Abstract

Image encryption with optical means has attracted attention due to its inherent multidimensionality and degrees of freedom, including phase, amplitude, polarization, and wavelength. In this paper, we propose an optical encoding system based on multiple intensity samplings of the complex-amplitude wavefront with axial translation of the image sensor. The optical encoding system is developed based on a single optical path, where multiple diffraction patterns, i.e., ciphertexts, are sequentially recorded through the axial translation of a CCD camera. During image decryption, an iterative phase retrieval algorithm is proposed for extracting the plaintext from ciphertexts. The results demonstrate that the proposed phase retrieval algorithm possesses a rapid convergence rate during image decryption, and high security can be achieved in the proposed optical cryptosystem. In addition, other advantages of the proposed method, such as high robustness against ciphertext contaminations, are also analyzed.

© 2013 Optical Society of America

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2012 (4)

E. Pérez-Cabré, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[CrossRef]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).
[CrossRef]

S. S. Gorthi and E. Schonbrun, “Phase imaging flow cytometry using a focus-stack collecting microscope,” Opt. Lett. 37, 707–709 (2012).
[CrossRef]

W. Chen and X. Chen, “Focal-plane detection and object reconstruction in the noninterferometric phase imaging,” J. Opt. Soc. Am. A 29, 585–592 (2012).
[CrossRef]

2011 (6)

2010 (7)

2009 (4)

H. E. Hwang, H. T. Chang, and W. N. Lie, “Fast double-phase retrieval in Fresnel domain using modified Gerchberg-Saxton algorithm for lensless optical security systems,” Opt. Express 17, 13700–13710 (2009).
[CrossRef]

K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express 17, 19662–19673 (2009).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

O. Matoba, T. Nomura, E. P. Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

2008 (2)

2007 (4)

2006 (1)

2005 (1)

2004 (2)

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

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

2003 (3)

2000 (1)

O. Matoba and B. Javidi, “Encrypted optical memory systems based on multidimensional keys for secure data storage and communications,” IEEE Circuits Devices Mag. 16(5), 8–15 (2000).

1999 (4)

1998 (2)

1997 (2)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[CrossRef]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[CrossRef]

1996 (1)

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

1995 (1)

1982 (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 35, 237–246 (1972).

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef]

Abril, H. C.

E. Pérez-Cabré, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[CrossRef]

Ahmad, M. A.

Alieva, T.

Almoro, P. F.

Anand, A.

A. Anand, V. Chhaniwal, and B. Javidi, “Quantitative cell imaging using single beam phase retrieval method,” J. Biomed. Opt. 16, 060503 (2011).
[CrossRef]

A. Anand and B. Javidi, “Three-dimensional microscopy with single-beam wavefront sensing and reconstruction from speckle fields,” Opt. Lett. 35, 766–768 (2010).
[CrossRef]

Arcos, S.

Bollaro, F.

Cabré, E. P.

O. Matoba, T. Nomura, E. P. Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Calvo, M. L.

Carnicer, A.

Castro, A.

Chang, H. T.

Chapman, H. N.

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Chatwin, C.

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Chen, W.

Chen, X.

Chhaniwal, V.

A. Anand, V. Chhaniwal, and B. Javidi, “Quantitative cell imaging using single beam phase retrieval method,” J. Biomed. Opt. 16, 060503 (2011).
[CrossRef]

Cho, M.

Dowling, T.

Faulkner, H. M. L.

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

Fienup, J. R.

Frauel, Y.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161, 777–778 (1948).
[CrossRef]

Gao, M.

J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

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 35, 237–246 (1972).

Glückstad, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Gorthi, S. S.

Goudail, F.

Gundu, P. N.

Guo, Q.

Han, P.

Hanson, S. G.

Hennelly, B.

Hennelly, B. M.

Hwang, H. E.

Javidi, B.

E. Pérez-Cabré, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[CrossRef]

A. Anand, V. Chhaniwal, and B. Javidi, “Quantitative cell imaging using single beam phase retrieval method,” J. Biomed. Opt. 16, 060503 (2011).
[CrossRef]

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

A. Anand and B. Javidi, “Three-dimensional microscopy with single-beam wavefront sensing and reconstruction from speckle fields,” Opt. Lett. 35, 766–768 (2010).
[CrossRef]

O. Matoba, T. Nomura, E. P. Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253–10265 (2007).
[CrossRef]

S. Kishk and B. Javidi, “Watermarking of three-dimensional objects by digital holography,” Opt. Lett. 28, 167–169 (2003).
[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical memory systems based on multidimensional keys for secure data storage and communications,” IEEE Circuits Devices Mag. 16(5), 8–15 (2000).

N. Towghi, B. Javidi, and Z. Luo, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915–1927 (1999).
[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical storage with wavelength-key and random phase codes,” Appl. Opt. 38, 6785–6790 (1999).
[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
[CrossRef]

F. Goudail, F. Bollaro, B. Javidi, and P. Réfrégier, “Influence of a perturbation in a double phase-encoding system,” J. Opt. Soc. Am. A 15, 2629–2638 (1998).
[CrossRef]

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[CrossRef]

P. Réfrégier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[CrossRef]

Joseph, J.

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).
[CrossRef]

Juvells, I.

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Kishk, S.

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

Kumar, A.

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).
[CrossRef]

Kumar, P.

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).
[CrossRef]

Lie, W. N.

Liu, S.

Liu, Z.

Luo, Z.

Matoba, O.

O. Matoba, T. Nomura, E. P. Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical memory systems based on multidimensional keys for secure data storage and communications,” IEEE Circuits Devices Mag. 16(5), 8–15 (2000).

O. Matoba and B. Javidi, “Encrypted optical storage with wavelength-key and random phase codes,” Appl. Opt. 38, 6785–6790 (1999).
[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
[CrossRef]

Matsushima, K.

Miao, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

Millan, M. S.

E. Pérez-Cabré, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[CrossRef]

Millán, M. S.

O. Matoba, T. Nomura, E. P. Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Nagahara, L. A.

J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Naughton, T. J.

Neild, A.

Ng, T. W.

Nomura, T.

O. Matoba, T. Nomura, E. P. Cabré, M. S. Millán, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Osten, W.

Paganin, D. M.

R. P. Yu, and D. M. Paganin, “Blind phase retrieval for aberrated linear shift-invariant imaging systems,” New J. Phys. 12, 073040 (2010).
[CrossRef]

Pedrini, G.

Pérez-Cabré, E.

E. Pérez-Cabré, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[CrossRef]

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

Quan, C.

W. Chen, C. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

Réfrégier, P.

Rodenburg, J. M.

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

Rodrigo, J. A.

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 35, 237–246 (1972).

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

Schonbrun, E.

Sheppard, C. J. R.

Sheridan, J. T.

Shi, Y.

Shimobaba, T.

Singh, K.

P. Kumar, A. Kumar, J. Joseph, and K. Singh, “Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack,” Opt. Lasers Eng. 50, 1196–1201 (2012).
[CrossRef]

Situ, G.

Stallings, W.

W. Stallings, Cryptography and Network Security: Principles and Practice, 4th ed. (Prentice-Hall, 2006).

Tay, C. J.

W. Chen, C. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

Towghi, N.

Usategui, M. M.

Vartanyants, I.

J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Wang, B.

Wang, R. K.

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Watson, I. A.

R. K. Wang, I. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. 35, 2464–2469 (1996).
[CrossRef]

Wu, C.

Xu, L.

Yamaguchi, I.

Yu, R. P.

R. P. Yu, and D. M. Paganin, “Blind phase retrieval for aberrated linear shift-invariant imaging systems,” New J. Phys. 12, 073040 (2010).
[CrossRef]

Zhang, F.

G. Pedrini, F. Zhang, and W. Osten, “Phase retrieval by pinhole scanning,” Opt. Lett. 36, 1113–1115 (2011).
[CrossRef]

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).
[CrossRef]

Zhang, J.

Zhang, R.

J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Zhang, T.

Zhang, Y.

Zou, J. M.

J. M. Zou, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

W. Chen, C. Quan, and C. J. Tay, “Extended depth of focus in a particle field measurement using a single-shot digital hologram,” Appl. Phys. Lett. 95, 201103 (2009).
[CrossRef]

IEEE Circuits Devices Mag. (1)

O. Matoba and B. Javidi, “Encrypted optical memory systems based on multidimensional keys for secure data storage and communications,” IEEE Circuits Devices Mag. 16(5), 8–15 (2000).

J. Biomed. Opt. (1)

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The plaintext (Baboon): http://sipi.usc.edu/database .

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Figures (8)

Fig. 1.
Fig. 1.

(a) Schematic optical setup for the proposed optical security system. (b) Schematic experimental setup for simultaneously recording three diffraction patterns without axial movements of the cameras. M, phase-only mask; P, plaintext; CCD, charge-coupled device; z1z5, axial distances. Three phase-only masks are used in the optical path, and it is straightforward to apply fewer or more phase-only masks in practical applications.

Fig. 2.
Fig. 2.

Flow chart for the proposed phase retrieval algorithm during image decryption.

Fig. 3.
Fig. 3.

(a) Plaintext (512×512 pixels and 8 bits); and phase-only masks (b) M1, (c) M2, and (d) M3.

Fig. 4.
Fig. 4.

(a)–(c) Three diffraction patterns (i.e., ciphertexts) sequentially recorded through the axial translation of CCD camera during image encryption.

Fig. 5.
Fig. 5.

(a) Decrypted image obtained by using correct security keys and (b) the corresponding relationship between the number of iterations and iterative errors (with a natural logarithm scale) during image decryption.

Fig. 6.
Fig. 6.

(a) Decrypted image obtained after 500 iterations by using a wrong axial distance z2 and (b) the corresponding relationship between the number of iterations and correlation coefficients. (c) Decrypted image obtained after 500 iterations by using a wrong wavelength and (d) the corresponding relationship between the number of iterations and correlation coefficients. The “CC” denotes correlation coefficient.

Fig. 7.
Fig. 7.

Decrypted images obtained after 500 iterations, respectively, by using the wrong phase-only mask (a) M2 or (c) M3; (b) and (d) are the corresponding relationships between the number of iterations and correlation coefficients obtained during image decryption, respectively, corresponding to (a) and (c).

Fig. 8.
Fig. 8.

(a) One typical ciphertext contaminated by the noise; (b) decrypted image obtained after 30 iterations with all ciphertexts contaminated by noise; (c) relationship between the number of iterations and the correlation coefficients during image decryption corresponding to (b). (d) Typical ciphertext contaminated by the occlusion; (e) decrypted image obtained after the 30 iterations with all ciphertexts contaminated by the occlusions; (f) relationship between iteration number and correlation coefficients during the decryption corresponding to (e).

Equations (14)

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O(x2,y2)=jλ++P(x1,y1)M1(x1,y1)exp[jk(x1x2)2+(y1y2)2+z12](x1x2)2+(y1y2)2+z12dx1dy1,
I(h)(ξ,η)=|FSPzi{[FSPz2({FSPz1[P(x1,y1)M1(x1,y1)]}M2(x2,y2))]M3(x3,y3)}|2,
O(1)(ξ,η)=FSPz3{[FSPz2({FSPz1[P(1)(n)(x1,y1)M1(x1,y1)]}M2(x2,y2))]M3(x3,y3,)}.
O(1)(ξ,η)¯=[I(1)(ξ,η)]1/2[O(1)(ξ,η)/|O(1)(ξ,η)|].
P(1)(n)(x1,y1)¯=(FSPz1{[FSPz2({FSPz3[O(1)(ξ,η)¯]}[M3(x3,y3)]*)][M2(x2,y2)]*})[M1(x1,y1)]*,
O(2)(ξ,η)=FSPz4{[FSPz2({FSPz1[|P(1)(n)(x1,y1)¯|M1(x1,y1)]}M2(x2,y2))]M3(x3,y3)}.
O(2)(ξ,η)¯=[I(2)(ξ,η)]1/2[O(2)(ξ,η)/|O(2)(ξ,η)|].
P(2)(n)(x1,y1)¯=(FSPz1{[FSPz2({FSPz4[O(2)(ξ,η)¯]}[M3(x3,y3)]*)][M2(x2,y2)]*})[M1(x1,y1)]*.
O(3)(ξ,η)=FSPz5{[FSPz2({FSPz1[|P(2)(n)(x1,y1)¯|M1(x1,y1)]}M2(x2,y2))]M3(x3,y3)}.
O(3)(ξ,η)¯=[I(3)(ξ,η)]1/2[O(3)(ξ,η)/|O(3)(ξ,η)|].
P(3)(n)(x1,y1)¯=(FSPz1{[FSPz2({FSPz5[O(3)(ξ,η)¯]}[M3(x3,y3)]*)][M2(x2,y2)]*})[M1(x1,y1)]*.
Error=x1,y1[|P(3)(n)(x1,y1)¯||P(3)(n1)(x1,y1)¯|]2.
CC=[cov(P,P)]/(σP×σP),
MSE=1M×Nμ=1Mν=1N[P(μ,ν)P(μ,ν)]2,

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