Abstract

The cross talk noise-to-signal ratio (NSR) of an angle-multiplexed holographic data storage system is studied, and we propose a method to determine the optimized multiplexing spacing with which the cross talk noise can be less than the conventional method. In our method, the optimization location at the image plane can be chosen arbitrarily, so the multiplexing of asymmetrical image patterns can be optimized. In particular, we investigate the 90° scheme and the transmission scheme angle multiplexing. For the 90° scheme, a holographic medium with a higher refractive index is recommended for cross talk-limited multiplexing. For the transmission scheme, a holographic medium with a lower refractive index is recommended for angular range-limited multiplexing. In addition, for the transmission scheme, a larger angle between the object arm and the reference arm results in less cross talk noise, whereas the highest storage density is achieved at a 45° angle.

© 2011 Optical Society of America

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References

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  1. H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds., Holographic Data Storage (Springer-Verlag, 2000).
  2. L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage system,” Proc. IEEE 92, 1231–1280 (2004).
    [CrossRef]
  3. F. H. Mok, M. C. Tackitt, and H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3 crystal,” Opt. Lett. 16, 605–607 (1991).
    [CrossRef] [PubMed]
  4. F. H. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
    [CrossRef] [PubMed]
  5. D. Psaltis, M. Levene, A. Pu, G. Barbastathis, and K. Curtis, “Holographic storage using shift multiplexing,” Opt. Lett. 20, 782–784 (1995).
    [CrossRef] [PubMed]
  6. G. Barbastathis, M. Levene, and D. Psaltis, “Shift multiplexing with spherical reference waves,” Appl. Opt. 35, 2403–2417(1996).
    [CrossRef] [PubMed]
  7. G. Barbastathis and D. Psaltis, “Shift-multiplexed holographic memory using the two-lambda method,” Opt. Lett. 21, 432–434(1996).
    [CrossRef] [PubMed]
  8. 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]
  9. C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, “Potentialities and limitations of hologram multiplexing using the phase-encoding technique,” Appl. Opt. 31, 5700–5705 (1992).
    [CrossRef] [PubMed]
  10. M. C. Bashaw, J. F. Heanue, A. Aharoni, J. F. Walkup, and L. Hesselink, “Cross-talk considerations for angular and phase-encoded multiplexing in volume holography,” J. Opt. Soc. Am. B 11, 1820–1836 (1994).
    [CrossRef]
  11. J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Sparse selection of reference beams for wavelength and angular-multiplexed volume holography,” J. Opt. Soc. Am. A 12, 1671–1676 (1995).
    [CrossRef]
  12. X. Yi, P. Yeh, C. Gu, and S. Campbell, “Crosstalk in volume holographic memory,” Proc. IEEE 87, 1912–1930 (1999).
    [CrossRef]
  13. C. Gu, J. Hong, I. McMichael, R. Saxena, and F. Mok, “Cross-talk-limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
    [CrossRef]
  14. K. Curtis and D. Psaltis, “Cross talk for angle- and wavelength-multiplexed image plane holograms,” Opt. Lett. 19, 1774–1776(1994).
    [CrossRef] [PubMed]
  15. X. Yi, S. Campbell, P. Yeh, and C. Gu, “Statistical analysis of cross-talk noise and storage capacity in volume holographic memory: image plane holograms,” Opt. Lett. 20, 779–781 (1995).
    [CrossRef] [PubMed]
  16. F. Dai and C. Gu, “Effect of Gaussian references on cross-talk noise reduction in volume holographic memory,” Opt. Lett. 22, 1802–1804 (1997).
    [CrossRef]
  17. M. A. Neifeld and M. McDonald, “Technique for controlling cross-talk noise in volume holography,” Opt. Lett. 21, 1298–1300(1996).
    [CrossRef] [PubMed]
  18. C. Gu and F. Dai, “Cross-talk noise reduction in volume holographic storage with an extended recording reference,” Opt. Lett. 20, 2336–2338 (1995).
    [CrossRef] [PubMed]
  19. F. Dai and C. Gu, “Statistical analysis on extended reference method for volume holographic data storage,” Opt. Eng. 36, 1691–1699 (1997).
    [CrossRef]
  20. C.-C. Sun, “Simplified model for diffraction analysis of volume holograms,” Opt. Eng. 42, 1184–1185 (2003).
    [CrossRef]

2004 (1)

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage system,” Proc. IEEE 92, 1231–1280 (2004).
[CrossRef]

2003 (1)

C.-C. Sun, “Simplified model for diffraction analysis of volume holograms,” Opt. Eng. 42, 1184–1185 (2003).
[CrossRef]

1999 (1)

X. Yi, P. Yeh, C. Gu, and S. Campbell, “Crosstalk in volume holographic memory,” Proc. IEEE 87, 1912–1930 (1999).
[CrossRef]

1997 (2)

F. Dai and C. Gu, “Statistical analysis on extended reference method for volume holographic data storage,” Opt. Eng. 36, 1691–1699 (1997).
[CrossRef]

F. Dai and C. Gu, “Effect of Gaussian references on cross-talk noise reduction in volume holographic memory,” Opt. Lett. 22, 1802–1804 (1997).
[CrossRef]

1996 (3)

1995 (4)

1994 (2)

1993 (1)

1992 (2)

1991 (2)

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

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]

Aharoni, A.

Barbastathis, G.

Bashaw, M. C.

Campbell, S.

Curtis, K.

Dai, F.

Denz, C.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, “Potentialities and limitations of hologram multiplexing using the phase-encoding technique,” Appl. Opt. 31, 5700–5705 (1992).
[CrossRef] [PubMed]

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]

Gu, C.

Heanue, J. F.

Hesselink, L.

Hong, J.

Levene, M.

McDonald, M.

McMichael, I.

Mok, F.

Mok, F. H.

Neifeld, M. A.

Orlov, S. S.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage system,” Proc. IEEE 92, 1231–1280 (2004).
[CrossRef]

Pauliat, G.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, “Potentialities and limitations of hologram multiplexing using the phase-encoding technique,” Appl. Opt. 31, 5700–5705 (1992).
[CrossRef] [PubMed]

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.

Roosen, G.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, “Potentialities and limitations of hologram multiplexing using the phase-encoding technique,” Appl. Opt. 31, 5700–5705 (1992).
[CrossRef] [PubMed]

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]

Saxena, R.

Stoll, H. M.

Sun, C.-C.

C.-C. Sun, “Simplified model for diffraction analysis of volume holograms,” Opt. Eng. 42, 1184–1185 (2003).
[CrossRef]

Tackitt, M. C.

Tschudi, T.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, “Potentialities and limitations of hologram multiplexing using the phase-encoding technique,” Appl. Opt. 31, 5700–5705 (1992).
[CrossRef] [PubMed]

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]

Walkup, J. F.

Yeh, P.

Yi, X.

Appl. Opt. (2)

J. Opt. Soc. Am. A (2)

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

Opt. Commun. (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]

Opt. Eng. (2)

F. Dai and C. Gu, “Statistical analysis on extended reference method for volume holographic data storage,” Opt. Eng. 36, 1691–1699 (1997).
[CrossRef]

C.-C. Sun, “Simplified model for diffraction analysis of volume holograms,” Opt. Eng. 42, 1184–1185 (2003).
[CrossRef]

Opt. Lett. (9)

Proc. IEEE (2)

X. Yi, P. Yeh, C. Gu, and S. Campbell, “Crosstalk in volume holographic memory,” Proc. IEEE 87, 1912–1930 (1999).
[CrossRef]

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage system,” Proc. IEEE 92, 1231–1280 (2004).
[CrossRef]

Other (1)

H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds., Holographic Data Storage (Springer-Verlag, 2000).

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Figures (11)

Fig. 1
Fig. 1

Schematic of an angle-multiplexing HDS. f 1 , f 2 , and f 3 are the focal lengths of lenses L 1 , L 2 , and L 3 , respectively. θ is the angle between the reference arm and the signal arm measured in air. The spectrum coordinate ( x , y , z ) (not shown in the figure) coincides with ( x , y , z ) , which is the coordinate of the holographic medium.

Fig. 2
Fig. 2

Two cases of the refraction between the air and a cubic holographic medium.

Fig. 3
Fig. 3

NSR as a function of both the location at the output plane ( y 2 / f 2 ) and the page level (i) for the 90 ° scheme optimized at y 2 = 0 .

Fig. 4
Fig. 4

NSR as a function of both the location at the output plane ( y 2 / f 2 ) and the page level (i) for the 90 ° scheme optimized at y 2 = 0.1 f 2 .

Fig. 5
Fig. 5

Mean NSR and AR as a function of the refractive index (n) for the 90 ° scheme.

Fig. 6
Fig. 6

Mean NSR and AR as a function of the optimization location ( y 2 / f 2 ) for the 90 ° scheme.

Fig. 7
Fig. 7

NSR as a function of both the location at the output plane ( y 2 / f 2 ) and the page level (i) for the transmission scheme optimized at y 2 = 0 .

Fig. 8
Fig. 8

NSR as a function of both the location at the output plane ( y 2 / f 2 ) and the page level (i) for the transmission scheme optimized at y 2 = 0.05 f 2 .

Fig. 9
Fig. 9

Mean NSR and AR as a function of the refractive index (n) for the transmission scheme.

Fig. 10
Fig. 10

Mean NSR and AR as a function of the angle between the object light and the reference light (θ).

Fig. 11
Fig. 11

Mean NSR and AR as a function of the optimization location ( y 2 / f 2 ) for the transmission scheme.

Equations (24)

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k x = k x , k y = k y , and k z = ( 2 π λ n ) 2 k x 2 k y 2 2 π λ n λ 4 π n ( k x 2 + k y 2 ) ,
k x = k x , k z = k z , and k y = ( 2 π λ n ) 2 k x 2 k z 2 2 π λ n λ 4 π n ( k x 2 + k z 2 ) .
S m = d x 0 d y 0 f m ( x 0 , y 0 ) exp [ j π z λ n f 1 2 ( x 0 2 + y 0 2 ) ] exp [ j 2 π λ f 1 ( x 0 x + y 0 y ) ] ,
k d x = 2 π x 2 λ f 2 , k d y = 2 π y 2 λ f 2 , and k d z = 2 π n λ ( 1 x 2 2 2 n 2 f 2 2 y 2 2 2 n f 2 2 ) .
g i ( x 2 , y 2 ) = m = M M f m ( f 1 f 2 x 2 λ f 1 2 π Δ K m i x , f 1 f 2 y 2 λ f 1 2 π Δ K m i y ) × sinc [ t 2 π ( Δ K m i z + x 2 Δ K m i x + y 2 Δ K m i y n f 2 + λ ( Δ K m i x 2 + Δ K m i y 2 ) 4 π n ) ] ,
m i | f m ( f 1 f 2 x 2 , f 1 f 2 y 2 λ f 1 2 π Δ K m i y ) · sinc [ t 2 π ( Δ K m i z + y 2 Δ K m i y n f 2 + λ Δ K m i y 2 4 π n ) ] | 2 ,
NSR i = m i sinc 2 [ t 2 π ( Δ K m i z + y 2 n f 2 Δ K m i y + λ 4 π n Δ K m i y 2 ) ] .
k y = 2 π λ f r y r cos θ 2 π λ ( 1 y r 2 2 f r 2 ) sin θ , and k z = 2 π λ f r y r sin θ + 2 π λ ( 1 y r 2 2 f r 2 ) cos θ ,
Δ K m i z = λ 4 π n ( k i y 2 k m y 2 ) .
NSR i = m i sinc 2 { t ( y m y i ) λ n f r sin θ cos θ · [ 1 + y 2 f 2 sin θ + y i f r ( cot θ y i 2 f r ) ( y m + y i 2 f r ) ( tan θ + y 2 f 2 cos θ + y i f r ) ] } ,
NSR i = m i sinc 2 { ( k m z k i z ) · [ 1 + λ 4 π n ( k i z + k m z ) ( y 2 n f 2 + ( λ 4 π n ) 2 ( k i z 2 k m z 2 ) ) ] } .
NSR i = m i sinc 2 { t ( y m y i ) λ f r [ 1 ( y m + y i 2 nf r ) ( y 2 nf 2 y i 2 y m 2 4 n 2 f r 2 ) ] } .
NSR i m i sinc 2 { t ( y m y i ) λ f r [ 1 y 2 n f 2 ( y m + y i 2 n f r ) ] } .
δ = λ f r t .
t δ λ f r [ 1 y 2 n f 2 ( 2 y m + δ 2 n f r ) ] = 1 .
δ = ( n 2 f 2 f r y 2 y m ) n 2 f 2 f r y 2 [ ( y 2 y m n 2 f 2 f r 1 ) 2 2 y 2 λ t n 2 f 2 ] 1 / 2 ,
y m + 1 = n 2 f 2 f r y 2 { 1 [ ( y 2 y m n 2 f 2 f r 1 ) 2 2 y 2 λ t n 2 f 2 ] 1 / 2 } .
y m 1 = n 2 f 2 f r y 2 { 1 [ ( y 2 y m n 2 f 2 f r 1 ) 2 + 2 y 2 λ t n 2 f 2 ] 1 / 2 } .
AR = ( y m = M y m = M ) / f r .
NSR i = m i sinc 2 { t ( y m y i ) λ n f r sin θ cos θ · [ 1 + y 2 f 2 sin θ + y i f r cot θ ( y m + y i 2 f r ) ( tan θ + y 2 f 2 cos θ ) ] } .
t δ + λ n f r sin θ cos θ · [ 1 + y 2 f 2 sin θ + ( y m + δ + f r ) cot θ ( 2 y m + δ + 2 f r ) ( tan θ + y 2 f 2 cos θ ) ] = 1 ,
δ + = B + B 2 4 A C 2 A , where     A = ( 2 cot θ tan θ ) 2 f r y 2 2 f r f 2 cos θ , B = 1 + y 2 f 2 sin θ + y m ( cot θ tan θ ) f r y m y 2 f r f 2 cos θ , C = λ n f r t · sin θ cos θ .
δ = B + B 2 4 A C 2 A , and A = 1 2 f r ( tan θ + y 2 f 2 cos θ ) , B = 1 + y 2 f 2 sin θ + y m ( cot θ tan θ ) f r y m y 2 f r f 2 cos θ , C = λ nf r t · sin θ cos θ .
δ + = δ 2 λ n f r t

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