Abstract

We described a method where the secret binary image that has been encoded into a single amplitude pattern in Fresnel domain can be recovered based on phase retrieval with an aperture-key and wavelength keys, and no holographic recording is needed in the encryption. The predesigned aperture-key not only realizes the intensity modulation of the encrypted image, but also helps to retrieve the secret image with high quality. All the necessary decryption keys can be kept in digital form that facilitates data transmission and loading in image retrieval process. Numerical simulation results are given for testing the validity and security of the proposed approach.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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2014 (3)

2013 (2)

2009 (2)

2007 (1)

2006 (1)

2004 (3)

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4798 (2004).
[Crossref]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).
[Crossref] [PubMed]

1999 (1)

1996 (1)

1995 (1)

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Alfalou, A.

Brasher, J. D.

Brosseau, C.

Castro, A.

Chang, H. T.

Chen, W.

Chen, X.

Faulkner, H. M. L.

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4798 (2004).
[Crossref]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

Fienup, J. R.

Frauel, Y.

Gao, Q.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Gong, Q.

Hwang, H. E.

Javidi, B.

Johnson, E. G.

Li, H.

Li, T.

Lie, W. N.

Matoba, O.

Naughton, T. J.

Peng, X.

Qin, Y.

Refregier, P.

Rodenburg, J. M.

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4798 (2004).
[Crossref]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Shi, Y.

Situ, G.

Wang, X.

Wang, Y.

Wang, Z.

Wei, H.

Zhang, J.

Zhang, P.

Zhang, S.

Adv. Opt. Photon. (2)

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4798 (2004).
[Crossref]

Opt. Express (4)

Opt. Lett. (7)

Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).

Phys. Rev. Lett. (1)

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

Other (1)

K. T. Alligood, T. D. Sauer, and J. A. Yorke, Chaos: An Introduction to Dynamical Systems (Springer, 2001).

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Figures (10)

Fig. 1
Fig. 1 Proposed schematic optical setup for binary images encryption without need of holographic recording.
Fig. 2
Fig. 2 (a) Plaintext, (b) one of the four CRPMs ( p 1 ), (c) aperture-key and (d) cyphertext.
Fig. 3
Fig. 3 The MSE curve of recovered images with the change of the scaling factor used for encryption. The attached three images arranged from left to right correspond to the scaling factors, 0.2, 1.0 and 2.0 respectively.
Fig. 4
Fig. 4 (a) MSE and (b) CC curves obtained by the proposed method. (c) MSE and (d) CC curves obtained by conventional GS-based PRA.
Fig. 5
Fig. 5 Retrieved image after (a) 50 iterations using the proposed method, (b) 1000 iterations using the conventional GS-based PRA.
Fig. 6
Fig. 6 Decrypted images after 200 iterations using a wrong CRPM. (a) p 1 with μ = 3.96 ( Δ μ = 0.01 ), (b) p 2 with x 0 = 0.23 ( Δ x 0 = 0.01 ), (c) p 3 with μ = 3.95 ( Δ μ = 0.01 ), (d) p 4 with x 0 = 0.16 ( Δ x 0 = 0.01 ).
Fig. 7
Fig. 7 Decrypted images after 100 iterations using a wrong key (a) λ 1 = 610 n m ( Δ λ 1 = 10 n m ) , (b) λ 2 = 660 n m ( Δ λ 2 = 10 n m ) , (c) z 1 = 51 c m ( Δ z 1 = 1 c m ) , (d) z 3 = 71 c m ( Δ z 3 = 1 c m ) .
Fig. 8
Fig. 8 Relations between MSE (between original and reconstructed data) and the scaling factor used for decryption.
Fig. 9
Fig. 9 Decrypted image after 100 iterations using (a) a circular aperture, (b) a relatively large rectangular aperture, (c) the upper half and (d) the lower half of the correct aperture-key.
Fig. 10
Fig. 10 Relations between CC and iteration number using different apertures.

Equations (8)

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I 0 ( x , y ) = | FrT z 2 , λ 1 { FrT z 1 , λ 1 { f ( x , y ) p 1 ( x , y ) } p 2 ( x , y ) } | 2
FrT z , λ { u ( x , y ) } = exp ( j k z ) j λ z u ( x , y ) exp { j π λ z [ ( x x ) 2 + ( y y ) 2 ] } d x d y
C ( x , y ) = | FrT z 2 , λ 1 { FrT z 1 , λ 1 { f ( x , y ) p 1 ( x , y ) } p 2 ( x , y ) } | 2 + α | FrT z 4 , λ 2 { FrT z 3 , λ 2 { a ( x , y ) p 3 ( x , y ) } p 4 ( x , y ) } | 2
I a ( x , y ) = | FrT z 4 , λ 2 { FrT z 3 , λ 2 { a ( x , y ) p 3 ( x , y ) } p 4 ( x , y ) } | 2
u n ( x , y ) = FrT z 2 , λ 1 { FrT z 1 , λ 1 { f n ( x , y ) p 1 ( x , y ) } p 2 ( x , y ) }
u n ( x , y ) = | C ( x , y ) α I a ( x , y ) | PR { u n ( x , y ) }
u n ( x , y ) = p 1 ( x , y ) FrT z 1 , λ 1 { p 2 ( x , y ) FrT z 2 , λ 1 { u n ( x , y ) } }
f n + 1 ( x , y ) = f n ( x , y ) + T ( x , y ) [ u n ( x , y ) a ( x , y ) f n ( x , y ) ]

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