Abstract

We compare the characteristics of cross talk for angular multiplexing and several phase-encoded multiplexing strategies for volume holography. We discuss the implications of these characteristics for holographic data storage and compare noise arising from cross talk with noise arising from scattering that is due to inhomogeneities within a holographic medium.

© 1994 Optical Society of America

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  1. L. Hesselink and M. C. Bashaw, "Optical memories implemented with photorefractive media," Opt. Quantum Electron. 25, S611–S661 (1993).
    [CrossRef]
  2. W. J. Burke and P. Sheng, "Crosstalk noise from multiple thick-phase holograms," J. Appl. Phys. 48, 681–685 (1977).
    [CrossRef]
  3. F. H. Mok, "Angle-multiplexed storage of 5000 holograms in lithium niobate," Opt. Lett. 18, 915–917 (1993).
    [CrossRef] [PubMed]
  4. Y. N. Denisyuk, "On the reproduction of the optical properties of an object by the wave field of its scattered radiation," Opt. Spectrosc. (USSR) 15, 279–284 (1963).
  5. G. A. Rakuljic, V. Leyva, and A. Yariv, "Optical data storage by using orthogonal wavelength-multiplexed volume holograms," Opt. Lett. 17, 1471–1473 (1992).
    [CrossRef]
  6. A. E. Krasnov, "Thick-film phase holograms recorded by means of coded reference waves," Sov. J. Quantum Electron. 7, 1147–1148 (1977).
    [CrossRef]
  7. D. Z. Anderson and D. M. Lininger, "Dynamic optical interconnects: volume holograms as two-port operators," Appl. Opt. 26, 5031–5038 (1987).
    [CrossRef] [PubMed]
  8. C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding technique," Opt. Commun. 85, 171–176 (1991).
    [CrossRef]
  9. Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, and S. H. Lee, "Incremental recording for photorefractive hologram multiplexing," Opt. Lett. 16, 1774–1776 (1991).
    [CrossRef] [PubMed]
  10. H. Lee and S. K. Jin, "Experimental study of volume holographic interconnects using random patterns," Appl. Phys. Lett. 62, 2191–2193 (1993).
    [CrossRef]
  11. L. d'Auria, J.-P. Huignard, C. Slezak, and E. Spitz, "Experimental holographic read-write memory using 3-D storage," Appl. Opt. 13, 808–818 (1974).
    [CrossRef]
  12. L. Hesselink, "Photorefractive fibres for optical data storage and processing," Int. J. Optoelectron. 5, 103–124 (1990).
  13. S. Tao, D. R. Selviah, and J. E. Midwinter, "Spationangu-lar multiplexed storage of 750 holograms in an FeiLiNbO3 crystal," Opt. Lett. 18, 912–914 (1993).
    [CrossRef]
  14. D. Gabor, "Associative holographic memories," IBM J. Res. Dev. 13, 156–159 (1969).
    [CrossRef]
  15. T. F. Krile, R. J. Marks II, J. F. Walkup, and M. O. Hagler, "Holographic representations of space-variant systems using phase-coded reference beams," Appl Opt. 16, 3131–3135 (1977).
    [CrossRef] [PubMed]
  16. T. F. Krile, M. O. Hagler, W. D. Redus, and J. F. Walkup, "Multiplex holography with chirp-modulated binary phase-coded reference-beam masks," Appl. Opt. 18, 52–56 (1979).
    [CrossRef] [PubMed]
  17. E. L. Kral, J. F. Walkup, and M. O. Hagler, "Correlation properties of random phase diffusers for multiplex holography," Appl. Opt. 21, 1281–1290 (1982).
    [CrossRef] [PubMed]
  18. V. N. Morozov, "Theory of holograms formed using coded reference beams," Sov. J. Quantum Electron. 7, 961–964 (1977).
    [CrossRef]
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  20. E. G. Ramberg, "Holographic information storage," RCA Rev. 33, 5–53 (1972).
  21. C. Gu, J. Hong, I. McMichael, R. Saxena, and F. Mok, "Crosstalk-limited storage capacity of volume holographic memory," J. Opt. Soc. Am. A 9, 1978–1983 (1992).
    [CrossRef]
  22. H. Lee, X.-G. Gu, and D. Psaltis, "Volume holographic interconnections with maximal capacity and minimal cross talk," J. Appl. Phys. 65, 2191–2193 (1989); D. Psaltis, D. Brady, X. G. Gu, and S. Lin, "Holography in artificial neural networks," Nature (London) 343, 325–330 (1990).
    [CrossRef]
  23. E. N. Leith, A. Kozma, J. Upatnieks, J. Marks, and N. Massey, "Holographic data storage in three-dimensional media," Appl. Opt. 5, 1303–1311 (1966).
    [CrossRef] [PubMed]
  24. A. Aharoni, M. C. Bashaw, and L. Hesselink, "Capacity considerations for multiplexed holographic optical data storage," in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1914, 56–65 (1993).
    [CrossRef]
  25. D. Gabor and G. W. Stroke, "The theory of deep holograms," Proc. R. Soc. London Ser. A 304, 275–289 (1968).
    [CrossRef]
  26. R. G. Ramberg, "The hologram-properties and applications," RCA Rev. 27, 467–499 (1966).
  27. H. W. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  28. L. Solymar and D. J. Cooke, Volume Holograpy and Volume Gratings (Academic, London, 1981).
  29. V. G. Sidorovich, "Diffraction efficiency of three-dimensional phase holograms," Sov. Phys. Tech. Phys. 21, 742–745 (1976).
  30. L. Solymar, "Two-dimensional N- coupled wave theory for volume holograms," Opt. Commun. 23, 199–202 (1977).
    [CrossRef]
  31. Y. L. Korzinin and V. I. Sukhanov, "Wave field scattered by a three-dimensional phase hologram in the spatial-frequency representation," Sov. Tech. Phys. Lett. 9, 538–540 (1983).
  32. Y. L. Korzinin and V. I. Sukhanov, "Light diffraction by 3-D holograms with a continuous spectrum of spatial frequencies. System of equations for coupled waves," Opt. Spectrosc. (USSR) 56, 467–469 (1985).
  33. Y. L. Korzinin and V. I. Sukhanov, "Light diffraction by 3-D holograms with a continuous spectrum of spatial frequencies," Opt. Spectrosc. (USSR) 56, 572–574 (1985).
  34. Y. L. Korzinin and V. I. Sukhanov, "Diffraction efficiency of a 3-D phase hologram of a diffuse object," Opt. Spectrosc. (USSR) 58, 86–88 (1985).
  35. Y. L. Korzinin, "Diffraction of a monochromatic wave of arbitrary shape by 3-D holograms with extended spatial-frequency spectrum," Opt. Spectrosc. (USSR) 59, 124–126 (1985).
  36. M. Segev and A. Yariv, "Phase conjugation involving incoherent counterpropagating beams in photorefractive media," Opt. Lett. 16, 1938–1940 (1991).
    [CrossRef] [PubMed]
  37. M. C. Bashaw, A. Aharoni, and L. Hesselink, "Limitations of phase-conjugate replay in volume-holographic phase-disturbing media," Opt. Lett. 18, 741–743 (1993).
    [CrossRef] [PubMed]
  38. N. V. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Sov. Tech. Phys. Lett. 2, 438–440 (1976).
  39. G. C. Valley and M. B. Klein, "Optimal properties of photorefractive materials for optical data processing," Opt. Eng. 22, 704–711 (1983).
    [CrossRef]
  40. D. W. Vahey, "A nonlinear coupled-wave theory of holographic storage in ferroelectric materials," J. Appl. Phys. 46, 3510–3515 (1975).
    [CrossRef]
  41. P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484–519 (1989).
    [CrossRef]
  42. C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Potentialities and limitations of hologram multiplexing by using the phase-encoding technique," Appl. Opt. 31, 5700–5705 (1992).
    [CrossRef] [PubMed]
  43. T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894–937 (1985).
    [CrossRef]
  44. D. Gabor, "Light and information," in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, pp. 109–153.
    [CrossRef]
  45. P. J. van Heerden, "Theory of optical information storage in solids," Appl. Opt. 2, 393–400 (1963).
    [CrossRef]
  46. V. V. Aristov and V. S. Shekhtman, "Properties of three-dimensional holograms," Sov. Phys. Usp. 14, 263–277 (1971).
    [CrossRef]
  47. T. Jannson, "Shannon number of an image and structural information capacity in volume holography," Opt. Acta 27, 1335–1344 (1980).
    [CrossRef]
  48. A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).
  49. A. Yariv, "Interpage and interpixel cross talk in orthogonal (wavelength-multiplexed) hologram," Opt. Lett. 18, 652–654 (1993).
    [CrossRef]

1993 (6)

1992 (3)

1991 (3)

1990 (1)

L. Hesselink, "Photorefractive fibres for optical data storage and processing," Int. J. Optoelectron. 5, 103–124 (1990).

1989 (2)

H. Lee, X.-G. Gu, and D. Psaltis, "Volume holographic interconnections with maximal capacity and minimal cross talk," J. Appl. Phys. 65, 2191–2193 (1989); D. Psaltis, D. Brady, X. G. Gu, and S. Lin, "Holography in artificial neural networks," Nature (London) 343, 325–330 (1990).
[CrossRef]

P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

1987 (1)

1985 (4)

Y. L. Korzinin and V. I. Sukhanov, "Light diffraction by 3-D holograms with a continuous spectrum of spatial frequencies. System of equations for coupled waves," Opt. Spectrosc. (USSR) 56, 467–469 (1985).

Y. L. Korzinin and V. I. Sukhanov, "Light diffraction by 3-D holograms with a continuous spectrum of spatial frequencies," Opt. Spectrosc. (USSR) 56, 572–574 (1985).

Y. L. Korzinin and V. I. Sukhanov, "Diffraction efficiency of a 3-D phase hologram of a diffuse object," Opt. Spectrosc. (USSR) 58, 86–88 (1985).

Y. L. Korzinin, "Diffraction of a monochromatic wave of arbitrary shape by 3-D holograms with extended spatial-frequency spectrum," Opt. Spectrosc. (USSR) 59, 124–126 (1985).

1983 (2)

Y. L. Korzinin and V. I. Sukhanov, "Wave field scattered by a three-dimensional phase hologram in the spatial-frequency representation," Sov. Tech. Phys. Lett. 9, 538–540 (1983).

G. C. Valley and M. B. Klein, "Optimal properties of photorefractive materials for optical data processing," Opt. Eng. 22, 704–711 (1983).
[CrossRef]

1982 (1)

1980 (1)

T. Jannson, "Shannon number of an image and structural information capacity in volume holography," Opt. Acta 27, 1335–1344 (1980).
[CrossRef]

1979 (1)

1977 (5)

T. F. Krile, R. J. Marks II, J. F. Walkup, and M. O. Hagler, "Holographic representations of space-variant systems using phase-coded reference beams," Appl Opt. 16, 3131–3135 (1977).
[CrossRef] [PubMed]

A. E. Krasnov, "Thick-film phase holograms recorded by means of coded reference waves," Sov. J. Quantum Electron. 7, 1147–1148 (1977).
[CrossRef]

W. J. Burke and P. Sheng, "Crosstalk noise from multiple thick-phase holograms," J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

V. N. Morozov, "Theory of holograms formed using coded reference beams," Sov. J. Quantum Electron. 7, 961–964 (1977).
[CrossRef]

L. Solymar, "Two-dimensional N- coupled wave theory for volume holograms," Opt. Commun. 23, 199–202 (1977).
[CrossRef]

1976 (2)

N. V. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Sov. Tech. Phys. Lett. 2, 438–440 (1976).

V. G. Sidorovich, "Diffraction efficiency of three-dimensional phase holograms," Sov. Phys. Tech. Phys. 21, 742–745 (1976).

1975 (1)

D. W. Vahey, "A nonlinear coupled-wave theory of holographic storage in ferroelectric materials," J. Appl. Phys. 46, 3510–3515 (1975).
[CrossRef]

1974 (1)

1972 (1)

E. G. Ramberg, "Holographic information storage," RCA Rev. 33, 5–53 (1972).

1971 (1)

V. V. Aristov and V. S. Shekhtman, "Properties of three-dimensional holograms," Sov. Phys. Usp. 14, 263–277 (1971).
[CrossRef]

1969 (2)

H. W. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

D. Gabor, "Associative holographic memories," IBM J. Res. Dev. 13, 156–159 (1969).
[CrossRef]

1968 (1)

D. Gabor and G. W. Stroke, "The theory of deep holograms," Proc. R. Soc. London Ser. A 304, 275–289 (1968).
[CrossRef]

1966 (2)

1963 (2)

Y. N. Denisyuk, "On the reproduction of the optical properties of an object by the wave field of its scattered radiation," Opt. Spectrosc. (USSR) 15, 279–284 (1963).

P. J. van Heerden, "Theory of optical information storage in solids," Appl. Opt. 2, 393–400 (1963).
[CrossRef]

van Heerden, P. J.

Aharoni, A.

M. C. Bashaw, A. Aharoni, and L. Hesselink, "Limitations of phase-conjugate replay in volume-holographic phase-disturbing media," Opt. Lett. 18, 741–743 (1993).
[CrossRef] [PubMed]

A. Aharoni, M. C. Bashaw, and L. Hesselink, "Capacity considerations for multiplexed holographic optical data storage," in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1914, 56–65 (1993).
[CrossRef]

Anderson, D. Z.

Aristov, V. V.

V. V. Aristov and V. S. Shekhtman, "Properties of three-dimensional holograms," Sov. Phys. Usp. 14, 263–277 (1971).
[CrossRef]

Bashaw, M. C.

M. C. Bashaw, A. Aharoni, and L. Hesselink, "Limitations of phase-conjugate replay in volume-holographic phase-disturbing media," Opt. Lett. 18, 741–743 (1993).
[CrossRef] [PubMed]

L. Hesselink and M. C. Bashaw, "Optical memories implemented with photorefractive media," Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

A. Aharoni, M. C. Bashaw, and L. Hesselink, "Capacity considerations for multiplexed holographic optical data storage," in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1914, 56–65 (1993).
[CrossRef]

Burke, W. J.

W. J. Burke and P. Sheng, "Crosstalk noise from multiple thick-phase holograms," J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

Cooke, D. J.

L. Solymar and D. J. Cooke, Volume Holograpy and Volume Gratings (Academic, London, 1981).

d’Auria, L.

Denisyuk, Y. N.

Y. N. Denisyuk, "On the reproduction of the optical properties of an object by the wave field of its scattered radiation," Opt. Spectrosc. (USSR) 15, 279–284 (1963).

Denz, C.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Potentialities and limitations of hologram multiplexing by using the phase-encoding technique," Appl. Opt. 31, 5700–5705 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding technique," Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Fainman, Y.

Ford, J. E.

Gabor, D.

D. Gabor, "Associative holographic memories," IBM J. Res. Dev. 13, 156–159 (1969).
[CrossRef]

D. Gabor and G. W. Stroke, "The theory of deep holograms," Proc. R. Soc. London Ser. A 304, 275–289 (1968).
[CrossRef]

D. Gabor, "Light and information," in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, pp. 109–153.
[CrossRef]

Gaylord, T. K.

T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gu, C.

Gu, X.-G.

H. Lee, X.-G. Gu, and D. Psaltis, "Volume holographic interconnections with maximal capacity and minimal cross talk," J. Appl. Phys. 65, 2191–2193 (1989); D. Psaltis, D. Brady, X. G. Gu, and S. Lin, "Holography in artificial neural networks," Nature (London) 343, 325–330 (1990).
[CrossRef]

Hagler, M. O.

Hesselink, L.

L. Hesselink and M. C. Bashaw, "Optical memories implemented with photorefractive media," Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

M. C. Bashaw, A. Aharoni, and L. Hesselink, "Limitations of phase-conjugate replay in volume-holographic phase-disturbing media," Opt. Lett. 18, 741–743 (1993).
[CrossRef] [PubMed]

L. Hesselink, "Photorefractive fibres for optical data storage and processing," Int. J. Optoelectron. 5, 103–124 (1990).

A. Aharoni, M. C. Bashaw, and L. Hesselink, "Capacity considerations for multiplexed holographic optical data storage," in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. Soc. Photo-Opt. Instrum. Eng. 1914, 56–65 (1993).
[CrossRef]

Hong, J.

Huignard, J.-P.

Jannson, T.

T. Jannson, "Shannon number of an image and structural information capacity in volume holography," Opt. Acta 27, 1335–1344 (1980).
[CrossRef]

Jin, S. K.

H. Lee and S. K. Jin, "Experimental study of volume holographic interconnects using random patterns," Appl. Phys. Lett. 62, 2191–2193 (1993).
[CrossRef]

Klein, M. B.

G. C. Valley and M. B. Klein, "Optimal properties of photorefractive materials for optical data processing," Opt. Eng. 22, 704–711 (1983).
[CrossRef]

Kogelnik, H. W.

H. W. Kogelnik, "Coupled wave theory for thick hologram gratings," Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Korzinin, Y. L.

Y. L. Korzinin and V. I. Sukhanov, "Diffraction efficiency of a 3-D phase hologram of a diffuse object," Opt. Spectrosc. (USSR) 58, 86–88 (1985).

Y. L. Korzinin, "Diffraction of a monochromatic wave of arbitrary shape by 3-D holograms with extended spatial-frequency spectrum," Opt. Spectrosc. (USSR) 59, 124–126 (1985).

Y. L. Korzinin and V. I. Sukhanov, "Light diffraction by 3-D holograms with a continuous spectrum of spatial frequencies. System of equations for coupled waves," Opt. Spectrosc. (USSR) 56, 467–469 (1985).

Y. L. Korzinin and V. I. Sukhanov, "Light diffraction by 3-D holograms with a continuous spectrum of spatial frequencies," Opt. Spectrosc. (USSR) 56, 572–574 (1985).

Y. L. Korzinin and V. I. Sukhanov, "Wave field scattered by a three-dimensional phase hologram in the spatial-frequency representation," Sov. Tech. Phys. Lett. 9, 538–540 (1983).

Kozma, A.

Kral, E. L.

Krasnov, A. E.

A. E. Krasnov, "Thick-film phase holograms recorded by means of coded reference waves," Sov. J. Quantum Electron. 7, 1147–1148 (1977).
[CrossRef]

Krile, T. F.

T. F. Krile, M. O. Hagler, W. D. Redus, and J. F. Walkup, "Multiplex holography with chirp-modulated binary phase-coded reference-beam masks," Appl. Opt. 18, 52–56 (1979).
[CrossRef] [PubMed]

T. F. Krile, R. J. Marks II, J. F. Walkup, and M. O. Hagler, "Holographic representations of space-variant systems using phase-coded reference beams," Appl Opt. 16, 3131–3135 (1977).
[CrossRef] [PubMed]

Kukhtarev, N. V.

N. V. Kukhtarev, "Kinetics of hologram recording and erasure in electrooptic crystals," Sov. Tech. Phys. Lett. 2, 438–440 (1976).

Lee, H.

H. Lee and S. K. Jin, "Experimental study of volume holographic interconnects using random patterns," Appl. Phys. Lett. 62, 2191–2193 (1993).
[CrossRef]

H. Lee, X.-G. Gu, and D. Psaltis, "Volume holographic interconnections with maximal capacity and minimal cross talk," J. Appl. Phys. 65, 2191–2193 (1989); D. Psaltis, D. Brady, X. G. Gu, and S. Lin, "Holography in artificial neural networks," Nature (London) 343, 325–330 (1990).
[CrossRef]

Lee, S. H.

Leith, E. N.

Leyva, V.

Lininger, D. M.

Ma, J.

Marks, J.

Marks II, R. J.

T. F. Krile, R. J. Marks II, J. F. Walkup, and M. O. Hagler, "Holographic representations of space-variant systems using phase-coded reference beams," Appl Opt. 16, 3131–3135 (1977).
[CrossRef] [PubMed]

Massey, N.

McMichael, I.

Midwinter, J. E.

Moharam, M. G.

T. K. Gaylord and M. G. Moharam, "Analysis and applications of optical diffraction by gratings," Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Mok, F.

Mok, F. H.

Morozov, V. N.

V. N. Morozov, "Theory of holograms formed using coded reference beams," Sov. J. Quantum Electron. 7, 961–964 (1977).
[CrossRef]

Pauliat, G.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Potentialities and limitations of hologram multiplexing by using the phase-encoding technique," Appl. Opt. 31, 5700–5705 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding technique," Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Psaltis, D.

H. Lee, X.-G. Gu, and D. Psaltis, "Volume holographic interconnections with maximal capacity and minimal cross talk," J. Appl. Phys. 65, 2191–2193 (1989); D. Psaltis, D. Brady, X. G. Gu, and S. Lin, "Holography in artificial neural networks," Nature (London) 343, 325–330 (1990).
[CrossRef]

Rakuljic, G. A.

Ramberg, E. G.

E. G. Ramberg, "Holographic information storage," RCA Rev. 33, 5–53 (1972).

Ramberg, R. G.

R. G. Ramberg, "The hologram-properties and applications," RCA Rev. 27, 467–499 (1966).

Redus, W. D.

Roosen, G.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Potentialities and limitations of hologram multiplexing by using the phase-encoding technique," Appl. Opt. 31, 5700–5705 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding technique," Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Sasaki, H.

Saxena, R.

Segev, M.

Selviah, D. R.

Shekhtman, V. S.

V. V. Aristov and V. S. Shekhtman, "Properties of three-dimensional holograms," Sov. Phys. Usp. 14, 263–277 (1971).
[CrossRef]

Sheng, P.

W. J. Burke and P. Sheng, "Crosstalk noise from multiple thick-phase holograms," J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

Sidorovich, V. G.

V. G. Sidorovich, "Diffraction efficiency of three-dimensional phase holograms," Sov. Phys. Tech. Phys. 21, 742–745 (1976).

Slezak, C.

Solymar, L.

L. Solymar, "Two-dimensional N- coupled wave theory for volume holograms," Opt. Commun. 23, 199–202 (1977).
[CrossRef]

L. Solymar and D. J. Cooke, Volume Holograpy and Volume Gratings (Academic, London, 1981).

Spitz, E.

Stroke, G. W.

D. Gabor and G. W. Stroke, "The theory of deep holograms," Proc. R. Soc. London Ser. A 304, 275–289 (1968).
[CrossRef]

Sukhanov, V. I.

Y. L. Korzinin and V. I. Sukhanov, "Light diffraction by 3-D holograms with a continuous spectrum of spatial frequencies," Opt. Spectrosc. (USSR) 56, 572–574 (1985).

Y. L. Korzinin and V. I. Sukhanov, "Light diffraction by 3-D holograms with a continuous spectrum of spatial frequencies. System of equations for coupled waves," Opt. Spectrosc. (USSR) 56, 467–469 (1985).

Y. L. Korzinin and V. I. Sukhanov, "Diffraction efficiency of a 3-D phase hologram of a diffuse object," Opt. Spectrosc. (USSR) 58, 86–88 (1985).

Y. L. Korzinin and V. I. Sukhanov, "Wave field scattered by a three-dimensional phase hologram in the spatial-frequency representation," Sov. Tech. Phys. Lett. 9, 538–540 (1983).

Taketomi, Y.

Tao, S.

Tschudi, T.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Potentialities and limitations of hologram multiplexing by using the phase-encoding technique," Appl. Opt. 31, 5700–5705 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase encoding technique," Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Upatnieks, J.

Vahey, D. W.

D. W. Vahey, "A nonlinear coupled-wave theory of holographic storage in ferroelectric materials," J. Appl. Phys. 46, 3510–3515 (1975).
[CrossRef]

Valley, G. C.

G. C. Valley and M. B. Klein, "Optimal properties of photorefractive materials for optical data processing," Opt. Eng. 22, 704–711 (1983).
[CrossRef]

VanderLugt, A.

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

Walkup, J. F.

Yariv, A.

Yeh, P.

P. Yeh, "Two-wave mixing in nonlinear media," IEEE J. Quantum Electron. 25, 484–519 (1989).
[CrossRef]

Appl Opt. (1)

T. F. Krile, R. J. Marks II, J. F. Walkup, and M. O. Hagler, "Holographic representations of space-variant systems using phase-coded reference beams," Appl Opt. 16, 3131–3135 (1977).
[CrossRef] [PubMed]

Appl. Opt. (7)

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Figures (11)

Fig. 1
Fig. 1

General schematic for holographic storage by angular multiplexing. A signal is generated by an illuminated amplitude spatial light modulator (ASLM), and reference beams are incident at different angles.

Fig. 2
Fig. 2

General schematic for holographic storage with controlled reference waves. A signal is generated by an illuminated amplitude spatial light modulator (ASLM), and reference beams are generated by an illuminated phase spatial light modulator (PSLM).

Fig. 3
Fig. 3

Slab geometry used in this evaluation.

Fig. 4
Fig. 4

Orientation on the Ewald circle of signal- and reference wave vectors.

Fig. 5
Fig. 5

Two-dimensional representation of the constituent grating vectors in reciprocal space for angular multiplexing.

Fig. 6
Fig. 6

Two-dimensional representation of the constituent grating vectors in reciprocal space for phase-encoded multiplexing.

Fig. 7
Fig. 7

Device architecture for the perpendicular geometry. The signal beam (S) is encoded with an amplitude spatial light modulator (ASLM), and the reference beam is encoded with a phase spatial light modulator (PSLM). All the lenses have focal length f and are arranged for Fourier holography. A signal pixel p corresponds to wave vector kp propagating at angle θp within the medium, and a reference pixel, or phase-code element, i corresponds to wave vector ki propagating at angle θi within the medium. Angular multiplexing is equivalent to having only one pixel i on for each reference wave, whereas for phase-encoded multiplexing all pixels are on.

Fig. 8
Fig. 8

Symmetrical bandwidth about perpendicular signal- and reference-wave-vector band centers.

Fig. 9
Fig. 9

Cross-talk-limited SNR for angular multiplexing in a 1-cm-long medium with an index of n = 2.5 at 500 nm. Here MR = 105. The SNR is plotted as a function of the signal bandwidth kpy/β. The dashed lines represent situations for which the second-order expansions are no longer valid and are included for comparison.

Fig. 10
Fig. 10

Interpixel cross talk that is due to the aperture of the medium itself, resulting in an overlap of the angular spectra of neighboring pixels.

Fig. 11
Fig. 11

SNR as a function of the number of pages MR = 105 and kpy/β = 0.1, when the maximum SNR for a single hologram without superposition, SNR1, is 105, 108, and 1011. The thin line (lower right-hand corner) represents the contribution to SNR that is due only to cross talk, the dashed lines represent the contribution to SNR that is due only to undesired scatter, and the thick lines represent the net SNR.

Tables (1)

Tables Icon

Table 1 Summary of XSR Estimates

Equations (104)

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SNR M R N ,
SNR M R N f d .
E ( r , t ) = A ( r ) exp ( i ω t ) ,
2 A ( r ) + ( r ) μ ( r ) ω 2 c 2 A ( r ) = 0 ,
β = n 0 ω c = 2 π n 0 λ ,
A ^ ( k ) = 1 ( 2 π ) 3 d 3 r exp ( - i k · r ) A ( r ) .
A ( r ) = d 3 k exp ( i k · r ) A ^ ( k ) .
d 2 A ^ c ( k , z ) d z 2 + 2 i k z d A ^ c ( k , z ) d z = ( k 2 - β 2 ) A ^ c ( k , z ) - 2 β 2 n 0 d k δ n ^ ( k - k ) A ^ c ( k , z )
δ n ^ ( K ) = n 1 ( K ) U ( A i ) d 3 k A ^ i * ( k - K ) A ^ i ( k ) × e ^ i ( k - K ) · e ^ i ( k )
U ( A i ) = 1 V d 3 r A i ( r ) 2 ,
A i ( r ) = S i ( r ) + R i ( r ) .
δ n ^ ( K ) = n 1 ( K ) U ( A i ) d 3 k R ^ i * ( k - K ) S ^ i ( k ) e ^ R i * ( k - K ) · e ^ S i ( k ) + n 1 ( K ) U ( A i ) d 3 k S ^ i * ( k - K ) × R ^ i ( k ) e ^ S i * ( k - K ) · e ^ R i ( k ) ,
δ n ( r ) = n 1 U ( R i + S i ) [ R i ( r ) S i * ( r ) + R i ( r ) * S i ( r ) ] ,
δ n ( r ) a 1 A * ( r ) A ( r ) .
K = k p - k i ,
d A ^ D ( k , z ) d z = i φ ( k ) c ( k ) A D ( k , z ) + i K ( k ) n 1 U 0 × [ S ^ i * ( R ^ i R ^ c ) ] ( k ) ,
φ ( k ) = β 2 - k 2 2 k = β 2 - k 2 2 k
c ( k ) = k z / k = cos ( θ k ) ,
K ( k ) = β 2 n 0 k z = 2 π λ c ( k )
( R ^ i R ^ c ) ( k ) = d 3 k R ^ i * ( k - k ) R ^ c ( k )
( S ^ i * f ^ ) ( k ) = d 3 k S ^ i ( k - k ) f ^ ( k ) ,
[ S ^ i * ( R ^ i R ^ c ) ] ( k ) = d 3 k d 3 k S ^ i ( k - k ) × R ^ i * ( k - k ) R ^ c ( k ) ,
S ^ ( k ) = S ^ ( θ k ) δ ( β - k 2 ) .
A ˜ ( k x , k y ) = d k z A ^ ( k x , k y , k z ) .
K ( k x , k y ) = β 2 n 0 1 ( β 2 - k x 2 - k y 2 ) 1 / 2 .
ξ ( k , L ) = φ ( k ) L 2 c ( k ) = β 2 - k 2 4 k z L .
A ˜ D ( k x , k y ) = i n 1 U 0 L K ( k x , k y ) d k z j N exp [ i ξ ( k , L ) ] × sinc [ ξ ( k , L ) ] [ S ^ j * ( R ^ j R ^ c ) ] ( k ) ,
R i ( r ) = R i exp ( i k i · r ) ,
R ^ i ( k ) = R i δ ( k - k i ) .
( R ^ i R ^ c ) ( k ) = R i * R c δ ( k - Δ k c i ) ,
Δ k c i = k c - k i ,
[ S ^ i * ( R ^ i R ^ c ) ] ( k ) = R i * R c S ^ i ( k - Δ k c i ) .
A ˜ D ( k p x , k p y ) = i n 1 L K ( k p x , k p y ) d k z exp [ i ξ ( k p , L ) ] × sinc [ ξ ( k p , L ) ] S ^ i ( k p - Δ k c i ) .
S ^ ( k p ) = 1 ( 2 π ) 2 d 2 r exp ( - i k p · r ) S ^ i ( r ) .
A ˜ D ( k p y ) = i n 1 L K ( k p y ) exp [ i ξ c i ( k p y ) ] × sinc [ ξ c i ( k p y ) ] S ^ i ( k p y - Δ k c i y ) ,
k - Δ k c i 2 = β 2
ξ c i ( k p y ) = - L 2 k p y Δ k c i y + 2 { [ β 2 - ( k p y - Δ k c i y ) 2 ] 1 / 2 + Δ k c i z } Δ k c i z - Δ k c i z 2 - Δ k c i z 2 4 { [ β 2 - ( k p y - Δ k c i y ) 2 ] 1 / 2 + Δ k c i z } .
ξ c i ( k p y ) π n λ sin ( θ i - θ p ) cos ( θ p ) L Δ θ c i .
Δ θ ( θ i , θ p ) λ n cos ( θ p ) sin ( θ i - θ p ) 1 L .
k i z = 2 π p i / L ,             - n L / λ p i n L / λ
0 π d θ Δ θ = M R .
k i z = 2 π p i / L ,             - N B 2 P i N B 2 .
k i z = 2 π m p i / L ,             - N B 2 m p i N B 2 m ,
ξ c j ( k p y = 0 ) Δ k c j z L / 2.
A ^ c ( k p y ) 2 = | n 1 β 2 n 0 k p z L S ^ c ( k p y ) | 2 ,
A ^ X ( k p y ) 2 = A ^ D ( k p y ) 2 - A ^ c ( k p y ) 2 .
XSR ( k p y ) A ^ X ( k p y ) 2 A ^ c ( k p y ) 2 ,
R i ( r ) = R 0 l M r i l exp ( i k l · r ) ,
R ^ i ( k ) = R 0 l r i l δ ( k - k l )
A ˜ D ( k p y ) = i n 1 L K ( k p y ) j N l M m M d k p z r j l * r c m × exp [ i ξ ( k p , L ) ] sinc [ ξ ( k p , L ) ] S ^ j ( k p - Δ k m l ) ,
A ^ D ( k p y ) = i n 1 β 2 n 0 k p z L j N l M m M r j l * r c m X m l ( k p y ) × S ^ j ( k p y - Δ k m l y ) ,
X m l ( k p y ) = exp [ i ξ m l ( k p y ) ] sinc [ ξ m l ( k p y ) ] ,
k p z β 2 - k p y 2 .
XSR ( k p y ) = | j N l M a j p r j l * r c l + j N l M m l M a j p m l r j l * r c m X m l | 2 - a c p 2 / a c p 2 ,
l M r j l * r c l = δ c j .
k i y = - β 2 - k i z 2 ,
Δ k m l y β 2 ( k m z 2 β 2 - k l z 2 β 2 ) .
ξ m l ( k p y ) = - L 2 [ ( k m z - k l z ) × ( 1 + k p y 2 k p z k m z + k l z β - k m z - k l z 2 k p z ) ] .
ξ m l ( k p y ) = - π ( p m - p l ) × ( 1 + k p y k p z p m + p l M R - β k p z p m - p l M R ) ,
r i l exp ( i ϕ i l ) δ i l ,
A ˜ D ( k p y ) = i n 1 β 2 n 0 k p z L j X c j ( k p y ) S ˜ j ( k p y - Δ k c j y ) .
XSR ( p c , k p y ) = j c X c j ( k p y ) 2 a j p c j 2 / a c p 2 .
X c j ( k s ) 2 sin 2 [ π ( p c - p j ) k p y k p z p c + p j M R ] / [ π ( p c - p j ) ] 2
( k p y k p z p c + p j M R ) 2 .
| ( p c - p j ) k p y k p z p c + p j M R | 1 ,
M t M R 2 p c | k p z k p y | .
M t = M t 2 + min [ M t 2 , ( N 2 - p c ) ] ,
X ( p c , k p y ) 2 = ( 2 p c M R k p y k p z ) 2 .
XSR ( p c , k p y ) = j c N X c j ( k p y ) 2
M t ( p c , k p y ) X ( p c , k p y ) 2
2 p c M R | k p y k p z | .
XSR ( N , k p y ) N M R k p y β .
SNR = M R N β k p y max .
XSR ( p c , k p y ) N 2 p c M R k p y β ,
r i l exp ( i ϕ i l ) / M .
XSR ( N , k p y ) = 1 N 2 j N l N m l N a j p m l 2 X m l ( k p y ) 2 / a c p 2 ,
XSR ( N , k p y ) = 1 N l N m l N X m l ( k p y ) 2 ,
XSR ( N , k p y ) 1 N p l = - N / 2 p l = N / 2 M t ( p l ) X ( p l , k p y ) 2 1 2 N M R k p y β ,
SNR 2 M R N β k p y max .
XSR ( k p ) = 1 M 2 | l N l M a j p exp [ i ( ϕ c l - ϕ j l - c j l ) ] | 2 - a c p 2 / a c p 2 .
XSR N M 2 ,
XSR ( k p y ) = 1 M 2 j c N l M a j p 2 / a c p 2 = N - 1 M .
SNR M N .
A ^ D ( k p y ) = i n 1 β 2 n 0 k z L j N l M n p l n 1 r j l * r c l S j ( k p y ) ,
R j l = r j l exp ( i k l · r ) .
r j l = r j l ( n 1 n 0 l ) 1 / 2 ,
l M ( n 0 l n 1 ) r j l * r c l = δ c j ,
A ^ D ( k p y ) = i n 1 β 2 n 0 k z L j N l M ( n p l n o l ) r j l * r c l S ^ j ( k p y ) ,
XSR ( N , k p y ) = | a c p + j N l M δ n p l n 0 l a j p r j l * r c l | 2 - a c p 2 / a c p 2 .
XSR ( N , k p y ) = N M 2 | l M δ n p l n 0 l exp ( ϕ c l - ϕ j l ) | 2 c j ,
XSR ( N , k p y ) = N M | δ n p l n 0 l | 2 ,
ξ c i ( k p y ) = - L 2 k p y Δ k c i y + 2 { [ β 2 - k p x 2 - ( k p y - Δ k c i y ) 2 ] 1 / 2 + Δ k c i z } Δ k c i z - Δ k c i y 2 - k c i z 2 4 { [ β 2 - k p x 2 - ( k p y - Δ k c i y ) 2 ] 1 / 2 + Δ k c i z } ,
k p x = 2 π u p / H ,             - n H / λ u p n H / λ ,
k p y = 2 π v p / W ,             - n W / λ v p n W / λ
k p y = 2 π p i / ( P L ) ,             - k p y max β P p i k p y max β P .
XSR ( N , P y ) N M R P y P R y ,
XSR ( N , P ) N M R P P R y P x ,
XSR ( N , P ) N M R ( P P R ) 1 / 2 ,
δ n ^ ( K ) = δ n ^ ( K ) * [ sinc ( K y W / 2 ) sinc ( K y H / 2 ) ] .
S ^ i ( k ) = S 0 p a i p δ ( k - k p ) .
S ^ i ( k ) = S 0 p a i p sinc [ ( k y - k p y ) W / 2 ] sinc [ ( k x - k p x ) H / 2 ] .
SNR = 1 / 2 .
n 1 ( k p - k i ) = ( k p - k i ) · c ^ 1 + k p - k i 2 / k D 2 ,
SNR = ( k p y max β N M R + B S 2 A D 2 + B R 2 A D 2 N 2 ) - 1 ,

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