Abstract

The reconstruction fidelity of gray-scale holographic images is analyzed quantitatively and assessed by use of proposed quantities, especially the correlation coefficient between the original and the retrieved images. The physical factors affecting the fidelity of photorefractive holograms are investigated experimentally, leading to results that are useful for the determination of the recording-beam ratio and the exposure dosage for high-fidelity retrieval. Investigation of the effects of noise on the fidelity of multiplexed holograms suggests that, if multiple-gray-scale data pages are multiplexed in a given volume, the total bit capacity may be competitive with that realized by means of storing binary pages.

© 1999 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. B. Tang, “Study on the quality of images retrieved from volume holograms,” Ph.D. dissertation (University of Science and Technology of China, Hefei, China, 1998).

1996 (4)

1994 (2)

1993 (3)

1992 (1)

1991 (1)

1989 (1)

1983 (1)

G. C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).
[CrossRef]

1979 (2)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

K. Bløtekjaer, “Limitations on holographic storage capacity of photochromic and photorefractive media,” Appl. Opt. 18, 57–67 (1979).
[CrossRef] [PubMed]

1969 (1)

H. Kogelink, “Coupled wave theory for thick holograms gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Aharoni, A.

Asthana, P.

Bashaw, M. C.

Bløtekjaer, K.

Burr, G.

F. H. Mok, D. Psaltis, G. Burr, “Spatially- and angle-multiplexed holographic random access memory,” in Photonics for Computers, Neural Networks, and Memories, W. J. Miceli, J. A. Neff, S. T. Kowel, eds., Proc. SPIE1773, 334–345 (1992).
[CrossRef]

Cai, L. Z.

L. Z. Cai, P. Yeh, H. K. Liu, “Mean fringe contrast, optimum beam ratio and maximum diffraction efficiency for volume gratings written by coupled waves,” Opt. Commun. 132, 48–54 (1996).
[CrossRef]

Chang, T. Y.

Chistian, W.

Denz, C.

Erbschloe, D. R.

D. R. Erbschloe, “Nonlinear effects in photorefractive crystals,” Ph.D. dissertation (Oxford University, Oxford, 1989), Chap. 2, pp. 90–95.

Fainman, Y.

Goggin, S. D. D.

Heanue, J. F.

Hesselink, L.

Hong, J. H.

Johnson, K. M.

Klein, M. B.

G. C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).
[CrossRef]

Kogelink, H.

H. Kogelink, “Coupled wave theory for thick holograms gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Lee, S. H.

Liu, H. K.

L. Z. Cai, P. Yeh, H. K. Liu, “Mean fringe contrast, optimum beam ratio and maximum diffraction efficiency for volume gratings written by coupled waves,” Opt. Commun. 132, 48–54 (1996).
[CrossRef]

Maniloff, E. S.

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

McDonald, M.

McMichael, I.

Mok, F. H.

F. H. Mok, M. C. Tackitt, N. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3 crystal,” Opt. Lett. 16, 605–607 (1991).
[CrossRef] [PubMed]

F. H. Mok, D. Psaltis, G. Burr, “Spatially- and angle-multiplexed holographic random access memory,” in Photonics for Computers, Neural Networks, and Memories, W. J. Miceli, J. A. Neff, S. T. Kowel, eds., Proc. SPIE1773, 334–345 (1992).
[CrossRef]

Neifeld, M. A.

Nordin, G. P.

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Pauliat, G.

Pletcher, D.

Pratt, W. K.

W. K. Pratt, Laser Communication Systems (Wiley, New York, 1969).

Psaltis, D.

A. Pu, D. Psaltis, “High-density recording in photopolymer-based holographic three-dimensional disks,” Appl. Opt. 35, 2389–2398 (1996).
[CrossRef] [PubMed]

F. H. Mok, D. Psaltis, G. Burr, “Spatially- and angle-multiplexed holographic random access memory,” in Photonics for Computers, Neural Networks, and Memories, W. J. Miceli, J. A. Neff, S. T. Kowel, eds., Proc. SPIE1773, 334–345 (1992).
[CrossRef]

Pu, A.

Sasaki, H.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Stoll, N. M.

Strasser, A. C.

Tackitt, M. C.

Tang, B.

B. Tang, “Study on the quality of images retrieved from volume holograms,” Ph.D. dissertation (University of Science and Technology of China, Hefei, China, 1998).

Tschudi, T.

Valley, G. C.

G. C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Walkup, J. F.

Yariv, A.

Yeh, P.

L. Z. Cai, P. Yeh, H. K. Liu, “Mean fringe contrast, optimum beam ratio and maximum diffraction efficiency for volume gratings written by coupled waves,” Opt. Commun. 132, 48–54 (1996).
[CrossRef]

Appl. Opt. (4)

Bell Syst. Tech. J. (1)

H. Kogelink, “Coupled wave theory for thick holograms gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

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

Opt. Commun. (1)

L. Z. Cai, P. Yeh, H. K. Liu, “Mean fringe contrast, optimum beam ratio and maximum diffraction efficiency for volume gratings written by coupled waves,” Opt. Commun. 132, 48–54 (1996).
[CrossRef]

Opt. Eng. (1)

G. C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).
[CrossRef]

Opt. Lett. (6)

Science (1)

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

Other (4)

F. H. Mok, D. Psaltis, G. Burr, “Spatially- and angle-multiplexed holographic random access memory,” in Photonics for Computers, Neural Networks, and Memories, W. J. Miceli, J. A. Neff, S. T. Kowel, eds., Proc. SPIE1773, 334–345 (1992).
[CrossRef]

W. K. Pratt, Laser Communication Systems (Wiley, New York, 1969).

D. R. Erbschloe, “Nonlinear effects in photorefractive crystals,” Ph.D. dissertation (Oxford University, Oxford, 1989), Chap. 2, pp. 90–95.

B. Tang, “Study on the quality of images retrieved from volume holograms,” Ph.D. dissertation (University of Science and Technology of China, Hefei, China, 1998).

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Figures (13)

Fig. 1
Fig. 1

Steady-state correlation coefficient CC versus the nominal beam ratio for different coupling strengths. Experimently measured results are also shown.

Fig. 2
Fig. 2

Correlation coefficient versus normalized exposure time for different beam ratios assuming (a) writing time constant inversely proportional to writing intensity, and (b) fixed writing time constant. (γL = 0.3).

Fig. 3
Fig. 3

Simulated probability distribution of the pixel intensity in a binary image with noise from a Gaussian distribution. The dashed curve represents σ0 = σ1, and the solid curve represents σ0 < σ1. The unequal standard deviations are supported by the experimental evidence.

Fig. 4
Fig. 4

Schematic diagram of the experimental setup. BS, beam splitter; K, electrical shutter; BE, beam expander; M, mirror; RM, rotary mirror; I, original image; L, lens; H, holographic recording medium.

Fig. 5
Fig. 5

(a) Primary image of the original mask and (b) its gray distribution (measured with a power meter).

Fig. 6
Fig. 6

Retrieved images (left) and their gray-scale distributions (right) for (a) β = 1:2 and (b) β = 1:30.

Fig. 7
Fig. 7

Measured and calculated correlation-coefficient CC values plotted versus the normalized exposure time t0.

Fig. 8
Fig. 8

Correlation-coefficient CC values as a function of the recording time. The measured diffraction-efficiency evolution curve is also shown.

Fig. 9
Fig. 9

Angular sensitivity curve for a 3-mm-thick LiNbO3 crystal. The full angular width of the main lobe ΔΘ is defined as the selective angle.

Fig. 10
Fig. 10

Selective property of the correlation-coefficient CC value. The simultaneously sampled diffraction efficiency is also shown.

Fig. 11
Fig. 11

(a) Correlation-coefficient CC value and (b) the NHN of the reconstructed image of H1 plotted versus the number of multiplexed holograms for different angular separations.

Fig. 12
Fig. 12

Probability distribution of gray-scale values of the first holographic image (after deducting noise from the primary image). The angular separation for angular multiplexing is (a) ΔΘ and (b) 2ΔΘ. Dashed curves, sampled immediately after recording; solid curves, sampled after the fifth hologram recorded.

Fig. 13
Fig. 13

Direct images of a SLM with four gray scales and their histograms (see text).

Tables (1)

Tables Icon

Table 1 MGSER’s of the Images from H1 for Multiplexing with Different Angular Separations

Equations (18)

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η0=βexpγL-121+β1+β exp2γL,
βn=2nβN-1.
ηn=βn1+βnexpγL-121+βn exp2γL.
γt=γ1-exp-t/τw.
τn=1+β1+βn τ0,
ηnt=βn1+βnexpγntL-121+βn exp2γntL,
γnt=γ1-exp-1+βn1+βtτ0.
CC=Gn-G¯Gn-G¯¯Gn2¯-G¯2(Gn2¯-G¯21/2
σn2=σtn2-σon2
σon=σonGnGn.
NHN=n=1N σnGmax-Gmin=n=1Nσtn2-σonGnGn21/2Gmax-Gmin.
BER=12-d12π σ1exp-I-I12/2σ12dI+d12π σ0exp-I-I02/2σ02dI,
dI1σ0+I0σ1σ0+σ1I1+I02.
BERexp-SNR2/2SNR2π1/2.
d1,2=-B±B2-4AC1/22A,
MGSER=1Nn=1N-1Gbn12π σnexp-G-Gn2/2σn2dG+-Gbn12π σn+1exp-G-Gn+12/2σn+12dG,
A=σn2-σn+12,B=2Gnσn+12-Gn+1σn2,C=Gn+12σn2-Gn2σn+12-2σn+12σn2 lnσn/σn+1.
PG=n=1412π σnexp-G-Gn2/2σn2.

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