Abstract

We present a new method using single-path beam-propagation-based imaging via aperture movement for optical encryption. The aperture is sequentially moved in the transverse domain, and a series of diffraction intensity patterns (i.e., ciphertexts) are correspondingly recorded during optical encryption. An iterative phase retrieval algorithm is applied for the decryption. It is illustrated that the proposed optical security system possesses several significant advantages, such as high flexibility and high security. The proposed optical security system also provides an effective channel to control information assignment and authentication.

© 2013 Optical Society of America

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References

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  1. J.  Miao, D.  Sayre, H. N.  Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662–1669 (1998).
    [CrossRef]
  2. P.  Thibault, M.  Dierolf, A.  Menzel, O.  Bunk, C.  David, F.  Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
    [CrossRef] [PubMed]
  3. M.  Dierolf, A.  Menzel, P.  Thibault, P.  Schneider, C. M.  Kewish, R.  Wepf, O.  Bunk, F.  Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
    [CrossRef] [PubMed]
  4. J. M.  Rodenburg, A. C.  Hurst, A. G.  Cullis, B. R.  Dobson, F.  Pfeiffer, O.  Bunk, C.  David, K.  Jefimovs, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
    [CrossRef] [PubMed]
  5. J. M.  Rodenburg, H. M. L.  Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4798 (2004).
    [CrossRef]
  6. H. M. L.  Faulkner, J. M.  Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
    [CrossRef] [PubMed]
  7. C. A.  Henderson, G. J.  Williams, A. G.  Peele, H. M.  Quiney, K. A.  Nugent, “Astigmatic phase retrieval: an experimental demonstration,” Opt. Express 17(14), 11905–11915 (2009).
    [CrossRef] [PubMed]
  8. R. W.  Gerchberg, W. O.  Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1972).
  9. J. R.  Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21(15), 2758–2769 (1982).
    [CrossRef] [PubMed]
  10. A.  Alfalou, C.  Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1(3), 589–636 (2009).
    [CrossRef]
  11. Y.  Zhang, B.  Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
    [CrossRef] [PubMed]
  12. P.  Refregier, B.  Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
    [CrossRef] [PubMed]
  13. G.  Situ, J.  Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).
    [CrossRef] [PubMed]
  14. X. F.  Meng, L. Z.  Cai, X. F.  Xu, X. L.  Yang, X. X.  Shen, G. Y.  Dong, Y. R.  Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31(10), 1414–1416 (2006).
    [CrossRef] [PubMed]
  15. W.  Chen, X.  Chen, C. J. R.  Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
    [CrossRef] [PubMed]
  16. Y.  Shi, T.  Li, Y.  Wang, Q.  Gao, S.  Zhang, H.  Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
    [CrossRef] [PubMed]
  17. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  18. W.  Chen, X.  Chen, A.  Anand, B.  Javidi, “Optical encryption using multiple intensity samplings in the axial domain,” J. Opt. Soc. Am. A 30(5), 806–812 (2013).
    [CrossRef] [PubMed]
  19. Z.  Liu, Q.  Guo, L.  Xu, M. A.  Ahmad, S.  Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18(11), 12033–12043 (2010).
    [CrossRef] [PubMed]
  20. B.  Hennelly, J. T.  Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28(4), 269–271 (2003).
    [CrossRef] [PubMed]
  21. L.  Waller, G.  Situ, J. W.  Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
    [CrossRef]
  22. B.  Javidi, “Nonlinear joint power spectrum based optical correlation,” Appl. Opt. 28(12), 2358–2367 (1989).
    [CrossRef] [PubMed]
  23. F. Sadjadi and B. Javidi, Physics of the Automatic Target Recognition (Springer, 2007).
  24. E.  Pérez-Cabré, M.  Cho, B.  Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36(1), 22–24 (2011).
    [CrossRef] [PubMed]
  25. E.  Pérez-Cabré, H. C.  Abril, M. S.  Millan, B.  Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14(9), 094001 (2012).
    [CrossRef]
  26. S.  Liu, Q.  Mi, B.  Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26(16), 1242–1244 (2001).
    [CrossRef] [PubMed]
  27. S.  Liu, L.  Yu, B.  Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase fltering,” Opt. Commun. 187(1-3), 57–63 (2001).
    [CrossRef]

2013

2012

L.  Waller, G.  Situ, J. W.  Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[CrossRef]

E.  Pérez-Cabré, H. C.  Abril, M. S.  Millan, B.  Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14(9), 094001 (2012).
[CrossRef]

2011

2010

2009

2008

P.  Thibault, M.  Dierolf, A.  Menzel, O.  Bunk, C.  David, F.  Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Y.  Zhang, B.  Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
[CrossRef] [PubMed]

2007

J. M.  Rodenburg, A. C.  Hurst, A. G.  Cullis, B. R.  Dobson, F.  Pfeiffer, O.  Bunk, C.  David, K.  Jefimovs, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[CrossRef] [PubMed]

2006

2004

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

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

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

2003

2001

S.  Liu, Q.  Mi, B.  Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26(16), 1242–1244 (2001).
[CrossRef] [PubMed]

S.  Liu, L.  Yu, B.  Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase fltering,” Opt. Commun. 187(1-3), 57–63 (2001).
[CrossRef]

1998

1995

1989

1982

1972

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

Abril, H. C.

E.  Pérez-Cabré, H. C.  Abril, M. S.  Millan, B.  Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14(9), 094001 (2012).
[CrossRef]

Ahmad, M. A.

Alfalou, A.

Anand, A.

Brosseau, C.

Bunk, O.

M.  Dierolf, A.  Menzel, P.  Thibault, P.  Schneider, C. M.  Kewish, R.  Wepf, O.  Bunk, F.  Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[CrossRef] [PubMed]

P.  Thibault, M.  Dierolf, A.  Menzel, O.  Bunk, C.  David, F.  Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

J. M.  Rodenburg, A. C.  Hurst, A. G.  Cullis, B. R.  Dobson, F.  Pfeiffer, O.  Bunk, C.  David, K.  Jefimovs, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[CrossRef] [PubMed]

Cai, L. Z.

Chapman, H. N.

Chen, W.

Chen, X.

Cho, M.

Cullis, A. G.

J. M.  Rodenburg, A. C.  Hurst, A. G.  Cullis, B. R.  Dobson, F.  Pfeiffer, O.  Bunk, C.  David, K.  Jefimovs, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[CrossRef] [PubMed]

David, C.

P.  Thibault, M.  Dierolf, A.  Menzel, O.  Bunk, C.  David, F.  Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

J. M.  Rodenburg, A. C.  Hurst, A. G.  Cullis, B. R.  Dobson, F.  Pfeiffer, O.  Bunk, C.  David, K.  Jefimovs, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[CrossRef] [PubMed]

Dierolf, M.

M.  Dierolf, A.  Menzel, P.  Thibault, P.  Schneider, C. M.  Kewish, R.  Wepf, O.  Bunk, F.  Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[CrossRef] [PubMed]

P.  Thibault, M.  Dierolf, A.  Menzel, O.  Bunk, C.  David, F.  Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Dobson, B. R.

J. M.  Rodenburg, A. C.  Hurst, A. G.  Cullis, B. R.  Dobson, F.  Pfeiffer, O.  Bunk, C.  David, K.  Jefimovs, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[CrossRef] [PubMed]

Dong, G. Y.

Faulkner, H. M. L.

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

H. M. L.  Faulkner, 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.

Fleischer, J. W.

L.  Waller, G.  Situ, J. W.  Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[CrossRef]

Gao, Q.

Gerchberg, R. W.

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

Guo, Q.

Henderson, C. A.

Hennelly, B.

Hurst, A. C.

J. M.  Rodenburg, A. C.  Hurst, A. G.  Cullis, B. R.  Dobson, F.  Pfeiffer, O.  Bunk, C.  David, K.  Jefimovs, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[CrossRef] [PubMed]

Javidi, B.

Jefimovs, K.

J. M.  Rodenburg, A. C.  Hurst, A. G.  Cullis, B. R.  Dobson, F.  Pfeiffer, O.  Bunk, C.  David, K.  Jefimovs, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[CrossRef] [PubMed]

Johnson, I.

J. M.  Rodenburg, A. C.  Hurst, A. G.  Cullis, B. R.  Dobson, F.  Pfeiffer, O.  Bunk, C.  David, K.  Jefimovs, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[CrossRef] [PubMed]

Kewish, C. M.

M.  Dierolf, A.  Menzel, P.  Thibault, P.  Schneider, C. M.  Kewish, R.  Wepf, O.  Bunk, F.  Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[CrossRef] [PubMed]

Li, H.

Li, T.

Liu, S.

Liu, Z.

Meng, X. F.

Menzel, A.

M.  Dierolf, A.  Menzel, P.  Thibault, P.  Schneider, C. M.  Kewish, R.  Wepf, O.  Bunk, F.  Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[CrossRef] [PubMed]

P.  Thibault, M.  Dierolf, A.  Menzel, O.  Bunk, C.  David, F.  Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Mi, Q.

Miao, J.

Millan, M. S.

E.  Pérez-Cabré, H. C.  Abril, M. S.  Millan, B.  Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14(9), 094001 (2012).
[CrossRef]

Nugent, K. A.

Peele, A. G.

Pérez-Cabré, E.

E.  Pérez-Cabré, H. C.  Abril, M. S.  Millan, B.  Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14(9), 094001 (2012).
[CrossRef]

E.  Pérez-Cabré, M.  Cho, B.  Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36(1), 22–24 (2011).
[CrossRef] [PubMed]

Pfeiffer, F.

M.  Dierolf, A.  Menzel, P.  Thibault, P.  Schneider, C. M.  Kewish, R.  Wepf, O.  Bunk, F.  Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[CrossRef] [PubMed]

P.  Thibault, M.  Dierolf, A.  Menzel, O.  Bunk, C.  David, F.  Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

J. M.  Rodenburg, A. C.  Hurst, A. G.  Cullis, B. R.  Dobson, F.  Pfeiffer, O.  Bunk, C.  David, K.  Jefimovs, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[CrossRef] [PubMed]

Quiney, H. M.

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, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[CrossRef] [PubMed]

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

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

Sayre, D.

Schneider, P.

M.  Dierolf, A.  Menzel, P.  Thibault, P.  Schneider, C. M.  Kewish, R.  Wepf, O.  Bunk, F.  Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[CrossRef] [PubMed]

Shen, X. X.

Sheppard, C. J. R.

Sheridan, J. T.

Shi, Y.

Situ, G.

L.  Waller, G.  Situ, J. W.  Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[CrossRef]

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

Thibault, P.

M.  Dierolf, A.  Menzel, P.  Thibault, P.  Schneider, C. M.  Kewish, R.  Wepf, O.  Bunk, F.  Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[CrossRef] [PubMed]

P.  Thibault, M.  Dierolf, A.  Menzel, O.  Bunk, C.  David, F.  Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Waller, L.

L.  Waller, G.  Situ, J. W.  Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[CrossRef]

Wang, B.

Wang, Y.

Wang, Y. R.

Wepf, R.

M.  Dierolf, A.  Menzel, P.  Thibault, P.  Schneider, C. M.  Kewish, R.  Wepf, O.  Bunk, F.  Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[CrossRef] [PubMed]

Williams, G. J.

Xu, L.

Xu, X. F.

Yang, X. L.

Yu, L.

S.  Liu, L.  Yu, B.  Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase fltering,” Opt. Commun. 187(1-3), 57–63 (2001).
[CrossRef]

Zhang, J.

Zhang, S.

Zhang, Y.

Zhu, B.

S.  Liu, L.  Yu, B.  Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase fltering,” Opt. Commun. 187(1-3), 57–63 (2001).
[CrossRef]

S.  Liu, Q.  Mi, B.  Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26(16), 1242–1244 (2001).
[CrossRef] [PubMed]

Adv. Opt. Photon.

Appl. Opt.

Appl. Phys. Lett.

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

J. Opt.

E.  Pérez-Cabré, H. C.  Abril, M. S.  Millan, B.  Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14(9), 094001 (2012).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photonics

L.  Waller, G.  Situ, J. W.  Fleischer, “Phase-space measurement and coherence synthesis of optical beams,” Nat. Photonics 6(7), 474–479 (2012).
[CrossRef]

Nature

M.  Dierolf, A.  Menzel, P.  Thibault, P.  Schneider, C. M.  Kewish, R.  Wepf, O.  Bunk, F.  Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[CrossRef] [PubMed]

Opt. Commun.

S.  Liu, L.  Yu, B.  Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase fltering,” Opt. Commun. 187(1-3), 57–63 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Y.  Shi, T.  Li, Y.  Wang, Q.  Gao, S.  Zhang, H.  Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
[CrossRef] [PubMed]

W.  Chen, X.  Chen, C. J. R.  Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35(22), 3817–3819 (2010).
[CrossRef] [PubMed]

E.  Pérez-Cabré, M.  Cho, B.  Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36(1), 22–24 (2011).
[CrossRef] [PubMed]

P.  Refregier, B.  Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
[CrossRef] [PubMed]

S.  Liu, Q.  Mi, B.  Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26(16), 1242–1244 (2001).
[CrossRef] [PubMed]

B.  Hennelly, J. T.  Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28(4), 269–271 (2003).
[CrossRef] [PubMed]

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

X. F.  Meng, L. Z.  Cai, X. F.  Xu, X. L.  Yang, X. X.  Shen, G. Y.  Dong, Y. R.  Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31(10), 1414–1416 (2006).
[CrossRef] [PubMed]

Y.  Zhang, B.  Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
[CrossRef] [PubMed]

Optik (Stuttg.)

R. W.  Gerchberg, 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.

J. M.  Rodenburg, A. C.  Hurst, A. G.  Cullis, B. R.  Dobson, F.  Pfeiffer, O.  Bunk, C.  David, K.  Jefimovs, I.  Johnson, “Hard-X-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[CrossRef] [PubMed]

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

Science

P.  Thibault, M.  Dierolf, A.  Menzel, O.  Bunk, C.  David, F.  Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Other

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

F. Sadjadi and B. Javidi, Physics of the Automatic Target Recognition (Springer, 2007).

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Figures (11)

Fig. 1
Fig. 1

Schematic experimental setup for the proposed optical security system with movable aperture: M, phase-only mask; A, Aperture; P, plaintext; CCD, charge-coupled device.

Fig. 2
Fig. 2

Flow chart for illustrating the decryption process.

Fig. 3
Fig. 3

Phase-only masks (a) M1 and (b) M2; schematic illustration of the movements of (c) rectangle-shaped aperture, (d) circle-shaped aperture and (e) triangle-shaped aperture; (f) an input image (i.e., the plaintext); and (g) one typical diffraction intensity pattern (i.e., ciphertext).

Fig. 4
Fig. 4

(a) The decrypted image obtained by using correct security keys, (b) a relationship between number of iterations and correlation coefficients, and (c) a relationship between the number of iterations and iterative errors (logarithm scale).

Fig. 5
Fig. 5

(a) A decrypted image obtained after 500 iterations, when there is an error of 10 nm in the light wavelength. (b) A decrypted image obtained after 500 iterations, when only the phase-only mask M2 is wrong.

Fig. 6
Fig. 6

The circle-shaped aperture and only five neighboring aperture positions: (a) The decrypted image obtained by using correct security keys, (b) a relationship between the number of iterations and iterative errors (with logarithm scale), (c) decrypted image obtained after 500 iterations using wrong wavelength, and (d) decrypted image obtained after 500 iterations using wrong phase-only mask M2.

Fig. 7
Fig. 7

Triangle-shaped aperture and only five neighboring aperture positions: (a) The decrypted image (MSE of 2.9003× 10 -7 ) obtained by using correct security keys, (b) a relationship between the number of iterations and iterative errors with logarithm scale (37 iterations are requested), (c) decrypted image (MSE of 6.2205× 10 3 ) obtained after 500 iterations using wrong wavelength, and (d) a decrypted image (MSE of 6.3076× 10 3 ) obtained after 500 iterations using wrong phase-only mask M2.

Fig. 8
Fig. 8

Sparse plaintext (sparse gray-scale image “Lena”) and only five neighboring triangle-shaped aperture positions: (a) The decrypted image obtained by using correct security keys, (b) a decrypted image obtained after 500 iterations using wrong wavelength, (c) the decrypted image obtained after 500 iterations using wrong phase-only mask M2, and (d), (e) and (f) the authentication distributions (normalized) obtained by the nonlinear correlation algorithm respectively corresponding to (a), (b) and (c).

Fig. 9
Fig. 9

Aperture array and only five neighboring aperture positions: (a) One simple aperture array, (b) decrypted image obtained by using correct security keys, (c) a relationship between the number of iterations and iterative errors (with logarithm scale), (d) the decrypted image obtained after 500 iterations using wrong wavelength, and (e) the decrypted image obtained after 500 iterations using wrong phase-only mask M2.

Fig. 10
Fig. 10

(a) Another aperture array (small apertures), (b) the decrypted image obtained by using all correct security keys, and (c) relationship between the number of iterations and iterative errors (logarithm scale).

Fig. 11
Fig. 11

Decrypted image obtained by using wrong aperture positions in aperture array.

Equations (5)

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O n (ξ,η)= FrT z 2 ,λ ( { FrT z 1 ,λ [ P n (x,y) M 1 (x,y) A j ( x,y ) ] } M 2 (μ,ν) ),
O n (ξ,η)= [ I j (ξ,η) ] 1/2 O n (ξ,η) / | O n (ξ,η) | .
O n (x,y)=[ FrT z 1 ,λ ( { FrT z 2 ,λ [ O n (ξ,η) ] } [ M 2 (μ,ν) ] * ) ] [ M 1 (x,y) ] * ,
P n (x,y)= P n (x,y)+ β A j ( x,y ) | A j ( x,y ) | 2 +α [ O n (x,y) P n (x,y) A j ( x,y ) ],
MSE= 1 M×N x=1 M y=1 N [ P( x,y )P'( x,y ) ] 2 ,

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