Abstract

Generally, the reconstruction of an object image from its diffraction field requires both the amplitude and the phase information of this field. We systematically investigated the effects of using only the real part, the imaginary part, or the phase information of the diffraction field to reconstruct the original image for both the binary and the gray-level images. We show that the phase information can yield a better result of image retrieval than the real or imaginary part and that the recovered image from the phase information is satisfactory especially for binary input. On the basis of this idea, a new technique of image encryption and watermarking by use of only one delivered image—the phase map of the diffraction field of the original image—through double random-phase encoding is proposed and verified by computer simulations with phase-shifting interferometry. This method can greatly cut down the communication load and is suitable for Internet transmission.

© 2005 Optical Society of America

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References

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2004

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2002

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1995

Bertaux, N.

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.

Du, J.

Frauel, Y.

Glückstad, J.

Guo, Y. K.

He, M. Z.

Hennelly, B.

Huang, Q.

Javidi, B.

Joseph, J.

Kishk, S.

Liu, Q.

Matoba, O.

Mc Donald, J. B.

Mifune, Y.

Mogensen, P. C.

Naughton, T. J.

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]

Refregier, P.

Sheridan, J. T.

Singh, K.

Tajahuerce, E.

Takai, N.

Unnikrishnan, G.

Yang, X. L.

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.

S. Kishk, B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462–5470 (2002).
[CrossRef] [PubMed]

E. Tajahuerce, B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595–6601 (2000).
[CrossRef]

Y. K. Guo, Q. Huang, J. Du, Y. Zhang, “Decomposition storage of information based on computer-generated hologram interference and its application in image encryption,” Appl. Opt. 40, 2860–2863 (2001).
[CrossRef]

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

L. Z. Cai, M. Z. He, Q. Liu, X. L. Yang, “Digital image encryption and watermarking by phase-shifting interferome-try,” Appl. Opt. 43, 3078–3084 (2004).
[CrossRef] [PubMed]

T. J. Naughton, J. B. Mc Donald, B. Javidi, “Efficient compression of Fresnel fields for Internet transmission of three-dimensional images,” Appl. Opt. 42, 4758–4764 (2003).
[CrossRef] [PubMed]

T. J. Naughton, Y. Frauel, B. Javidi, E. Tajahuerce, “Compression of digital holograms for three-dimensional object reconstruction and recognition,” Appl. Opt. 41, 4124–4132 (2002).
[CrossRef] [PubMed]

P. C. Mogensen, J. Glückstad, “Phase-only optical decryption of a fixed mask,” Appl. Opt. 40, 1226–1235 (2001).
[CrossRef]

O. Matoba, T. J. Naughton, Y. Frauel, N. Bertaux, B. Javidi, “Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram,” Appl. Opt. 41, 6187–6192 (2002).
[CrossRef] [PubMed]

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 (6)

Fig. 1
Fig. 1

Scheme of the image encryption and watermarking system by PSI. BE, beam expander; BS, beam splitter; M, mirror; PR, phase retarder.

Fig. 2
Fig. 2

(a) Binary image to be hidden, (b) gray-level image to be hidden, and (c) host image C(x, y).

Fig. 3
Fig. 3

Image encryption and decryption results by use of a binary hidden image. (a) Transmitted real part; (b) retrieved image from (a); (c) binarized image from (b); (d) transmitted imaginary part; (e) retrieved image from (d); (f) binarized image from (e); (g) transmitted phase map; (h) retrieved image from (g); (i) binarized image from (h).

Fig. 4
Fig. 4

Image encryption and decryption results by use of a gray-level hidden image. (a) Transmitted real part; (b) retrieved image from (a); (c) transmitted imaginary part; (d) retrieved image from (c); (e) transmitted phase map; (f) retrieved image from (e).

Fig. 5
Fig. 5

Similar results as in Fig. 3 but with watermarking. Here the encrypted images in the left column are embedded by the host image in Fig. 2(c).

Fig. 6
Fig. 6

Similar results as in Fig. 4 but with watermarking. Here the encrypted images in the left column are embedded by the host image in Fig. 2(c).

Tables (1)

Tables Icon

Table 1 Calculation Results of the Normalized MSEs in Image Encryption for Binary and Gray-Level Images

Equations (10)

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U 2 ( x 2 , y 2 ) = exp ( i k d 1 ) i λ d 1 t ( x 1 , y 1 ) exp [ i 2 π p ( x 1 , y 1 ) ] × exp { i π λ d 1 [ ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 ] } d x 1 d y 1 ,
U ( x , y ) = exp ( i k d 2 ) i λ d 2 U 2 ( x 2 , y 2 ) exp [ i 2 π q ( x 2 , y 2 ) ] × exp { i π λ d 2 [ ( x x 2 ) 2 + ( y y 2 ) 2 ] } d x 2 d y 2 .
I 1 ( x , y ) = A 2 ( x , y ) + A r 2 + 2 A r A ( x , y ) cos ϕ ( x , y ) , I 2 ( x , y ) = A 2 ( x , y ) + A r 2 + 2 A r A ( x , y ) sin ϕ ( x , y ) , I 3 ( x , y ) = A 2 ( x , y ) + A r 2 2 A r A ( x , y ) cos ϕ ( x , y ) , I 4 ( x , y ) = A 2 ( x , y ) + A r 2 2 A r A ( x , y ) sin ϕ ( x , y ) ,
U ( x , y ) = 1 4 A r [ ( I 1 I 3 ) + i ( I 2 I 4 ) ] .
I 1 = I 1 I 3 + I 0 ,
I 1 I 3 = c A cos ϕ = 1 2 c [ A exp ( i ϕ ) + A exp ( i ϕ ) ] ,
ϕ ( x , y ) = i ln ( I 1 I 3 ) + i ( I 2 I 4 ) 4 A r A ( x , y ) ,
I ( x , y ) = I ( x , y ) + α C ( x , y )
ϕ ( x , y ) = ϕ ( x , y ) + α C ( x , y ) ,
MSE = x = 0 M 1 y = 0 N 1 [ | f ( x , y ) f r ( x , y ) | 2 ] x = 0 M 1 y = 0 N 1 [ | f ( x , y ) | 2 ] ,

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