Abstract

We study the interpixel cross talk introduced to digital holographic data storage by use of a multilevel phase mask at the data-input plane. We evaluate numerically the intensity distribution at the output detector for Fourier plane hologram storage in a limited-aperture storage medium. Only the effect at an output pixel of interpixel cross talk from the four horizontal and vertical neighboring pixels is considered, permitting systematic evaluation of all possibilities. For random two-level and pseudorandom six-level phase masks, the influence of the pixel fill factor, as well as the aperture size of the storage medium, is studied. Our simulations show that, for a given aperture size, a random two-level mask is more susceptible to interpixel cross talk than is a pseudorandom six-level mask. Decreasing the pixel fill factor below 94% with a pseudorandom six-level phase mask makes it theoretically possible to have a system with no errors from interpixel cross talk if one particular 5-pixel pattern is forbidden through modulation coding. Reducing the input fill factor below 85% means that no patterns need to be excluded.

© 1997 Optical Society of America

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References

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    [CrossRef]
  2. L. Hesselink and M. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, 611–651 (1993).
    [CrossRef]
  3. F. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
    [CrossRef] [PubMed]
  4. J. Heanue, M. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
    [CrossRef] [PubMed]
  5. G. Sincerbox, “Holographic storage revisited,” in Current Trends in Optics, C. Dainty, ed. (Academic, New York, 1994), pp. 195 –207.
  6. G. W. Burr, F. H. Mok, and D. Psaltis, “Angle and space multiplexed holographic storage using 90 degree geometry,” Opt. Commun. 117, 49–55 (1995).
    [CrossRef]
  7. 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, and G. Wittmann, “A precision tester for studies of holographic optical storage materials and recording physics,” Appl. Opt. 35, 2360–2373 (1996).
    [CrossRef] [PubMed]
  8. G. W. Burr, F. H. Mok, and D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics (CLEO’96), Vol. 9 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CMB7, p. 9.
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    [CrossRef]
  13. X. Yi, P. Yeh, and C. Gu, “Statistical analysis of cross-talk noise and storage capacity in volume holographic memory,” Opt. Lett. 19, 1580–1582 (1994).
    [CrossRef] [PubMed]
  14. J. Hong, I. McMichael, and J. Ma, “Influence of phase masks on cross talk in holographic memory,” Opt. Lett. 21, 1694–1696 (1996).
    [CrossRef] [PubMed]
  15. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  16. E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, New York, 1974).

1996 (2)

1995 (1)

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

1994 (2)

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

X. Yi, P. Yeh, and C. Gu, “Statistical analysis of cross-talk noise and storage capacity in volume holographic memory,” Opt. Lett. 19, 1580–1582 (1994).
[CrossRef] [PubMed]

1993 (2)

L. Hesselink and 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]

1979 (1)

1972 (2)

1969 (1)

1963 (1)

Bashaw, M.

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

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

Bernal, M.-P.

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, New York, 1974).

Burkhardt, C. B.

Burr, G. W.

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

Coufal, H.

Firester, A. H.

Fox, E. C.

Goodman, J. W.

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

Grygier, R. K.

Gu, C.

Heanue, J.

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

Hesselink, L.

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

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

Hill, B.

Hoffnagle, J. A.

Hong, J.

Jefferson, C. M.

Kato, M.

Ma, J.

Macfarlane, R. M.

McMichael, I.

Mok, F.

Mok, F. H.

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

Nakayama, Y.

Psaltis, D.

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

Shelby, R. M.

Sincerbox, G. T.

Stewart, W. C.

van Heerden, P. J.

Wimmer, P.

Wittmann, G.

Yeh, P.

Yi, X.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

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

Opt. Lett. (3)

Opt. Quantum Electron. (1)

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

Science (1)

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

Other (4)

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

G. W. Burr, F. H. Mok, and D. Psaltis, “Storage of 10,000 holograms in LiNbO3:Fe,” in Conference on Lasers and Electro-Optics (CLEO’96), Vol. 9 of 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).

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, New York, 1974).

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Figures (13)

Fig. 1
Fig. 1

Digital holographic data-storage system in a 4 f configuration. In this study, the SLM and the phase mask are considered perfectly aligned and in the object Fourier plane of the lens L1. The storage medium, with a cross section D2, is located in the common Fourier plane (FP) of the lenses L1 and L2. The CCD camera is placed in the image Fourier plane of L2. A hologram is formed when the object beam and the reference beam interfere in the holographic storage medium.

Fig. 2
Fig. 2

Output signal of a single SLM pixel in the CCD plane for three different aperture sizes: (a) f/D = 14, (b) f/D = 23, and (c) f/D = 47. The signal consists of a main lobe and a series of smaller sidelobes extending in the x and y axes of the plane. The signals have been normalized to 1 and only a range from 0 to 0.5 is shown to emphasize the lower-signal lobes. The structure is due to the diffraction effect from the cross-sectional area of the storage medium, which is acting as a low-pass spatial filter.

Fig. 3
Fig. 3

Intensity of the Fourier spectrum of one SLM pixel as a function of the ratio f/D.

Fig. 4
Fig. 4

CCD pixel locations in which signal power is computed for a single input SLM pixel, to show roll-off of the point-spread function.

Fig. 5
Fig. 5

Neighbor-to-center contrast evaluated in the CCD pixel locations shown in Fig. 4 for several storage-medium cross-sectional apertures.

Fig. 6
Fig. 6

Thirteen unique patterns of neighbor pixels considered in this study for the evaluation of interpixel cross talk, shown for the case of a central 0. For the case of a two-level phase mask, there are 26 more similar patterns corresponding to a central pixel 1 and phase 0 (superscript plus) or a central pixel 1 and phase π (superscript minus). In the case of a six-level phase mask there are only 13 additional patterns, corresponding to a central pixel 1 and no phase. For the pseudorandom mask, a plus or a minus in neighboring pixels represents a phase shift of ±π/3 with respect to the central pixel.

Fig. 7
Fig. 7

Output signal of the central pixel in pattern I1+ by use of a two-level phase mask and f/D = 37.6 plotted versus the number of subdivisions per pixel edge.

Fig. 8
Fig. 8

Output-signal values for the interpixel cross-talk patterns of a two-level phase mask as a function of f/D. Interpixel cross talk is found for f/D values greater than or equal to 34.9. In the plot, only the five interpixel cross-talk patterns found for f/D = 34.9 are analyzed, but as f/D increases above 40 the number of patterns that produce interpixel cross talk increases beyond those shown here.

Fig. 9
Fig. 9

Output-signal values in the 10 worst-case patterns with a two-level phase mask as a function of the SLM phase pixel fill factor at f/D = 37.6. If the linear fill factor is less than or equal to 0.94 and patterns L0 and M1- are removed, there is no overlap between the 0 and the 1 patterns.

Fig. 10
Fig. 10

Output-signal values for the five interpixel cross-talk patterns with a pseudorandom six-level phase mask as a function of f/D. In contrast to the case of a two-level phase mask, there is no crossover between patterns at f/D = 34.9. When the value of f/D is greater than or equal to 43.4, five out of 26 patterns introduce interpixel cross talk.

Fig. 11
Fig. 11

Output-signal values for the five interpixel cross-talk patterns plotted versus the SLM phase pixel fill factor. In this case, f/D = 47 and a pseudorandom six-level phase mask is used. A system with no intrinsic errors is nominally achieved by elimination of pattern M1 for a linear fill factor less than 0.94. An error-free system can also be obtained without eliminating any patterns if the SLM pixel fill factor is less than 85%.

Fig. 12
Fig. 12

Six unique amplitude-only 5-pixel patterns. Note that there is no phase information in the patterns. As before, there are six additional patterns for a central 1 pixel.

Fig. 13
Fig. 13

Output-signal values for the 12 different no-phase-mask patterns plotted as a function of the fill factor for f/D = 37.6. (In the graph there are only 11 patterns since pattern M0, corresponding to the five off pixels, is always zero). No errors from interpixel cross talk are seen when there is no phase mask in the system.

Equations (6)

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

U0x, y, z=0=m=-P1P1n=-P2P2 cmn expiΦmn×rectx-mΓΓrecty-nΓΓ,
Ucx, y, z=2f=iΓ2λfm=-P1P1n=-P2P2 cmn expiΦmn×exp-i2πxmΓλfexp-i2πynΓλf×sincΓxπfsincΓyλf,
sincx1x=0sinπx/πxotherwise.
Px, y=rectx/Drecty/D,
Udx, y, z=4f=-Γ2m=-P1P1n=-P2P2 cmn expiΦmn×Ix+mΓIy+nΓ,
Ir=-α+αsincΓsexp-i2πrsds,

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