Abstract

We propose a method using phase encryption and hologram multiplexing to encode positional information into the hologram, which can be used during readout to find the correct position of the reference beam. We also include a method to align the position of the phase code in the reference beam during readout, with which we achieved approximately 1/100 hologram size (4.4μm) precision electronically, without the need of a precise mechanical hologram positioning device. We prove the feasibility of the method with experiments.

© 2010 Optical Society of America

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References

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  1. P. Réfrégier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767-769 (1995).
    [CrossRef] [PubMed]
  2. X. Tan, O. Matoba, Y. Okada-Shudo, M. Ide, T. Shimura, and K. Kuroda, “Secure optical memory system with polarization encryption,” Appl. Opt. 40, 2310-2315 (2001).
    [CrossRef]
  3. C. Denz, T. Dellwig, J. Lembcke, and T. Tschudi, “Parallel optical image addition and subtraction in a dynamic photorefractive memory by phase-code multiplexing,” Opt. Lett. 21, 278-280 (1996).
    [CrossRef] [PubMed]
  4. C. Denz, K.-O. Müller, F. Visinka, G. Berger, and T. Tschudi, “Beyond volume holographic storage--applications of phase-coded multiplexing to image processing and encryption,” Proc. SPIE 4110, 254-261 (2000).
    [CrossRef]
  5. C. C. Chang, K. L. Russel, and G. W. Hu, “Optical holographic memory using angular-rotationally phase-coded multiplexing in a LiNbO3:Fe crystal,” Appl. Phys. B 72, 307-310(2001).
  6. B. Wang, C.-C. Sun, W.-C. Su, and A. E. T. Chiou, “Shift-tolerance property of an optical double-random phase-encoding encryption system,” Appl. Opt. 39, 4788-4793(2000).
    [CrossRef]
  7. H. Horimai and X. Tan, “Collinear technology for a holographic versatile disk,” Appl. Opt. 45, 910-914 (2006).
    [CrossRef] [PubMed]
  8. Z. Göröcs, G. Erdei, T. Sarkadi, F. Ujhelyi, J. Reményi, P. Koppa, and E. Lőrincz, “Hybrid multinary modulation using a phase modulating spatial light modulator and a low-pass spatial filter,” Opt. Lett. 32, 2336-2338 (2007).
    [CrossRef] [PubMed]
  9. Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253-10265
    [CrossRef] [PubMed]

2007 (1)

2006 (1)

2001 (2)

X. Tan, O. Matoba, Y. Okada-Shudo, M. Ide, T. Shimura, and K. Kuroda, “Secure optical memory system with polarization encryption,” Appl. Opt. 40, 2310-2315 (2001).
[CrossRef]

C. C. Chang, K. L. Russel, and G. W. Hu, “Optical holographic memory using angular-rotationally phase-coded multiplexing in a LiNbO3:Fe crystal,” Appl. Phys. B 72, 307-310(2001).

2000 (2)

C. Denz, K.-O. Müller, F. Visinka, G. Berger, and T. Tschudi, “Beyond volume holographic storage--applications of phase-coded multiplexing to image processing and encryption,” Proc. SPIE 4110, 254-261 (2000).
[CrossRef]

B. Wang, C.-C. Sun, W.-C. Su, and A. E. T. Chiou, “Shift-tolerance property of an optical double-random phase-encoding encryption system,” Appl. Opt. 39, 4788-4793(2000).
[CrossRef]

1996 (1)

1995 (1)

Berger, G.

C. Denz, K.-O. Müller, F. Visinka, G. Berger, and T. Tschudi, “Beyond volume holographic storage--applications of phase-coded multiplexing to image processing and encryption,” Proc. SPIE 4110, 254-261 (2000).
[CrossRef]

Castro, A.

Chang, C. C.

C. C. Chang, K. L. Russel, and G. W. Hu, “Optical holographic memory using angular-rotationally phase-coded multiplexing in a LiNbO3:Fe crystal,” Appl. Phys. B 72, 307-310(2001).

Chiou, A. E. T.

Dellwig, T.

Denz, C.

C. Denz, K.-O. Müller, F. Visinka, G. Berger, and T. Tschudi, “Beyond volume holographic storage--applications of phase-coded multiplexing to image processing and encryption,” Proc. SPIE 4110, 254-261 (2000).
[CrossRef]

C. Denz, T. Dellwig, J. Lembcke, and T. Tschudi, “Parallel optical image addition and subtraction in a dynamic photorefractive memory by phase-code multiplexing,” Opt. Lett. 21, 278-280 (1996).
[CrossRef] [PubMed]

Erdei, G.

Frauel, Y.

Göröcs, Z.

Horimai, H.

Hu, G. W.

C. C. Chang, K. L. Russel, and G. W. Hu, “Optical holographic memory using angular-rotationally phase-coded multiplexing in a LiNbO3:Fe crystal,” Appl. Phys. B 72, 307-310(2001).

Ide, M.

Javidi, B.

Koppa, P.

Kuroda, K.

Lembcke, J.

Lorincz, E.

Matoba, O.

Müller, K.-O.

C. Denz, K.-O. Müller, F. Visinka, G. Berger, and T. Tschudi, “Beyond volume holographic storage--applications of phase-coded multiplexing to image processing and encryption,” Proc. SPIE 4110, 254-261 (2000).
[CrossRef]

Naughton, T. J.

Okada-Shudo, Y.

Réfrégier, P.

Reményi, J.

Russel, K. L.

C. C. Chang, K. L. Russel, and G. W. Hu, “Optical holographic memory using angular-rotationally phase-coded multiplexing in a LiNbO3:Fe crystal,” Appl. Phys. B 72, 307-310(2001).

Sarkadi, T.

Shimura, T.

Su, W.-C.

Sun, C.-C.

Tan, X.

Tschudi, T.

C. Denz, K.-O. Müller, F. Visinka, G. Berger, and T. Tschudi, “Beyond volume holographic storage--applications of phase-coded multiplexing to image processing and encryption,” Proc. SPIE 4110, 254-261 (2000).
[CrossRef]

C. Denz, T. Dellwig, J. Lembcke, and T. Tschudi, “Parallel optical image addition and subtraction in a dynamic photorefractive memory by phase-code multiplexing,” Opt. Lett. 21, 278-280 (1996).
[CrossRef] [PubMed]

Ujhelyi, F.

Visinka, F.

C. Denz, K.-O. Müller, F. Visinka, G. Berger, and T. Tschudi, “Beyond volume holographic storage--applications of phase-coded multiplexing to image processing and encryption,” Proc. SPIE 4110, 254-261 (2000).
[CrossRef]

Wang, B.

Appl. Opt. (3)

Appl. Phys. B (1)

C. C. Chang, K. L. Russel, and G. W. Hu, “Optical holographic memory using angular-rotationally phase-coded multiplexing in a LiNbO3:Fe crystal,” Appl. Phys. B 72, 307-310(2001).

Opt. Express (1)

Opt. Lett. (3)

Proc. SPIE (1)

C. Denz, K.-O. Müller, F. Visinka, G. Berger, and T. Tschudi, “Beyond volume holographic storage--applications of phase-coded multiplexing to image processing and encryption,” Proc. SPIE 4110, 254-261 (2000).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Simulation images of a phase code. (a) SLM page used for generating the phase code. (b) Intensity distribution of the phase code at the hologram plane. Note the 1 pixel wide zero-intensity gaps where the phase changes rapidly.

Fig. 2
Fig. 2

Simplified 1D grating structure sketch of R in and R out . A and B are the amplitude modulation values, and 0 and π ϵ are the phase modulation values. δ represents the horizontal shift of the hologram between the write-in and the readout and, thus, the shift of the phase modulation in the reference beams.

Fig. 3
Fig. 3

Optical setup for measurements. α 10 ° is the angle between the reference and the object beams.

Fig. 4
Fig. 4

(a) SLM pattern used for the modulation of the object beam, (b) SLM page used for the modulation of the reference beam, (c) CCD image with zero horizontal shift of the phase code, and (d) CCD image with a 4 pixel horizontal shift of the phase code.

Fig. 5
Fig. 5

Intensity dependency of the tracking image points on the CCD for 1D horizontal shift. (a) First-order diffraction spots. (b) Second-order diffraction spots.

Fig. 6
Fig. 6

SLM pattern used (a) for the modulation of the object beam during data write-in, (b) for the modulation of the reference beam during data write-in, (c) for the modulation of the object beam during marker write-in, and (d) for the modulation of the reference beam during marker write-in.

Fig. 7
Fig. 7

Computer simulations for the lateral shift dependence of the zeroth- and ± 2 nd-order diffracted light intensities with the use of a 6 × 6 chessboardlike phase code with 5 pixel sized squares. The figure in the middle ( 0 , 0 ) is the (horizontal, vertical) shift-intensity curve of the zeroth order, while the others are the respective ± 2 nd diffraction orders around the zeroth order. For example, the top left ( 2 , 2 ) is the intensity values of the 2 nd, 2 nd diffraction order of the 2D grating created by the various horizontal and vertical shifts.

Fig. 8
Fig. 8

(a) CCD image of the positional markers without any positional shift, (b) CCD image with a vertical shift of + 1 pixel on the SLM, (c) CCD image with a vertical shift of 1 pixel on the SLM, and (d) CCD image with a horizontal shift and a vertical shift of 1 pixel on the SLM.

Fig. 9
Fig. 9

Error function showing the difference between the calculated and the measured shifts (Error), and the normalized Gaussian function ( σ = 0.2902 ) fitted to the error data. Ranges corresponding to individual SLM pixels on the modulator are also shown.

Fig. 10
Fig. 10

Reconstructed hologram of the data page [Fig. 6a] that was recorded using phase-code multiplexing to the same spot where the sync marks were written with a shift-sensitive code.

Equations (15)

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E 0 ( x 0 , y 0 ) = D 0 ( x 0 , y 0 ) exp [ i π f 0 ( x 0 , y 0 ) ] ,
I 1 ( x 1 , y 1 ) = F { E 0 ( x 0 , y 0 ) } R in * ( x 1 , y 1 ) .
E 2 ( x 2 , y 2 ) = F { F { E 0 ( x 0 , y 0 ) } R in * ( x 1 , y 1 ) R out ( x 1 , y 1 ) } .
E 2 ( x 2 , y 2 ) = E 0 ( x 0 , y 0 ) * F { exp [ i π r diff ( x , y ) ] } ,
I 1 ( x 1 , y 1 ) = F { E 0 , 1 ( x 0 , y 0 ) } R in , 1 * ( x 1 , y 1 ) + F { E 0 , 2 ( x 0 , y 0 ) } R in , 2 * ( x 1 , y 1 ) .
E 2 , 1 ( x 2 , y 2 ) = E 0 , 1 ( x 0 , y 0 ) + E 0 , 2 ( x 0 , y 0 ) * F { exp [ i π r diff ( x , y ) ] } ,
E 2 , 2 ( x 2 , y 2 ) = E 0 , 2 ( x 0 , y 0 ) + E 0 , 1 ( x 0 , y 0 ) * F { exp [ i π r diff ( x , y ) ] } ,
R in ( x , y ) = [ r code ( x δ , y ) × ( A B ) + B ] × exp [ i ( π ϵ ) r code ( x δ , y ) ] ,
R out ( x , y ) = [ r code ( x , y ) × ( A B ) + B ] × exp [ i ( π ϵ ) r code ( x , y ) ] ,
E 2 ( x 2 , y 2 ) = E 0 ( x 0 , y 0 ) * F { R out ( x , y ) × R in * ( x , y ) } .
I + ( δ ) ( 2 C 2 + 2 D 2 ) + ( 2 C 2 2 D 2 ) cos ( π δ a ) + 4 C D sin ( π δ a ) ,
I ( δ ) ( 2 C 2 + 2 D 2 ) + ( 2 C 2 2 D 2 ) cos ( π δ a ) 4 C D sin ( π δ a ) .
I + ( δ ) ( 2 C 2 + 2 D 2 ) + ( 2 C 2 2 D 2 ) cos ( 2 π δ a ) + 4 C D sin ( 2 π δ a ) ,
I ( δ ) ( 2 C 2 + 2 D 2 ) + ( 2 C 2 2 D 2 ) cos ( 2 π δ a ) 4 C D sin ( 2 π δ a ) ,
Error ( h shift , v shift ) = m , n = 2 m , n = 2 ( I m , n Sim ( h shift , v shift ) I m , n Meas ) 2 ,

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