Abstract

For analysis of effective phase-code multiplexing in a holographic memory system four types of phase code are generated and used as a reference beam. In computer simulations the size of the address beam is fixed at 32 × 32 pixels, and 0%, 5%, 10%, 15%, 20%, and 25% phase-error rates in a pixel are purposely added to the real phase values for consideration of the nonlinear phase-modulation characteristics of a practical spatial light modulator. Cross talk and signal-to-noise ratios (SNR’s) are comparatively analyzed for these phase codes by calculation of the autocorrelation and the cross correlation. The pseudorandom code (PSR) has the lowest cross-correlation mean value of 0.067 among the four types of phase code, which means that the SNR of the PSR is higher than with other phase codes. Also, the standard deviation of the PSR, indicating the degree of recalled data degradation, has the lowest value, at 0.0113.

© 2000 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. H. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
    [CrossRef] [PubMed]
  2. G. A. Rakuljic, V. Leyva, A. Yariv, “Optical data storage by orthogonal wavelength-multiplexed volume holograms,” Opt. Lett. 17, 1471–1473 (1992).
    [CrossRef]
  3. C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
    [CrossRef]
  4. S. G. Kim, K. T. Kim, E. S. Kim, “Non-mechanical angular multiplexed holographic memory system using a moving window on a liquid crystal display,” Jpn. J. Appl. Phys. 38, L38–L40 (1999).
    [CrossRef]
  5. T. F. Krile, M. O. Hagler, W. D. Redus, J. F. Walkup, “Multiplex holography with chirp-modulated binary phase coded reference-beam masks,” Appl. Opt. 16, 3131–3135 (1977).
    [CrossRef] [PubMed]
  6. E. L. Kral, J. F. Walkup, M. O. Hagler, “Correlation properties of random phase diffusers for multiplex holography,” Appl. Opt. 21, 1281–1290 (1982).
    [CrossRef] [PubMed]
  7. Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett. 16, 1774–1776 (1991).
    [CrossRef] [PubMed]
  8. M. C. Bashaw, J. F. Heanue, A. Aharoni, J. F. Walkup, L. Hesselink, “Cross-talk considerations for angular and phase-encoded multiplexing in volume holography,” J. Opt. Soc. Am. B 11, 1820–1836 (1994).
    [CrossRef]
  9. A. Arvillas, D. Maritsas, “Partitioning the period of a class of m-sequences and application to pseudo random number generation,” J. Assoc. Comput. Mach. 25, 675–686 (1978).
    [CrossRef]
  10. V. Morozov, K. Johnson, A. Lahrichi, “Pseudorandom codes for volume holographic storage application,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 144–151.

1999 (1)

S. G. Kim, K. T. Kim, E. S. Kim, “Non-mechanical angular multiplexed holographic memory system using a moving window on a liquid crystal display,” Jpn. J. Appl. Phys. 38, L38–L40 (1999).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1991 (2)

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Y. Taketomi, J. E. Ford, H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, “Incremental recording for photorefractive hologram multiplexing,” Opt. Lett. 16, 1774–1776 (1991).
[CrossRef] [PubMed]

1982 (1)

1978 (1)

A. Arvillas, D. Maritsas, “Partitioning the period of a class of m-sequences and application to pseudo random number generation,” J. Assoc. Comput. Mach. 25, 675–686 (1978).
[CrossRef]

1977 (1)

Aharoni, A.

Arvillas, A.

A. Arvillas, D. Maritsas, “Partitioning the period of a class of m-sequences and application to pseudo random number generation,” J. Assoc. Comput. Mach. 25, 675–686 (1978).
[CrossRef]

Bashaw, M. C.

Denz, C.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Fainman, Y.

Ford, J. E.

Hagler, M. O.

Heanue, J. F.

Hesselink, L.

Johnson, K.

V. Morozov, K. Johnson, A. Lahrichi, “Pseudorandom codes for volume holographic storage application,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 144–151.

Kim, E. S.

S. G. Kim, K. T. Kim, E. S. Kim, “Non-mechanical angular multiplexed holographic memory system using a moving window on a liquid crystal display,” Jpn. J. Appl. Phys. 38, L38–L40 (1999).
[CrossRef]

Kim, K. T.

S. G. Kim, K. T. Kim, E. S. Kim, “Non-mechanical angular multiplexed holographic memory system using a moving window on a liquid crystal display,” Jpn. J. Appl. Phys. 38, L38–L40 (1999).
[CrossRef]

Kim, S. G.

S. G. Kim, K. T. Kim, E. S. Kim, “Non-mechanical angular multiplexed holographic memory system using a moving window on a liquid crystal display,” Jpn. J. Appl. Phys. 38, L38–L40 (1999).
[CrossRef]

Kral, E. L.

Krile, T. F.

Lahrichi, A.

V. Morozov, K. Johnson, A. Lahrichi, “Pseudorandom codes for volume holographic storage application,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 144–151.

Lee, S. H.

Leyva, V.

Ma, J.

Maritsas, D.

A. Arvillas, D. Maritsas, “Partitioning the period of a class of m-sequences and application to pseudo random number generation,” J. Assoc. Comput. Mach. 25, 675–686 (1978).
[CrossRef]

Mok, F. H.

Morozov, V.

V. Morozov, K. Johnson, A. Lahrichi, “Pseudorandom codes for volume holographic storage application,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 144–151.

Pauliat, G.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Rakuljic, G. A.

Redus, W. D.

Roosen, G.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Sasaki, H.

Taketomi, Y.

Tschudi, T.

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Walkup, J. F.

Yariv, A.

Appl. Opt. (2)

J. Assoc. Comput. Mach. (1)

A. Arvillas, D. Maritsas, “Partitioning the period of a class of m-sequences and application to pseudo random number generation,” J. Assoc. Comput. Mach. 25, 675–686 (1978).
[CrossRef]

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

Jpn. J. Appl. Phys. (1)

S. G. Kim, K. T. Kim, E. S. Kim, “Non-mechanical angular multiplexed holographic memory system using a moving window on a liquid crystal display,” Jpn. J. Appl. Phys. 38, L38–L40 (1999).
[CrossRef]

Opt. Commun. (1)

C. Denz, G. Pauliat, G. Roosen, T. Tschudi, “Volume hologram multiplexing using a deterministic phase encoding method,” Opt. Commun. 85, 171–176 (1991).
[CrossRef]

Opt. Lett. (3)

Other (1)

V. Morozov, K. Johnson, A. Lahrichi, “Pseudorandom codes for volume holographic storage application,” in Joint International Symposium on Optical Memory and Optical Data Storage, Vol. 12 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 144–151.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (17)

Fig. 1
Fig. 1

Hologram memory system with phase-code multiplexing. f, focal length; L, lens; PR, photorefractive; PSLM, phase SLM; ASLM, amplitude SLM.

Fig. 2
Fig. 2

Some examples of phase codes (32 × 32).

Fig. 3
Fig. 3

Feedback shifter register.

Fig. 4
Fig. 4

Flow chart of the two-dimensional pseudorandom phase-code generation.

Fig. 5
Fig. 5

SNR considering phase error rate.

Fig. 6
Fig. 6

(a) Autocorrelation of PUR, (b) cross correlation of PUR.

Fig. 7
Fig. 7

(a) Autocorrelation of EQR, (b) cross correlation of EQR.

Fig. 8
Fig. 8

(a) Autocorrelation of HAM, (b) Cross correlation of HAM.

Fig. 9
Fig. 9

(a) Autocorrelation of PSR, (b) cross correlation of PSR.

Fig. 10
Fig. 10

Cross-correlation result of PUR.

Fig. 11
Fig. 11

Cross-correlation result of EQR.

Fig. 12
Fig. 12

Cross-correlation result of HAM.

Fig. 13
Fig. 13

Cross-correlation result of PSR.

Fig. 14
Fig. 14

Average of cross-correlation dependence on number of pixels.

Fig. 15
Fig. 15

Standard deviation of cross-correlation dependence on number of pixels.

Fig. 16
Fig. 16

SNR dependence on phase-coding schemes.

Fig. 17
Fig. 17

SNR dependence on number of pixels.

Tables (2)

Tables Icon

Table 1 Number of Address Beams for Five Types of Phase Code (Address Size is 32 × 32 Pixels)

Tables Icon

Table 2 Average and Standard Deviations for Cross Correlation

Equations (12)

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

MPUR=2!n2.
MB-EQR=m2!m22!m22!,
MEQR=m2!m22!m22!n/m2.
MHAM=2n.
MPSR=22m-12m-1n-1.
gx, y=fx, y+ex, y,
FT|gx, y|2=-- GifX, fY×Gj*ξ-fX, η-fYdξdη,
FT|gx, y|21  if i=j0  if ij.
SNRdB=10 log10Ai/Ci,
Exmx=- xpxdx,
σx2=Ex-mx2=-x-mx2pxdx=Ex2-2xmx+mx2,
σx=Ex2-2xmx+mx21/2.

Metrics