Abstract

We investigate the effects of interpixel cross talk and detector noise on the areal storage density of holographic data storage. A numerical simulation is used to obtain the bit-error rate (BER) as a function of hologram aperture, pixel fill factors, and additive Gaussian intensity noise. We consider the effect of interpixel cross talk at an output pixel from all possible configurations of its 12 closest-neighbor pixels. Experimental verification of this simulation procedure is shown for several fill-factor combinations. The simulation results show that areal density is maximized when the aperture coincides with the zero order of the spatial light modulator (SLM) (Nyquist sampling condition) and the CCD fill factor is large. Additional numerical analysis including finite SLM contrast and fixed-pattern noise show that, if the fixed-pattern noise reaches 6% of the mean signal level, the SLM contrast has to be larger than 6:1 to maintain high areal density. We also investigate the improvement of areal density when error-prone pixel combinations are forbidden by using coding schemes. A trade-off between an increase in areal density and the redundancy of a coding scheme that avoids isolated-on pixels occurs at a code rate of approximately 83%.

© 1998 Optical Society of America

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References

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  1. L. Hesselink, M. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, 611–651 (1993).
    [CrossRef]
  2. F. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
    [CrossRef] [PubMed]
  3. J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
    [CrossRef] [PubMed]
  4. G. Sincerbox, “Holographic storage revisited,” in Current Trends in Optics, J. C. Dainty, ed. (Academic, New York, 1994), pp. 195–207.
  5. G. W. Burr, F. H. Mok, D. Psaltis, “Angle and space multiplexed holographic storage using 90 degree geometry,” Opt. Commun. 117, 49–55 (1995).
    [CrossRef]
  6. M.-P. Bernal, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, R. M. Macfarlane, R. M. Shelby, G. T. Sincerbox, P. Wimmer, G. Wittmann, “A precision tester for studies of holographic optical storage materials and recording physics,” Appl. Opt. 35, 2360–2373 (1996).
    [CrossRef] [PubMed]
  7. G. W. Burr, F. H. Mok, D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CMB7, p. 9.
  8. 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]
  9. G. Barbastathis, “Intelligent holographic databases,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1998).
  10. J. Hong, I. McMichael, J. Ma, “Influence of phase masks on cross talk in holographic memory,” Opt. Lett. 21, 1694–1696 (1996).
    [CrossRef] [PubMed]
  11. M.-P. Bernal, G. W. Burr, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, E. Oesterschulze, R. M. Shelby, G. T. Sincerbox, M. Quintanilla, “Effects of multilevel phase masks on interpixel cross talk in digital holographic data storage,” Appl. Opt. 36, 3107–3115 (1997).
    [CrossRef] [PubMed]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  13. G. W. Burr, “Volume holographic storage using the 90° geometry,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1996).
  14. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, New York, 1992).
  15. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1989).
  16. G. W. Burr, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, “Noise reduction of page-oriented data storage by inverse filtering during recording,” Opt. Lett. 23, 289–291 (1998).
    [CrossRef]
  17. 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]
  18. J. Ashley, B. Marcus, “Two-dimensional low-pass filtering codes,” IEEE Trans. Commun. 46, 724–727 (1998).
    [CrossRef]

1998 (2)

1997 (2)

1996 (2)

1995 (2)

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

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]

1994 (1)

J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

1993 (2)

L. Hesselink, M. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, 611–651 (1993).
[CrossRef]

F. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
[CrossRef] [PubMed]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, New York, 1992).

Ashley, J.

Barbastathis, G.

G. Barbastathis, “Intelligent holographic databases,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1998).

Bashaw, M.

J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

L. Hesselink, M. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, 611–651 (1993).
[CrossRef]

Bashaw, M. C.

Bernal, M.-P.

Burr, G. W.

G. W. Burr, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, “Noise reduction of page-oriented data storage by inverse filtering during recording,” Opt. Lett. 23, 289–291 (1998).
[CrossRef]

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]

M.-P. Bernal, G. W. Burr, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, E. Oesterschulze, R. M. Shelby, G. T. Sincerbox, M. Quintanilla, “Effects of multilevel phase masks on interpixel cross talk in digital holographic data storage,” Appl. Opt. 36, 3107–3115 (1997).
[CrossRef] [PubMed]

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

G. W. Burr, “Volume holographic storage using the 90° geometry,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1996).

G. W. Burr, F. H. Mok, D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CMB7, p. 9.

Coufal, H.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1989).

Goodman, J. W.

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

Grygier, R. K.

Heanue, J.

J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Heanue, J. F.

Hesselink, L.

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]

J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

L. Hesselink, M. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, 611–651 (1993).
[CrossRef]

Hoffnagle, J. A.

Hong, J.

Jefferson, C. M.

Ma, J.

Macfarlane, R. M.

Marcus, B.

McMichael, I.

Mok, F.

Mok, F. H.

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

G. W. Burr, F. H. Mok, D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CMB7, p. 9.

Oesterschulze, E.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1989).

Psaltis, D.

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

G. W. Burr, F. H. Mok, D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CMB7, p. 9.

Quintanilla, M.

Shelby, R. M.

Sincerbox, G.

G. Sincerbox, “Holographic storage revisited,” in Current Trends in Optics, J. C. Dainty, ed. (Academic, New York, 1994), pp. 195–207.

Sincerbox, G. T.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1989).

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1989).

Wimmer, P.

Wittmann, G.

Appl. Opt. (2)

IEEE Trans. Commun. (1)

J. Ashley, B. Marcus, “Two-dimensional low-pass filtering codes,” IEEE Trans. Commun. 46, 724–727 (1998).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

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

Opt. Lett. (4)

Opt. Quantum Electron. (1)

L. Hesselink, M. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, 611–651 (1993).
[CrossRef]

Science (1)

J. Heanue, M. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Other (7)

G. Sincerbox, “Holographic storage revisited,” in Current Trends in Optics, J. C. Dainty, ed. (Academic, New York, 1994), pp. 195–207.

G. W. Burr, F. H. Mok, D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics, Vol. 7 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CMB7, p. 9.

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

G. W. Burr, “Volume holographic storage using the 90° geometry,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1996).

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley, New York, 1992).

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, New York, 1989).

G. Barbastathis, “Intelligent holographic databases,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1998).

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Figures (8)

Fig. 1
Fig. 1

Schematic of a 4f configuration used for holographic data storage.

Fig. 2
Fig. 2

Thirteen-pixel pattern used to study interpixel cross talk. The coherent contribution of these 12 nearest neighbors is evaluated over the central pixel.

Fig. 3
Fig. 3

Example of a discrete histogram for SLM and CCD fill factors of 100% and the Nyquist aperture.

Fig. 4
Fig. 4

Experimental validation of the proposed algorithm. Experiments on the BER versus the aperture were performed in the PRISM tester for two situations: (a) SLM and CCD fill factors of 100%. (b) SLM linear fill factor of 50% and CCD fill factor of 100%.

Fig. 5
Fig. 5

BER as a function of the CCD and the SLM linear fill factors for (a) the Nyquist aperture and (b) twice the Nyquist aperture. The detector-noise level is 5% of the incoming signal level (before losses derived from diffraction and CCD dead space).

Fig. 6
Fig. 6

Areal density as a function of the aperture for (a) the best combination of fill factors (obtained with BER maps such as those shown in Fig. 5), (b) a SLM linear fill factor of 90% and a CCD linear fill factor of 87%, and (c) a SLM linear fill factor of 60% and a CCD linear fill factor of 40% (corresponding to the DEMON system8).

Fig. 7
Fig. 7

Areal density as a function of the fixed-pattern noise for different SLM contrast levels at the Nyquist aperture and with large fill factors (SLM, 90%; CCD, 87%).

Fig. 8
Fig. 8

Areal density as a function of the BER with the Nyquist aperture and large fill factors (SLM, 90%; CCD, 87%) when (a) all possible 13-pixel pattern combinations are considered, (b) all the combinations with an isolated-on pixel (the four closest neighbors to the center are off) are forbidden, and (c) both isolated-on and isolated-off pixels (central pixels off; four nearest neighbors on) are forbidden.

Equations (16)

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U 0 x ,   y ,   z = 0 = rect x g SLM Γ rect y g SLM Γ .
Uc x ,   y ,   z = 2 f = g SLM 2 Γ 2 i λ f sinc g SLM Γ x λ f sinc g SLM Γ y λ f ,
P x ,   y = rect x D rect y D .
U d x ,   y ,   z = 4 f = - g SLM 2 Γ 2 I x I y ,
I v = - α + α sinc Γ g SLM s exp - i 2 π vs d s , α D 2 λ f .
U T x ,   y = c 02 U d x ,   y + 2 Γ + c - 20 U d x - 2 Γ ,   y + i = - 1 1 j = - 1 1   c ij U d x - i Γ ,   y - j Γ + c 20 U d x + 2 Γ ,   y + c 0 - 2 U d x ,   y - 2 Γ .
I T = x m = - g CCD Γ / 2 + g CCD Γ / 2 y m = - g CCD Γ / 2 + g CCD Γ / 2   | U T x m ,   y m ,   z = 4 f | 2 .
BER = 1 4 1 d 0 i = 1 N 0   w i , 0   erfc Θ - μ i , 0 2 σ d + 1 d 1 i = 1 N 1   w i , 1   erfc μ i , 1 - Θ 2 σ d ,
n d = σ d n s ,
n s = P ref h ν   η hologram η opt η e t int 1 N ON ,
η hologram = M / # M 2 .
M M / #   σ d n d P ref h ν   t int 2 N p   η e η opt 1 / 2 .
D = number of pixels hologram number of holograms aperture area .
D = M / # N p P ref h ν σ d n d   η opt η e t int 2 1 / 2 D 2 .
σ ON = σ d + σ p ,
σ OFF = σ d + σ p / c ,

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