Abstract

We demonstrate a method to optimize the reconstruction of a hologram when the storage device has a limited dynamic range and a minimum grain size. The optimal solution at the recording plane occurs when the object wave has propagated an intermediate distance between the near and far fields. This distance corresponds to an optimal order and magnification of the fractional Fourier transform of the object.

© 2011 Optical Society of America

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2011

E. Sejdić, I. Djurović, and L. Stanković, Signal Process. 91, 1351 (2011).
[CrossRef]

2010

J. Sha, J.-K. Lee, S. Kang, V. M. Prabhu, C. L. Soles, P. V. Bonnesen, and C. K. Ober, Chem. Mater. 22, 3093 (2010).
[CrossRef]

2009

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photon. 3, 211 (2009).
[CrossRef]

2008

N. Singh and A. Sinha, Opt. Lasers Eng. 46, 117 (2008).
[CrossRef]

2004

2003

N. K. Nischal, J. Joseph, and K. Singh, Opt. Eng. 42, 1583 (2003).
[CrossRef]

2002

D. Psaltis, Science 298, 1359 (2002).
[CrossRef] [PubMed]

2001

J. Sang-il, B. You-Seok, and L. Soo-Young, Opt. Commun. 198, 57 (2001).
[CrossRef]

1998

K. Buse, A. Adibi, and D. Psaltis, Nature 393, 665 (1998).
[CrossRef]

G. W. Burr, J. J. Ashley, B. Marcus, C. M. Jefferson, J. A. Hoffnagle, and H. J. Coufal, Proc. SPIE 3468, 64 (1998).
[CrossRef]

1997

K. Buse, Appl. Phys. B 64, 273 (1997).
[CrossRef]

1996

H. Ramenah, P. Bertrand, E. H. Soubari, and P. Meyrueis, Opt. Lasers Eng. 28, 589 (1996).
[CrossRef]

1995

1993

D. Mendlovic and H. M. Ozatkas, J. Opt. Soc. Am. A 10, 1875 (1993).
[CrossRef]

A. M. Eskicioglu and P. S. Fisher, NASA Conf. Publ. 3191, 49 (1993).

1983

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University, 1983).

1980

1977

A. Yariv, Opt. Commun. 21, 49 (1977).
[CrossRef]

1971

Adibi, A.

K. Buse, A. Adibi, and D. Psaltis, Nature 393, 665 (1998).
[CrossRef]

Ashley, J. J.

G. W. Burr, J. J. Ashley, B. Marcus, C. M. Jefferson, J. A. Hoffnagle, and H. J. Coufal, Proc. SPIE 3468, 64 (1998).
[CrossRef]

Barsi, C.

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photon. 3, 211 (2009).
[CrossRef]

Bertrand, P.

H. Ramenah, P. Bertrand, E. H. Soubari, and P. Meyrueis, Opt. Lasers Eng. 28, 589 (1996).
[CrossRef]

Bonnesen, P. V.

J. Sha, J.-K. Lee, S. Kang, V. M. Prabhu, C. L. Soles, P. V. Bonnesen, and C. K. Ober, Chem. Mater. 22, 3093 (2010).
[CrossRef]

Burr, G. W.

G. W. Burr, J. J. Ashley, B. Marcus, C. M. Jefferson, J. A. Hoffnagle, and H. J. Coufal, Proc. SPIE 3468, 64 (1998).
[CrossRef]

Buse, K.

K. Buse, A. Adibi, and D. Psaltis, Nature 393, 665 (1998).
[CrossRef]

K. Buse, Appl. Phys. B 64, 273 (1997).
[CrossRef]

Coufal, H. J.

G. W. Burr, J. J. Ashley, B. Marcus, C. M. Jefferson, J. A. Hoffnagle, and H. J. Coufal, Proc. SPIE 3468, 64 (1998).
[CrossRef]

Djurovic, I.

E. Sejdić, I. Djurović, and L. Stanković, Signal Process. 91, 1351 (2011).
[CrossRef]

Eskicioglu, A. M.

A. M. Eskicioglu and P. S. Fisher, NASA Conf. Publ. 3191, 49 (1993).

Feinberg, J.

Fisher, P. S.

A. M. Eskicioglu and P. S. Fisher, NASA Conf. Publ. 3191, 49 (1993).

Fleischer, J. W.

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photon. 3, 211 (2009).
[CrossRef]

Greer, M. O.

He, Q.

Hoffnagle, J. A.

G. W. Burr, J. J. Ashley, B. Marcus, C. M. Jefferson, J. A. Hoffnagle, and H. J. Coufal, Proc. SPIE 3468, 64 (1998).
[CrossRef]

Jefferson, C. M.

G. W. Burr, J. J. Ashley, B. Marcus, C. M. Jefferson, J. A. Hoffnagle, and H. J. Coufal, Proc. SPIE 3468, 64 (1998).
[CrossRef]

Jin, G.

Jones, R.

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University, 1983).

Joseph, J.

N. K. Nischal, J. Joseph, and K. Singh, Opt. Eng. 42, 1583 (2003).
[CrossRef]

Kang, S.

J. Sha, J.-K. Lee, S. Kang, V. M. Prabhu, C. L. Soles, P. V. Bonnesen, and C. K. Ober, Chem. Mater. 22, 3093 (2010).
[CrossRef]

Lee, J.-K.

J. Sha, J.-K. Lee, S. Kang, V. M. Prabhu, C. L. Soles, P. V. Bonnesen, and C. K. Ober, Chem. Mater. 22, 3093 (2010).
[CrossRef]

Lee, W. H.

Marcus, B.

G. W. Burr, J. J. Ashley, B. Marcus, C. M. Jefferson, J. A. Hoffnagle, and H. J. Coufal, Proc. SPIE 3468, 64 (1998).
[CrossRef]

Mendlovic, D.

Meyrueis, P.

H. Ramenah, P. Bertrand, E. H. Soubari, and P. Meyrueis, Opt. Lasers Eng. 28, 589 (1996).
[CrossRef]

Nischal, N. K.

N. K. Nischal, J. Joseph, and K. Singh, Opt. Eng. 42, 1583 (2003).
[CrossRef]

Ober, C. K.

J. Sha, J.-K. Lee, S. Kang, V. M. Prabhu, C. L. Soles, P. V. Bonnesen, and C. K. Ober, Chem. Mater. 22, 3093 (2010).
[CrossRef]

Ozaktas, H. M.

Ozatkas, H. M.

Prabhu, V. M.

J. Sha, J.-K. Lee, S. Kang, V. M. Prabhu, C. L. Soles, P. V. Bonnesen, and C. K. Ober, Chem. Mater. 22, 3093 (2010).
[CrossRef]

Psaltis, D.

D. Psaltis, Science 298, 1359 (2002).
[CrossRef] [PubMed]

K. Buse, A. Adibi, and D. Psaltis, Nature 393, 665 (1998).
[CrossRef]

Ramenah, H.

H. Ramenah, P. Bertrand, E. H. Soubari, and P. Meyrueis, Opt. Lasers Eng. 28, 589 (1996).
[CrossRef]

Sang-il, J.

J. Sang-il, B. You-Seok, and L. Soo-Young, Opt. Commun. 198, 57 (2001).
[CrossRef]

Sejdic, E.

E. Sejdić, I. Djurović, and L. Stanković, Signal Process. 91, 1351 (2011).
[CrossRef]

Sha, J.

J. Sha, J.-K. Lee, S. Kang, V. M. Prabhu, C. L. Soles, P. V. Bonnesen, and C. K. Ober, Chem. Mater. 22, 3093 (2010).
[CrossRef]

Singh, K.

N. K. Nischal, J. Joseph, and K. Singh, Opt. Eng. 42, 1583 (2003).
[CrossRef]

Singh, N.

N. Singh and A. Sinha, Opt. Lasers Eng. 46, 117 (2008).
[CrossRef]

Sinha, A.

N. Singh and A. Sinha, Opt. Lasers Eng. 46, 117 (2008).
[CrossRef]

Soles, C. L.

J. Sha, J.-K. Lee, S. Kang, V. M. Prabhu, C. L. Soles, P. V. Bonnesen, and C. K. Ober, Chem. Mater. 22, 3093 (2010).
[CrossRef]

Soo-Young, L.

J. Sang-il, B. You-Seok, and L. Soo-Young, Opt. Commun. 198, 57 (2001).
[CrossRef]

Soubari, E. H.

H. Ramenah, P. Bertrand, E. H. Soubari, and P. Meyrueis, Opt. Lasers Eng. 28, 589 (1996).
[CrossRef]

Stankovic, L.

E. Sejdić, I. Djurović, and L. Stanković, Signal Process. 91, 1351 (2011).
[CrossRef]

Wan, W.

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photon. 3, 211 (2009).
[CrossRef]

Wang, Z.

Wu, M.

Wykes, C.

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University, 1983).

Yariv, A.

A. Yariv, Opt. Commun. 21, 49 (1977).
[CrossRef]

You-Seok, B.

J. Sang-il, B. You-Seok, and L. Soo-Young, Opt. Commun. 198, 57 (2001).
[CrossRef]

Appl. Opt.

Appl. Phys. B

K. Buse, Appl. Phys. B 64, 273 (1997).
[CrossRef]

Chem. Mater.

J. Sha, J.-K. Lee, S. Kang, V. M. Prabhu, C. L. Soles, P. V. Bonnesen, and C. K. Ober, Chem. Mater. 22, 3093 (2010).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

NASA Conf. Publ.

A. M. Eskicioglu and P. S. Fisher, NASA Conf. Publ. 3191, 49 (1993).

Nat. Photon.

C. Barsi, W. Wan, and J. W. Fleischer, Nat. Photon. 3, 211 (2009).
[CrossRef]

Nature

K. Buse, A. Adibi, and D. Psaltis, Nature 393, 665 (1998).
[CrossRef]

Opt. Commun.

A. Yariv, Opt. Commun. 21, 49 (1977).
[CrossRef]

J. Sang-il, B. You-Seok, and L. Soo-Young, Opt. Commun. 198, 57 (2001).
[CrossRef]

Opt. Eng.

N. K. Nischal, J. Joseph, and K. Singh, Opt. Eng. 42, 1583 (2003).
[CrossRef]

Opt. Lasers Eng.

N. Singh and A. Sinha, Opt. Lasers Eng. 46, 117 (2008).
[CrossRef]

H. Ramenah, P. Bertrand, E. H. Soubari, and P. Meyrueis, Opt. Lasers Eng. 28, 589 (1996).
[CrossRef]

Opt. Lett.

Proc. SPIE

G. W. Burr, J. J. Ashley, B. Marcus, C. M. Jefferson, J. A. Hoffnagle, and H. J. Coufal, Proc. SPIE 3468, 64 (1998).
[CrossRef]

Science

D. Psaltis, Science 298, 1359 (2002).
[CrossRef] [PubMed]

Signal Process.

E. Sejdić, I. Djurović, and L. Stanković, Signal Process. 91, 1351 (2011).
[CrossRef]

Other

R. Jones and C. Wykes, Holographic and Speckle Interferometry (Cambridge University, 1983).

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Figures (3)

Fig. 1
Fig. 1

Reflection-type setup for quantification of holographic storage efficiency. In the optimal configuration, a thin spherical lens (position z 0 , focal length f) minimizes the reconstruction error.

Fig. 2
Fig. 2

Input (dashed red) and readout (blue) simulation results for a rectangle signal. (a) Reconstruction of real-space hologram ( α = 0 ). Diffusion effects on the storage device induce reconstruction error on the edges. (b) Fourier transform of the rectangular signal. Green line shows the saturation level of the device. (c), (d) Reconstruction of Fourier-space hologram ( α = 1 ) after (c) diffusion and (d) saturation on the device.

Fig. 3
Fig. 3

Reconstruction error of a rectangular signal. (a) Error as a function of fractional order α and magnification M, (b) field at recording device for optimal configuration for free-space propagation (black, narrow profile) and single-lens configuration (blue), (c), (d) reconstructed (readout) output fields for (c) free-space and (d) single-lens configurations.

Equations (6)

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

F = P ( d z 0 ) [ exp ( i k ( x 2 + y 2 ) 2 f ) P ( z 0 ) ] .
I = | A WR + W e i k 0 · x | 2 = I 0 + 2 R e [ W A WR e i k 0 · x ] .
[ F M α ( f ) ] ( u ) = K α ( u M , x ) f ( x ) d x ,
K α ( u , x ) = k = 0 ψ k ( u ) e i k α π / 2 ψ k ( x ) ,
min F L ( R 2 ) I OUT I OBJ ,
min ( α , M ) [ 0 , 1 ] × R + | F 1 H F ( A OBJ ) | 2 | A OBJ | 2 .

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