Abstract

A method for both image encryption and watermarking by three-step phase-shifting interferometry is proposed. The image to be hidden is stored in three interferograms and then can be reconstructed by use of one random phase mask, several specific geometric parameters, and a certain algorithm. To further increase the security of the hidden image and confuse unauthorized receivers, images with the same or different content can be added to the interferograms, and these images will have no or only a small effect on the retrieval of the hidden image, owing to the specific property of this algorithm. All these features and the utility of this method for image retrieval from parts of interferograms are verified by computer simulations. This technique uses intensity maps as decrypted images for delivery, and both encryption and decryption can be conveniently achieved digitally. It is particularly suitable for the remote transmission of secret information via the Internet.

© 2004 Optical Society of America

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References

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2003

2002

L. Yu, X. Peng, L. Cai, “Parameterized multi-dimensional data encryption by digital optics,” Opt. Commun. 203, 67–77 (2002).
[CrossRef]

N. Takai, Y. Mifune, “Digital watermarking by a holographic technique,” Appl. Opt. 41, 865–873 (2002).
[CrossRef] [PubMed]

2001

2000

1999

1995

Cai, L.

L. Yu, X. Peng, L. Cai, “Parameterized multi-dimensional data encryption by digital optics,” Opt. Commun. 203, 67–77 (2002).
[CrossRef]

Cai, L. Z.

L. Z. Cai, Q. Liu, X. L. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. 19, 1808–1810 (2003).
[CrossRef]

Du, J.

Guo, Y. K.

Hennelly, B.

Huang, Q.

Javidi, B.

Joseph, J.

Kishk, S.

Liu, Q.

L. Z. Cai, Q. Liu, X. L. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. 19, 1808–1810 (2003).
[CrossRef]

Matoba, O.

Mifune, Y.

Nomura, T.

Peng, X.

L. Yu, X. Peng, L. Cai, “Parameterized multi-dimensional data encryption by digital optics,” Opt. Commun. 203, 67–77 (2002).
[CrossRef]

Réfrégier, P.

Sheridan, J. T.

Singh, K.

Tajahuerce, E.

Takai, N.

Unnikrishnan, G.

Yang, X. L.

L. Z. Cai, Q. Liu, X. L. Yang, “Phase-shift extraction and wave-front reconstruction in phase-shifting interferometry with arbitrary phase steps,” Opt. Lett. 19, 1808–1810 (2003).
[CrossRef]

Yu, L.

L. Yu, X. Peng, L. Cai, “Parameterized multi-dimensional data encryption by digital optics,” Opt. Commun. 203, 67–77 (2002).
[CrossRef]

Zhang, Y.

Appl. Opt.

Opt. Commun.

L. Yu, X. Peng, L. Cai, “Parameterized multi-dimensional data encryption by digital optics,” Opt. Commun. 203, 67–77 (2002).
[CrossRef]

Opt. Lett.

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Figures (7)

Fig. 1
Fig. 1

Schematic of image encryption by phase-shifting interferometry.

Fig. 2
Fig. 2

Image to be hidden and transmitted.

Fig. 3
Fig. 3

Results of digital image encryption and decryption: (a), (b), (c) interferograms I 1, I 2, and I 3, respectively; (d) correctly retrieved image; (e) retrieved image when mask G2 is not used; (f) retrieved image with mask G2 shifted transversely by one pixel; (g), (h), (i) retrieved images when λ, d 1, and d 2 have relative errors 0.23%, 0.3%, and 0.28%, respectively.

Fig. 4
Fig. 4

Results similar to those in Fig. 3 but with the same facial pattern a 1(x, y) added to I 1, I 2, and I 3 in (a), (b), and (c), respectively. The parameters are the same as those in Fig. 3.

Fig. 5
Fig. 5

Results similar to those in Fig. 3 but with different facial patterns a 1(x, y), a 2(x, y), and a 3(x, y) added to I 1, I 2, and I 3 in (a), (b), and (c), respectively. The parameters are the same as those in Fig. 3, except that the relative error for d 2 in (i) now is 0.27%.

Fig. 6
Fig. 6

Ability of this method for image retrieval from parts of interferograms when the same content image, a 1(x, y), is used. (a)–(d) use 400 × 400 pixels, where (a), (b), and (c) are parts of I 1 + a 1, I 2 + a 1, and I 3 + a 1, respectively. (d) Retrieved hidden image; (e)–(h) similar to (a)–(d) but for 300 × 300 pixels. All the images were sized to have the same printed dimensions.

Fig. 7
Fig. 7

Results similar to those in Fig. 6 but with three different content images. (a)–(d) use 400 × 400 pixels; (e)–(h) use 300 × 300 pixels.

Equations (8)

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ux2, y2=expikd1iλd1  t0x1, y1×expi2πpx1, y1expiπλd1×x2-x12+y2-y12dx1dy1,
ux, y=expikd2iλd2  ux2, y2×expi2πqx2, y2expiπλd2×x-x22+y-y22dx2dy2,
Inx, y=A2x, y+Ar2+2ArAx, ycosφ-δn.
ux, y=14ArI1-I3+i2I2-I1-I3.
I1x, y=I1x, y+αax, y, I2x, y=I2x, y+αax, y,I3x, y=I3x, y+αax, y,
I1x, y=I1x, y+α1a1x, y, I2x, y=I2x, y+α2a2x, y, I3x, y=I3x, y+α3a3x, y,
ux, y=ux, y+Δux, y,
Δux, y=α1a1-α3a3+i2α2a2-α1a1-α3a3

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