Abstract

What we believe to be a new technique, based on a modified Gerchberg–Saxton algorithm (MGSA) and a phase modulation scheme in the Fresnel-transform domain, is proposed to reduce cross talks existing in multiple-image encryption and multiplexing. First, each plain image is encoded and multiplexed into a phase function by using the MGSA and a different wavelength/position parameter. Then all the created phase functions are phase modulated to result in different shift amounts of the reconstruction images before being combined together into a single phase-only function. Simulation results show that the cross talks between multiplexed images have been significantly reduced, compared with prior methods [Opt. Lett. 30, 1306 (2005) ; J. Opt. A 8, 391 (2006) ], thus presenting high promise in increasing the multiplexing capacity and encrypting grayscale and color images.

© 2009 Optical Society of America

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References

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  1. G. Situ and J. Zhang, Opt. Lett. 30, 1306 (2005).
    [CrossRef] [PubMed]
  2. G. Situ and J. Zhang, J. Opt. A 8, 391 (2006).
    [CrossRef]
  3. J. F. Heanue, M. C. Bashaw, and L. Hesselink, Appl. Opt. 34, 6012 (1995).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. G. Situ and J. Zhang, Opt. Lett. 29, 1584 (2004).
    [CrossRef] [PubMed]
  9. Z. Liu and S. Liu, Opt. Commun. 275, 324 (2007).
    [CrossRef]
  10. R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 34, 275 (1971).
  11. R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).
  12. H. E. Hwang, H. T. Chang, and W. N. Lie, Opt. Express 17, 13700 (2009).
    [CrossRef] [PubMed]

2009 (1)

2007 (1)

Z. Liu and S. Liu, Opt. Commun. 275, 324 (2007).
[CrossRef]

2006 (2)

2005 (1)

2004 (1)

2002 (2)

1997 (1)

1995 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

1971 (1)

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 34, 275 (1971).

Bashaw, M. C.

Berger, G.

Chang, H. T.

Chien, H. C.

Denz, C.

Dietz, M.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 34, 275 (1971).

Heanue, J. F.

Hesselink, L.

Hwang, H. E.

Javidi, B.

Kuo, C. J.

Li, L.

Lie, W. N.

Liu, S.

Z. Liu and S. Liu, Opt. Commun. 275, 324 (2007).
[CrossRef]

Liu, Z.

Z. Liu and S. Liu, Opt. Commun. 275, 324 (2007).
[CrossRef]

Lu, W. C.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 34, 275 (1971).

Situ, G.

Yeh, C. H.

Zhang, G.

Zhang, J.

Zhang, X.

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Figures (4)

Fig. 1
Fig. 1

Block diagram of the proposed MGSA based on FrT domain.

Fig. 2
Fig. 2

(a) Block diagram of the proposed multiple-image encryption and multiplexing. (b) Wavelength demultiplexing and (c) position demultiplexing for an optical decryption system based on one POF and lensless Fresnel domain.

Fig. 3
Fig. 3

(a) Nine images for encryption; (b) and (e) g 6 ( x 1 , y 1 ) and g 3 ( x 1 , y 1 ) for wavelength and position multiplexing, respectively; (c) and (f) decryption results corresponding to images in (b) and (e); (d) and (g) the enlarged version of the selected region in (c) and (f), respectively.

Fig. 4
Fig. 4

Comparison between the proposed method and Situ and Zhang’s [1, 2] in terms of correlation coefficient.

Equations (6)

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FrT { exp [ j ψ λ n ( x 0 , y 0 ) ] ; λ n ; z } = g ̂ n λ ( x 1 , y 1 ) exp [ j ψ g ̂ n λ ( x 1 , y 1 ) ] ,
FrT { exp [ j ψ z n ( x 0 , y 0 ) ] ; λ ; z n } = g ̂ n z ( x 1 , y 1 ) exp [ j ψ g ̂ n z ( x 1 , y 1 ) ] ,
FrT { exp [ j ψ λ n ( x 0 , y 0 ) ] ; λ n ; z } = g ̂ n λ ( x 1 μ n , y 1 ν n ) exp [ j ϕ ( x 1 , y 1 ) ] ,
ψ λ n ( x 0 , y 0 ) = ψ λ n ( x 0 , y 0 ) + 2 π ( μ n x 0 + ν n y 0 ) λ n z ,
ψ T λ ( x 0 , y 0 ) = arg { n = 1 N exp [ j ψ λ n ( x 0 , y 0 ) ] | n = 1 N exp [ j ψ λ n ( x 0 , y 0 ) ] | } ,
| FrT { exp [ j ψ T λ ( x 0 , y 0 ) ] ; λ n ; z } | = | g ̂ n λ ( x 1 μ n , y 1 ν n ) exp [ j ψ g ̂ n λ ( x 1 μ n , y 1 ν n ) ] + n λ n ( x 1 , y 1 ) | | g ̂ n λ ( x 1 μ n , y 1 ν n ) | + | n λ n ( x 1 , y 1 ) | ,

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