Abstract

In a spectroholographic storage system the defocusing method is often used to obtain spectrum uniformity and improve the quality of the recorded information. However, defocusing introduces vignette and stronger interpixel cross talk in the marginal field of view. We report a method that defocuses the aperture and medium together. Based on the pixel spread function, two inequalities are introduced to estimate the upper and lower bounds of the energy received at the CCD. We balance the spectrum uniformity with interpixel cross talk and vignette and then allow the designer to select optimal structure values of the defocusing spectroholographic storage system, i.e., the defocusing value, aperture size, and fill factors for the spatial light modulator and CCD.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. H. J. Coufal, D. Psaltis, and G. Sincerbox, eds., Holographic Data Storage (Springer-Verlag, 2000).
  2. G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, M. Jurich, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, R. M. Macfarlane, and R. M. Shelby, "Progress in read-write fast-access volume holographic data storage," Proc. SPIE 4459, 290-304 (2001).
    [CrossRef]
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  4. R. K. Kostuk, M. P. Bernal Artajona, and Q. Gao, "Beam conditioning techniques for holographic recording systems," in Holographic Data Storage, H. J. Coufal, D. Psaltis, and G. Sincerbox, eds. (Springer-Verlag, 2000).
  5. Q. Gao and R. Kostuk, "Improvement to holographic digital data-storage systems with random and pseudorandom phase masks," Appl. Opt. 36, 4853-4861 (1997).
    [CrossRef] [PubMed]
  6. G. W. Burr, C. M. Jefferson, H. Coufal, M. Jurich, J. A. Hoffnagle, R. M. Macfarlane, and R. M. Shelby, "Volume holographic data storage at an areal density of 250 gigapixels/in.2," Opt. Lett. 26, 444-446 (2001).
    [CrossRef]
  7. Z. Wang, G. Jin, Q. He, and M. Wu, "Comparisons of defocusing and fractional Fourier transform in spectro-holographic storage," Appl. Opt. 43, 4896-4901 (2004).
    [CrossRef] [PubMed]
  8. V. Vadde and B. B. K. V. Kumar, "Channel modeling and estimation for intrapage equalization in pixel-matched volume holographic data storage," Appl. Opt. 38, 4374-4386 (1999).
    [CrossRef]
  9. M.-P. Bernal, G. W. Burr, H. Coufal, and M. Quintanilla, "Balancing inter-pixel crosstalk and thermal noise to optimize areal density in holographic storage systems," Appl. Opt. 37, 5377-5385 (1998).
    [CrossRef]
  10. J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, 2001), Chap. 9.
  11. K. R. Castleman, Digital Image Processing (Prentice-Hall, 1996), Chap. 12.

2004 (1)

2001 (2)

G. W. Burr, C. M. Jefferson, H. Coufal, M. Jurich, J. A. Hoffnagle, R. M. Macfarlane, and R. M. Shelby, "Volume holographic data storage at an areal density of 250 gigapixels/in.2," Opt. Lett. 26, 444-446 (2001).
[CrossRef]

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, M. Jurich, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, R. M. Macfarlane, and R. M. Shelby, "Progress in read-write fast-access volume holographic data storage," Proc. SPIE 4459, 290-304 (2001).
[CrossRef]

1999 (1)

1998 (1)

1997 (1)

Appl. Opt. (4)

Opt. Lett. (1)

Proc. SPIE (1)

G. W. Burr, E. Mecher, T. Juchem, H. Coufal, C. M. Jefferson, M. Jurich, F. Gallego, K. Meerholz, N. Hampp, J. A. Hoffnagle, R. M. Macfarlane, and R. M. Shelby, "Progress in read-write fast-access volume holographic data storage," Proc. SPIE 4459, 290-304 (2001).
[CrossRef]

Other (5)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

R. K. Kostuk, M. P. Bernal Artajona, and Q. Gao, "Beam conditioning techniques for holographic recording systems," in Holographic Data Storage, H. J. Coufal, D. Psaltis, and G. Sincerbox, eds. (Springer-Verlag, 2000).

J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, 2001), Chap. 9.

K. R. Castleman, Digital Image Processing (Prentice-Hall, 1996), Chap. 12.

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Defocusing 4f system for spectroholographic storage. Data are imprinted onto an object beam by shining laser light through a SLM. A pair of lenses images the data through the defocused storage material onto a CCD.

Fig. 2
Fig. 2

Nine pixel pattern used to study interpixel cross talk. The linear fill factors are defined as Γ S L M _ X = τ x / T x and Γ S L M _ Y = τ y / T y .

Fig. 3
Fig. 3

Intensity distribution at CCD | U 3 ( x ) | 2 , different values for c, κ = 1 .

Fig. 4
Fig. 4

Intensity distribution at CCD | U 3 ( x ) | 2 , different values for κ, c = 0 .

Fig. 5
Fig. 5

Consideration of the SLM linear fill factor Γ 0 ( κ , 1 ) .

Fig. 6
Fig. 6

Digitalization effects in the time (left column) and frequency (right column) domains ( d = 1 / T , τ = T , τ = T ) . (a) Focus recording c = 0 , (b) defocusing case c = 1 , (c) defocusing case c = 2 . (Amplitude of every figure is normalized by its peak value.)

Fig. 7
Fig. 7

Relative cross talk versus aperture κ ( c = 0 ) . (a) E x (1), (b) E y (1).

Fig. 8
Fig. 8

Interpixel cross talk E x ( 1 ) , E y ( 1 ) and energy I x ( 0 ) , I y ( 0 ) versus relative position c x and c y for κ x = 0.568 and κ y = 0.483 . (a) Relative cross talk E x ( 1 ) versus c x , (b) energy I x ( 0 ) versus c x , (c) relative cross talk E y ( 1 ) versus c y , (d) energy I y ( 0 ) versus c y .

Fig. 9
Fig. 9

Spectral distribution of (a) the focus plane ( δ = 0 ) and (b) the recording plane ( δ = 0.32 δ s p e c i a l _ y ) for κ x = 0.568 , κ y = 0.483 , f 1 = 154.6   mm , λ = 532 × 10 6   mm , M = 512 , N = 384 , τ x = 16 × 10 3   mm , τ y = 23 × 10 3   mm , T x = T y = 26 × 10 3   mm , and a ( m , n ) = 1 , m = 25 m , m = 2 0 , 19 ,   .   .   .   , 20 ; n = 25 n , n = 15 , 14 ,   .   .   .   , 15 and 0 otherwise. (Parameters are accordant to our storage system.)

Fig. 10
Fig. 10

Optimization of the aperture and defocusing.

Tables (2)

Tables Icon

Table 1 Energy I ( p , q ) of the Central Viewing Field and Marginal Viewing Fields

Tables Icon

Table 2 Interpixel Cross Talk of the Central and Marginal Viewing Fields

Equations (18)

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

U 2 ( x 2 , y 2 ) = C τ x τ y m = M M n = N N α ( m , n ) P x P y × sinc ( τ x f ε ) sinc ( τ y f η ) ,
{ P x = exp ( i π m 2 T x 2 δ λ f 1 ) exp ( i 2 π m T x f ε ) P y = exp ( i π n 2 T y 2 δ λ f 1 ) exp ( i 2 π n T y f η ) , { f ε = x 2 δ m T x λ f 1 f η = y 2 δ n T y λ f 1 ,
U 3 ( x ) = 1 / 2 1 / 2 exp ( i 2 π κ x c x x u ) sinc [ 2 κ x ( x x u ) ] d x u 1 / 2 1 / 2 sinc ( 2 κ x x u ) d x u ,
c x = δ 0.5 d x m T x .
U 3 ( x , y ) = m = M M n = N N α ( m , n ) U 3 ( x + m Γ S L M _ X ) × U 3 ( y + n Γ S L M _ Y ) .
I ( p , q ) = a b c d | m = M M n = N N α ( m , n ) U 3 ( x + m Γ S L M _ X ) × U 3 ( y + n Γ S L M _ Y ) | 2 d x d y ,
I ( p , q ) = a b | U 3 ( x ) | 2 d x c d | U 3 ( y ) | 2 d y = d e f I x ( p ) I y ( q ) .
E ( p , q ) = I x ( p ) I x ( 0 ) I y ( q ) I y ( 0 ) = d e f E x ( p ) E y ( q ) .
I ( p , q ) a b c d ( m = M M n = N N α ( m , n ) | U 3 ( x + m Γ S L M _ X ) | × | U 3 ( y + n Γ S L M _ Y ) | ) 2 d x d y ( m = M M n = N N ( a b c d α 2 ( m , n ) | U 3 ( x + m Γ S L M _ X ) | 2 × | U 3 ( y + n Γ S L M _ Y ) | 2 d x d y ) 1 / 2 ) 2 .
U 3 ( x + m Γ S L M _ X ) U 3 ( y + n Γ S L M _ Y ) = C U 3 ( x + m Γ S L M _ X ) × U 3 ( y + n Γ S L M _ Y ) ,
I ( 0 , 0 ) ( m = 1 1 n = 1 1 ( α ( m , n ) I x ( m ) I y ( n ) ) 1 / 2 ) 2 ,
g = | m = M M n = N N α ( m , n ) U 3 ( x + m Γ S L M _ X ) × U 3 ( y + n Γ S L M _ Y ) | ,
I ( p , q ) 1 ( b a ) ( d c ) | a b c d | m = M M n = N N α ( m , n ) × U 3 ( x + m Γ S L M _ X ) U 3 ( y + n Γ S L M _ Y ) | d x d y | 2 .
Γ 0 ( κ , Γ C C D ) = d e f 2 Γ C C D 2 b ( κ ) ,
δ = min { c x 0.5 d x M T x , c y 0.5 d y N T y } .
I ˜ ( x ) m = δ ( x m T ) ,
m = δ ( x m / T ) .
δ = min ( c x 0.5 d x M T x , c y 0.5 d y N T y ) = c y 0.5 d y N T y ,

Metrics