Abstract

The cross talk between holograms recorded in a phase-code multiplexing system is analyzed. The signal-to-noise ratio (SNR) is derived for the original image of a finite contrast ratio in the presence of a phase-shift error of the reference beam. It is shown that one particular code in the Walsh–Hadamard code set can be the dominant cross-talk noise source. We experimentally measured the SNR of the holograms recorded in an 8-bit phase-code multiplexing system by varying the contrast ratio of the original image. We show good agreement between experiment and theory. The existence of one bad code is also shown experimentally.

© 2004 Optical Society of America

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Corrections

Hyun Kim and Yeon H. Lee, "Cross talk between holograms of finite contrast in a phase-code multiplexing system: erratum," Opt. Lett. 29, 647-647 (2004)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-29-6-647

References

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  1. C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Opt. Commun. 85, 171 (1991).
    [CrossRef]
  2. C. Alves, G. Pauliat, and G. Roosen, Opt. Lett. 19, 1894 (1994).
    [CrossRef]
  3. C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Appl. Opt. 31, 5700 (1992).
    [CrossRef] [PubMed]
  4. K. Curtis and D. Psaltis, J. Opt. Soc. Am. A 10, 2547 (1993).
    [CrossRef]
  5. C. Alves, L. Gerard, G. Pauliat, and G. Roosen, in Optical Computing, B. S. Wherrett and P. Chavel, eds., Vol. 139 of Institute of Physics Conference Series (Institute of Physics, London, 1995).
  6. A. Yariv and P. Yeh, Optical Waves in Crystal (Wiley, New York, 1984), Chap. 5.
  7. M. Yamauchi and T. Eiju, Opt. Commun. 115, 19 (1995).
    [CrossRef]
  8. J.-S. Jang and D.-H. Shin, Opt. Lett. 26, 1797 (2001).
    [CrossRef]

2001 (1)

1995 (1)

M. Yamauchi and T. Eiju, Opt. Commun. 115, 19 (1995).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1991 (1)

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Opt. Commun. 85, 171 (1991).
[CrossRef]

Alves, C.

C. Alves, G. Pauliat, and G. Roosen, Opt. Lett. 19, 1894 (1994).
[CrossRef]

C. Alves, L. Gerard, G. Pauliat, and G. Roosen, in Optical Computing, B. S. Wherrett and P. Chavel, eds., Vol. 139 of Institute of Physics Conference Series (Institute of Physics, London, 1995).

Curtis, K.

Denz, C.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Appl. Opt. 31, 5700 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Opt. Commun. 85, 171 (1991).
[CrossRef]

Eiju, T.

M. Yamauchi and T. Eiju, Opt. Commun. 115, 19 (1995).
[CrossRef]

Gerard, L.

C. Alves, L. Gerard, G. Pauliat, and G. Roosen, in Optical Computing, B. S. Wherrett and P. Chavel, eds., Vol. 139 of Institute of Physics Conference Series (Institute of Physics, London, 1995).

Jang, J.-S.

Pauliat, G.

C. Alves, G. Pauliat, and G. Roosen, Opt. Lett. 19, 1894 (1994).
[CrossRef]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Appl. Opt. 31, 5700 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Opt. Commun. 85, 171 (1991).
[CrossRef]

C. Alves, L. Gerard, G. Pauliat, and G. Roosen, in Optical Computing, B. S. Wherrett and P. Chavel, eds., Vol. 139 of Institute of Physics Conference Series (Institute of Physics, London, 1995).

Psaltis, D.

Roosen, G.

C. Alves, G. Pauliat, and G. Roosen, Opt. Lett. 19, 1894 (1994).
[CrossRef]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Appl. Opt. 31, 5700 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Opt. Commun. 85, 171 (1991).
[CrossRef]

C. Alves, L. Gerard, G. Pauliat, and G. Roosen, in Optical Computing, B. S. Wherrett and P. Chavel, eds., Vol. 139 of Institute of Physics Conference Series (Institute of Physics, London, 1995).

Shin, D.-H.

Tschudi, T.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Appl. Opt. 31, 5700 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Opt. Commun. 85, 171 (1991).
[CrossRef]

Yamauchi, M.

M. Yamauchi and T. Eiju, Opt. Commun. 115, 19 (1995).
[CrossRef]

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystal (Wiley, New York, 1984), Chap. 5.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystal (Wiley, New York, 1984), Chap. 5.

Appl. Opt. (1)

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

Opt. Commun. (2)

M. Yamauchi and T. Eiju, Opt. Commun. 115, 19 (1995).
[CrossRef]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Opt. Commun. 85, 171 (1991).
[CrossRef]

Opt. Lett. (2)

Other (2)

C. Alves, L. Gerard, G. Pauliat, and G. Roosen, in Optical Computing, B. S. Wherrett and P. Chavel, eds., Vol. 139 of Institute of Physics Conference Series (Institute of Physics, London, 1995).

A. Yariv and P. Yeh, Optical Waves in Crystal (Wiley, New York, 1984), Chap. 5.

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Figures (6)

Fig. 1
Fig. 1

Experimental setup: M, mirrors; B.E., beam expander; B.S., beam splitter.

Fig. 2
Fig. 2

Walsh–Hadamard 8-bit code pattern.

Fig. 3
Fig. 3

Eight images recorded and restored with no phase-shift error in the reference beam.

Fig. 4
Fig. 4

Eight images recorded and restored with a phase-shift error of =-30°.

Fig. 5
Fig. 5

Seven images recorded and restored with a phase-shift error of =-30°, where the first code was intentionally avoided when we recorded the hologram.

Fig. 6
Fig. 6

Intensity SNR versus intensity contrast of the original image. Solid and dashed curves, theory; circles with error bars, experiment.

Equations (5)

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Az=Γn=1NSmRn2Sm2+Rn2+Γm=1mmMn=1NSmRn expjϕmn*Sm2+Rn2Rnexpjϕmn,
Bz=Γn=1NSmONRn2SmON2+Rn2+Γ2m=1mmMn=1NSmONRn2 expjϕmn-ϕmnSmON2+Rn2+SmOFFRn2 expjϕmn-ϕmnSmOFF2+Rn2=ΓSONK1N+12ΓSONK1+SOFFK2m=1mmMn=1N×expjϕmn-ϕmn,
Cz=ΓSOFFK2N+cross talk.
SNRm=1=TK1+14E1TK1+K2K2+14E1TK1+K2,
SNRm1=TK1+14E2TK1+K2K2+14E2TK1+K2,

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