Abstract

We introduce the technique of wavelength multiplexing into a double random-phase encoding system to achieve multiple-image encryption. Each primary image is first encrypted by the double phase encoding method and then superposed to yield the final enciphered image. We analyze the minimum separation between two adjacent multiplexing wavelengths through cross talk and the multiplexing capacity through the correlation coefficient. Computer simulations are performed to demonstrate the concept. This technique can be used for hiding multiple images as well.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Réfrégier and B. Javidi, Opt. Lett. 20, 767 (1995).
    [CrossRef]
  2. B. Javidi, G. Zhang, and J. Li, Appl. Opt. 36, 1054 (1997).
    [CrossRef] [PubMed]
  3. O. Matoba and B. Javidi, Appl. Opt. 38, 6785 (1999).
    [CrossRef]
  4. O. Matoba and B. Javidi, Opt. Lett. 24, 762 (1999).
    [CrossRef]
  5. O. Matoba and B. Javidi, Appl. Opt. 38, 7288 (1999).
    [CrossRef]
  6. B. M. Hennelly and J. B. Sheridan, Optik (Stuttgart) 114, 251 (2003).
    [CrossRef]
  7. G. Situ and J. Zhang, Opt. Lett. 29, 1584 (2004).
    [CrossRef] [PubMed]
  8. B. M. Hennelly and J. B. Sheridan, Opt. Eng. 43, 2239 (2004).
    [CrossRef]
  9. G. Situ and J. Zhang, Opt. Commun. 232, 115 (2004).
    [CrossRef]
  10. S. Lai and M. A. Neifeld, Opt. Commun. 178, 283 (2000).
    [CrossRef]
  11. S. Kishk and B. Javidi, Appl. Opt. 41, 5462 (2002).
    [CrossRef] [PubMed]
  12. S. Kishk and B. Javidi, Opt. Lett. 28, 167 (2003).
    [CrossRef] [PubMed]
  13. G. Situ and J. Zhang, Opt. Commun. 245, 55 (2005).
    [CrossRef]
  14. I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking (Morgan Kaufmann, San Diego, Calif., 2002).
  15. U. Schnars and W. P. O. Jüptner, Meas. Sci. Technol. 13, 85 (2002).
    [CrossRef]
  16. D. Lande, J. F. Heanue, M. C. Bashaw, and L. Hesselink, Opt. Lett. 21, 1780 (1996).
    [CrossRef] [PubMed]
  17. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 2002).

2005 (1)

G. Situ and J. Zhang, Opt. Commun. 245, 55 (2005).
[CrossRef]

2004 (3)

G. Situ and J. Zhang, Opt. Lett. 29, 1584 (2004).
[CrossRef] [PubMed]

B. M. Hennelly and J. B. Sheridan, Opt. Eng. 43, 2239 (2004).
[CrossRef]

G. Situ and J. Zhang, Opt. Commun. 232, 115 (2004).
[CrossRef]

2003 (2)

B. M. Hennelly and J. B. Sheridan, Optik (Stuttgart) 114, 251 (2003).
[CrossRef]

S. Kishk and B. Javidi, Opt. Lett. 28, 167 (2003).
[CrossRef] [PubMed]

2002 (2)

S. Kishk and B. Javidi, Appl. Opt. 41, 5462 (2002).
[CrossRef] [PubMed]

U. Schnars and W. P. O. Jüptner, Meas. Sci. Technol. 13, 85 (2002).
[CrossRef]

2000 (1)

S. Lai and M. A. Neifeld, Opt. Commun. 178, 283 (2000).
[CrossRef]

1999 (3)

1997 (1)

1996 (1)

1995 (1)

Bashaw, M. C.

Bloom, J. A.

I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking (Morgan Kaufmann, San Diego, Calif., 2002).

Cox, I. J.

I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking (Morgan Kaufmann, San Diego, Calif., 2002).

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 2002).

Heanue, J. F.

Hennelly, B. M.

B. M. Hennelly and J. B. Sheridan, Opt. Eng. 43, 2239 (2004).
[CrossRef]

B. M. Hennelly and J. B. Sheridan, Optik (Stuttgart) 114, 251 (2003).
[CrossRef]

Hesselink, L.

Javidi, B.

Jüptner, W. P. O.

U. Schnars and W. P. O. Jüptner, Meas. Sci. Technol. 13, 85 (2002).
[CrossRef]

Kishk, S.

Lai, S.

S. Lai and M. A. Neifeld, Opt. Commun. 178, 283 (2000).
[CrossRef]

Lande, D.

Li, J.

Matoba, O.

Miller, M. L.

I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking (Morgan Kaufmann, San Diego, Calif., 2002).

Neifeld, M. A.

S. Lai and M. A. Neifeld, Opt. Commun. 178, 283 (2000).
[CrossRef]

Réfrégier, P.

Schnars, U.

U. Schnars and W. P. O. Jüptner, Meas. Sci. Technol. 13, 85 (2002).
[CrossRef]

Sheridan, J. B.

B. M. Hennelly and J. B. Sheridan, Opt. Eng. 43, 2239 (2004).
[CrossRef]

B. M. Hennelly and J. B. Sheridan, Optik (Stuttgart) 114, 251 (2003).
[CrossRef]

Situ, G.

G. Situ and J. Zhang, Opt. Commun. 245, 55 (2005).
[CrossRef]

G. Situ and J. Zhang, Opt. Lett. 29, 1584 (2004).
[CrossRef] [PubMed]

G. Situ and J. Zhang, Opt. Commun. 232, 115 (2004).
[CrossRef]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 2002).

Zhang, G.

Zhang, J.

G. Situ and J. Zhang, Opt. Commun. 245, 55 (2005).
[CrossRef]

G. Situ and J. Zhang, Opt. Commun. 232, 115 (2004).
[CrossRef]

G. Situ and J. Zhang, Opt. Lett. 29, 1584 (2004).
[CrossRef] [PubMed]

Appl. Opt. (4)

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Jüptner, Meas. Sci. Technol. 13, 85 (2002).
[CrossRef]

Opt. Commun. (3)

G. Situ and J. Zhang, Opt. Commun. 245, 55 (2005).
[CrossRef]

G. Situ and J. Zhang, Opt. Commun. 232, 115 (2004).
[CrossRef]

S. Lai and M. A. Neifeld, Opt. Commun. 178, 283 (2000).
[CrossRef]

Opt. Eng. (1)

B. M. Hennelly and J. B. Sheridan, Opt. Eng. 43, 2239 (2004).
[CrossRef]

Opt. Lett. (5)

Optik (Stuttgart) (1)

B. M. Hennelly and J. B. Sheridan, Optik (Stuttgart) 114, 251 (2003).
[CrossRef]

Other (2)

I. J. Cox, M. L. Miller, and J. A. Bloom, Digital Watermarking (Morgan Kaufmann, San Diego, Calif., 2002).

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 2002).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Optical setup for the lensless security system based on double random-phase encoding in the Fresnel domain.

Fig. 2
Fig. 2

Primary secret image for (a) Alice and (b) Bob in computer simulations.

Fig. 3
Fig. 3

Decrypted secret images with (a) λ 1 and (b) λ 2 .

Fig. 4
Fig. 4

Behavior of ρ versus N.

Equations (8)

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

u 1 ( x , y ) = FRT λ 1 { f 1 ( x , y ) exp [ j 2 π ϕ ( x , y ) ] ; z 1 } ,
g 1 ( x 0 , y 0 ) = FRT λ 1 { u 1 ( x , y ) exp [ j 2 π ψ ( x , y ) ] ; z 2 } .
γ = λ 1 λ 2 n λ 2 1 n λ 1 1
f ̂ 1 ( x , y ) = f 1 ( x , y ) + n 1 ( x , y ) ,
n 1 ( x , y ) = FRT λ 1 { FRT λ 1 { g 2 * ( x 0 , y 0 ) ; z 2 } exp [ j 2 π ψ ( x , y ) ] ; z 1 } exp [ j 2 π ϕ ( x , y ) ]
g ( x 0 , y 0 ) = k = 1 N g k ( x 0 , y 0 ) ,
n m ( x , y ) = k m FRT λ m { FRT λ m { g k * ( x 0 , y 0 ) ; z 2 } exp [ j 2 π γ m ψ ( x , y ) ] ; z 1 } exp [ j 2 π γ m ϕ ( x , y ) ] ,
ρ m = E { [ f m E [ f m ] ] [ f ̂ m E [ f ̂ m ] ] } { E { [ f m E [ f m ] ] 2 } E { [ f ̂ m E [ f ̂ m ] ] 2 } } 1 2 ,

Metrics