Abstract

An experimental procedure for determining the relation between the number of stored holograms and the raw bit-error rate (BER) (the BER before error correction) of a holographic storage system is described. Compared with conventional recording schedules that equalize the diffraction efficiency, scheduling of recording exposures to achieve a uniform raw BER is shown to improve capacity. The experimentally obtained capacity versus the raw-BER scaling is used to study the effects of modulation and error-correction coding in holographic storage. The use of coding is shown to increase the number of holograms that can be stored; however, the redundancy associated with coding incurs a capacity cost per hologram. This trade-off is quantified, and an optimal working point for the overall system is identified. This procedure makes it possible to compare, under realistic conditions, system choices whose impact cannot be fully analyzed or simulated. Using LiNbO3 in the 90° geometry, we implement this capacity-estimation procedure and compare several block-based modulation codes and thresholding techniques on the basis of total user capacity.

© 1998 Optical Society of America

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References

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  1. D. Psaltis, F. Mok, “Holographic memories,” Sci. Am. 273 (5), 70–76 (1995).
    [CrossRef]
  2. J. F. Heanue, M. C. Bashaw, L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
    [CrossRef] [PubMed]
  3. M. A. Neifeld, M. McDonald, “Error correction for increasing the usable capacity of photorefractive memories,” Opt. Lett. 19, 1483–1485 (1994).
    [CrossRef] [PubMed]
  4. 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]
  5. 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]
  6. 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, 1–6 (1993).
  7. C. Gu, F. Dai, J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” Electron. Lett. 32, 1400–1402 (1996).
    [CrossRef]
  8. D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
    [CrossRef]
  9. F. H. Mok, G. W. Burr, D. Psaltis, “System metric for holographic memory systems,” Opt. Lett. 21, 896–898 (1996).
    [CrossRef] [PubMed]
  10. 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).
    [CrossRef]
  11. G. W. Burr, “Volume holographic storage using the 90° geometry,” Ph.D. thesis (California Institute of Technology, Pasadena, California, 1996).
  12. M.-P. Bernal, G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, R. M. Shelby, M. Quintanilla, “Experimental study of the effects of a six-level phase mask on a digital holographic storage system,” Appl. Opt. 37, 2094–2101 (1998).
    [CrossRef]
  13. I. S. Reed, G. Solomon, “Polynomial codes over certain finite fields,” J. Soc. Indust. Appl. Math. 8, 300–304 (1960).
    [CrossRef]
  14. M. M. Wang, S. C. Esener, F. B. McCormick, I. Cokgor, A. S. Dvornikov, P. M. Rentzepis, “Experimental characterization of a two-photon memory,” Opt. Lett. 22, 558–560 (1997).
    [CrossRef] [PubMed]
  15. X. A. Shen, A.-D. Nguyen, J. W. Perry, D. L. Huestis, R. Kachru, “Time-domain holographic digital memory,” Science 278, 96–100 (1997).
    [CrossRef]
  16. A. Pu, D. Psaltis, “High-density recording in photopolymer-based holographic three-dimensional disks,” Appl. Opt. 35, 2389–2398 (1996).
    [CrossRef] [PubMed]
  17. G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, “Noise reduction for page-oriented data storage by inverse filtering during recording,” Opt. Lett. 23, 289–291 (1998).
    [CrossRef]

1998

1997

1996

1995

1994

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

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

1993

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, 1–6 (1993).

1988

1960

I. S. Reed, G. Solomon, “Polynomial codes over certain finite fields,” J. Soc. Indust. Appl. Math. 8, 300–304 (1960).
[CrossRef]

Ashley, J.

Bashaw, M. C.

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

Bernal, M.-P.

Brady, D.

Burr, G. W.

Campbell, S.

Cokgor, I.

Coufal, H.

Dai, F.

C. Gu, F. Dai, J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” Electron. Lett. 32, 1400–1402 (1996).
[CrossRef]

Dvornikov, A. S.

Esener, S. C.

Grygier, R. K.

Gu, C.

C. Gu, F. Dai, J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” Electron. Lett. 32, 1400–1402 (1996).
[CrossRef]

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, 1–6 (1993).

Heanue, J. F.

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

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

Hoffnagle, J. A.

Hong, J.

C. Gu, F. Dai, J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” Electron. Lett. 32, 1400–1402 (1996).
[CrossRef]

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, 1–6 (1993).

Huestis, D. L.

X. A. Shen, A.-D. Nguyen, J. W. Perry, D. L. Huestis, R. Kachru, “Time-domain holographic digital memory,” Science 278, 96–100 (1997).
[CrossRef]

Jefferson, C. M.

Kachru, R.

X. A. Shen, A.-D. Nguyen, J. W. Perry, D. L. Huestis, R. Kachru, “Time-domain holographic digital memory,” Science 278, 96–100 (1997).
[CrossRef]

Lin, S.-H.

Marcus, B.

McCormick, F. B.

McDonald, M.

McMichael, I.

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, 1–6 (1993).

Mok, F.

D. Psaltis, F. Mok, “Holographic memories,” Sci. Am. 273 (5), 70–76 (1995).
[CrossRef]

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, 1–6 (1993).

Mok, F. H.

Neifeld, M. A.

Nguyen, A.-D.

X. A. Shen, A.-D. Nguyen, J. W. Perry, D. L. Huestis, R. Kachru, “Time-domain holographic digital memory,” Science 278, 96–100 (1997).
[CrossRef]

Perry, J. W.

X. A. Shen, A.-D. Nguyen, J. W. Perry, D. L. Huestis, R. Kachru, “Time-domain holographic digital memory,” Science 278, 96–100 (1997).
[CrossRef]

Psaltis, D.

Pu, A.

Quintanilla, M.

Reed, I. S.

I. S. Reed, G. Solomon, “Polynomial codes over certain finite fields,” J. Soc. Indust. Appl. Math. 8, 300–304 (1960).
[CrossRef]

Rentzepis, P. M.

Saxena, R.

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, 1–6 (1993).

Shelby, R. M.

Shen, X. A.

X. A. Shen, A.-D. Nguyen, J. W. Perry, D. L. Huestis, R. Kachru, “Time-domain holographic digital memory,” Science 278, 96–100 (1997).
[CrossRef]

Solomon, G.

I. S. Reed, G. Solomon, “Polynomial codes over certain finite fields,” J. Soc. Indust. Appl. Math. 8, 300–304 (1960).
[CrossRef]

Wagner, K.

Wang, M. M.

Yeh, P.

Yi, X.

Appl. Opt.

Electron. Lett.

C. Gu, F. Dai, J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” Electron. Lett. 32, 1400–1402 (1996).
[CrossRef]

J. Opt. Soc. Am. A

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, 1–6 (1993).

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. Opt. Soc. Am. B

J. Soc. Indust. Appl. Math.

I. S. Reed, G. Solomon, “Polynomial codes over certain finite fields,” J. Soc. Indust. Appl. Math. 8, 300–304 (1960).
[CrossRef]

Opt. Lett.

Sci. Am.

D. Psaltis, F. Mok, “Holographic memories,” Sci. Am. 273 (5), 70–76 (1995).
[CrossRef]

Science

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

X. A. Shen, A.-D. Nguyen, J. W. Perry, D. L. Huestis, R. Kachru, “Time-domain holographic digital memory,” Science 278, 96–100 (1997).
[CrossRef]

Other

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

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Figures (12)

Fig. 1
Fig. 1

Evolution of the diffraction efficiency (top) and the raw BER (bottom) for the first hologram in a recording schedule. The raw BER is the BER presented to the ECC, which must then correct down to the user-BER specification. The arrow on the raw-BER axis points in the direction of a lower (better) raw BER.

Fig. 2
Fig. 2

Measurement of the raw BER as a function of the readout exposure time and a quadratic fit. The camera-integration time is 16.66 ms.

Fig. 3
Fig. 3

Number of holograms that can be stored (M) as a function of the total recording exposure time t meas (expressed in units of the erasure-time constant τ e ). The different curves correspond to raw-BER values ranging from 3 × 10-7 to 3 × 10-3. All the curves represent the 6:8 modulation code.

Fig. 4
Fig. 4

Expected diffraction efficiency and the raw BER as a function of hologram number for a flat-BER and a flat-η schedule. Because the last hologram does not need as much diffraction efficiency as the first, the dynamic range can be taken away from the last hologram and used to store additional holograms. The arrow on the raw-BER axis points in the direction of a lower (better) BER. (This graph is an illustration, not measured data.)

Fig. 5
Fig. 5

Measured data for the number of holograms that can be stored (M) as a function of the raw BER with a flat-BER and a flat-η schedule. The flat-BER schedule takes the dynamic range from holograms that are under (better than) the raw-BER specification to maximize the number of stored holograms.

Fig. 6
Fig. 6

Measured raw BER at a constant diffracted energy as a function of the readout power. Because scatter noise is not significant, the raw BER is independent of the readout power.

Fig. 7
Fig. 7

Code rate of the RS ECC as a function of the lowest (worst) correctable raw BER for different numbers of bits per ECC symbol. The codes correct to a 10-12 user BER and are of maximal length for the symbol size.

Fig. 8
Fig. 8

Raw BER versus the signal strength in the presence of a constant noise floor. Two modulation codes (6:8 and 8:12) are compared with global, local, and adaptive thresholding.

Fig. 9
Fig. 9

Number of holograms that can be stored (M) as a function of the raw BER. Long recording schedules are assumed (saturation region of Fig. 4). Several modulation codes and thresholding schemes are compared, combining results from two separate experiments.

Fig. 10
Fig. 10

Number of user and ECC bits that can be stored (r code × M) as a function of the raw BER. Here a low code rate is traded off against high performance (permitting more stored holograms). The error bars from Fig. 9 still apply but have been omitted for readability.

Fig. 11
Fig. 11

Total user capacity in bits (r ECC × r code × M) as a function of the raw BER for an output user-BER specification of 10-12. An optimal working point for the system can be identified. Error bars have been omitted for readability.

Fig. 12
Fig. 12

Total user capacity in bits (r ECC × r code × M) expressed as a function of the number of holograms that can be stored (M). Recording too many holograms reduces capacity because the code-rate expense of the required ECC code outpaces the increase in the number of holograms. Error bars have been omitted for readability.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

SNR = SM - 2 N 1 M - 2 + N floor ,
M max = M max 1 - SNR t SNR 0 .
η = M / # 2 M 2 .
M / # A 0 τ r τ e .
t M = τ e M + X ,
t 1 = τ e ln X + 1 X .
M = τ e t M - X ,
t m = t m + 1 exp t m + 1 / τ e ,
η 1 η M = t 1 t M 2 1 - τ chosen / τ e ,

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