Abstract

We propose an optical architecture that encodes a primary image to stationary white noise by using two statistically independent random phase codes. The encoding is done in the fractional Fourier domain. The optical distribution in any two planes of a quadratic phase system (QPS) are related by fractional Fourier transform of the appropriately scaled distribution in the two input planes. Thus a QPS offers a continuum of planes in which encoding can be done. The six parameters that characterize the QPS in addition to the random phase codes form the key to the encrypted image. The proposed method has an enhanced security value compared with earlier methods. Experimental results in support of the proposed idea are presented.

© 2000 Optical Society of America

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References

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1999

1998

1997

1995

Hua, J.

Javidi, B.

Joseph, J.

Kutay, M. A.

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, San Diego, Calif., 1999), Vol. 106, Chap. 4, pp. 239–291.
[CrossRef]

Li, G.

Liu, L.

Matoba, O.

Mendlovic, D.

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, San Diego, Calif., 1999), Vol. 106, Chap. 4, pp. 239–291.
[CrossRef]

Ozaktas, H. M.

H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, San Diego, Calif., 1999), Vol. 106, Chap. 4, pp. 239–291.
[CrossRef]

Réfrégier, P.

Singh, K.

Unnikrishnan, G.

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Figures (6)

Fig. 1
Fig. 1

Optical setup for encryption.

Fig. 2
Fig. 2

Schematic of the encryption system.

Fig. 3
Fig. 3

Schematic of the decryption system.

Fig. 4
Fig. 4

Optical setup for decryption.

Fig. 5
Fig. 5

Experimental setup: BS’s, beam splitters, BE, beam expander; M’s, mirrors; R1, R2, random phase masks; L1–L3, lenses; PRC, photorefractive crystal; O, object transparency.

Fig. 6
Fig. 6

(a) Primary image used for the study, (b) encrypted image, (c) decrypted image with the correct key, (d) decrypted image with the correct random phase codes but the wrong QPS parameters.

Equations (7)

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

gu=Kfxexpiϕ1x×expiπa2x2+b2u2tan α-i2πabuxsin αdx,
a2=1λf1-d2f1-d11f12-f1-d1f1-d21/2,
α=arccosf1-d1f1-d2f1,
b2=1λf1-d1f1-d21f12-f1-d1f1-d21/2.
Ψy=Kguexpiϕ2u×expiπc2u2+d2y2tan β-i2πcduysin βdu,
gdu=KΨ*y×expiπd2y2+c2u2tan β-i2πcduysin βdy.
fdx=Kgduexpiϕ2u×expiπb2u2+a2x2tan α-i2πabuxsin αdu.

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