Abstract

Digital super-resolution holographic data storage based on Hermitian symmetry is proposed to store digital data in a tiny area of a medium. In general, reducing a recording area with an aperture leads to the improvement in the storage capacity of holographic data storage. Conventional holographic data storage systems however have a limitation in reducing a recording area. This limitation is called a Nyquist size. Unlike the conventional systems, our proposed system can overcome the limitation with the help of a digital holographic technique and digital signal processing. Experimental result shows that the proposed system can record and retrieve a hologram in a smaller area than the Nyquist size on the basis of Hermitian symmetry.

© 2017 Optical Society of America

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References

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2017 (1)

2016 (3)

2015 (3)

2014 (4)

2013 (3)

T. Ochiai, D. Barada, T. Fukuda, Y. Hayasaki, K. Kuroda, and T. Yatagai, “Angular multiplex recording of data pages by dual-channel polarization holography,” Opt. Lett. 38(5), 748–750 (2013).
[Crossref] [PubMed]

M. Bunsen, S. Umetsu, M. Takabayashi, and A. Okamoto, “Method of phase and amplitude modulation/demodulation using datapages with embedded phase-shift for holographic data storage,” Jpn. J. Appl. Phys. 52, 09LD04 (2013).
[Crossref]

S. Yoshida, H. Kurata, S. Ozawa, K. Okubo, S. Horiuchi, Z. Ushiyama, M. Yamamoto, S. Koga, and A. Tanaka, “High-density holographic data storage using three-dimensional shift multiplexing with spherical reference wave,” Jpn. J. Appl. Phys. 52, 09LD07 (2013).
[Crossref]

2011 (1)

2010 (1)

2009 (3)

2008 (2)

L. Dhar, K. Curtis, and T. Fäche, “Holographic data storage: Coming of age,” Nat. Photonics 2, 403–405 (2008).
[Crossref]

G. Berger, M. Dietz, and C. Denz, “Hybrid multinary modulation codes for page-oriented holographic data storage,” J. Opt. A: Pure Appl. Opt. 10, 115305 (2008).
[Crossref]

2007 (2)

2005 (1)

H. Horimai, X. Tan, and J. Li, “Collinear holography,” Opt. Lett. 44(13), 2575–2579 (2005).

2004 (1)

2003 (1)

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20(3), 21–36 (2003).
[Crossref]

2002 (1)

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143 (2002).
[Crossref]

2001 (1)

2000 (1)

1999 (1)

1998 (2)

1995 (1)

1992 (1)

1991 (1)

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

1982 (1)

Anderson, K.

Andrés, P.

Araiza-E, M.

Arrizón, V.

Awatsuji, Y.

Ayres, M.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).
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Barada, D.

Barbastathis, G.

Barking, G.

Berger, G.

G. Berger, M. Dietz, and C. Denz, “Hybrid multinary modulation codes for page-oriented holographic data storage,” J. Opt. A: Pure Appl. Opt. 10, 115305 (2008).
[Crossref]

Bernal, M.-P.

Bo, F.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143 (2002).
[Crossref]

Bracewell, R. B.

R. B. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, 1986).

Bunsen, M.

M. Bunsen, S. Umetsu, M. Takabayashi, and A. Okamoto, “Method of phase and amplitude modulation/demodulation using datapages with embedded phase-shift for holographic data storage,” Jpn. J. Appl. Phys. 52, 09LD04 (2013).
[Crossref]

Burr, G. W.

Campos, J.

Cao, L.

Carrada, R.

Chi, S.

Cho, S. L.

Chou, S. F.

Climent, V.

Cottrell, D. M.

Coufal, H.

Curtis, K.

L. Dhar, K. Curtis, and T. Fäche, “Holographic data storage: Coming of age,” Nat. Photonics 2, 403–405 (2008).
[Crossref]

K. Anderson and K. Curtis, “Polytopic multiplexing,” Opt. Lett. 29(12), 1402–1404 (2004).
[Crossref] [PubMed]

D. Psaltis, M. Levene, A. Pu, G. Barbastathis, and K. Curtis, “Holographic storage using shift multiplexing,” Opt. Lett. 20(7), 782–784 (1995).
[Crossref] [PubMed]

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).
[Crossref]

Davis, J. A.

Denz, C.

G. Berger, M. Dietz, and C. Denz, “Hybrid multinary modulation codes for page-oriented holographic data storage,” J. Opt. A: Pure Appl. Opt. 10, 115305 (2008).
[Crossref]

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

Dhar, L.

L. Dhar, K. Curtis, and T. Fäche, “Holographic data storage: Coming of age,” Nat. Photonics 2, 403–405 (2008).
[Crossref]

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).
[Crossref]

Dietz, M.

G. Berger, M. Dietz, and C. Denz, “Hybrid multinary modulation codes for page-oriented holographic data storage,” J. Opt. A: Pure Appl. Opt. 10, 115305 (2008).
[Crossref]

Eldar, Y. C.

Fäche, T.

L. Dhar, K. Curtis, and T. Fäche, “Holographic data storage: Coming of age,” Nat. Photonics 2, 403–405 (2008).
[Crossref]

Fujii, M.

Fukuda, T.

Fukumoto, A.

González, L. A.

Goodman, J. W.

Gu, H.

Hara, M.

Hayasaki, Y.

Hayashi, K.

He, Q.

Hill, A.

K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).
[Crossref]

Hirooka, K.

Hoffnagle, J. A.

Horimai, H.

H. Horimai, X. Tan, and J. Li, “Collinear holography,” Opt. Lett. 44(13), 2575–2579 (2005).

Horiuchi, S.

S. Yoshida, Y. Takahata, S. Horiuchi, and M. Yamamoto, “Spatial run-length limited code for reduction of hologram size in holographic data storage,” Opt. Commun,  358, 103–107 (2016).
[Crossref]

S. Yoshida, H. Kurata, S. Ozawa, K. Okubo, S. Horiuchi, Z. Ushiyama, M. Yamamoto, S. Koga, and A. Tanaka, “High-density holographic data storage using three-dimensional shift multiplexing with spherical reference wave,” Jpn. J. Appl. Phys. 52, 09LD07 (2013).
[Crossref]

Hosaka, M.

Y. Nakamura, H. Shimada, T. Ishii, H. Ishihara, M. Hosaka, and T. Hoshizawa, “High-density recording method with RLL coding for holographic memory system,” in Nonlinear Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMB5.
[Crossref]

Hoshizawa, T.

Y. Nakamura, H. Shimada, T. Ishii, H. Ishihara, M. Hosaka, and T. Hoshizawa, “High-density recording method with RLL coding for holographic memory system,” in Nonlinear Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMB5.
[Crossref]

Hsu, K. Y.

Imbe, M.

M. Imbe and T. Nomura, “Selective calculation for the improvement of reconstructed images in single-exposure generalized phase-shifting digital holography,” Opt. Eng. 53(4), 044102 (2014).
[Crossref]

Ina, H.

Ishihara, H.

Y. Nakamura, H. Shimada, T. Ishii, H. Ishihara, M. Hosaka, and T. Hoshizawa, “High-density recording method with RLL coding for holographic memory system,” in Nonlinear Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMB5.
[Crossref]

Ishii, N.

Ishii, T.

Y. Nakamura, H. Shimada, T. Ishii, H. Ishihara, M. Hosaka, and T. Hoshizawa, “High-density recording method with RLL coding for holographic memory system,” in Nonlinear Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMB5.
[Crossref]

Ishioka, K.

Ito, K.

Javidi, B.

Jefferson, M.

Jin, G.

Kakue, T.

Kamijo, K.

Kang, M. G.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20(3), 21–36 (2003).
[Crossref]

Kawano, K.

Kikuchi, H.

King, B. M.

Kinoshita, N.

M. Sawada, N. Kinoshita, T. Muroi, M. Motohashi, and N. Saito, “Rotation spacing and multiplexing number in angle-peristrophic multiplexing holographic memory,” Jpn. J. Appl. Phys. 54, 09MA03 (2015).
[Crossref]

N. Kinoshita, T. Muroi, N. Ishii, K. Kamijo, H. Kikuchi, N. Shimidzu, and O. Matoba, “Half-data-page insertion method for increasing recording density in angular multiplexing holographic memory,” Appl. Opt. 50(16), 2361–2369 (2011).
[Crossref] [PubMed]

Kobayashi, S.

Koga, S.

S. Yoshida, H. Kurata, S. Ozawa, K. Okubo, S. Horiuchi, Z. Ushiyama, M. Yamamoto, S. Koga, and A. Tanaka, “High-density holographic data storage using three-dimensional shift multiplexing with spherical reference wave,” Jpn. J. Appl. Phys. 52, 09LD07 (2013).
[Crossref]

Kubota, T.

Kurata, H.

S. Yoshida, H. Kurata, S. Ozawa, K. Okubo, S. Horiuchi, Z. Ushiyama, M. Yamamoto, S. Koga, and A. Tanaka, “High-density holographic data storage using three-dimensional shift multiplexing with spherical reference wave,” Jpn. J. Appl. Phys. 52, 09LD07 (2013).
[Crossref]

Kuroda, K.

Lancis, J.

Levene, M.

Leyva, V.

Li, J.

Lin, C. M.

Lin, J. H.

Lin, S. H.

Liu, C.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143 (2002).
[Crossref]

Liu, J.

Liu, Z.

C. Liu, Z. Liu, F. Bo, Y. Wang, and J. Zhu, “Super-resolution digital holographic imaging method,” Appl. Phys. Lett. 81(17), 3143 (2002).
[Crossref]

Martínez-León, L.

Matoba, O.

Minabe, J.

Moreno, I.

Motohashi, M.

M. Sawada, N. Kinoshita, T. Muroi, M. Motohashi, and N. Saito, “Rotation spacing and multiplexing number in angle-peristrophic multiplexing holographic memory,” Jpn. J. Appl. Phys. 54, 09MA03 (2015).
[Crossref]

Muroi, T.

M. Sawada, N. Kinoshita, T. Muroi, M. Motohashi, and N. Saito, “Rotation spacing and multiplexing number in angle-peristrophic multiplexing holographic memory,” Jpn. J. Appl. Phys. 54, 09MA03 (2015).
[Crossref]

N. Kinoshita, T. Muroi, N. Ishii, K. Kamijo, H. Kikuchi, N. Shimidzu, and O. Matoba, “Half-data-page insertion method for increasing recording density in angular multiplexing holographic memory,” Appl. Opt. 50(16), 2361–2369 (2011).
[Crossref] [PubMed]

Nakamura, Y.

Y. Nakamura, H. Shimada, T. Ishii, H. Ishihara, M. Hosaka, and T. Hoshizawa, “High-density recording method with RLL coding for holographic memory system,” in Nonlinear Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMB5.
[Crossref]

Neifeld, M. A.

Nishio, K.

Nobukawa, T.

Nomura, T.

Ochiai, T.

Ogasawara, Y.

Okamoto, A.

M. Bunsen, S. Umetsu, M. Takabayashi, and A. Okamoto, “Method of phase and amplitude modulation/demodulation using datapages with embedded phase-shift for holographic data storage,” Jpn. J. Appl. Phys. 52, 09LD04 (2013).
[Crossref]

Okubo, K.

S. Yoshida, H. Kurata, S. Ozawa, K. Okubo, S. Horiuchi, Z. Ushiyama, M. Yamamoto, S. Koga, and A. Tanaka, “High-density holographic data storage using three-dimensional shift multiplexing with spherical reference wave,” Jpn. J. Appl. Phys. 52, 09LD07 (2013).
[Crossref]

Ozawa, S.

S. Yoshida, H. Kurata, S. Ozawa, K. Okubo, S. Horiuchi, Z. Ushiyama, M. Yamamoto, S. Koga, and A. Tanaka, “High-density holographic data storage using three-dimensional shift multiplexing with spherical reference wave,” Jpn. J. Appl. Phys. 52, 09LD07 (2013).
[Crossref]

Park, M. K.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20(3), 21–36 (2003).
[Crossref]

Park, S. C.

S. C. Park, M. K. Park, and M. G. Kang, “Super-resolution image reconstruction: a technical overview,” IEEE Signal Process. Mag. 20(3), 21–36 (2003).
[Crossref]

Pauliat, G.

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

Psaltis, D.

Pu, A.

Quintanilla, M.

Rakuljic, G. A.

Roosen, G.

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

Ruiz, U.

Saito, N.

M. Sawada, N. Kinoshita, T. Muroi, M. Motohashi, and N. Saito, “Rotation spacing and multiplexing number in angle-peristrophic multiplexing holographic memory,” Jpn. J. Appl. Phys. 54, 09MA03 (2015).
[Crossref]

Sawada, M.

M. Sawada, N. Kinoshita, T. Muroi, M. Motohashi, and N. Saito, “Rotation spacing and multiplexing number in angle-peristrophic multiplexing holographic memory,” Jpn. J. Appl. Phys. 54, 09MA03 (2015).
[Crossref]

Shimada, H.

Y. Nakamura, H. Shimada, T. Ishii, H. Ishihara, M. Hosaka, and T. Hoshizawa, “High-density recording method with RLL coding for holographic memory system,” in Nonlinear Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMB5.
[Crossref]

Shimidzu, N.

Shimozato, Y.

Su, W. C.

Sun, C. C.

Tahara, T.

Tajahuerce, E.

Takabayashi, M.

M. Bunsen, S. Umetsu, M. Takabayashi, and A. Okamoto, “Method of phase and amplitude modulation/demodulation using datapages with embedded phase-shift for holographic data storage,” Jpn. J. Appl. Phys. 52, 09LD04 (2013).
[Crossref]

Takahata, Y.

S. Yoshida, Y. Takahata, S. Horiuchi, and M. Yamamoto, “Spatial run-length limited code for reduction of hologram size in holographic data storage,” Opt. Commun,  358, 103–107 (2016).
[Crossref]

Takashima, Y.

Takeda, M.

Tan, Q.

Tan, X.

H. Horimai, X. Tan, and J. Li, “Collinear holography,” Opt. Lett. 44(13), 2575–2579 (2005).

Tanaka, A.

S. Yoshida, H. Kurata, S. Ozawa, K. Okubo, S. Horiuchi, Z. Ushiyama, M. Yamamoto, S. Koga, and A. Tanaka, “High-density holographic data storage using three-dimensional shift multiplexing with spherical reference wave,” Jpn. J. Appl. Phys. 52, 09LD07 (2013).
[Crossref]

Tanaka, K.

Tokuyama, K.

Tschudi, T.

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

Umetsu, S.

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Figures (11)

Fig. 1
Fig. 1 Reducing a recording area with an aperture in holographic data storage.
Fig. 2
Fig. 2 Schematic of digital super-resolution holographic data storage.
Fig. 3
Fig. 3 Schematic of a numerical simulation based on spatial frequency filtering.
Fig. 4
Fig. 4 Signal beam in a numerical simulation. (a) Data page. (b) Random phase mask. (c) Fourier spectrum of a signal beam.
Fig. 5
Fig. 5 Simulation result without the restoration process. (a) Aperture for spatial frequency filtering. (b) Intensity and (c) complex amplitude distributions of a filtered signal beam in an output plane.
Fig. 6
Fig. 6 Simulation result with the restoration process. (a) Restored Fourier spectrum and (b) the intensity distribution of a restored signal beam in an output plane.
Fig. 7
Fig. 7 Simulation result in a conventional holographic data storage system. (a) Aperture for spatial frequency filtering and (b) intensity distribution of a filtered signal beam in an output plane.
Fig. 8
Fig. 8 Experimental setup for demonstrating digital super-resolution holographic data storage.
Fig. 9
Fig. 9 Phase holograms for signal and reference beams: (a) encoded phase pattern and (b) computer-generated reference pattern.
Fig. 10
Fig. 10 Fourier spectrum of phase holograms: (a) encoded phase pattern and (b) computer-generated reference pattern.
Fig. 11
Fig. 11 Experimental results. (a) Retrieved data and (b) Fourier spectrum of a filtered signal beam without the restoration process. (c) Retrieved data and (d) Fourier spectrum of a restored signal beam. (e) Retrieved data and (f) Fourier spectrum of a filtered signal beam without recording a hologram in conventional holographic data storage.

Equations (20)

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w = f λ d ,
s ( x , y ) = a page ( x , y ) exp { i ϕ rand ( x , y ) } ,
A ( u , v ) = rect ( 2 ( u c w / 4 ) c w ) rect ( v c w ) ,
S h ( u , v ) = S ( u , v ) A ( u , v ) ,
S ( u , v ) = S * ( u , v ) ,
s h ( x , y ) = [ S ( u , v ) A ( u , v ) ] = s ( x , y ) [ A ( u , v ) ] ,
O ( u , v ) = S ( u , v ) A ( u , v ) + S * ( u , v ) A ( u , v ) = S ( u , v ) { A ( u , v ) + A ( u , v ) } = S ( u , v ) { rect ( u c w ) rect ( v c w ) } .
| o ( x , y ) | 2 = | [ O ( u , v ) ] | 2 = | s ( x , y ) [ rect ( u c w ) rect ( v c w ) ] | 2 .
SER = E symbol N symbol × 100 [ % ] ,
ψ ( x , y ) = a page ( x , y ) { ϕ rand ( x , y ) + ϕ linear ( x , y ) } ,
ϕ linear ( x , y ) = 2 π ( f x 1 x + f y 1 y ) .
s ( x , y ) = sin { 1 a page ( x , y ) } π { 1 a page ( x , y ) } π exp [ i { ϕ rand ( x , y ) + ϕ linear ( x , y ) } ] .
s ( x , y ) = a page ( x , y ) exp [ i { ϕ rand ( x , y ) + ϕ linear ( x , y ) } ] = s ( x , y ) exp { i ϕ linear ( x , y ) } ,
s h ( x , y ) = s ( x , y ) exp { i ϕ linear ( x , y ) } [ A ( u f x1 , v f y1 ) ] = s h ( x , y ) exp { i ϕ linear ( x , y ) }
p ( x , y ) = exp { i 2 π ( f x 2 x + f y 2 y ) } ,
I ( x , y ) = | s h ( x , y ) + p ( x , y ) | 2 = B ( x , y ) + s h ( x , y ) p * ( x , y ) + s h * ( x , y ) p ( x , y ) ,
I ( x , y ) = B ( x , y ) + s h ( x , y ) exp [ i 2 π { ( f x 1 f x 2 ) x + ( f y 1 f y 2 ) y } ] + s h * ( x , y ) exp [ i 2 π { ( f x 1 f x 2 ) x ( f y 1 f y 2 ) y } ] = B ( x , y ) + s h ( x , y ) exp [ i 2 π { f x s x + f y s y } ] + s h * ( x , y ) exp [ i 2 π { f x s x f y s y } ] ,
f x s = f x 1 f x 2
f y s = f y 1 f y 2 ,
[ I ( x , y ) ] = [ B ( x , y ) ] + S h ( u f x s , v f y s ) + S h * ( u f x s , v f y s ) ,

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