Abstract

A lensless optical security system based on double random-phase encoding in the Fresnel domain is proposed. This technique can encrypt a primary image to random noise by use of two statistically independent random-phase masks in the input and transform planes, respectively. In this system the positions of the significant planes and the operation wavelength, as well as the phase codes, are used as keys to encrypt and recover the primary image. Therefore higher security is achieved. The sensitivity of the decrypted image to shifting along the propagation direction and to the wavelength are also investigated.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Réfrégier and B. Javidi, Opt. Lett. 20, 767 (1995).
    [CrossRef]
  2. N. Towghi, B. Javidi, and Z. Luo, J. Opt. Soc. Am. A 16, 1915 (1999).
    [CrossRef]
  3. G. Unnikrishnan, J. Joseph, and K. Singh, Opt. Lett. 25, 887 (2000).
    [CrossRef]
  4. B. Zhu, S. Liu, and Q. Ran, Opt. Lett. 25, 1159 (2000).
    [CrossRef]
  5. S. Liu, L. Yu, and B. Zhu, Opt. Commun. 187, 57 (2001).
    [CrossRef]
  6. B. Hennelly and J. B. Sheridan, Opt. Lett. 28, 269 (2003).
    [CrossRef] [PubMed]
  7. P. C. Mogensen and J. Glückstad, Opt. Lett. 25, 566 (2000).
    [CrossRef]
  8. X. Peng, L. Yu, and L. Cai, Opt. Express 10, 41 (2002), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  9. G. Situ and J. Zhang, Optik 114, 473 (2003).
    [CrossRef]
  10. G. Situ and J. Zhang, Opt. Commun. 232, 115 (2004).
    [CrossRef]
  11. O. Matoba and B. Javidi, Opt. Lett. 24, 762 (1999).
    [CrossRef]
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  13. D. Mendlovic, Z. Zalevsky, and N. Konforti, J. Mod. Opt. 44, 407 (1997).
    [CrossRef]
  14. D. G. Manolakis, V. K. Ingle, and S. M. Kogon, Statistical and Adaptive Signal Processing (McGraw-Hill, New York, 2000).

2004 (1)

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

2003 (2)

2002 (1)

2001 (1)

S. Liu, L. Yu, and B. Zhu, Opt. Commun. 187, 57 (2001).
[CrossRef]

2000 (3)

1999 (2)

1997 (1)

D. Mendlovic, Z. Zalevsky, and N. Konforti, J. Mod. Opt. 44, 407 (1997).
[CrossRef]

1995 (1)

Cai, L.

Glückstad, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hennelly, B.

Ingle, V. K.

D. G. Manolakis, V. K. Ingle, and S. M. Kogon, Statistical and Adaptive Signal Processing (McGraw-Hill, New York, 2000).

Javidi, B.

Joseph, J.

Kogon, S. M.

D. G. Manolakis, V. K. Ingle, and S. M. Kogon, Statistical and Adaptive Signal Processing (McGraw-Hill, New York, 2000).

Konforti, N.

D. Mendlovic, Z. Zalevsky, and N. Konforti, J. Mod. Opt. 44, 407 (1997).
[CrossRef]

Liu, S.

S. Liu, L. Yu, and B. Zhu, Opt. Commun. 187, 57 (2001).
[CrossRef]

B. Zhu, S. Liu, and Q. Ran, Opt. Lett. 25, 1159 (2000).
[CrossRef]

Luo, Z.

Manolakis, D. G.

D. G. Manolakis, V. K. Ingle, and S. M. Kogon, Statistical and Adaptive Signal Processing (McGraw-Hill, New York, 2000).

Matoba, O.

Mendlovic, D.

D. Mendlovic, Z. Zalevsky, and N. Konforti, J. Mod. Opt. 44, 407 (1997).
[CrossRef]

Mogensen, P. C.

Peng, X.

Ran, Q.

Réfrégier, P.

Sheridan, J. B.

Singh, K.

Situ, G.

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

G. Situ and J. Zhang, Optik 114, 473 (2003).
[CrossRef]

Towghi, N.

Unnikrishnan, G.

Yu, L.

Zalevsky, Z.

D. Mendlovic, Z. Zalevsky, and N. Konforti, J. Mod. Opt. 44, 407 (1997).
[CrossRef]

Zhang, J.

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

G. Situ and J. Zhang, Optik 114, 473 (2003).
[CrossRef]

Zhu, B.

S. Liu, L. Yu, and B. Zhu, Opt. Commun. 187, 57 (2001).
[CrossRef]

B. Zhu, S. Liu, and Q. Ran, Opt. Lett. 25, 1159 (2000).
[CrossRef]

J. Mod. Opt. (1)

D. Mendlovic, Z. Zalevsky, and N. Konforti, J. Mod. Opt. 44, 407 (1997).
[CrossRef]

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

Opt. Commun. (2)

S. Liu, L. Yu, and B. Zhu, Opt. Commun. 187, 57 (2001).
[CrossRef]

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

Opt. Express (1)

Opt. Lett. (6)

Optik (1)

G. Situ and J. Zhang, Optik 114, 473 (2003).
[CrossRef]

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

D. G. Manolakis, V. K. Ingle, and S. M. Kogon, Statistical and Adaptive Signal Processing (McGraw-Hill, New York, 2000).

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 of the proposed security system.

Fig. 2
Fig. 2

(a) Primary image for computer simulations and (b) encrypted image.

Fig. 3
Fig. 3

Behavior of the SNR versus Δλ.

Fig. 4
Fig. 4

Behavior of the SNR versus Δz.

Equations (9)

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

ux,y=fx,yexpjϕx,y×hx,y;x,y;z1;λdxdy,
hx,y;x,y;z1;λ=expj2πz1/λjλz1×expjπλz1x-x2+y-y2
ux,y=FrTλfx,yexpjϕx,y;z1,
gx0,y0=FrTλux,yexpjψx,y;z2.
vx,y=FrTλg*x0,y0;z2.
fˆx,y=FrTλvx,yexpjψx,y;z1.
SNR=10 logfx,y2dxdyfx,y-fˆx,y2dxdy,
hx,y;x0,y0;z2,λ+Δλ=expj2πz2/λ+Δλjλ+Δλz2×expjπλ+Δλz2x-x02+y-y02.
1λ+Δλ=1λ-Δλλλ+Δλ.

Metrics