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

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References

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  1. B. Javidi, J. L. Horner, Opt. Eng. 33, 1752 (1994).
    [CrossRef]
  2. J. L. Horner, B. Javadi, in Optical Pattern Recognition, B. Javidi, 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, J. R. Fienup, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, San Diego, Calif., 1987), pp. 195– 230.
  7. J. L. Horner, P. D. Gianino, Appl. Opt. 23, 812 (1984).
    [CrossRef] [PubMed]

1994

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

1984

1968

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

Dainty, J. C.

J. C. Dainty, 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, 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, J. L. Horner, Opt. Eng. 33, 1752 (1994).
[CrossRef]

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

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

Javadi, B.

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

Javidi, B.

B. Javidi, 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.

IEEE Trans. Syst. Sci. Cybernet.

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

Opt. Eng.

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

Other

J. L. Horner, B. Javadi, in Optical Pattern Recognition, B. Javidi, 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, J. R. Fienup, in Image Recovery: Theory and Application, H. Stark, ed. (Academic, San Diego, Calif., 1987), pp. 195– 230.

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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)

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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 .

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