Abstract

We propose a new optical encoding method of images for security applications. The encoded image is obtained by random-phase encoding in both the input and the Fourier planes. We analyze the statistical properties of this technique and show that the encoding converts the input signal to stationary white noise and that the reconstruction method is robust.

© 1995 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Double image encryption based on random phase encoding in the fractional Fourier domain

Ran Tao, Yi Xin, and Yue Wang
Opt. Express 15(24) 16067-16079 (2007)

Optical encryption by double-random phase encoding in the fractional Fourier domain

G. Unnikrishnan, J. Joseph, and K. Singh
Opt. Lett. 25(12) 887-889 (2000)

Encrypted optical memory using double-random phase encoding

Bahram Javidi, Guanshen Zhang, and Jian Li
Appl. Opt. 36(5) 1054-1058 (1997)

References

  • View by:
  • |
  • |
  • |

  1. B. Javidi and J. L. Horner, Opt. Eng. 33, 1752 (1994).
    [Crossref]
  2. J. L. Horner and B. Javadi, in Optical Pattern Recognition, B. Javidi and Ph. Refregier, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2237, 193 (1994).
  3. E. T. Jaynes, IEEE Trans. Syst. Sci. Cybernet. 4, 227 (1968).
    [Crossref]
  4. G. Jumarie, Relative Information (Springer-Verlag, Berlin, 1990), pp. 33– 34.
  5. M. H. Hayes, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, San Diego, Calif., 1987), pp. 195– 230.
  6. J. C. Dainty and J. R. Fienup, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, San Diego, Calif., 1987), pp. 195– 230.
  7. J. L. Horner and P. D. Gianino, Appl. Opt. 23, 812 (1984).
    [Crossref] [PubMed]

1994 (1)

B. Javidi and J. L. Horner, Opt. Eng. 33, 1752 (1994).
[Crossref]

1984 (1)

1968 (1)

E. T. Jaynes, IEEE Trans. Syst. Sci. Cybernet. 4, 227 (1968).
[Crossref]

Dainty, J. C.

J. C. Dainty and J. R. Fienup, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, San Diego, Calif., 1987), pp. 195– 230.

Fienup, J. R.

J. C. Dainty and J. R. Fienup, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, San Diego, Calif., 1987), pp. 195– 230.

Gianino, P. D.

Hayes, M. H.

M. H. Hayes, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, San Diego, Calif., 1987), pp. 195– 230.

Horner, J. L.

B. Javidi and J. L. Horner, Opt. Eng. 33, 1752 (1994).
[Crossref]

J. L. Horner and P. D. Gianino, Appl. Opt. 23, 812 (1984).
[Crossref] [PubMed]

J. L. Horner and B. Javadi, in Optical Pattern Recognition, B. Javidi and Ph. Refregier, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2237, 193 (1994).

Javadi, B.

J. L. Horner and B. Javadi, in Optical Pattern Recognition, B. Javidi and Ph. Refregier, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2237, 193 (1994).

Javidi, B.

B. Javidi and J. L. Horner, Opt. Eng. 33, 1752 (1994).
[Crossref]

Jaynes, E. T.

E. T. Jaynes, IEEE Trans. Syst. Sci. Cybernet. 4, 227 (1968).
[Crossref]

Jumarie, G.

G. Jumarie, Relative Information (Springer-Verlag, Berlin, 1990), pp. 33– 34.

Appl. Opt. (1)

IEEE Trans. Syst. Sci. Cybernet. (1)

E. T. Jaynes, IEEE Trans. Syst. Sci. Cybernet. 4, 227 (1968).
[Crossref]

Opt. Eng. (1)

B. Javidi and J. L. Horner, Opt. Eng. 33, 1752 (1994).
[Crossref]

Other (4)

J. L. Horner and B. Javadi, in Optical Pattern Recognition, B. Javidi and Ph. Refregier, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2237, 193 (1994).

G. Jumarie, Relative Information (Springer-Verlag, Berlin, 1990), pp. 33– 34.

M. H. Hayes, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, San Diego, Calif., 1987), pp. 195– 230.

J. C. Dainty and J. R. Fienup, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, San Diego, Calif., 1987), pp. 195– 230.

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 (5)

Fig. 1
Fig. 1

Image to be encoded.

Fig. 2
Fig. 2

Optical implementation of the proposed encoding method. ψ(x) is the input image, and the phase mask is exp[−i2πn(x)]. At the output one obtains f(x)exp[i2πn(x)], which leads to f(x) since the CCD array measures |f(x)|2 and f(x) is a positive image.

Fig. 3
Fig. 3

Real part of the encoded image.

Fig. 4
Fig. 4

Imaginary part of the encoded image.

Fig. 5
Fig. 5

Decoded image with an input multiplicative noise.

Equations (4)

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

ψ ( x ) = { f ( x ) exp [ i 2 π n ( x ) ] } * h ( x ) ,
h * ( x ξ ) h ( y ξ ) = 1 N δ x y ,
δ x y = { 1 if x y = 0 0 otherwise .
ψ * ( x ) ψ ( y ) = 1 N ξ = 0 N 1 | f ( ξ ) | 2 δ x y .

Metrics