Abstract

A new phase-to-amplitude data page conversion method is proposed for efficient recovery of the data encoded in phase-modulated data pages used in holographic storage and optical encryption. The method is based on the interference between the data page and its copy shifted by an integral number of pixels. Key properties such as Fourier plane homogeneity, bit error rate, and positioning tolerances are investigated by computer modeling, and a comparison is provided with amplitude-modulated data page holographic storage with and without static phase masks. The feasibility and the basic properties of the proposed method are experimentally demonstrated. The results show that phase-modulated data pages can be used efficiently with reduced system complexity.

© 2007 Optical Society of America

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References

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  1. J. Joseph and D. A. Waldman, "Homogenized Fourier transform holographic data storage using phase spatial light modulators and methods for recovery of data from the phase image," Appl. Opt. 45, 6374-6380 (2006).
    [CrossRef] [PubMed]
  2. Y. Takeda, Y. Oshida, and Y. Miyamura, "Random phase shifters for Fourier transformed holograms," Appl. Opt. 11, 818-822 (1972).
    [CrossRef] [PubMed]
  3. M. P. Bernal, G. W. Burr, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, R. M. Macfarlane, R. M. Shelby, and 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]
  4. L. Domján, P. Koppa, G. Szarvas, and J. Reményi, "Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane light homogenization in holographic data storage," Optik (Stuttgart) 113, 382-390 (2002).
    [CrossRef]
  5. R. John, J. Joseph, and K. Singh, "Phase-image-based content-addressable holographic data storage," Opt. Commun. 232, 99-106 (2004).
    [CrossRef]
  6. P. C. Mogensen and J. Glückstad, "Phase-only optical encryption," Opt. Lett. 25, 566-568 (2000).
    [CrossRef]
  7. X. Tan, O. Matoba, T. Shimura, K. Kuroda, and B. Javidi, "Secure optical storage that uses fully phase encryption," Appl. Opt. 39, 6689-6694 (2000).
    [CrossRef]
  8. D.-H. Seo and S.-J. Kim, "Interferometric phase-only optical encryption of a reference wave," Opt. Lett. 28, 304-306 (2003).
    [CrossRef] [PubMed]
  9. F. Zernike, "How I discovered phase contrast," Science 121, 345-349 (1955).
    [CrossRef] [PubMed]
  10. L. G. Neto, "Implementation of image encryption using phase contrast techniques," Proc. SPIE 3386, 284-289 (1998).
    [CrossRef]
  11. J. Glückstad and P. C. Mogensen, "Optimal phase contrast in common-path interferometry," Appl. Opt. 40, 268-282 (2001).
    [CrossRef]
  12. P. Koppa, J. Reményi, F. Ujhelyi, and G. Erdei, "Method and system for parallel optical decoding of digital phase image to intensity image," European patent application 06013569.6-2210 (2006).
  13. P. Várhegyi, P. Koppa, F. Ujhelyi, and E. Lörincz, "System modeling and optimization of Fourier holographic memory," Appl. Opt. 44, 3024-3031 (2005).
    [CrossRef] [PubMed]
  14. P. Várhegyi, Á. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, E. Lörincz, G. Szarvas, and P. S. Ramanujam, "Saturation effect in azobenzene polymers used for polarization holography," J. Appl. Phys. B 76, 397-402 (2003).
    [CrossRef]
  15. A. D. S. Jayalath and C. Tellambura, "Peak-to-average power ratio of a Zipper signal," in IEEE VTS 54th Vehicular Technology Conference (IEEE, 2001), pp. 1111-1114.
  16. J. Reményi, P. Várhegyi, L. Domján, and E. Lörincz, "Amplitude, phase, and hybrid ternary modulation modes of a twisted-nematic liquid-crystal display at 400 nm," Appl. Opt. 42, 3428-3434 (2003).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

2004 (1)

R. John, J. Joseph, and K. Singh, "Phase-image-based content-addressable holographic data storage," Opt. Commun. 232, 99-106 (2004).
[CrossRef]

2003 (3)

2002 (1)

L. Domján, P. Koppa, G. Szarvas, and J. Reményi, "Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane light homogenization in holographic data storage," Optik (Stuttgart) 113, 382-390 (2002).
[CrossRef]

2001 (1)

2000 (2)

1998 (2)

1972 (1)

1955 (1)

F. Zernike, "How I discovered phase contrast," Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Bernal, M. P.

Burr, G. W.

Coufal, H.

Domján, L.

J. Reményi, P. Várhegyi, L. Domján, and E. Lörincz, "Amplitude, phase, and hybrid ternary modulation modes of a twisted-nematic liquid-crystal display at 400 nm," Appl. Opt. 42, 3428-3434 (2003).
[CrossRef] [PubMed]

L. Domján, P. Koppa, G. Szarvas, and J. Reményi, "Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane light homogenization in holographic data storage," Optik (Stuttgart) 113, 382-390 (2002).
[CrossRef]

Erdei, G.

P. Koppa, J. Reményi, F. Ujhelyi, and G. Erdei, "Method and system for parallel optical decoding of digital phase image to intensity image," European patent application 06013569.6-2210 (2006).

Glückstad, J.

Hoffnagle, J. A.

Javidi, B.

Jayalath, A. D. S.

A. D. S. Jayalath and C. Tellambura, "Peak-to-average power ratio of a Zipper signal," in IEEE VTS 54th Vehicular Technology Conference (IEEE, 2001), pp. 1111-1114.

Jefferson, C. M.

John, R.

R. John, J. Joseph, and K. Singh, "Phase-image-based content-addressable holographic data storage," Opt. Commun. 232, 99-106 (2004).
[CrossRef]

Joseph, J.

Kerekes, Á.

P. Várhegyi, Á. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, E. Lörincz, G. Szarvas, and P. S. Ramanujam, "Saturation effect in azobenzene polymers used for polarization holography," J. Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Kim, S.-J.

Koppa, P.

P. Várhegyi, P. Koppa, F. Ujhelyi, and E. Lörincz, "System modeling and optimization of Fourier holographic memory," Appl. Opt. 44, 3024-3031 (2005).
[CrossRef] [PubMed]

P. Várhegyi, Á. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, E. Lörincz, G. Szarvas, and P. S. Ramanujam, "Saturation effect in azobenzene polymers used for polarization holography," J. Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

L. Domján, P. Koppa, G. Szarvas, and J. Reményi, "Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane light homogenization in holographic data storage," Optik (Stuttgart) 113, 382-390 (2002).
[CrossRef]

P. Koppa, J. Reményi, F. Ujhelyi, and G. Erdei, "Method and system for parallel optical decoding of digital phase image to intensity image," European patent application 06013569.6-2210 (2006).

Kuroda, K.

Lörincz, E.

Macfarlane, R. M.

Matoba, O.

Miyamura, Y.

Mogensen, P. C.

Neto, L. G.

L. G. Neto, "Implementation of image encryption using phase contrast techniques," Proc. SPIE 3386, 284-289 (1998).
[CrossRef]

Oshida, Y.

Quintanilla, M.

Ramanujam, P. S.

P. Várhegyi, Á. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, E. Lörincz, G. Szarvas, and P. S. Ramanujam, "Saturation effect in azobenzene polymers used for polarization holography," J. Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Reményi, J.

J. Reményi, P. Várhegyi, L. Domján, and E. Lörincz, "Amplitude, phase, and hybrid ternary modulation modes of a twisted-nematic liquid-crystal display at 400 nm," Appl. Opt. 42, 3428-3434 (2003).
[CrossRef] [PubMed]

L. Domján, P. Koppa, G. Szarvas, and J. Reményi, "Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane light homogenization in holographic data storage," Optik (Stuttgart) 113, 382-390 (2002).
[CrossRef]

P. Koppa, J. Reményi, F. Ujhelyi, and G. Erdei, "Method and system for parallel optical decoding of digital phase image to intensity image," European patent application 06013569.6-2210 (2006).

Sajti, S.

P. Várhegyi, Á. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, E. Lörincz, G. Szarvas, and P. S. Ramanujam, "Saturation effect in azobenzene polymers used for polarization holography," J. Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Seo, D.-H.

Shelby, R. M.

Shimura, T.

Singh, K.

R. John, J. Joseph, and K. Singh, "Phase-image-based content-addressable holographic data storage," Opt. Commun. 232, 99-106 (2004).
[CrossRef]

Szarvas, G.

P. Várhegyi, Á. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, E. Lörincz, G. Szarvas, and P. S. Ramanujam, "Saturation effect in azobenzene polymers used for polarization holography," J. Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

L. Domján, P. Koppa, G. Szarvas, and J. Reményi, "Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane light homogenization in holographic data storage," Optik (Stuttgart) 113, 382-390 (2002).
[CrossRef]

Takeda, Y.

Tan, X.

Tellambura, C.

A. D. S. Jayalath and C. Tellambura, "Peak-to-average power ratio of a Zipper signal," in IEEE VTS 54th Vehicular Technology Conference (IEEE, 2001), pp. 1111-1114.

Ujhelyi, F.

P. Várhegyi, P. Koppa, F. Ujhelyi, and E. Lörincz, "System modeling and optimization of Fourier holographic memory," Appl. Opt. 44, 3024-3031 (2005).
[CrossRef] [PubMed]

P. Várhegyi, Á. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, E. Lörincz, G. Szarvas, and P. S. Ramanujam, "Saturation effect in azobenzene polymers used for polarization holography," J. Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

P. Koppa, J. Reményi, F. Ujhelyi, and G. Erdei, "Method and system for parallel optical decoding of digital phase image to intensity image," European patent application 06013569.6-2210 (2006).

Várhegyi, P.

Waldman, D. A.

Zernike, F.

F. Zernike, "How I discovered phase contrast," Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Appl. Opt. (7)

J. Appl. Phys. B (1)

P. Várhegyi, Á. Kerekes, S. Sajti, F. Ujhelyi, P. Koppa, E. Lörincz, G. Szarvas, and P. S. Ramanujam, "Saturation effect in azobenzene polymers used for polarization holography," J. Appl. Phys. B 76, 397-402 (2003).
[CrossRef]

Opt. Commun. (1)

R. John, J. Joseph, and K. Singh, "Phase-image-based content-addressable holographic data storage," Opt. Commun. 232, 99-106 (2004).
[CrossRef]

Opt. Lett. (2)

Optik (1)

L. Domján, P. Koppa, G. Szarvas, and J. Reményi, "Ternary phase-amplitude modulation with twisted nematic liquid crystal displays for Fourier-plane light homogenization in holographic data storage," Optik (Stuttgart) 113, 382-390 (2002).
[CrossRef]

Proc. SPIE (1)

L. G. Neto, "Implementation of image encryption using phase contrast techniques," Proc. SPIE 3386, 284-289 (1998).
[CrossRef]

Science (1)

F. Zernike, "How I discovered phase contrast," Science 121, 345-349 (1955).
[CrossRef] [PubMed]

Other (2)

P. Koppa, J. Reményi, F. Ujhelyi, and G. Erdei, "Method and system for parallel optical decoding of digital phase image to intensity image," European patent application 06013569.6-2210 (2006).

A. D. S. Jayalath and C. Tellambura, "Peak-to-average power ratio of a Zipper signal," in IEEE VTS 54th Vehicular Technology Conference (IEEE, 2001), pp. 1111-1114.

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Figures (8)

Fig. 1
Fig. 1

Principle of phase-to-amplitude conversion showing (a) the amplitude and (b) the intensity of the input and output for a simple image.

Fig. 2
Fig. 2

Block diagram of the simulation process. FFT, fast Fourier transform.

Fig. 3
Fig. 3

Simulated image of the phase-to-amplitude conversion of a 128 by 128 pixel data page with 0.9 Fourier filtering and a 28% white rate: (a) The whole output image, (b) its magnified top right corner, (c) the Fourier plane intensity distribution, and (d) the pixel histogram are shown. The BER is 2.7 × 10 12 , the histogram spacing is 64, and the PAR is 20.5.

Fig. 4
Fig. 4

Simulated image of the phase-to-amplitude conversion of a 128 by 128 pixel data page with 0.685 Fourier filtering and a 50% white rate. (a) The whole output image, (b) its magnified top right corner, (c) the Fourier plane intensity distribution, and (d) the pixel histogram are shown. The BER is 0.00964, the histogram spacing is 46 , and the PAR in the Fourier plane is 20.5.

Fig. 5
Fig. 5

Simulated image of a conventional amplitude data page without a phase mask with 0.685 Fourier filtering and a 50% white rate. (a) The whole output image, (b) its magnified top right corner, the Fourier plane intensity distribution in (c) linear and (d) logarithmic scale, and (e) the pixel histogram are shown. The BER is 0.43, the histogram spacing is 175 , and the PAR is 18,000.

Fig. 6
Fig. 6

Simulation results on the reconstruction of holograms with positioning errors with respect to the recording position. (a) The reconstructed image of a simple interferometric phase-to-amplitude conversion at a 1% shift, (b) the image reconstructed with the new method for a 9% shift, and (c) the histogram spacing as a function of the misalignment for the new method.

Fig. 7
Fig. 7

(a) Schematic system diagram of our experimental setup. (b) The phase-to-amplitude conversion part in detail also shows the polarization of the beams. (c) Orientation and geometry of the birefringent plate. BE, beam expander; CP, circular polarizer; BIS, birefringent image splitter; P, polarizer; O and E, ordinary and extraordinary polarizations, respectively.

Fig. 8
Fig. 8

Typical output images obtained in the experiment (a) without and (b) with phase-to-amplitude conversion, and (c) a typical intensity distribution in the Fourier plane. Note that in the experiment a large Fourier filter (about 5 × the Nyquist aperture) was used; thus the experimental images seem sharper than the simulated ones.

Tables (1)

Tables Icon

Table 1 Summary of Simulation Results for Different Data Pages and Phase Masks with 0.685 Fourier Filtering and a 50% White Rate

Equations (4)

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

E k , j out = E k , j in + E k + 1 , j + 1 in ,
I k , j out | E k , j out | 2 = | E k , j in | 2 + | E k + 1 , j + 1 in | 2 + E k , j in * E k + 1 , j + 1 in + E k , j in E k + 1 , j + 1 in * = E 0 2 ( 2 ± 2 ) .
E k + 1 , j + 1 in = E k , j out E k , j in .
PAR = I peak I average .

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