Abstract

We present two different channel models (the magnitude model and the intensity model) for a pixel-matched volume holographic data storage system that employs the 4-focal-length architecture. First, a framework to describe the channel models is developed. We evaluate the linearity of the channel models by comparing data values obtained from diffraction-limited interference with data values predicted by the channel models. The models are evaluated for linearity and equalization gain under different storage and read-back conditions, such as fill factors, apertures, and contrast ratios. Bit error rate results obtained by use of linear equalization methods in conjunction with the channel models developed are also presented. Our results suggest that the magnitude model leads to better performance when the fill factors are small, whereas the intensity model appears to be more appropriate for the high-fill-factor cases. The magnitude model, when suitable, appears to provide a storage density improvement of as great as 65%, whereas the intensity model seems capable of providing as much as 15% density gain through deconvolution. The optimum aperture for storage seems to be close to the Nyquist aperture.

© 1999 Optical Society of America

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References

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  1. L. Hesselink, M. C. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, S611–S661 (1993).
    [CrossRef]
  2. V. Vadde, B. V. K. Vijaya Kumar, “Channel estimation and intra-page equalization for digital volume holographic data storage,” in Optical Data Storage 1997 Topical Meeting, H. Birecki, Z. Kwiecien, eds., Proc. SPIE3109, 250–255 (1997).
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    [CrossRef]
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    [CrossRef] [PubMed]
  12. C. Miller, B. Hunt, M. A. Neifeld, W. Marcellin, “Binary image reconstruction via 2-D Viterbi search,” in Proceedings of the International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997).
    [CrossRef]
  13. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
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    [CrossRef]
  16. C. Gu, F. Dai, J. Hong, “Statistics of both optical and electronic noise in digital volume holographic data storage,” Electron. Lett. 32, 1400–1402 (1996).
    [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. G. P. Agrawal, Fiber Optic Communication Systems (Wiley, New York, 1992).
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    [CrossRef] [PubMed]
  21. U. Efron, Spatial Light Modulator Technology (Marcel Dekker, New York, 1994).
  22. J. A. Neff, R. A. Athale, S. H. Lee, “Two dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
    [CrossRef]

1998 (1)

1997 (1)

1996 (5)

1995 (1)

1994 (2)

1993 (1)

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

1992 (2)

1990 (1)

J. A. Neff, R. A. Athale, S. H. Lee, “Two dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

Agrawal, G. P.

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

Athale, R. A.

J. A. Neff, R. A. Athale, S. H. Lee, “Two dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

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]

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

Bernal, M.-P.

Brady, D.

Burr, G. W.

Chugg, K. M.

Coufal, H.

Curtis, K.

Dai, F.

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

Daniel, E. D.

C. D. Mee, E. D. Daniel, Magnetic Storage Handbook (McGraw-Hill, New York, 1996).

Efron, U.

U. Efron, Spatial Light Modulator Technology (Marcel Dekker, New York, 1994).

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Grygier, R. K.

Gu, C.

Gurkan, K.

Heanue, J. F.

Hesselink, L.

Hoffnagle, J. A.

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 storage,” Appl. Opt. 36, 3107–3115 (1997).
[CrossRef] [PubMed]

V. Vadde, B. V. K. Vijaya Kumar, G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, “A figure-of-merit for the optical aperture used in digital volume holographic data storage,” in Optical Data Storage ’98, S. Kubota, T. D. Milster, P. J. Wehrenberg, eds., Proc. SPIE3401, 194–200 (1998).
[CrossRef]

Hong, J.

Hunt, B.

C. Miller, B. Hunt, M. A. Neifeld, W. Marcellin, “Binary image reconstruction via 2-D Viterbi search,” in Proceedings of the International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997).
[CrossRef]

Jefferson, C. M.

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 storage,” Appl. Opt. 36, 3107–3115 (1997).
[CrossRef] [PubMed]

V. Vadde, B. V. K. Vijaya Kumar, G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, “A figure-of-merit for the optical aperture used in digital volume holographic data storage,” in Optical Data Storage ’98, S. Kubota, T. D. Milster, P. J. Wehrenberg, eds., Proc. SPIE3401, 194–200 (1998).
[CrossRef]

King, B. M.

Lee, S. H.

J. A. Neff, R. A. Athale, S. H. Lee, “Two dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

Ma, J.

Marcellin, W.

C. Miller, B. Hunt, M. A. Neifeld, W. Marcellin, “Binary image reconstruction via 2-D Viterbi search,” in Proceedings of the International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997).
[CrossRef]

McMichael, I.

Mee, C. D.

C. D. Mee, E. D. Daniel, Magnetic Storage Handbook (McGraw-Hill, New York, 1996).

Miller, C.

C. Miller, B. Hunt, M. A. Neifeld, W. Marcellin, “Binary image reconstruction via 2-D Viterbi search,” in Proceedings of the International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997).
[CrossRef]

Mok, F.

Neff, J. A.

J. A. Neff, R. A. Athale, S. H. Lee, “Two dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

Neifeld, M. A.

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]

C. Miller, B. Hunt, M. A. Neifeld, W. Marcellin, “Binary image reconstruction via 2-D Viterbi search,” in Proceedings of the International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997).
[CrossRef]

Oesterschulze, E.

Psaltis, D.

Quintanilla, M.

Saxena, R.

Shelby, R. M.

Sincerbox, G. T.

Sornat, G.

Vadde, V.

V. Vadde, B. V. K. Vijaya Kumar, “Channel estimation and intra-page equalization for digital volume holographic data storage,” in Optical Data Storage 1997 Topical Meeting, H. Birecki, Z. Kwiecien, eds., Proc. SPIE3109, 250–255 (1997).

V. Vadde, B. V. K. Vijaya Kumar, G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, “A figure-of-merit for the optical aperture used in digital volume holographic data storage,” in Optical Data Storage ’98, S. Kubota, T. D. Milster, P. J. Wehrenberg, eds., Proc. SPIE3401, 194–200 (1998).
[CrossRef]

Vijaya Kumar, B. V. K.

V. Vadde, B. V. K. Vijaya Kumar, G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, “A figure-of-merit for the optical aperture used in digital volume holographic data storage,” in Optical Data Storage ’98, S. Kubota, T. D. Milster, P. J. Wehrenberg, eds., Proc. SPIE3401, 194–200 (1998).
[CrossRef]

V. Vadde, B. V. K. Vijaya Kumar, “Channel estimation and intra-page equalization for digital volume holographic data storage,” in Optical Data Storage 1997 Topical Meeting, H. Birecki, Z. Kwiecien, eds., Proc. SPIE3109, 250–255 (1997).

Yeh, P.

Yi, X.

Appl. Opt. (3)

Electron. Lett. (1)

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

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

Opt. Lett. (5)

Opt. Quantum Electron. (1)

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

Proc. IEEE (1)

J. A. Neff, R. A. Athale, S. H. Lee, “Two dimensional spatial light modulators: a tutorial,” Proc. IEEE 78, 826–855 (1990).
[CrossRef]

Other (8)

U. Efron, Spatial Light Modulator Technology (Marcel Dekker, New York, 1994).

V. Vadde, B. V. K. Vijaya Kumar, “Channel estimation and intra-page equalization for digital volume holographic data storage,” in Optical Data Storage 1997 Topical Meeting, H. Birecki, Z. Kwiecien, eds., Proc. SPIE3109, 250–255 (1997).

C. Miller, B. Hunt, M. A. Neifeld, W. Marcellin, “Binary image reconstruction via 2-D Viterbi search,” in Proceedings of the International Conference on Image Processing (Institute of Electrical and Electronics Engineers, New York, 1997).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978).

V. Vadde, B. V. K. Vijaya Kumar, G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, “A figure-of-merit for the optical aperture used in digital volume holographic data storage,” in Optical Data Storage ’98, S. Kubota, T. D. Milster, P. J. Wehrenberg, eds., Proc. SPIE3401, 194–200 (1998).
[CrossRef]

C. D. Mee, E. D. Daniel, Magnetic Storage Handbook (McGraw-Hill, New York, 1996).

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

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of a digital volume HDSS in the 4-f L architecture.

Fig. 2
Fig. 2

Holographic storage system modeled as a communication channel.

Fig. 3
Fig. 3

Magnitude channel model that employs positive square roots of received pixel values.

Fig. 4
Fig. 4

Intensity channel model that employs received pixel values as a linear superposition of input image.

Fig. 5
Fig. 5

5 × 5 pixel pattern used to compute CCD output value for different ISI combinations.

Fig. 6
Fig. 6

Channel linearity plot for magnitude and intensity models: (a) and (b), SLM areal fill factor at 1.0, CCD fill factor at 0.25, amplitude CR at 3, Nyquist aperture. (c) and (d), SLM fill factor at 1.0, CCD areal fill factor at 0.95, amplitude CR at 3, Nyquist aperture.

Fig. 7
Fig. 7

Preequalization and postequalization BER as a function of SNR for channels dominated by optical and electronic noise. MZFE and IZFE refer to ZFE on the magnitude model and the intensity model, respectively. (a) and (b), SLM areal fill factor at 1, CCD areal fill factor at 0.4, Nyquist aperture, amplitude CR = 3. (c) and (d), SLM areal fill factor at 1, CCD areal fill factor at 0.8, Nyquist aperture, amplitude CR at 3.

Fig. 8
Fig. 8

FOM plotted for an OND channel (top) and an END channel (bottom) as a function of the SLM areal fill factor. A target BER of 10-3 along with a CCD areal fill factor of 0.3, an aperture width of 1.0W, and amplitude CR at 3 are assumed.

Fig. 9
Fig. 9

Dependence of the FOM on the areal CCD fill factor for an OND channel (top) and an END channel (bottom). A target BER of 10-3 along with a SLM areal fill factor of 0.9, an aperture width of 1.0W, and an amplitude CR at 3 are assumed.

Fig. 10
Fig. 10

Storage density gain obtained by use of the appropriate (i.e., better) channel model plotted as a function of the target BER. An OND channel is considered here. Top, low CCD fill factor; bottom, high CCD fill factor.

Fig. 11
Fig. 11

Storage density gain obtained by use of the appropriate (i.e., better) channel model plotted versus the target BER. An OND channel is considered here.

Fig. 12
Fig. 12

FOM plotted for an OND channel (top) and an END channel (bottom) versus the normalized aperture width (for SLM areal fill factor at 1, CCD areal fill factor at 0.8, amplitude CR at 3). The target BER assumed is 10-3.

Fig. 13
Fig. 13

FOM plotted for an OND channel (top) and an END channel (bottom) as a function of the contrast ratio (with SLM areal fill factor at 1, CCD areal fill factor at 0.8, aperture width is W). The FOM target BER assumed is 10-3.

Equations (41)

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

ν=ErONErOFF,
α1=δx1/Δx1.
α2=δx2/Δx2.
g1x, y=FxλfL, yλfL,
g2x, y=f-x, -y * sincxdλfL, ydλfL,
hx, y=sincxdλfL, ydλfL.
g2x, y=rectx-pΔx1δx1, y-qΔy1δy1 * sin cxdλfL, ydλfL.
rk, l=-+-+g2x, yrectx-kΔx2δx2, y-lΔy2δy2+nok, l2dxdy+nek, l,
rk, l=-+-+ pq ap, qrectx-pΔx1δx1, y-qΔy1δy1 * sincxdλfL, ydλfL×rectx-kΔx2δx2, y-lΔy2δy2+nok, l2dxdy+ne[k, l],
r=a * hM+nM,
r=a * hI+nI,
hMk, l=-+-+rectxδx1, yδy1 * sincxdλfL, ydλfL×rectx-kΔx2δx2, y-lΔy2δy2dxdy,
hMk, l=x=k-α2/2Δx2k+α2/2Δx2y=l-α2/2Δy2l+α2/2Δy2rectxδx1, yδy1* sincxdλfL, ydλfLdxdy,
hIk, l=x=k-α2/2Δx2k+α2/2Δx2y=l-α2/2Δy2l+α2/2Δy2×rectxδx1, yδy1 * sincxdλfL, ydλfL2dxdy.
hM=00-0.030000.020.150.020-0.030.151.00.15-0.0300.020.150.02000-0.0300.
XX0XXX111X01110X111XXX0XX, XX1XXX000X10001X000XXX1XX.
no=ni+jnq,
Idetk, l=|rk, l+nik, l+jnqk, l|2+nek, l,
SNR=μ1/σ1,
σ12=4σo2σo2+μ1+σe2,
σ124σo2μ1+σe2.
μ1σo+μ0σ1σo+σ1.
FOME=σe/d2.
FOMo=2σoμ1d2.
SNR=μ1/σ1,
Idet=|r+ni+jnq|2+ne=r+ni2+2rni+nq2+ne.
xn=ni2+2rni+nq2+ne.
σn2=Exn2-Exn2,
Exn=Eni2+2rEni+Enq2+Ene.
Exn=2σo2,
Exn2=Eni2+2rni+nq2+ne2.
Exn2=Eni4+4rni2+nq4+ne2+4ni2rni+2ni2nq2+2ni2ne+4rninq2+4rnine+2nq2ne.
Exn2=Eni4+E4rni2+Enq4+Ene2+E2ni2nq2.
Ex2=σ2,  Ex4=3σ4,
Exn2=3σo4+4rσo2+3σo4+σe2+2σo4=8σo4+4rσo2+σe2.
σn2=4σo4+4rσo2+σe2.
Exn=EIENni2+2rENni+ENnq2+ENne.
Exn2=EIENni4+EN4rni2+ENnq4+ENne2+EN2ni2nq2=8σo4+4EIrσo2+σe2.
σn2=Exn2-Exn2=4σo4+4aσo2+σe2.
μ1=a+2σo2.
σn2=4σo4+4μ1σo2+σe2.

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