Abstract

In spectroholographic storage systems the defocusing method is often used for spectrum uniformity and quality improvement of recorded information. The same purpose is served by the fractional Fourier transform (FRFT) storage system. To simplify the numerical analysis, we derive the expressions of the Fraunhofer spectrum and the reconstructed image at the detected plane (CCD) for both cases instead of using the Fresnel spectrum and the FRFT spectrum. The recording aperture, spectrum uniformity, and reconstructed information of both systems are investigated. A numerical comparison is also presented.

© 2004 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  2. R. K. Kostuk, M. P. Bernal Artajona, Q. Gao, “Beam conditioning techniques for holographic recording systems,” in Holographic Data Storage, H. J. Coufal, D. Psaltis, G. Sincerbox, eds. (Springer-Verlag, Berlin, 2000).
    [CrossRef]
  3. S. Jin, Y.-S. Bae, S.-Y. Lee, “Holographic data storage with fractional Fourier transform,” Opt. Commun. 198, 57–63 (2001).
    [CrossRef]
  4. A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1988).
  5. S. Feijun, S. Jutamulia, Advanced Optical Information Processing (Peking University Press, Beijing, 1998).
  6. L. M. Bernardo, O. D. D. Soares, “Fractional Fourier transforms and imaging,” J. Opt. Soc. Am. A 11, 2622–2626 (1994).
    [CrossRef]
  7. G. W. Burr, T. Weiss, “Compensation of pixel misregistration in volume holographic data storage,” Opt. Lett. 26, 542–544 (2001).
    [CrossRef]
  8. P. Pellat-Finet, “Fresnel diffraction and the fractional order Fourier transform,” Opt. Lett. 19, 1388–1390 (1994).
    [CrossRef] [PubMed]
  9. V. Vadde, B. B. K. Vijaya Kumar, “Channel modeling and estimates for intrapage equalization in pixel-matched volume holographic data storage,” Appl. Opt. 38, 4374–4386 (1999).
    [CrossRef]
  10. M.-P. Bernal, G. W. Burr, H. Coufal, M. Quintanilla, “Balancing interpixel cross talk and detector noise to optimize areal density in holographic storage systems,” Appl. Opt. 37, 5377–5385 (1998).
    [CrossRef]

2001 (2)

S. Jin, Y.-S. Bae, S.-Y. Lee, “Holographic data storage with fractional Fourier transform,” Opt. Commun. 198, 57–63 (2001).
[CrossRef]

G. W. Burr, T. Weiss, “Compensation of pixel misregistration in volume holographic data storage,” Opt. Lett. 26, 542–544 (2001).
[CrossRef]

1999 (1)

1998 (1)

1994 (2)

Bae, Y.-S.

S. Jin, Y.-S. Bae, S.-Y. Lee, “Holographic data storage with fractional Fourier transform,” Opt. Commun. 198, 57–63 (2001).
[CrossRef]

Bernal, M.-P.

Bernal Artajona, M. P.

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

Bernardo, L. M.

Burr, G. W.

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1988).

Coufal, H.

Feijun, S.

S. Feijun, S. Jutamulia, Advanced Optical Information Processing (Peking University Press, Beijing, 1998).

Gao, Q.

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

Goodman, J. W.

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

Jin, S.

S. Jin, Y.-S. Bae, S.-Y. Lee, “Holographic data storage with fractional Fourier transform,” Opt. Commun. 198, 57–63 (2001).
[CrossRef]

Jutamulia, S.

S. Feijun, S. Jutamulia, Advanced Optical Information Processing (Peking University Press, Beijing, 1998).

Kostuk, R. K.

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

Lee, S.-Y.

S. Jin, Y.-S. Bae, S.-Y. Lee, “Holographic data storage with fractional Fourier transform,” Opt. Commun. 198, 57–63 (2001).
[CrossRef]

Pellat-Finet, P.

Quintanilla, M.

Soares, O. D. D.

Vadde, V.

Vijaya Kumar, B. B. K.

Weiss, T.

Appl. Opt. (2)

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

Opt. Commun. (1)

S. Jin, Y.-S. Bae, S.-Y. Lee, “Holographic data storage with fractional Fourier transform,” Opt. Commun. 198, 57–63 (2001).
[CrossRef]

Opt. Lett. (2)

Other (4)

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1988).

S. Feijun, S. Jutamulia, Advanced Optical Information Processing (Peking University Press, Beijing, 1998).

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

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

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Figures (4)

Fig. 1
Fig. 1

(a) Defocusing recording system and (b) the FRFT recording system. Our sign conventions are based on those given in Ref. 4.

Fig. 2
Fig. 2

Intensity distribution at CCD |U 3′|2.

Fig. 3
Fig. 3

Spectral distribution of (a) δ = 0, (b) defocusing δ = (d y /D y ), (c) FRFT defocusing δ = (d y /D y ). κ x = κ y = 1, 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, am, n= 1,m=25m, m=-20, -19,, 20;n=25n, n=-15, -14,, 150,others.

Fig. 4
Fig. 4

Relative error ψ(ε, 0.4).

Equations (12)

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U2x2, y2=C0 t1x1, y1expik2f1Δff1x12+y12-2x1x2+y1y2dx1dy1, t1x1, y1=m=-MMn=-NN am, nrectx1-mTxτx×recty1-mTyτy,
U2x2=C expik2f1δm2Tx2-2x2mTx -+rectxτx× expikδ2f1 x2-ikf1x2-δmTxxdx,
U2x2=C exp- ikm2Tx2δ2f1exp-i2πmTxfετx×sincτxfε|fε= x2-δmTxλf1.
U3x=C λf1κxτx-τx/2τx/2expi2πκxcxxuτx ×sinc2κxx-xuτxdxu,
U2x2, y2=C expik cos αx22+y222f˜ sin α  t1x1, y1 ×expik2cos αx12+y12f˜ sin α- 2x1x2+y1y2f˜ sin αdx1dy1 f˜=f1 sin α,
U2ε, α=C -+rectxτxexpikf1 sin2 α εxdx=Cτx sincτxfεfε= ελf1 sin2 α,ε=x2-mTx cos α,
C=C0 expik2f1 sin2 α-m2Tx2 cos α sin2 α-2εmTx sin2 α+ε2 cos α.
d1 tan-U+f1 tan-U=d/2 d1 tan-U+d1 tan-U=d/2 tan U=tan U-d1 tan U/f1.
U3x=C λf1κxτx-τx/2τx/2expi2πκrxcxxuτx×sinc2κrxx-xuτxdxu,
y1ε, δ= -+ rectxτxexpikδ2f1 x2-ikf1 εxdx, y2ε=-+ rectxτxexp- ikf1 εxdx,
ψε, δ= y1ε, δ-y2εy1ε, δ.
am, n= 1,m=25m, m=-20, -19,, 20;n=25n, n=-15, -14,, 150,others.

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