Abstract

A paraxial solution to the coaxial holographic storage algorithm is proposed based on the scalar diffraction theory and a VOHIL model (volume hologram being an integrator of the lights emitted from elementary light sources), which can give insight into the optical characteristics of the collinear holographic storage system in an effective way, including the point spread function and shift selectivity. The paraxial solution shows that the reference pattern is the key issue in the point spread function. Thus, the bit error rate of the system can be improved by changing the reference pattern. The proposed solution will be useful in the design of a new reference pattern to perform a high-quality readout pattern in the coaxial holographic storage system.

© 2007 Optical Society of America

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  1. P. J. van Heerden, "Theory of optical information storage in solids," Appl. Opt. 2, 393-400 (1963).
    [CrossRef]
  2. G. Barbastathis and D. Psaltis, "Volume holographic multiplexing methods," in Holographic Data Storage, H. J. Coufal, D. Psaltis, and G. T. Sincerbox, eds. (Springer-Verlag, 2000) pp.21-22.
  3. L. Hesselink, S. S. Orlov, and M. C. Bashaw, "Holographic data storage systems," inProceedings of IEEE 92, 1231-1280 (2004).
    [CrossRef]
  4. E. N. Leith, A. Kozma, J. Marks, and N. Massey, "Holographic data storage in three-dimensional media," Appl. Opt. 5, 1303-1311 (1966).
    [CrossRef] [PubMed]
  5. H. Horimai, "Collinear holography," Proc. 5th Pacific Rim Conference on Lasers and Electro-Optics 1, 376-377 (2003).
  6. H. Horimai and X. Tan, "Advanced collinear holography," Opt. Rev. 12, 90-92 (2005).
    [CrossRef]
  7. H. Horimai, X. D. Tan, and J. Li, "Collinear holography," Appl. Opt. 44, 2575-2579 (2005).
    [CrossRef] [PubMed]
  8. K. Tanaka, H. Mori, M. Hara, K. Hirooka, A. Fukumoto, and K. Watanabe, "High density recording of 270 Gbits/inch2 in a coaxial holographic storage system," Tech. Digest of ISOM 2007, MO-D-03.
  9. H. Horimai and X. Tan, "Holographic versatile disc system," Proc. of SPIE 5939, 593901(2005).
    [CrossRef]
  10. T. Shimura, S. Ichimura, Y. Ashizuka, R. Fujimura, K. Kuroda, X. D. Tan, and H. Horimai, "Shift selectivity of the collinear holographic storage system," Proc. of SPIE 6282, 62820s (2006).
    [CrossRef]
  11. T. Shimura, S. Ichimura, R. Fujimura, K. Kuroda, X. D. Tan and H. Horimai, "Analysis of a collinear holographic storage system: introduction of pixel spread function," Opt. Letters 31, 1208-1210 (2006).
    [CrossRef]
  12. H. Horimai and J. Li, "A novel collinear optical setup for holographic data storage system," in Proc. of SPIE 5380, 297-303 (2004).
    [CrossRef]
  13. S. R. Lambourdiere, A. Fukumoto, K. Tanaka, and K. Watanabe, "Simulation of holographic data storage for the optical collinear system," Jpn. J. Appl. Phys. 45, 1246-1252 (2006).
    [CrossRef]
  14. C. C. Sun, "A simplified model for diffraction analysis of volume holograms," Opt. Eng. 42, 1184-1185 (2003).
    [CrossRef]
  15. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2002).

2006

T. Shimura, S. Ichimura, Y. Ashizuka, R. Fujimura, K. Kuroda, X. D. Tan, and H. Horimai, "Shift selectivity of the collinear holographic storage system," Proc. of SPIE 6282, 62820s (2006).
[CrossRef]

T. Shimura, S. Ichimura, R. Fujimura, K. Kuroda, X. D. Tan and H. Horimai, "Analysis of a collinear holographic storage system: introduction of pixel spread function," Opt. Letters 31, 1208-1210 (2006).
[CrossRef]

S. R. Lambourdiere, A. Fukumoto, K. Tanaka, and K. Watanabe, "Simulation of holographic data storage for the optical collinear system," Jpn. J. Appl. Phys. 45, 1246-1252 (2006).
[CrossRef]

2005

H. Horimai and X. Tan, "Advanced collinear holography," Opt. Rev. 12, 90-92 (2005).
[CrossRef]

H. Horimai and X. Tan, "Holographic versatile disc system," Proc. of SPIE 5939, 593901(2005).
[CrossRef]

H. Horimai, X. D. Tan, and J. Li, "Collinear holography," Appl. Opt. 44, 2575-2579 (2005).
[CrossRef] [PubMed]

2004

L. Hesselink, S. S. Orlov, and M. C. Bashaw, "Holographic data storage systems," inProceedings of IEEE 92, 1231-1280 (2004).
[CrossRef]

2003

C. C. Sun, "A simplified model for diffraction analysis of volume holograms," Opt. Eng. 42, 1184-1185 (2003).
[CrossRef]

1966

1963

Ashizuka, Y.

T. Shimura, S. Ichimura, Y. Ashizuka, R. Fujimura, K. Kuroda, X. D. Tan, and H. Horimai, "Shift selectivity of the collinear holographic storage system," Proc. of SPIE 6282, 62820s (2006).
[CrossRef]

Bashaw, M. C.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, "Holographic data storage systems," inProceedings of IEEE 92, 1231-1280 (2004).
[CrossRef]

Fujimura, R.

T. Shimura, S. Ichimura, R. Fujimura, K. Kuroda, X. D. Tan and H. Horimai, "Analysis of a collinear holographic storage system: introduction of pixel spread function," Opt. Letters 31, 1208-1210 (2006).
[CrossRef]

T. Shimura, S. Ichimura, Y. Ashizuka, R. Fujimura, K. Kuroda, X. D. Tan, and H. Horimai, "Shift selectivity of the collinear holographic storage system," Proc. of SPIE 6282, 62820s (2006).
[CrossRef]

Fukumoto, A.

S. R. Lambourdiere, A. Fukumoto, K. Tanaka, and K. Watanabe, "Simulation of holographic data storage for the optical collinear system," Jpn. J. Appl. Phys. 45, 1246-1252 (2006).
[CrossRef]

Hesselink, L.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, "Holographic data storage systems," inProceedings of IEEE 92, 1231-1280 (2004).
[CrossRef]

Horimai, H.

T. Shimura, S. Ichimura, R. Fujimura, K. Kuroda, X. D. Tan and H. Horimai, "Analysis of a collinear holographic storage system: introduction of pixel spread function," Opt. Letters 31, 1208-1210 (2006).
[CrossRef]

T. Shimura, S. Ichimura, Y. Ashizuka, R. Fujimura, K. Kuroda, X. D. Tan, and H. Horimai, "Shift selectivity of the collinear holographic storage system," Proc. of SPIE 6282, 62820s (2006).
[CrossRef]

H. Horimai and X. Tan, "Holographic versatile disc system," Proc. of SPIE 5939, 593901(2005).
[CrossRef]

H. Horimai and X. Tan, "Advanced collinear holography," Opt. Rev. 12, 90-92 (2005).
[CrossRef]

H. Horimai, X. D. Tan, and J. Li, "Collinear holography," Appl. Opt. 44, 2575-2579 (2005).
[CrossRef] [PubMed]

Ichimura, S.

T. Shimura, S. Ichimura, R. Fujimura, K. Kuroda, X. D. Tan and H. Horimai, "Analysis of a collinear holographic storage system: introduction of pixel spread function," Opt. Letters 31, 1208-1210 (2006).
[CrossRef]

T. Shimura, S. Ichimura, Y. Ashizuka, R. Fujimura, K. Kuroda, X. D. Tan, and H. Horimai, "Shift selectivity of the collinear holographic storage system," Proc. of SPIE 6282, 62820s (2006).
[CrossRef]

Kozma, A.

Kuroda, K.

T. Shimura, S. Ichimura, R. Fujimura, K. Kuroda, X. D. Tan and H. Horimai, "Analysis of a collinear holographic storage system: introduction of pixel spread function," Opt. Letters 31, 1208-1210 (2006).
[CrossRef]

T. Shimura, S. Ichimura, Y. Ashizuka, R. Fujimura, K. Kuroda, X. D. Tan, and H. Horimai, "Shift selectivity of the collinear holographic storage system," Proc. of SPIE 6282, 62820s (2006).
[CrossRef]

Lambourdiere, S. R.

S. R. Lambourdiere, A. Fukumoto, K. Tanaka, and K. Watanabe, "Simulation of holographic data storage for the optical collinear system," Jpn. J. Appl. Phys. 45, 1246-1252 (2006).
[CrossRef]

Leith, E. N.

Li, J.

Marks, J.

Massey, N.

Orlov, S. S.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, "Holographic data storage systems," inProceedings of IEEE 92, 1231-1280 (2004).
[CrossRef]

Shimura, T.

T. Shimura, S. Ichimura, R. Fujimura, K. Kuroda, X. D. Tan and H. Horimai, "Analysis of a collinear holographic storage system: introduction of pixel spread function," Opt. Letters 31, 1208-1210 (2006).
[CrossRef]

T. Shimura, S. Ichimura, Y. Ashizuka, R. Fujimura, K. Kuroda, X. D. Tan, and H. Horimai, "Shift selectivity of the collinear holographic storage system," Proc. of SPIE 6282, 62820s (2006).
[CrossRef]

Sun, C. C.

C. C. Sun, "A simplified model for diffraction analysis of volume holograms," Opt. Eng. 42, 1184-1185 (2003).
[CrossRef]

Tan, X.

H. Horimai and X. Tan, "Holographic versatile disc system," Proc. of SPIE 5939, 593901(2005).
[CrossRef]

H. Horimai and X. Tan, "Advanced collinear holography," Opt. Rev. 12, 90-92 (2005).
[CrossRef]

Tan, X. D.

T. Shimura, S. Ichimura, Y. Ashizuka, R. Fujimura, K. Kuroda, X. D. Tan, and H. Horimai, "Shift selectivity of the collinear holographic storage system," Proc. of SPIE 6282, 62820s (2006).
[CrossRef]

T. Shimura, S. Ichimura, R. Fujimura, K. Kuroda, X. D. Tan and H. Horimai, "Analysis of a collinear holographic storage system: introduction of pixel spread function," Opt. Letters 31, 1208-1210 (2006).
[CrossRef]

H. Horimai, X. D. Tan, and J. Li, "Collinear holography," Appl. Opt. 44, 2575-2579 (2005).
[CrossRef] [PubMed]

Tanaka, K.

S. R. Lambourdiere, A. Fukumoto, K. Tanaka, and K. Watanabe, "Simulation of holographic data storage for the optical collinear system," Jpn. J. Appl. Phys. 45, 1246-1252 (2006).
[CrossRef]

van Heerden, P. J.

Watanabe, K.

S. R. Lambourdiere, A. Fukumoto, K. Tanaka, and K. Watanabe, "Simulation of holographic data storage for the optical collinear system," Jpn. J. Appl. Phys. 45, 1246-1252 (2006).
[CrossRef]

Appl. Opt.

Jpn. J. Appl. Phys.

S. R. Lambourdiere, A. Fukumoto, K. Tanaka, and K. Watanabe, "Simulation of holographic data storage for the optical collinear system," Jpn. J. Appl. Phys. 45, 1246-1252 (2006).
[CrossRef]

Opt. Eng.

C. C. Sun, "A simplified model for diffraction analysis of volume holograms," Opt. Eng. 42, 1184-1185 (2003).
[CrossRef]

Opt. Letters

T. Shimura, S. Ichimura, R. Fujimura, K. Kuroda, X. D. Tan and H. Horimai, "Analysis of a collinear holographic storage system: introduction of pixel spread function," Opt. Letters 31, 1208-1210 (2006).
[CrossRef]

Opt. Rev.

H. Horimai and X. Tan, "Advanced collinear holography," Opt. Rev. 12, 90-92 (2005).
[CrossRef]

Proc. of SPIE

H. Horimai and X. Tan, "Holographic versatile disc system," Proc. of SPIE 5939, 593901(2005).
[CrossRef]

T. Shimura, S. Ichimura, Y. Ashizuka, R. Fujimura, K. Kuroda, X. D. Tan, and H. Horimai, "Shift selectivity of the collinear holographic storage system," Proc. of SPIE 6282, 62820s (2006).
[CrossRef]

Proceedings of IEEE

L. Hesselink, S. S. Orlov, and M. C. Bashaw, "Holographic data storage systems," inProceedings of IEEE 92, 1231-1280 (2004).
[CrossRef]

Other

H. Horimai, "Collinear holography," Proc. 5th Pacific Rim Conference on Lasers and Electro-Optics 1, 376-377 (2003).

K. Tanaka, H. Mori, M. Hara, K. Hirooka, A. Fukumoto, and K. Watanabe, "High density recording of 270 Gbits/inch2 in a coaxial holographic storage system," Tech. Digest of ISOM 2007, MO-D-03.

H. Horimai and J. Li, "A novel collinear optical setup for holographic data storage system," in Proc. of SPIE 5380, 297-303 (2004).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 2002).

G. Barbastathis and D. Psaltis, "Volume holographic multiplexing methods," in Holographic Data Storage, H. J. Coufal, D. Psaltis, and G. T. Sincerbox, eds. (Springer-Verlag, 2000) pp.21-22.

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Figures (8)

Fig. 1.
Fig. 1.

Transmission model of the collinear algorithm for (a) writing process and (b) reading process.

Fig. 2.
Fig. 2.

Four different reference patterns: (a) radial line, (b) multi-ring, (c) horizontal lines. and (d) vertical lines.

Fig. 3.
Fig. 3.

Calculation of intensity of the PSF for the four different reference patterns in Fig. 2.

Fig. 4
Fig. 4

Four whirl structures used for the reference patterns.

Fig. 5.
Fig. 5.

Calculation of intensity of the PSFs in comparison with that of the radial pattern.

Fig. 6.
Fig. 6.

Reference patterns and corresponding simulated diffracted patterns on the output plane: (a) radial pattern, (b) extended radial pattern, and (c) cross-whirl pattern.

Fig. 7.
Fig. 7.

Relative diffraction intensity vs. displacement of the disc.

Fig. 8.
Fig. 8.

The 1-D PSF of the holographic discs in different thickness.

Equations (19)

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U disk ( u , v , Δ z ) = exp ( jk Δ z ) j λ Δ z U f ( u , v ) exp ( j k 2 Δ z ( u 2 + v 2 ) ) ,
U f ( u , v ) = exp ( ik 2 f ) j λ f U i ( x , y ) exp ( j 2 π λ f ( xu + yv ) ) dx dy .
S ( u , v , Δ z ) = exp ( jk ( 2 f + Δ z ) ) f Δ z { U s ( x , y ) } exp ( j k 2 Δ z ( u 2 + v 2 ) )
= exp ( jk ( 2 f + Δ z ) ) j λ f { U s ( x , y ) exp ( j π Δ z λ f 2 ( x 2 + y 2 ) ) } ,
R ( u , v , Δ z ) = exp ( jk ( 2 f + Δ z ) ) j λ f { U r ( x , y ) exp ( j π Δ z λ f 2 ( x 2 + y 2 ) ) } ,
P ( u , v , Δ z ) = exp ( jk ( 2 f + Δ z ) ) j λ f { U p ( x , y ) exp ( j π Δ z λ f 2 ( x 2 + y 2 ) ) } ,
I = R 2 + S 2 + R * S + R S * .
D = ( R 2 + S 2 ) P + PR * S + PRS * .
U df ( u , v , Δ z ) = exp ( jk 2 f ) λ 2 f Δ z { { U p ( x , y ) exp ( j π Δ z λ f 2 ( x 2 + y 2 ) ) } { U r * ( x , y ) exp ( j π Δ z λ f 2 ( x 2 + y 2 ) ) } { U s ( x , y ) exp ( j π Δ z λ f 2 ( x 2 + y 2 ) ) } } exp ( jk 2 Δ z ( u 2 + v 2 ) ) .
U d ( ξ , η , Δ z ) = exp ( jk 4 f ) ( λ f ) 2 exp [ j π Δ z λ f 2 ( ξ 2 + η 2 ) ] [ U p ( ξ , η ) exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) ]
[ U r * ( ξ , η ) exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) ] [ U s ( ξ , η ) exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) ] .
U det ( ξ , η ) = exp ( jk 4 f ) ( λ f ) 2 T T exp [ j π Δ z λ f 2 ( ξ 2 + η 2 ) ] { [ U p ( ξ , η ) exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) ] [ U r * ( ξ , η ) exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) ] [ U s ( ξ , η ) exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) ] } d Δ z .
PSF ( ξ , η ) = exp ( jk 4 f ) ( λ f ) 2 T T exp [ j π Δ z λ f 2 ( ξ 2 + η 2 ) ] · { δ ( ξ , η ) psfz ( ξ , η , Δ z ) } d Δ z ,
psfz = [ U p ( ξ , η ) exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) ] [ U r * ( ξ , η ) exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) ] .
SNR = ( m 1 m 0 ) ( σ 0 2 + σ 1 2 ) 1 2 ,
D det ( ξ , η , Δ u , Δ v ) =
exp ( jk 4 f ) ( λ f ) 2 exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) { [ U p ( ξ , η ) exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) ] [ exp ( j 2 π λ f ( Δ u ξ + Δ v η ) ) U R ( ξ , η ) * exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) ] [ exp ( j 2 π λ f ( Δ u ξ + Δ v η ) ) U s ( ξ , η ) exp ( j π Δ z λ f 2 ( ξ 2 + η 2 ) ) ] } d Δ z .
D det ( ξ , η , Δ u , Δ v ) =
2 T exp ( jk 4 f ) ( λ f ) 2 exp ( j 2 π λ f ( Δ u . ξ + Δ v . η ) ) { U S ( ξ + ξ 2 , η + η 2 ) U R * ( ξ 2 ξ 1 , η 2 η 1 ) U P ( ξ 1 , η 1 ) exp ( j 2 π λ f ( Δ u · ξ 1 + Δ v · η 1 ) ) sin c [ 2 T λ f 2 ( ξ · ξ 2 + η · η 2 ξ 2 ξ 1 η 2 · η 1 ) ] } d η 1 d η 2 d ζ 1 d ξ 2 ,

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