Abstract

We study the use of error-correction coding (ECC) and two-dimensional interleaving for volume holographic memory (VHM) systems suffering from both random and systematic errors. The bit-error rate (BER) is used as the data-fidelity measure and as a design metric for optical 4f systems. The correlated error patterns arising from both lens aberrations and misalignment errors are analyzed, and we discuss the information theoretic storage capacity of VHM in the presence of such correlated error patterns. The performance of interleaving and ECC is analyzed from both BER and storage-capacity perspectives. Magnification, rotation, tilt, and defocus errors are also studied, and an experimental demonstration that combines ECC with two-dimensional interleaving is included.

© 1998 Optical Society of America

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  1. J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Opt. Eng. 34, 2193–2203 (1995).
    [CrossRef]
  2. R. M. Shelby, J. A. Hoffnagle, G. W. Burr, C. M. Jefferson, M.-P. Bernal, H. Coufal, R. K. Grygier, H. Günther, R. M. Macfarlane, G. T. Sincerbox, “Pixel-matched holographic data storage with megabit pages,” Opt. Lett. 22, 1509–1511 (1997).
    [CrossRef]
  3. I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375–2379 (1996).
    [CrossRef] [PubMed]
  4. G. A. Rakuljic, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
    [CrossRef] [PubMed]
  5. T. F. Krile, R. J. Marks, J. F. Walkup, M. O. Hagler, “Holographic representations of space-variant systems using phase-coded reference beams,” Appl. Opt. 16, 3131–3135 (1977).
    [CrossRef] [PubMed]
  6. J. T. LaMacchia, D. L. White, “Coded multiple exposure holograms,” Appl. Opt. 7, 91–94 (1968).
    [CrossRef] [PubMed]
  7. P. J. van Heerden, “A new optical method of storing and retrieving information,” Appl. Opt. 2, 387–392 (1963).
    [CrossRef]
  8. G. W. Burr, F. H. Mok, D. Psaltis, “Angle and space multiplexed holographic storage using the 90° geometry,” Opt. Commun. 117, 49–55 (1995).
    [CrossRef]
  9. F. Vachss, I. McMichael, J. Hong, “Cross-erasure noise in high-density holographic-storage systems,” J. Opt. Soc. Am. B 14, 1187–1198 (1997).
    [CrossRef]
  10. A. A. Freschi, P. M. Garcia, I. Rasnik, J. Frejlich, “Avoiding hologram bending in photorefractive crystals,” Opt. Lett. 21, 152–154 (1996).
    [CrossRef] [PubMed]
  11. S. Campbell, S.-H. Lin, X. Yi, P. Yeh, “Absorption effects in photorefractive volume-holographic memory systems. I. Beam depletion,” J. Opt. Soc. Am. B 13, 2209–2217 (1996);“Absorption effects in photorefractive volume-holographic memory systems. II. Material heating,” J. Opt. Soc. Am. B 13, 2218–2228 (1996).
    [CrossRef]
  12. X. Yi, P. Yeh, C. Gu, “Cross-talk noise in volume holographic memory with spherical reference beams,” Opt. Lett. 20, 1812–1814 (1995).
    [CrossRef] [PubMed]
  13. H. Zhou, F. Zhao, F. T. S. Yu, “Effects of recording–erasure dynamics of storage capacity of a wavelength-multiplexed reflection-type photorefractive hologram,” Appl. Opt. 33, 4339–4344 (1994).
    [CrossRef] [PubMed]
  14. J. T. Gallo, C. M. Verber, “Model for the effects of material shrinkage on volume holograms,” Appl. Opt. 33, 6797–6804 (1994).
    [CrossRef] [PubMed]
  15. E. S. Maniloff, K. M. Johnson, “Effects of scattering on the dynamics of holographic recording and erasure in photorefractive lithium niobate,” J. Appl. Phys. 73, 541–547 (1993).
    [CrossRef]
  16. C. Gu, J. Hong, I. McMichael, R. Saxena, F. Mok, “Cross-talk-limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
    [CrossRef]
  17. C. Gu, J. Hong, “Noise gratings formed during the multiple exposure schedule in photorefractive media,” Opt. Commun. 93, 213–218 (1992).
    [CrossRef]
  18. M. A. Neifeld, K. M. Chugg, B. M. King, “Parallel data detection in page-oriented optical memory,” Opt. Lett. 21, 1481–1483 (1996).
    [CrossRef] [PubMed]
  19. J. F. Heanue, K. Gürkan, L. Hesselink, “Signal detection for page-access optical memories with intersymbol interference,” Appl. Opt. 35, 2431–2438 (1996).
    [CrossRef] [PubMed]
  20. J. F. Heanue, M. C. Bashaw, L. Hesselink, “Channel codes for digital holographic data storage,” J. Opt. Soc. Am. A 12, 2432–2439 (1995).
    [CrossRef]
  21. M. Aguilar, M. Carrascosa, F. Agulló-López, “Optimization of selective erasure in photorefractive memories,” J. Opt. Soc. Am. B 14, 110–115 (1997).
    [CrossRef]
  22. A. Yariv, “Interpage and interpixel cross talk in orthogonal (wavelength-multiplexed) holograms,” Opt. Lett. 18, 652–654 (1993).
    [CrossRef] [PubMed]
  23. K. Rastani, “Storage capacity and cross talk in angularly multiplexed holograms: two case studies,” Appl. Opt. 32, 3772–3778 (1993).
    [CrossRef] [PubMed]
  24. M. A. Neifeld, W.-C. Chou, “Information theoretic limits to the capacity of volume holographic optical memory,” Appl. Opt. 36, 514–517 (1997).
    [CrossRef] [PubMed]
  25. K. M. Chugg, “Performance of optimal digital page detection in a two-dimensional ISI/AWGN channel,” in Conference Record of the Thirtieth Asilomar Conference on Signals, Systems and Computers, A. Singh, ed. (IEEE Computer Society, Los Alamitos, Calif., 1997), Vol. 2, pp. 958–962.
    [CrossRef]
  26. Z. Wen, Y. Tao, X. Yang, “Crosstalk in phase-coded holographic memories using different orthogonal codes,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications III, Proc. SPIE3137, 123–133 (1997).
    [CrossRef]
  27. M. A. Neifeld, M. McDonald, “Technique for controlling cross-talk noise in volume holography,” Opt. Lett. 21, 1298–1300 (1996).
    [CrossRef] [PubMed]
  28. C. Gu, F. Dai, “Cross-talk noise reduction in volume holographic storage with an extended recording reference,” Opt. Lett. 20, 2336–2338 (1995).
    [CrossRef] [PubMed]
  29. F. Dai, C. Gu, “Effect of Gaussian references on cross-talk noise reduction in volume holographic memory,” Opt. Lett. 22, 1802–1804 (1997).
    [CrossRef]
  30. M. A. Neifeld, J. D. Hayes, “Error-correction schemes for volume optical memories,” Appl. Opt. 34, 8183–8191 (1995).
    [CrossRef] [PubMed]
  31. B. J. Goertzen, P. A. Mitkas, “Error-correcting code for volume holographic storage of a relational database,” Opt. Lett. 20, 1655–1657 (1995).
    [CrossRef] [PubMed]
  32. G. W. Burr, J. Ashley, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, B. Marcus, “Modulation coding for pixel-matched holographic data storage,” Opt. Lett. 22, 639–641 (1997).
    [CrossRef] [PubMed]
  33. E. S. Bjornson, M. C. Bashaw, L. Hesselink, “Digital quasi-phase-matched two-color nonvolatile holographic storage,” Appl. Opt. 36, 3090–3106 (1997).
    [CrossRef] [PubMed]
  34. D. Brady, D. Psaltis, “Control of volume holograms,” J. Opt. Soc. Am. A 9, 1167–1182 (1992).
    [CrossRef]
  35. U. Efron, ed., Spatial Light Modulator Technology–Materials, Devices, and Applications (Marcel Dekker, New York, 1995).
  36. zemax Optical Design Program: User’s Guide, 5th ed. (Focus Software, Inc., P.O. Box 18228, Tucson, Ariz., 85731, 1996).
  37. M. A. Neifeld, M. McDonald, “Optical design for page access to volume optical media,” Appl. Opt. 35, 2418–2430 (1996).
    [CrossRef] [PubMed]
  38. M.-P. Bernal, H. Coufal, J. A. Hoffnagle, R. M. Macfarlane, R. M. Shelby, G. T. Sincerbox, P. Wimmer, G. Wittmann, “Precision tester for studies of holographic data storage materials and recording physics,” Appl. Opt. 35, 2360–2374 (1996).
    [CrossRef] [PubMed]
  39. Y. Ichioka, T. Iwaki, K. Matsuoka, “Optical information processing and beyond,” Proc. IEEE 84, 694–719 (1996).
    [CrossRef]
  40. K. Bløtekjaer, “Limitations on holographic storage capacity of photochromic and photorefractive media,” Appl. Opt. 18, 57–67 (1979).
    [CrossRef] [PubMed]
  41. H.-Y. S. Li, D. Psaltis, “Alignment sensitivity of holographic three-dimensional disks,” J. Opt. Soc. Am. A 12, 1902–1912 (1995).
    [CrossRef]
  42. C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
    [CrossRef]
  43. S. V. Miridonov, A. V. Khomenko, D. Tentori, A. A. Kamshilin, “Information capacity of holograms in photorefractive crystals,” Opt. Lett. 19, 502–504 (1994).
    [CrossRef] [PubMed]
  44. T. M. Cover, J. A. Thomas, Elements of Information Theory, 1st ed. (Wiley, New York, 1991).
    [CrossRef]
  45. K. Kamra, A. Kumar, K. Singh, “Novel optical photorefractive storage–retrieval system using speckle coding technique in beam-fanning geometry,” J. Mod. Opt. 43, 365–371 (1996).
    [CrossRef]
  46. S. W. McLaughlin, A. R. Calderbank, R. Laroia, J. Gerpheide, A. Jain, “Partial response modulation codes for electron trapping optical memory (ETOM),” in Optical Data Storage ’95, G. R. Knight, H. Ooki, eds., Proc. SPIE2514, 82–90 (1995).
    [CrossRef]
  47. B. H. Olson, S. C. Esener, “Partial response precoding for parallel-readout optical memories,” Opt. Lett. 19, 661–663 (1994).
    [CrossRef] [PubMed]
  48. C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Potentialities and limitations of hologram multiplexing using the phase-encoding technique,” Appl. Opt. 31, 5700–5705 (1992).
    [CrossRef] [PubMed]
  49. S. Lin, D. J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).
  50. M. A. Neifeld, M. McDonald, “Error correction for increasing the usable capacity of photorefractive memories,” Opt. Lett. 19, 1483–1485 (1994).
    [CrossRef] [PubMed]
  51. S. B. Wicker, V. K. Bhargava, eds., Reed-Solomon Codes and Their Applications (Institute of Electrical and Electronics Engineers, New York, 1994).
  52. J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).
  53. J. D. Roberts, A. Ryley, D. M. Jones, D. Burke, “Analysis of error-correction constraints in an optical disk,” Appl. Opt. 35, 3915–3924 (1996).
    [CrossRef] [PubMed]
  54. M. A. Neifeld, S. K. Sridharan, “Parallel error correction using spectral Reed–Solomon codes,” J. Opt. Commun. 18, 144–150 (1997).
  55. T. K. Matsushima, T. Matsushima, S. Hirasawa, “Parallel encoder and decoder architecture for cyclic codes,” IEICE Trans. Fund. Electron. Commun. Comput. Sci. E79-A, 1313–1323 (1996).

1997 (8)

1996 (12)

A. A. Freschi, P. M. Garcia, I. Rasnik, J. Frejlich, “Avoiding hologram bending in photorefractive crystals,” Opt. Lett. 21, 152–154 (1996).
[CrossRef] [PubMed]

M. A. Neifeld, M. McDonald, “Technique for controlling cross-talk noise in volume holography,” Opt. Lett. 21, 1298–1300 (1996).
[CrossRef] [PubMed]

M. A. Neifeld, K. M. Chugg, B. M. King, “Parallel data detection in page-oriented optical memory,” Opt. Lett. 21, 1481–1483 (1996).
[CrossRef] [PubMed]

S. Campbell, S.-H. Lin, X. Yi, P. Yeh, “Absorption effects in photorefractive volume-holographic memory systems. I. Beam depletion,” J. Opt. Soc. Am. B 13, 2209–2217 (1996);“Absorption effects in photorefractive volume-holographic memory systems. II. Material heating,” J. Opt. Soc. Am. B 13, 2218–2228 (1996).
[CrossRef]

T. K. Matsushima, T. Matsushima, S. Hirasawa, “Parallel encoder and decoder architecture for cyclic codes,” IEICE Trans. Fund. Electron. Commun. Comput. Sci. E79-A, 1313–1323 (1996).

Y. Ichioka, T. Iwaki, K. Matsuoka, “Optical information processing and beyond,” Proc. IEEE 84, 694–719 (1996).
[CrossRef]

K. Kamra, A. Kumar, K. Singh, “Novel optical photorefractive storage–retrieval system using speckle coding technique in beam-fanning geometry,” J. Mod. Opt. 43, 365–371 (1996).
[CrossRef]

M.-P. Bernal, H. Coufal, J. A. Hoffnagle, R. M. Macfarlane, R. M. Shelby, G. T. Sincerbox, P. Wimmer, G. Wittmann, “Precision tester for studies of holographic data storage materials and recording physics,” Appl. Opt. 35, 2360–2374 (1996).
[CrossRef] [PubMed]

I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375–2379 (1996).
[CrossRef] [PubMed]

M. A. Neifeld, M. McDonald, “Optical design for page access to volume optical media,” Appl. Opt. 35, 2418–2430 (1996).
[CrossRef] [PubMed]

J. F. Heanue, K. Gürkan, L. Hesselink, “Signal detection for page-access optical memories with intersymbol interference,” Appl. Opt. 35, 2431–2438 (1996).
[CrossRef] [PubMed]

J. D. Roberts, A. Ryley, D. M. Jones, D. Burke, “Analysis of error-correction constraints in an optical disk,” Appl. Opt. 35, 3915–3924 (1996).
[CrossRef] [PubMed]

1995 (8)

1994 (5)

1993 (3)

1992 (5)

1979 (1)

1977 (1)

1968 (1)

1963 (1)

1949 (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[CrossRef]

Aguilar, M.

Agulló-López, F.

Ashley, J.

Bashaw, M. C.

Bernal, M.-P.

Bjornson, E. S.

Bløtekjaer, K.

Brady, D.

Burke, D.

Burr, G. W.

Calderbank, A. R.

S. W. McLaughlin, A. R. Calderbank, R. Laroia, J. Gerpheide, A. Jain, “Partial response modulation codes for electron trapping optical memory (ETOM),” in Optical Data Storage ’95, G. R. Knight, H. Ooki, eds., Proc. SPIE2514, 82–90 (1995).
[CrossRef]

Campbell, S.

Carrascosa, M.

Chang, T. Y.

I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375–2379 (1996).
[CrossRef] [PubMed]

J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Opt. Eng. 34, 2193–2203 (1995).
[CrossRef]

Chou, W.-C.

Christian, W.

I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375–2379 (1996).
[CrossRef] [PubMed]

J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Opt. Eng. 34, 2193–2203 (1995).
[CrossRef]

Chugg, K. M.

M. A. Neifeld, K. M. Chugg, B. M. King, “Parallel data detection in page-oriented optical memory,” Opt. Lett. 21, 1481–1483 (1996).
[CrossRef] [PubMed]

K. M. Chugg, “Performance of optimal digital page detection in a two-dimensional ISI/AWGN channel,” in Conference Record of the Thirtieth Asilomar Conference on Signals, Systems and Computers, A. Singh, ed. (IEEE Computer Society, Los Alamitos, Calif., 1997), Vol. 2, pp. 958–962.
[CrossRef]

Costello, D. J.

S. Lin, D. J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).

Coufal, H.

Cover, T. M.

T. M. Cover, J. A. Thomas, Elements of Information Theory, 1st ed. (Wiley, New York, 1991).
[CrossRef]

Dai, F.

Denz, C.

Esener, S. C.

Frejlich, J.

Freschi, A. A.

Gallo, J. T.

Garcia, P. M.

Gerpheide, J.

S. W. McLaughlin, A. R. Calderbank, R. Laroia, J. Gerpheide, A. Jain, “Partial response modulation codes for electron trapping optical memory (ETOM),” in Optical Data Storage ’95, G. R. Knight, H. Ooki, eds., Proc. SPIE2514, 82–90 (1995).
[CrossRef]

Goertzen, B. J.

Grygier, R. K.

Gu, C.

Günther, H.

Gürkan, K.

Hagler, M. O.

Hayes, J. D.

Heanue, J. F.

Hesselink, L.

Hirasawa, S.

T. K. Matsushima, T. Matsushima, S. Hirasawa, “Parallel encoder and decoder architecture for cyclic codes,” IEICE Trans. Fund. Electron. Commun. Comput. Sci. E79-A, 1313–1323 (1996).

Hoffnagle, J. A.

Hong, J.

Hong, J. H.

I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375–2379 (1996).
[CrossRef] [PubMed]

J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Opt. Eng. 34, 2193–2203 (1995).
[CrossRef]

Ichioka, Y.

Y. Ichioka, T. Iwaki, K. Matsuoka, “Optical information processing and beyond,” Proc. IEEE 84, 694–719 (1996).
[CrossRef]

Iwaki, T.

Y. Ichioka, T. Iwaki, K. Matsuoka, “Optical information processing and beyond,” Proc. IEEE 84, 694–719 (1996).
[CrossRef]

Jain, A.

S. W. McLaughlin, A. R. Calderbank, R. Laroia, J. Gerpheide, A. Jain, “Partial response modulation codes for electron trapping optical memory (ETOM),” in Optical Data Storage ’95, G. R. Knight, H. Ooki, eds., Proc. SPIE2514, 82–90 (1995).
[CrossRef]

Jefferson, C. M.

Johnson, K. M.

E. S. Maniloff, K. M. Johnson, “Effects of scattering on the dynamics of holographic recording and erasure in photorefractive lithium niobate,” J. Appl. Phys. 73, 541–547 (1993).
[CrossRef]

Jones, D. M.

Kamra, K.

K. Kamra, A. Kumar, K. Singh, “Novel optical photorefractive storage–retrieval system using speckle coding technique in beam-fanning geometry,” J. Mod. Opt. 43, 365–371 (1996).
[CrossRef]

Kamshilin, A. A.

Khomenko, A. V.

King, B. M.

Krile, T. F.

Kumar, A.

K. Kamra, A. Kumar, K. Singh, “Novel optical photorefractive storage–retrieval system using speckle coding technique in beam-fanning geometry,” J. Mod. Opt. 43, 365–371 (1996).
[CrossRef]

LaMacchia, J. T.

Laroia, R.

S. W. McLaughlin, A. R. Calderbank, R. Laroia, J. Gerpheide, A. Jain, “Partial response modulation codes for electron trapping optical memory (ETOM),” in Optical Data Storage ’95, G. R. Knight, H. Ooki, eds., Proc. SPIE2514, 82–90 (1995).
[CrossRef]

Leyva, V.

Li, H.-Y. S.

Lin, S.

S. Lin, D. J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).

Lin, S.-H.

Macfarlane, R. M.

Maniloff, E. S.

E. S. Maniloff, K. M. Johnson, “Effects of scattering on the dynamics of holographic recording and erasure in photorefractive lithium niobate,” J. Appl. Phys. 73, 541–547 (1993).
[CrossRef]

Marcus, B.

Marks, R. J.

Matsuoka, K.

Y. Ichioka, T. Iwaki, K. Matsuoka, “Optical information processing and beyond,” Proc. IEEE 84, 694–719 (1996).
[CrossRef]

Matsushima, T.

T. K. Matsushima, T. Matsushima, S. Hirasawa, “Parallel encoder and decoder architecture for cyclic codes,” IEICE Trans. Fund. Electron. Commun. Comput. Sci. E79-A, 1313–1323 (1996).

Matsushima, T. K.

T. K. Matsushima, T. Matsushima, S. Hirasawa, “Parallel encoder and decoder architecture for cyclic codes,” IEICE Trans. Fund. Electron. Commun. Comput. Sci. E79-A, 1313–1323 (1996).

McDonald, M.

McLaughlin, S. W.

S. W. McLaughlin, A. R. Calderbank, R. Laroia, J. Gerpheide, A. Jain, “Partial response modulation codes for electron trapping optical memory (ETOM),” in Optical Data Storage ’95, G. R. Knight, H. Ooki, eds., Proc. SPIE2514, 82–90 (1995).
[CrossRef]

McMichael, I.

Miridonov, S. V.

Mitkas, P. A.

Mok, F.

Mok, F. H.

G. W. Burr, F. H. Mok, D. Psaltis, “Angle and space multiplexed holographic storage using the 90° geometry,” Opt. Commun. 117, 49–55 (1995).
[CrossRef]

Neifeld, M. A.

Olson, B. H.

Paek, E. G.

J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Opt. Eng. 34, 2193–2203 (1995).
[CrossRef]

Pauliat, G.

Pletcher, D.

Proakis, J. G.

J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).

Psaltis, D.

Rakuljic, G. A.

Rasnik, I.

Rastani, K.

Roberts, J. D.

Roosen, G.

Ryley, A.

Saxena, R.

Shannon, C. E.

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[CrossRef]

Shelby, R. M.

Sincerbox, G. T.

Singh, K.

K. Kamra, A. Kumar, K. Singh, “Novel optical photorefractive storage–retrieval system using speckle coding technique in beam-fanning geometry,” J. Mod. Opt. 43, 365–371 (1996).
[CrossRef]

Sridharan, S. K.

M. A. Neifeld, S. K. Sridharan, “Parallel error correction using spectral Reed–Solomon codes,” J. Opt. Commun. 18, 144–150 (1997).

Tao, Y.

Z. Wen, Y. Tao, X. Yang, “Crosstalk in phase-coded holographic memories using different orthogonal codes,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications III, Proc. SPIE3137, 123–133 (1997).
[CrossRef]

Tentori, D.

Thomas, J. A.

T. M. Cover, J. A. Thomas, Elements of Information Theory, 1st ed. (Wiley, New York, 1991).
[CrossRef]

Tschudi, T.

Vachss, F.

van Heerden, P. J.

Verber, C. M.

Walkup, J. F.

Wen, Z.

Z. Wen, Y. Tao, X. Yang, “Crosstalk in phase-coded holographic memories using different orthogonal codes,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications III, Proc. SPIE3137, 123–133 (1997).
[CrossRef]

White, D. L.

Wimmer, P.

Wittmann, G.

Yang, X.

Z. Wen, Y. Tao, X. Yang, “Crosstalk in phase-coded holographic memories using different orthogonal codes,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications III, Proc. SPIE3137, 123–133 (1997).
[CrossRef]

Yariv, A.

Yeh, P.

Yi, X.

Yu, F. T. S.

Zhao, F.

Zhou, H.

Appl. Opt. (16)

P. J. van Heerden, “A new optical method of storing and retrieving information,” Appl. Opt. 2, 387–392 (1963).
[CrossRef]

J. T. LaMacchia, D. L. White, “Coded multiple exposure holograms,” Appl. Opt. 7, 91–94 (1968).
[CrossRef] [PubMed]

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

K. Bløtekjaer, “Limitations on holographic storage capacity of photochromic and photorefractive media,” Appl. Opt. 18, 57–67 (1979).
[CrossRef] [PubMed]

K. Rastani, “Storage capacity and cross talk in angularly multiplexed holograms: two case studies,” Appl. Opt. 32, 3772–3778 (1993).
[CrossRef] [PubMed]

H. Zhou, F. Zhao, F. T. S. Yu, “Effects of recording–erasure dynamics of storage capacity of a wavelength-multiplexed reflection-type photorefractive hologram,” Appl. Opt. 33, 4339–4344 (1994).
[CrossRef] [PubMed]

J. T. Gallo, C. M. Verber, “Model for the effects of material shrinkage on volume holograms,” Appl. Opt. 33, 6797–6804 (1994).
[CrossRef] [PubMed]

M. A. Neifeld, W.-C. Chou, “Information theoretic limits to the capacity of volume holographic optical memory,” Appl. Opt. 36, 514–517 (1997).
[CrossRef] [PubMed]

E. S. Bjornson, M. C. Bashaw, L. Hesselink, “Digital quasi-phase-matched two-color nonvolatile holographic storage,” Appl. Opt. 36, 3090–3106 (1997).
[CrossRef] [PubMed]

M. A. Neifeld, J. D. Hayes, “Error-correction schemes for volume optical memories,” Appl. Opt. 34, 8183–8191 (1995).
[CrossRef] [PubMed]

M.-P. Bernal, H. Coufal, J. A. Hoffnagle, R. M. Macfarlane, R. M. Shelby, G. T. Sincerbox, P. Wimmer, G. Wittmann, “Precision tester for studies of holographic data storage materials and recording physics,” Appl. Opt. 35, 2360–2374 (1996).
[CrossRef] [PubMed]

I. McMichael, W. Christian, D. Pletcher, T. Y. Chang, J. H. Hong, “Compact holographic storage demonstrator with rapid access,” Appl. Opt. 35, 2375–2379 (1996).
[CrossRef] [PubMed]

M. A. Neifeld, M. McDonald, “Optical design for page access to volume optical media,” Appl. Opt. 35, 2418–2430 (1996).
[CrossRef] [PubMed]

J. F. Heanue, K. Gürkan, L. Hesselink, “Signal detection for page-access optical memories with intersymbol interference,” Appl. Opt. 35, 2431–2438 (1996).
[CrossRef] [PubMed]

J. D. Roberts, A. Ryley, D. M. Jones, D. Burke, “Analysis of error-correction constraints in an optical disk,” Appl. Opt. 35, 3915–3924 (1996).
[CrossRef] [PubMed]

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

IEICE Trans. Fund. Electron. Commun. Comput. Sci. (1)

T. K. Matsushima, T. Matsushima, S. Hirasawa, “Parallel encoder and decoder architecture for cyclic codes,” IEICE Trans. Fund. Electron. Commun. Comput. Sci. E79-A, 1313–1323 (1996).

J. Appl. Phys. (1)

E. S. Maniloff, K. M. Johnson, “Effects of scattering on the dynamics of holographic recording and erasure in photorefractive lithium niobate,” J. Appl. Phys. 73, 541–547 (1993).
[CrossRef]

J. Mod. Opt. (1)

K. Kamra, A. Kumar, K. Singh, “Novel optical photorefractive storage–retrieval system using speckle coding technique in beam-fanning geometry,” J. Mod. Opt. 43, 365–371 (1996).
[CrossRef]

J. Opt. Commun. (1)

M. A. Neifeld, S. K. Sridharan, “Parallel error correction using spectral Reed–Solomon codes,” J. Opt. Commun. 18, 144–150 (1997).

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (3)

Opt. Commun. (2)

C. Gu, J. Hong, “Noise gratings formed during the multiple exposure schedule in photorefractive media,” Opt. Commun. 93, 213–218 (1992).
[CrossRef]

G. W. Burr, F. H. Mok, D. Psaltis, “Angle and space multiplexed holographic storage using the 90° geometry,” Opt. Commun. 117, 49–55 (1995).
[CrossRef]

Opt. Eng. (1)

J. H. Hong, I. McMichael, T. Y. Chang, W. Christian, E. G. Paek, “Volume holographic memory systems: techniques and architectures,” Opt. Eng. 34, 2193–2203 (1995).
[CrossRef]

Opt. Lett. (14)

G. A. Rakuljic, V. Leyva, A. Yariv, “Optical data storage by using orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
[CrossRef] [PubMed]

A. Yariv, “Interpage and interpixel cross talk in orthogonal (wavelength-multiplexed) holograms,” Opt. Lett. 18, 652–654 (1993).
[CrossRef] [PubMed]

S. V. Miridonov, A. V. Khomenko, D. Tentori, A. A. Kamshilin, “Information capacity of holograms in photorefractive crystals,” Opt. Lett. 19, 502–504 (1994).
[CrossRef] [PubMed]

B. H. Olson, S. C. Esener, “Partial response precoding for parallel-readout optical memories,” Opt. Lett. 19, 661–663 (1994).
[CrossRef] [PubMed]

M. A. Neifeld, M. McDonald, “Error correction for increasing the usable capacity of photorefractive memories,” Opt. Lett. 19, 1483–1485 (1994).
[CrossRef] [PubMed]

B. J. Goertzen, P. A. Mitkas, “Error-correcting code for volume holographic storage of a relational database,” Opt. Lett. 20, 1655–1657 (1995).
[CrossRef] [PubMed]

X. Yi, P. Yeh, C. Gu, “Cross-talk noise in volume holographic memory with spherical reference beams,” Opt. Lett. 20, 1812–1814 (1995).
[CrossRef] [PubMed]

C. Gu, F. Dai, “Cross-talk noise reduction in volume holographic storage with an extended recording reference,” Opt. Lett. 20, 2336–2338 (1995).
[CrossRef] [PubMed]

A. A. Freschi, P. M. Garcia, I. Rasnik, J. Frejlich, “Avoiding hologram bending in photorefractive crystals,” Opt. Lett. 21, 152–154 (1996).
[CrossRef] [PubMed]

M. A. Neifeld, M. McDonald, “Technique for controlling cross-talk noise in volume holography,” Opt. Lett. 21, 1298–1300 (1996).
[CrossRef] [PubMed]

M. A. Neifeld, K. M. Chugg, B. M. King, “Parallel data detection in page-oriented optical memory,” Opt. Lett. 21, 1481–1483 (1996).
[CrossRef] [PubMed]

G. W. Burr, J. Ashley, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, B. Marcus, “Modulation coding for pixel-matched holographic data storage,” Opt. Lett. 22, 639–641 (1997).
[CrossRef] [PubMed]

R. M. Shelby, J. A. Hoffnagle, G. W. Burr, C. M. Jefferson, M.-P. Bernal, H. Coufal, R. K. Grygier, H. Günther, R. M. Macfarlane, G. T. Sincerbox, “Pixel-matched holographic data storage with megabit pages,” Opt. Lett. 22, 1509–1511 (1997).
[CrossRef]

F. Dai, C. Gu, “Effect of Gaussian references on cross-talk noise reduction in volume holographic memory,” Opt. Lett. 22, 1802–1804 (1997).
[CrossRef]

Proc. IEEE (1)

Y. Ichioka, T. Iwaki, K. Matsuoka, “Optical information processing and beyond,” Proc. IEEE 84, 694–719 (1996).
[CrossRef]

Proc. IRE (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[CrossRef]

Other (9)

S. Lin, D. J. Costello, Error Control Coding: Fundamentals and Applications (Prentice-Hall, Englewood Cliffs, N.J., 1983).

S. B. Wicker, V. K. Bhargava, eds., Reed-Solomon Codes and Their Applications (Institute of Electrical and Electronics Engineers, New York, 1994).

J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).

T. M. Cover, J. A. Thomas, Elements of Information Theory, 1st ed. (Wiley, New York, 1991).
[CrossRef]

K. M. Chugg, “Performance of optimal digital page detection in a two-dimensional ISI/AWGN channel,” in Conference Record of the Thirtieth Asilomar Conference on Signals, Systems and Computers, A. Singh, ed. (IEEE Computer Society, Los Alamitos, Calif., 1997), Vol. 2, pp. 958–962.
[CrossRef]

Z. Wen, Y. Tao, X. Yang, “Crosstalk in phase-coded holographic memories using different orthogonal codes,” in Photorefractive Fiber and Crystal Devices: Materials, Optical Properties, and Applications III, Proc. SPIE3137, 123–133 (1997).
[CrossRef]

U. Efron, ed., Spatial Light Modulator Technology–Materials, Devices, and Applications (Marcel Dekker, New York, 1995).

zemax Optical Design Program: User’s Guide, 5th ed. (Focus Software, Inc., P.O. Box 18228, Tucson, Ariz., 85731, 1996).

S. W. McLaughlin, A. R. Calderbank, R. Laroia, J. Gerpheide, A. Jain, “Partial response modulation codes for electron trapping optical memory (ETOM),” in Optical Data Storage ’95, G. R. Knight, H. Ooki, eds., Proc. SPIE2514, 82–90 (1995).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

VHM system configuration comprising a SLM, a CCD, the storage medium, and a pair of Fourier transformation lenses.

Fig. 2
Fig. 2

(a) Images of SLM corner pixels on the CCD plane given a 0.10% magnification error. The images partition the CCD pixel area into four regions (measured in percent). (b) pdf of the corner pixel with 0.10% magnification error. (c) pdf of a corner pixel storing 3000 pages with 0.10% magnification error and circuit thermal noise.

Fig. 3
Fig. 3

(a) pdf of a center pixel with 0.10% magnification error, 10% shift error, and 4800 stored pages. (b) pdf of a corner pixel with 0.10% magnification error, 10% shift error, and 4800 stored pages. (c) Raw BER contour plot on a 512 × 512 pixel page given 0.10% magnification error, 10% shift error, and 4800 stored pages.

Fig. 4
Fig. 4

Page-average raw BER versus the CCD position for the minimum-worst-spot design (solid curves) and the approximate BER design (dashed curve). The solid curves are parameterized by the CCD fill factor.

Fig. 5
Fig. 5

Information theoretic capacity versus the number of stored pages given no systematic error (circles), 0.1% magnification error (mag err) (squares), and 0.1% magnification error plus 10% shift error (triangles).

Fig. 6
Fig. 6

Storage capacity versus the number of holographic pages determined by use of RS ECC. The output BER equals 10-12, γ = 2.304 × 108, and all pixels are assumed to be iid.

Fig. 7
Fig. 7

Interleaving schematic: (a) Depiction of a 14-bit burst error in the first 21 bits. (b) Depiction of an n = 7 symbol/code word ECC with m = 3 bits/symbol by use of serially transmitting code words, resulting in a six-symbol burst. (c) Three-code-word interleaving by use of an n = 7 symbol ECC with 3 bits/symbol. After deinterleaving the six symbol errors are distributed as 2 symbol errors/code word.

Fig. 8
Fig. 8

(a) Output BER performance of serial (dashed curves) and matched (solid curves) interleavers for different magnification errors. A RS n = 31 code is used to store 4800 pages. (b) Ratio of the serial BER(out) to the matched BER(out) versus the magnification error for four different RS n = 31 codes. (c) Ratio of the standard deviation σ of BER(out) to the mean μ of BER(out) versus the magnification error for serial (dashed curves) and matched (solid curves) interleavers.

Fig. 9
Fig. 9

(a) Storage capacity of matched, serial, center, and magnification–shift (mag-shift) interleavers obtained with a variety of RS ECC. This plot is based on a 0.1% magnification error and a required output BER of 10-12. (b) Optimum storage capacity of serial, matched, and tilt interleavers by use of n = 127 RS codes and their associated capacity gains with respect to the use of a serial interleaver for different magnification errors and a required output BER of 10-12.

Fig. 10
Fig. 10

Optimum storage capacity of serial, matched, and mag-shift interleavers by use of n = 31 RS ECC and their associated capacity gains with respect to the use of a serial interleaver for combinations of different magnification and shift errors to achieve an output BER of 10-12.

Fig. 11
Fig. 11

(a) Image captured by the CCD camera for a well-aligned system. The enlarged area shows local pixels with renormalized contrast levels. (b) Image captured by the CCD camera given a 19.4% shift error. The enlarged area shows local pixels with renormalized contrast levels. (c) Experimental output signal histograms. The filled circles indicate a well-aligned system, and the open circles represent the system with 19.4% shift error.

Fig. 12
Fig. 12

(a) Pixel error pattern measured for a well-aligned system. The dots mark the pixels that are in error. (b) Pixel error pattern measured for a system with a 0.045° in-plane CCD rotation error. The dots mark the pixels that are in error.

Fig. 13
Fig. 13

Experimental output BER performance measured by use of serial (ser) and center (cen) interleaving schemes with five different RS n = 31 codes.

Tables (5)

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Table 1 Optimum Storage Capacities Achievable for Five Different Interleavers and Four RS Code-Word Lengths n Given Various Degrees of Magnification Error and BER(out) = 10-12

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Table 2 Optimum Storage Capacities Achievable for Five Different Interleavers and Two RS Code-Word Lengths n Given Various Degrees of Tilt Error with BER(out) = 10-12

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Table 3 Optimum Storage Capacities Achievable for Five Different Interleavers and Two RS Code-Word Lengths n Given Various Degrees of Defocus Error with BER(out) = 10-12

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Table 4 Optimum Storage Capacities Achievable for Five Different Interleavers and n = 63 RS ECC Given Various Combinations of Shift and Magnification Error with BER(out) = 10-12

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Table 5 Optimum Storage Capacities Achievable for Three Different Interleavers and Two RS Code-Word Lengths n Given Various Combinations of Shift and Magnification Error with BER(out) = 10-12 for a 1024 × 1024 Pixel/Page System

Equations (5)

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I X ;   Y =   f x ,   y log 2 f x ,   y f x f y d x d y ,
I X ;   Y = i = 0,1   π i     f y | x = i log 2 f y | x = i f y d y ,
R max = max π 0 , π 1 I X ;   Y .
C = MN 2 R max M ,
I X ;   Y I ˜ X ;   Y = i = 1 N 2   I X i ;   Y i , I X i ;   Y i = x i X i     p x i f y i log f y i | x i f y i d y i ,

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