6, 193 (1970).
[CrossRef]

Spiller, E.

W. Martienssen, E. Spiller, Phys. Rev. 145, 285 (1966).
[CrossRef]

Stewart, W. C.

R. D. Lohman, R. S. Mezrich, W. C. Stewart, Electronics, 18January, 61 (1971).

W. C. Stewart, L. S. Cosentino, Appl. Opt. 9, 2271 (1970).
[CrossRef] [PubMed]

Taylor, G. W.

S. A. Keneman, G. W. Taylor, A. Miller, W. H. Fonger, Appl. Phys. Lett. 17, 173 (1970).
[CrossRef]

Thust, W.

U. Schmidt, W. Thust, IEEE J. Quantum Electron. QE-5, 351 (1969).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S. A. Keneman, G. W. Taylor, A. Miller, W. H. Fonger, Appl. Phys. Lett. 17, 173 (1970).
[CrossRef]

Bell Lab. Rec. (1)

L. K. Anderson, Bell Lab. Rec. 46, 319 (1968).

Bell Syst. Tech. J. (1)

F. M. Smits, L. E. Gallaher, Bell Syst. Tech. J. 46, 1267 (1967).

Electronics (2)

A. H. Meitzler, J. R. Maldonado, Electronics, February, 34 (1971).

R. D. Lohman, R. S. Mezrich, W. C. Stewart, Electronics, 18January, 61 (1971).

IEEE J. Quantum Electron. (1)

U. Schmidt, W. Thust, IEEE J. Quantum Electron. QE-5, 351 (1969).
[CrossRef]

J. Am. Ceramic Bull. (1)

G. H. Heartling, C. E. Land, J. Am. Ceramic Bull. 49, 6 (1970).

J. Appl. Phys. (2)

A. H. Eschenfelder, J. Appl. Phys. 41, 1372 (1970).
[CrossRef]

J. A. Rajchman, J. Appl. Phys. 41, 1376 (1970).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. E Sci. Instrum. (1)

K. Biedermann, N.-E. Molin, J. Phys. E Sci. Instrum. 3, 669 (1970).
[CrossRef]

J. Quantum Electron. (1)

A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, L. Z. Sokolava, J. Quantum Electron. QE-6, 193 (1970).
[CrossRef]

Laser Focus (1)

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

Laser-Tech. Sect. (1)

L. K. Anderson, Laser-Tech. Sect. 62 (1970).

Opt. Comm. (1)

G. Groh, G. Marie, Opt. Comm. 2, 133 (1970).
[CrossRef]

Philips Res. Repts. (1)

G. Marie, Philips Res. Repts. 22, 110 (1967).

Phys. Rev. (1)

W. Martienssen, E. Spiller, Phys. Rev. 145, 285 (1966).
[CrossRef]

Rad. Electron. Eng. (1)

R. M. Langdon, Rad. Electron. Eng. 38, 369 (1969).
[CrossRef]

Other (2)

U. Schmidt, in Optical Processing of Information, D. K. Pollack, C. J. Koester, J. T. Tippett, Eds. (Spartan Books, Washington, D.C., 1963), pp. 98–103.

H. Schlitt, Systemtheorie für regellose Vorgänge (Springer, Berlin, 1960).

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Figures (12)

Fig. 1
Fig. 1

Holographic storage system for transparent data input.

Fig. 2
Fig. 2

Holographic storage system for reflective data input.

Fig. 3
Fig. 3

Object wave irradiance in the hologram plane for the case of in-phase data input.

Fig. 4
Fig. 4

Mean object wave irradiance in the hologram plane for the data mask with random phase distribution.

Fig. 5
Fig. 5

Probability density of the normalized hologram irradiance for various exposure ratios.

Fig. 6
Fig. 6

Relative power of the light of which the intensities exceed the saturation value IHmax for various exposure ratios L.

Fig. 7
Fig. 7

Intensity distributions in the hologram plane.

Fig. 8
Fig. 8

Relative receiving signal as a function of the relative size of a detector.

Fig. 9
Fig. 9

Separation of reconstructed image and broadened zero order (Mx = number of holes in one column of the data mask).

Fig. 10
Fig. 10

Maximum angle between incident waves in the hologram plane.

Fig. 11
Fig. 11

Crosstalk by overlapping of the holograms.

Fig. 12
Fig. 12

Crosstalk by overlapping of the image points in the detector plane.

Equations (54)

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B I ( x I , y I ) = ν , μ rect ( x I - Δ I · ν D I ) rect ( y I - Δ I · μ D I ) .
I H I ( x H , y H ) = 1 2 A 2 4 π 2 F [ B ( x I , y I ) ] F * [ B ( x I , y I ) ] .
I H I ( x H , y H ) = k 2 8 π 2 f 2 A 2 D I 4 sinc 2 ( k D I 2 f x H ) sinc 2 ( k D I 2 f y H ) × sin 2 ( k / 2 f ) M Δ I x H · sin 2 ( k / 2 f ) M Δ I y H sin 2 ( k / 2 f ) Δ I x H · sin 2 ( k / 2 f ) Δ I y H ;             ( k = 2 π / λ ) .
B ( x I , y I ) = ν , μ exp ( i φ ν , μ ) rect ( x I - Δ I ν D I ) rect ( y I - Δ I ν D I ) ,
I H I ( x H , y H ) = k 2 A 2 8 π 2 f 2 D I 4 sinc 2 ( k D I 2 f x H ) sinc 2 ( k D I 2 f y H ) × | ν , μ exp [ i φ ν , μ - i k f Δ I ( x H · ν + y H · μ ) ] | 2 ,
I H I ( x H , y H ) = k 2 A 2 8 π 2 f 2 D I 4 M 2 sinc 2 ( k D I 2 f x H ) · sinc 2 ( k D I 2 f y H ) .
P [ I H ( x H , y H ) I H ( x H , y H ) ] = exp [ - I H ( x H , y H ) I H ( x H , y H ) ] .
R ( x H , y H ) = R exp [ - 4 D R 2 ( x H 2 + y H 2 ) + i k x H sin γ 0 ] .
P Ref = 1 2 R 2 ( π / 8 ) D R 2
P Data = 1 2 M 2 A 2 D I 2 ,
L = P Data P Ref = 8 π M 2 A 2 D I 2 R 2 D R 2 .
- + sinc 2 ( k D I 2 f x H ) d x H = - + exp ( - k 2 D I 2 4 π f 2 x H 2 ) d x H .
D H I 2 = D R 2 = ( 32 π f 2 ) / ( k 2 D I 2 ) .
I H ( x H , y H ) = L I H ( 0 , 0 ) M 2 ( 1 + L ) exp [ - 8 D R 2 ( x H 2 + y H 2 ) ] × | ν , μ exp [ i φ ν , μ - i k f Δ I ( x H ν + y H μ ) ] - i M L exp ( - i k x H sin γ 0 ) | 2 ,
I H ( 0 , 0 ) = 1 2 R 2 ( 1 + L ) .
P [ I H ( x H , y H ) ] = 1 + L L exp [ ( 8 / D R 2 ) ( x H 2 + y H 2 ) ] I H ( 0 , 0 ) × exp [ - 1 L - I H ( x H , y H ) I H ( 0 , 0 ) 1 + L L ] exp [ 8 D R 2 ( x H 2 + y H 2 ) ] × I 0 { 2 ( 1 + L ) 1 2 L exp [ 4 D R 2 ( x H 2 + y H 2 ) ] [ I H ( x H , y H ) I H ( 0 , 0 ) ] 1 2 } ,
P ( I H > I H max ) = 1 P total - + d x H d y H I H max I H ( x H , y H ) × p [ I H ( x H , y H ) ] d I H ( x H , y H ) = L 1 + L exp ( - 1 L ) 0 exp ( - t ) d t × 1 + L L exp ( t ) I H max I H ( 0 , 0 ) z exp ( - z ) I 0 ( 2 L z ) d z .
t H ( x H , y H ) = t H 0 - ( t H 0 / I H max ) · I H ( x H , y H ) ,
i t H 0 ( 2 L ) 1 2 M ( 1 + L ) / 2 3 I H ( 0 , 0 ) / 2 3 I H max exp [ - 12 D R 2 ( x H 2 + y H 2 ) ] × ν , μ exp [ i φ ν , μ - i k f Δ I ( x H ν + y H μ ) ] .
L t H 0 2 ( 1 + L ) 3 π D R 2 24 I H ( 0 , 0 ) 3 I H 2 max ,
η H D = t H 0 2 L ( 1 + L ) 2 1 3 I H ( 0 , 0 ) 2 I H 2 max .
η H T = t H 0 2 P 2 total ( 8 π D R 2 ) 2 1 3 1 I H 2 max L [ 1 + ( L / η D ) ] 3 .
L = 0.5 η D .
η H T max = t H 0 2 P 2 total ( 8 π D R 2 ) 2 4 81 η D 1 I H 2 max = t H 0 2 I H ( 0 , 0 ) 2 I H 2 max 1 9 η D ( 1 + 1 2 η D ) 2 .
η H D = t H 0 2 ( 1 / 12 ) [ I H ( 0 , 0 ) 2 / I H 2 max ]
D H = D R / 3.
I D ( x D , y D ) = P Ref · η H D M 2 8 π D D 2 × | ν , μ exp { i φ ν , μ - 4 D D 2 [ ( x D + Δ I ν ) 2 + ( y D + Δ I μ ) 2 ] } | 2 .
D D = 3.8 f / k D R = ( 6 / π ) 1 2 D I
P D = P Ref · η H D M 2 8 π D D 2 × - ( s / 2 ) β D D D ( s / 2 ) β D D D d x D - ( s / 2 ) β D D D ( s / 2 ) β D D D d y D exp [ - 8 D D 2 ( x D 2 + y D 2 ) ] .
P D max = ( P Ref × η H D ) / M 2 .
P D ( s β D ) / P D max = ( 4 / π ) erf 2 [ 2 s β D ]
t H 0 2 M 2 P 2 total ( 8 π D R 2 ) 2 2 3 I H 2 max L [ 1 + ( L / η D ) ] 3 4 π erf 2 [ 2 s β D ] .
η D = η D 0 × ( π / 6 β D 2 ) .
[ η D 0 erf 2 ( 2 s β D ) ] / β D .
γ 0 3 ( B x / 2 f ) ,
F 0 = γ 0 / λ = 3 B x / 2 λ f .
γ max = ( 1 / 2 f ) [ ( 4 B x ) 2 + B y 2 ] 1 2 .
γ max = 1 3 γ 0 ( 16 + α 2 ) 1 2 .
F max = 1 3 F 0 ( 16 + α 2 ) 1 2 .
M 2 = ( 4 α / 16 + α 2 ) [ ( λ f / Δ I ) F max ] 2 .
M max 2 = 1 2 ( λ f / Δ I ) F max ) 2 .
const . ν , μ exp { - i φ ν , μ - i k f Δ I [ ( x H + δ x H ) ν + ( y H + δ y H ) μ ] } × exp [ - 4 D R 2 ( x H + δ x H ) 2 + ( y H + δ x H ) 2 ] × sinc [ k D I 2 f ( x H + δ x H ) ] sinc [ k D I 2 f ( y H + δ y H ) ] × exp [ - 4 D R 2 ( x H 2 + y H 2 ) ] .
P D ( δ x H , δ y H ) = P D ( 0 , 0 ) exp { - 16 9 D H 2 [ ( δ x H ) 2 + ( δ y H ) 2 ] } .
c H 1.0 = exp [ - ( 16 / 9 ) β H 2 ]
c H 1.1 = exp [ - ( 32 / 9 ) β H 2 ] .
P D ( δ x D , δ y D ) - ( s / 2 ) β D D D ( s / 2 ) β D D D d x D d y D × exp { - 8 D D 2 [ ( x D - δ x D ) 2 + ( y D - δ y D ) 2 ] } .
c P 1.0 = erf [ 2 β D ( s + 2 ) ] - erf [ 2 β D ( s - 2 ) ] 2 erf ( 2 s β D ) .
c P 11 = { erf [ 2 β D ( s + 2 ) ] - erf [ 2 β D ( s - 2 ) ] } 2 4 erf 2 ( 2 β D s )
s H = M 2 / ( β H D H ) 2
s H = 4 M 2 / π D H 2
s H = ( 4 / π ) β H 2 s H .
s H = π 2 F max 2 α 4 ( 16 + α 2 ) × 1 β H 2 β D 2 .
s H = π 2 32 F max 2 1 β H 2 β D 2 = 0.137 F max 2 .
c = ( A H π 2 F max 2 α ) / [ 4 ( 16 + α 2 ) ] × 1 / ( β D 2 β H 2 ) ,

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