Abstract

The ptychographic scanning operation is introduced into digital holography to expand the field-of-view (FOV). An optical image encryption method based on this technique is further proposed and analyzed. The plaintext is moved sequentially in the way of ptychographic scanning and corresponding pairs of phase-shifted interferograms are recorded as ciphertexts. Then the holographic processing and the ptychographic iterative reconstruction are both employed to retrieve the plaintext. Numerical experiments demonstrate that the proposed system possesses high security level and wide FOV. The proposed method might also be used for other potential applications, such as three-dimensional information encryption and image hiding.

© 2014 Optical Society of America

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2014 (1)

S. Liu, C. Guo, and J. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
[CrossRef]

2013 (6)

J. Zang, Z. Xie, and Y. Zhang, “Optical image encryption with spatially incoherent illumination,” Opt. Lett. 38, 1289–1291 (2013).
[CrossRef]

Y. Wang, T. Li, Q. Gao, S. Zhang, and Y. Shi, “Application of diffractive optical elements for controlling the light beam in ptychography,” Opt. Eng. 52, 091720 (2013).
[CrossRef]

Y. Shi, Y. Wang, and S. Zhang, “Generalized ptychography with divers’ probes,” Chin. Phys. Lett. 30, 054203 (2013).
[CrossRef]

Y. Shi, Y. Wang, T. Li, Q. Gao, H. Wan, S. Zhang, and Z. Wu, “Ptychographic imaging algorithm with a single random phase encoding,” Chin. Phys. Lett. 30, 074203 (2013).
[CrossRef]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
[CrossRef]

W. Chen, G. Situ, and X. Chen, “High-flexibility optical encryption via aperture movement,” Opt. Express 21, 24680–24691 (2013).
[CrossRef]

2012 (2)

H. Di, K. Zheng, X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, T. C. Poon, and C. Zhou, “Multiple-image encryption by compressive holography,” Appl. Opt. 51, 1000–1009 (2012).
[CrossRef]

W. Chen and X. Chen, “Structured-illumination-based diffractive imaging and its application to optical image encryption,” Opt. Commun. 285, 2044–2047 (2012).
[CrossRef]

2010 (4)

2009 (4)

2008 (2)

2007 (2)

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier-transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

2006 (2)

2004 (3)

2003 (2)

L. Yu and L. Cai, “Multidimensional data encryption with digital holography,” Opt. Commun. 215, 271–284 (2003).
[CrossRef]

B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier-domains,” Opt. Lett. 28, 269–271 (2003).
[CrossRef]

2001 (2)

S. Liu, Q. Mi, and B. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).
[CrossRef]

S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier-transforms with random phase filtering,” Opt. Commun. 187, 57–63 (2001).
[CrossRef]

2000 (4)

1995 (1)

1982 (1)

W. Hoppe, “Trace structure analysis, ptychography, phase tomography,” Ultramicroscopy 10, 187–198 (1982).
[CrossRef]

Ahmad, M. A.

Alexandrov, S. A.

Alfalou, A.

Brosseau, C.

Bunk, O.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Cai, L.

Chen, L.

Chen, W.

Chen, X.

Clemente, P.

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

David, C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Di, H.

Di, J.

Dobson, B. R.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Dong, G.

Durán, V.

Fan, Q.

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]

Gao, Q.

Y. Wang, T. Li, Q. Gao, S. Zhang, and Y. Shi, “Application of diffractive optical elements for controlling the light beam in ptychography,” Opt. Eng. 52, 091720 (2013).
[CrossRef]

Y. Shi, Y. Wang, T. Li, Q. Gao, H. Wan, S. Zhang, and Z. Wu, “Ptychographic imaging algorithm with a single random phase encoding,” Chin. Phys. Lett. 30, 074203 (2013).
[CrossRef]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
[CrossRef]

Guo, C.

S. Liu, C. Guo, and J. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
[CrossRef]

Guo, Q.

Gutzler, T.

Han, Y.

Y. Han and Y. Zhang, “Optical image encryption based on two beams’ interference,” Opt. Commun. 283, 1690–1692 (2010).
[CrossRef]

Hennelly, B.

Hillman, T. R.

Hoppe, W.

W. Hoppe, “Trace structure analysis, ptychography, phase tomography,” Ultramicroscopy 10, 187–198 (1982).
[CrossRef]

Hurst, A. C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Javidi, B.

Jefimovs, K.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Jiang, H.

Johnson, I.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Joseph, J.

Kim, D. H.

Kim, H.

Kim, T.

Kim, Y. S.

Lam, E. Y.

Lancis, J.

Lee, Y. H.

Li, H.

Li, T.

Y. Shi, Y. Wang, T. Li, Q. Gao, H. Wan, S. Zhang, and Z. Wu, “Ptychographic imaging algorithm with a single random phase encoding,” Chin. Phys. Lett. 30, 074203 (2013).
[CrossRef]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
[CrossRef]

Y. Wang, T. Li, Q. Gao, S. Zhang, and Y. Shi, “Application of diffractive optical elements for controlling the light beam in ptychography,” Opt. Eng. 52, 091720 (2013).
[CrossRef]

Liu, J.

Liu, S.

S. Liu, C. Guo, and J. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
[CrossRef]

Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18, 12033–12043 (2010).
[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier-transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier-transforms with random phase filtering,” Opt. Commun. 187, 57–63 (2001).
[CrossRef]

S. Liu, Q. Mi, and B. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).
[CrossRef]

Liu, Z.

Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18, 12033–12043 (2010).
[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier-transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

Matoba, O.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000).
[CrossRef]

Meng, X.

Mi, Q.

Millan, M. Í. S.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Nomura, T.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25, 28–30 (2000).
[CrossRef]

Perez-Cabre, E.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[CrossRef]

Pfeiffer, F.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Poon, T. C.

Refregier, P.

Rodenburg, J. M.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[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]

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, 2008), pp. 87–184.

Sampson, D. D.

Shen, X.

Sheppard, C. J. R.

Sheridan, J.

S. Liu, C. Guo, and J. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
[CrossRef]

Sheridan, J. T.

Shi, Y.

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
[CrossRef]

Y. Shi, Y. Wang, T. Li, Q. Gao, H. Wan, S. Zhang, and Z. Wu, “Ptychographic imaging algorithm with a single random phase encoding,” Chin. Phys. Lett. 30, 074203 (2013).
[CrossRef]

Y. Wang, T. Li, Q. Gao, S. Zhang, and Y. Shi, “Application of diffractive optical elements for controlling the light beam in ptychography,” Opt. Eng. 52, 091720 (2013).
[CrossRef]

Y. Shi, Y. Wang, and S. Zhang, “Generalized ptychography with divers’ probes,” Chin. Phys. Lett. 30, 054203 (2013).
[CrossRef]

Singh, K.

Situ, G.

Sun, W.

Tajahuerce, E.

Torres-Company, V.

Unnikrishnan, G.

Verrall, S. C.

Wan, H.

Y. Shi, Y. Wang, T. Li, Q. Gao, H. Wan, S. Zhang, and Z. Wu, “Ptychographic imaging algorithm with a single random phase encoding,” Chin. Phys. Lett. 30, 074203 (2013).
[CrossRef]

Wang, B.

Wang, Y.

Y. Shi, Y. Wang, T. Li, Q. Gao, H. Wan, S. Zhang, and Z. Wu, “Ptychographic imaging algorithm with a single random phase encoding,” Chin. Phys. Lett. 30, 074203 (2013).
[CrossRef]

Y. Shi, Y. Wang, and S. Zhang, “Generalized ptychography with divers’ probes,” Chin. Phys. Lett. 30, 054203 (2013).
[CrossRef]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
[CrossRef]

Y. Wang, T. Li, Q. Gao, S. Zhang, and Y. Shi, “Application of diffractive optical elements for controlling the light beam in ptychography,” Opt. Eng. 52, 091720 (2013).
[CrossRef]

N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhao, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13424 (2009).
[CrossRef]

X. Meng, L. Cai, X. Xu, X. Yang, X. Shen, G. Dong, and Y. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31, 1414–1416 (2006).
[CrossRef]

Wu, Z.

Y. Shi, Y. Wang, T. Li, Q. Gao, H. Wan, S. Zhang, and Z. Wu, “Ptychographic imaging algorithm with a single random phase encoding,” Chin. Phys. Lett. 30, 074203 (2013).
[CrossRef]

Xie, J.

Xie, Z.

Xu, L.

Xu, X.

Yang, X.

Yu, L.

L. Yu and L. Cai, “Multidimensional data encryption with digital holography,” Opt. Commun. 215, 271–284 (2003).
[CrossRef]

S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier-transforms with random phase filtering,” Opt. Commun. 187, 57–63 (2001).
[CrossRef]

Zang, J.

Zhang, J.

Zhang, P.

Zhang, S.

Y. Wang, T. Li, Q. Gao, S. Zhang, and Y. Shi, “Application of diffractive optical elements for controlling the light beam in ptychography,” Opt. Eng. 52, 091720 (2013).
[CrossRef]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425–1427 (2013).
[CrossRef]

Y. Shi, Y. Wang, and S. Zhang, “Generalized ptychography with divers’ probes,” Chin. Phys. Lett. 30, 054203 (2013).
[CrossRef]

Y. Shi, Y. Wang, T. Li, Q. Gao, H. Wan, S. Zhang, and Z. Wu, “Ptychographic imaging algorithm with a single random phase encoding,” Chin. Phys. Lett. 30, 074203 (2013).
[CrossRef]

Zhang, X.

Zhang, Y.

Zhao, D.

Zhao, H.

Zhao, J.

Zheng, K.

Zhou, C.

Zhu, B.

S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier-transforms with random phase filtering,” Opt. Commun. 187, 57–63 (2001).
[CrossRef]

S. Liu, Q. Mi, and B. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).
[CrossRef]

Zhu, N.

Adv. Opt. Photon. (1)

Appl. Opt. (4)

Chin. Phys. Lett. (2)

Y. Shi, Y. Wang, and S. Zhang, “Generalized ptychography with divers’ probes,” Chin. Phys. Lett. 30, 054203 (2013).
[CrossRef]

Y. Shi, Y. Wang, T. Li, Q. Gao, H. Wan, S. Zhang, and Z. Wu, “Ptychographic imaging algorithm with a single random phase encoding,” Chin. Phys. Lett. 30, 074203 (2013).
[CrossRef]

Opt. Commun. (5)

Y. Han and Y. Zhang, “Optical image encryption based on two beams’ interference,” Opt. Commun. 283, 1690–1692 (2010).
[CrossRef]

L. Yu and L. Cai, “Multidimensional data encryption with digital holography,” Opt. Commun. 215, 271–284 (2003).
[CrossRef]

W. Chen and X. Chen, “Structured-illumination-based diffractive imaging and its application to optical image encryption,” Opt. Commun. 285, 2044–2047 (2012).
[CrossRef]

S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier-transforms with random phase filtering,” Opt. Commun. 187, 57–63 (2001).
[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier-transform,” Opt. Commun. 275, 324–329 (2007).
[CrossRef]

Opt. Eng. (1)

Y. Wang, T. Li, Q. Gao, S. Zhang, and Y. Shi, “Application of diffractive optical elements for controlling the light beam in ptychography,” Opt. Eng. 52, 091720 (2013).
[CrossRef]

Opt. Express (5)

Opt. Laser Technol. (1)

S. Liu, C. Guo, and J. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014).
[CrossRef]

Opt. Lett. (13)

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

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

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier-domain,” Opt. Lett. 25, 887–889 (2000).
[CrossRef]

S. Liu, Q. Mi, and B. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).
[CrossRef]

L. Chen and D. Zhao, “Optical image encryption with Hartley transforms,” Opt. Lett. 31, 3438–3440 (2006).
[CrossRef]

B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier-domains,” Opt. Lett. 28, 269–271 (2003).
[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
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Figures (10)

Fig. 1.
Fig. 1.

Schematic experimental setup for optical encryption of unlimited-size image based on ptychographic scanning digital holography: BS, beam splitter; d1, d2, and d3, diffraction distance; M1, M2, and M3, phase-only masks.

Fig. 2.
Fig. 2.

(a) Illumination on the object plane in the classical DH system and (b) Illustration for the P-scanning operation on the object plane. (c) Effect of the P-scanning.

Fig. 3.
Fig. 3.

Flow chart of the decryption procedure.

Fig. 4.
Fig. 4.

(a) Secret image, (b) illumination on the object plane, and (c) using P-scanning mode (3×3 scanning positions and 50% overlapped rate).

Fig. 5.
Fig. 5.

(a)–(c) Phase-only masks M1, M2, and M3, (512×512 pixels). (d) and (e) Typical pair of ciphertexts (512×512 pixels) corresponding to 0 and π phase delays, respectively. (f) Correct decrypted image (1024×1024 pixels and the iterations are 100). (g) Co curve of the decryption.

Fig. 6.
Fig. 6.

Co values between the decrypted results and the original image when the scanning errors (Se) change from 1.0mm to +1.0mm, and some typical examples are also presented.

Fig. 7.
Fig. 7.

(a)–(c) Three complex probes (phase term, blue: π/2; green: 0; red: π/2). (d) and (e) Decrypted images when using correct and incorrect probes, respectively.

Fig. 8.
Fig. 8.

Co curves of adjacent positions in the single ptychographic and the P-scanning DH method, respectively.

Fig. 9.
Fig. 9.

Decrypted images when using (a) a wrong phase-only mask M3 and (b) a wrong diffractive distance d3 (error=1mm), (c) a wrong wavelength λ (error=5nm), (d) a wrong phase-only mask M2, and (e) a wrong diffractive distance d2 (error=1mm).

Fig. 10.
Fig. 10.

Robustness of the proposed method against noise attack and occlusion: (a) ciphertext with random noise (SNR=5), (b) decrypted image from (a), (c) ciphertext with 6.25% occlusion, and (d) decrypted image from (c).

Equations (10)

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{IDn0=|Onc|2+|R|2+OncR*+Onc*RIDnπ=|Onc|2+|R|2OncR*Onc*R,
R=FrTλ,d[exp(iM3)].
Ognck=FrTλ,d2{FrTλ,d1[Pn·Ognk·exp(iM1)]·exp(iM2)},
|Onc|2=IDn0+IDnπ2|R|2.
O^gnck=|Onc|2·Ognck|Ognck|.
OgnRk=FrTλ,d11{FrTλ,d21(O^gnck)·exp(iM2)}·exp(iM1),
O^gk=Ogk+|Pn||Pn,max|Pn*|Pn|2+δ(OgRkPn·Ogk),
Co(f,fo)=cov(f,fo)(σf·σfo)1,
Single ptychographic method:{N1=|Ψ(A+B)|2N2=|Ψ(B+C)|2P-scanning DH method:{N˜1=|Ψ(A+B)+X1|2N˜2=|Ψ(B+C)+X2|2,
Se=SpSd.

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