Abstract

An optical three-dimensional (3D) display system interfaced with digital data transmission is proposed. In this system, an original 3D object is encrypted by use of a random phase mask and then the encrypted pattern is recorded as a digital hologram. The digital hologram key is also recorded for optical decryption. Both the encrypted digital hologram and the digital hologram key are transmitted to a receiver through a conventional communication data channel. At the receiver, the 3D scene is reconstructed and displayed optically in a retrieval system based on a joint-transform correlation. Experimental results are presented. We investigate the influence of quantization of the joint power spectrum in the optical correlator on the quality of the reconstructed image.

© 2004 Optical Society of America

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References

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  1. B. Javidi, F. Okano, eds., Three-Dimensional TV, Video and Display (Springer-Verlag, Berlin, 2002).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  13. O. Matoba, B. Javidi, “Optical retrieval of encrypted digital holograms for secure real-time display,” Opt. Lett. 27, 321–323 (2002).
    [CrossRef]
  14. N. Yoshikawa, M. Itoh, T. Yatagai, “Binary computer-generated holograms for security applications from a synthetic double-exposure method by electron-beam lithography,” Opt. Lett. 23, 1483–1485 (1998).
    [CrossRef]
  15. D. Mas, J. Garcia, C. Ferreira, L. B. Bernardo, F. Marinho, “Fast algorithms for free-space calculation,” Opt. Commun. 164, 233–245 (1999).
    [CrossRef]
  16. L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford U. Press, New York, 1996).

2003 (1)

2002 (2)

2001 (1)

2000 (2)

1999 (3)

D. Mas, J. Garcia, C. Ferreira, L. B. Bernardo, F. Marinho, “Fast algorithms for free-space calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

O. Matoba, B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
[CrossRef]

1998 (2)

1997 (1)

1995 (1)

1994 (1)

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Arai, J.

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

J. Arai, F. Okano, H. Hoshino, I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37, 2034–2045 (1998).
[CrossRef]

Bernardo, L. B.

D. Mas, J. Garcia, C. Ferreira, L. B. Bernardo, F. Marinho, “Fast algorithms for free-space calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Bertaux, N.

Ferreira, C.

D. Mas, J. Garcia, C. Ferreira, L. B. Bernardo, F. Marinho, “Fast algorithms for free-space calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Frauel, Y.

Garcia, J.

D. Mas, J. Garcia, C. Ferreira, L. B. Bernardo, F. Marinho, “Fast algorithms for free-space calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Grunnet-Jepsen, A.

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford U. Press, New York, 1996).

Horner, J. L.

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

Hoshino, H.

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

J. Arai, F. Okano, H. Hoshino, I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37, 2034–2045 (1998).
[CrossRef]

Ichioka, Y.

Ishida, K.

Itoh, M.

Javidi, B.

Kondou, N.

Kumagai, T.

Marinho, F.

D. Mas, J. Garcia, C. Ferreira, L. B. Bernardo, F. Marinho, “Fast algorithms for free-space calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Mas, D.

D. Mas, J. Garcia, C. Ferreira, L. B. Bernardo, F. Marinho, “Fast algorithms for free-space calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Matoba, O.

McDonald, J. B.

Miyatake, S.

Miyazaki, D.

Morimoto, T.

Naughton, T. J.

Okano, F.

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

J. Arai, F. Okano, H. Hoshino, I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37, 2034–2045 (1998).
[CrossRef]

Réfrégier, P.

Solymar, L.

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford U. Press, New York, 1996).

Tajahuerce, E.

Tanida, J.

Webb, D. J.

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford U. Press, New York, 1996).

Yamada, K.

Yamaguchi, I.

Yatagai, T.

Yoshikawa, N.

Yuyama, I.

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

J. Arai, F. Okano, H. Hoshino, I. Yuyama, “Gradient-index lens-array method based on real-time integral photography for three-dimensional images,” Appl. Opt. 37, 2034–2045 (1998).
[CrossRef]

Zhang, T.

Appl. Opt. (6)

Opt. Commun. (1)

D. Mas, J. Garcia, C. Ferreira, L. B. Bernardo, F. Marinho, “Fast algorithms for free-space calculation,” Opt. Commun. 164, 233–245 (1999).
[CrossRef]

Opt. Eng. (2)

B. Javidi, J. L. Horner, “Optical pattern recognition for validation and security verification,” Opt. Eng. 33, 1752–1756 (1994).
[CrossRef]

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1999).
[CrossRef]

Opt. Lett. (5)

Other (2)

L. Solymar, D. J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford U. Press, New York, 1996).

B. Javidi, F. Okano, eds., Three-Dimensional TV, Video and Display (Springer-Verlag, Berlin, 2002).

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Figures (11)

Fig. 1
Fig. 1

Schematic of the proposed 3D display system with digital data transmission by use of an encrypted digital hologram.

Fig. 2
Fig. 2

Recording system of an encrypted digital hologram of a 3D object. RPM, random phase mask.

Fig. 3
Fig. 3

Reconstruction system of a 3D object by an optical correlator: KH, BS, EDH, and HK denote a key digital hologram, a beam splitter, an encrypted digital hologram, and a digital hologram key, respectively.

Fig. 4
Fig. 4

Numerical results. Example of (a) the original image and (b) its encrypted image.

Fig. 5
Fig. 5

Reconstructed images at several quantization levels: (a) double precision, (b) 12-bit, (c) 10-bit, (d) 8-bit, (e) 6-bit, and (d) 5-bit quantization.

Fig. 6
Fig. 6

RMS errors as a function of the number of quantization levels.

Fig. 7
Fig. 7

Images reconstructed at longitudinal positions (a) z = -99 mm, (b) z = -100 mm, and (c) z = -101 mm.

Fig. 8
Fig. 8

RMS as a function of reconstructed longitudinal position.

Fig. 9
Fig. 9

Experimental setup for 3D optical reconstruction and display of data.

Fig. 10
Fig. 10

Experimental results: (a) original image; (b), (c) images reconstructed by the correct and by an incorrect key hologram, respectively.

Fig. 11
Fig. 11

Experimental results of 3D optical reconstruction at different longitudinal z positions: (a) original image; reconstructed images (b) at the correct longitudinal position and (c) at an incorrect longitudinal position by use of the correct digital hologram key.

Equations (14)

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

fx, y= ozξ, ηgzx-ξ, y-ηdξdη=ozx, ygzx, y,
gzx, y=expjπλzx2+y2
ex, y=fx, ymx, y,
Isx, y=|ex, y+rx, y|2=|ex, y|2+|rx, y|2+e*x, yrx, y+ex, yr*x, y,
Ikx, y=|mx, y+rx, y|2=|mx, y|2+|rx, y|2+m*x, yrx, y+mx, yr*x, y,
sx, y=Isx-α, y+Ikx, y.
tx, y=ex-α, y+mx, y,
|Tfx, fy|2=|Efx, fyexpjαfx+Mfx, fy|2=|Efx, fy|2+|Mfx, fy|2+Efx, fyM*fx, fyexpjαfx+E*fx, fyMfx, fyexp-jαfx=|Efx, fy|2+|Mfx, fy|2+Ffx, fyexpjαfx+F*fx, fyexp-jαfx,
ox, y=ex, yex, y+mx, ymx, y+fx-α, y+f*x+α, y,
Oξ, η=eξ, ηeξ, ηgξ, η+mξ, ηmξ, ηgξ, η+fξ-α, ηgξ, η+f*ξ+α, ηgξ, η=eξ, ηeξ, ηgξ, η+mξ, ηmξ, ηgξ, η+fξ-α, ηgξ, η+o*ξ+α, η.
Oξ, η=eξ, ηeξ, ηg*ξ, η+mξ, ηmξ, ηg*ξ, η+fξ-α, ηg*ξ, η+f*ξ+α, ηg*ξ, η=eξ, ηeξ, ηg*ξ, η+mξ, ηmξ, ηg*ξ, η+oξ-α, η+f*ξ+α, ηg*ξ, η.
RMS=i=1NOni2-Oqi22N1/2.
Δx2/λz=0.019.
zMΔx2λ.

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