Abstract

Ptychography is combined with optical image encryption for the first time. Due to the nature of ptychography, not only is the interferometric optical setup that is usually adopted not required any more, but also the encryption for a complex-valued image is achievable. Considering that the probes overlapping with each other is the crucial factor in ptychography, their complex-amplitude functions can serve as a kind of secret keys that lead to the enlarged key space and the enhanced system security. Further, since only introducing the probes into the input of common system is required, it is convenient to combine ptychography with many existing optical image encryption systems for varied security applications.

© 2013 Optical Society of America

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M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Commun. 3, 730 (2012).
[CrossRef]

2010

2009

2008

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[CrossRef]

2007

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, Ultramicroscopy 107, 227 (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, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

2004

H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef]

1982

W. Hoppe, Ultramicroscopy 10, 187 (1982).
[CrossRef]

1969

W. Hoppe, Acta Crystallogr. A 25, 495 (1969).

Alfalou, A.

Brosseau, C.

Bunk, O.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Chen, W.

Chen, X.

Clemente, P.

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, Ultramicroscopy 107, 227 (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, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Dierolf, M.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[CrossRef]

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, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Durán, V.

Faulkner, H. M. L.

H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef]

Hoppe, W.

W. Hoppe, Ultramicroscopy 10, 187 (1982).
[CrossRef]

W. Hoppe, Acta Crystallogr. A 25, 495 (1969).

Humphry, M. J.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Commun. 3, 730 (2012).
[CrossRef]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, Opt. Lett. 35, 2585 (2010).
[CrossRef]

Hurst, A. C.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Commun. 3, 730 (2012).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, Ultramicroscopy 107, 227 (2007).
[CrossRef]

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, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

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, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Kraus, B.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Commun. 3, 730 (2012).
[CrossRef]

Lancis, J.

Maiden, A. M.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Commun. 3, 730 (2012).
[CrossRef]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, Opt. Lett. 35, 2585 (2010).
[CrossRef]

Menzel, A.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[CrossRef]

Pfeiffer, F.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Rodenburg, J. M.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Commun. 3, 730 (2012).
[CrossRef]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, Opt. Lett. 35, 2585 (2010).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, Ultramicroscopy 107, 227 (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, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef]

J. M. Rodenburg, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, 2008), Vol. 150, pp. 87–184.

Sheppard, C. J. R.

Tajahuerce, E.

Thibault, P.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[CrossRef]

Torres-Company, V.

Acta Crystallogr. A

W. Hoppe, Acta Crystallogr. A 25, 495 (1969).

Adv. Opt. Photon.

Nat. Commun.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, Nat. Commun. 3, 730 (2012).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

H. M. L. Faulkner and J. M. Rodenburg, Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef]

Science

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, Science 321, 379 (2008).
[CrossRef]

Ultramicroscopy

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, Ultramicroscopy 107, 227 (2007).
[CrossRef]

W. Hoppe, Ultramicroscopy 10, 187 (1982).
[CrossRef]

Other

J. M. Rodenburg, in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, 2008), Vol. 150, pp. 87–184.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of optical image encryption via ptychography: an example with random-phase encoding in both the input and the Fourier planes.

Fig. 2.
Fig. 2.

(a) Amplitude, (b) phase term of the secret image, (c) one of phase keys, and (d) a typical diffraction pattern.

Fig. 3.
Fig. 3.

Four employed probes. (a)–(d) Amplitudes and (e)–(h) phase distributions of the probes.

Fig. 4.
Fig. 4.

Amplitude and phase function, respectively, of the decrypted complex-valued images corresponding to three different types of probes: (a), (b) pure amplitude; (c), (d) phase only; and (e), (h) complex amplitude.

Fig. 5.
Fig. 5.

Diversity of the probes was tested with other series of probes: (a)–(d) K1, (e)–(h) K2, and (i)–(l) K3.

Fig. 6.
Fig. 6.

Security enhancement due to ptychography.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

IDi=|FT{FT{Pi·fo·exp[jM1]}·exp[jM2]}|2,
IDigk=|FT{FT{Pi·figk·exp[jM1]}·exp[jM2]}|2.
IDik=[IDio]1/2·[IDigk/|IDigk|].
figNk=FT1{FT1IDik·exp[jM2]}·exp[jM1].
f(i+1)gk=figk+βPi(figNk+figkPi)/(Pi+α),
Co(f,fo)=cov(f,fo)(σf·σfo)1,

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