Abstract

Recent advances in ptychographic imaging have shown how the technique extends naturally to mixed state experiments, for example when the illuminating radiation is partially coherent or when the object being imaged is laterally vibrating. To date, experiments using this mixed-state form of ptychography have relied on decomposition of the illumination ‘probe’ into multiple modes. In this paper we demonstrate, for the first time, ptychographic imaging with the simultaneous presence of both multiple probe and multiple object states. Our results prompt a discussion of uniqueness in the reconstructed images, and we show mathematically how ambiguities can arise. This leads us to extend the reconstruction process to include additional constraints that break these ambiguities, allowing interpretation of mixed object states that are not orthogonal.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Quantitative birefringence distribution measurement using mixed-state ptychography

Xuejie Zhang, Bei Cheng, Cheng Liu, Weixing Shen, and Jianqiang Zhu
Opt. Express 25(25) 30851-30861 (2017)

X-ray ptychography using a distant analyzer

Esther H. R. Tsai, Ana Diaz, Andreas Menzel, and Manuel Guizar-Sicairos
Opt. Express 24(6) 6441-6450 (2016)

Holography-guided ptychography with soft X-rays

Piet Hessing, Bastian Pfau, Erik Guehrs, Michael Schneider, Laura Shemilt, Jan Geilhufe, and Stefan Eisebitt
Opt. Express 24(2) 1840-1851 (2016)

References

  • View by:
  • |
  • |
  • |

  1. J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. A 339(1655), 521–553 (1992).
    [Crossref]
  2. 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(3), 034801 (2007).
    [Crossref] [PubMed]
  3. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
    [Crossref] [PubMed]
  4. 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]
  5. J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
    [Crossref]
  6. M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16(10), 7264–7278 (2008).
    [Crossref] [PubMed]
  7. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
    [Crossref] [PubMed]
  8. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
    [Crossref] [PubMed]
  9. A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
    [Crossref] [PubMed]
  10. J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
    [Crossref] [PubMed]
  11. M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
    [Crossref] [PubMed]
  12. A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
    [Crossref] [PubMed]
  13. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
    [Crossref] [PubMed]
  14. K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(2), 529–534 (2010).
    [Crossref] [PubMed]
  15. A. M. Maiden, G. R. Morrison, B. Kaulich, A. Gianoncelli, and J. M. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
    [Crossref] [PubMed]
  16. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
    [Crossref] [PubMed]
  17. P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
    [Crossref] [PubMed]
  18. J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112(11), 113901 (2014).
    [Crossref] [PubMed]
  19. J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Continuous scanning mode for ptychography,” Opt. Lett. 39(20), 6066–6069 (2014).
    [Crossref] [PubMed]
  20. D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
    [Crossref] [PubMed]
  21. S. M. Solís, F. M. Santoyo, and M. S. Hernández-Montes, “3D displacement measurements of the tympanic membrane with digital holographic interferometry,” Opt. Express 20(5), 5613–5621 (2012).
    [Crossref] [PubMed]
  22. D. Boss, A. Hoffmann, B. Rappaz, C. Depeursinge, P. J. Magistretti, D. Van de Ville, and P. Marquet, “Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering,” PLoS One 7(8), e40667 (2012).
    [Crossref] [PubMed]
  23. D. B. Williams and C. B. Carter, Transmission Electron Microscopy: A Textbook for Materials Science (New York: Plenum Press, 1949).
  24. H. Yoshimura, T. Asakura, and N. Takai, “Spatial coherence properties of light from optical fibres,” Opt. Quantum Electron. 24(6), 631–646 (1992).
    [Crossref]
  25. B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104(17), 171104 (2014).
    [Crossref]
  26. J. R. Fienup, “Invariant error metrics for image reconstruction,” Appl. Opt. 36(32), 8352–8357 (1997).
    [Crossref] [PubMed]
  27. A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774 (1997).
    [Crossref]
  28. D. L. Misell, “On the validity of the weak-phase and other approximations in the analysis of electron microscope images,” J. Phys. D Appl. Phys. 9(13), 1849–1866 (1976).
    [Crossref]
  29. E. Wolf, “New theory of partial coherence in the space-frequency domain Part I: spectra and cross spectra of steady-state sources,” J. Opt. Soc. Am. 72(3), 343–351 (1982).
    [Crossref]

2015 (1)

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref] [PubMed]

2014 (4)

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112(11), 113901 (2014).
[Crossref] [PubMed]

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Continuous scanning mode for ptychography,” Opt. Lett. 39(20), 6066–6069 (2014).
[Crossref] [PubMed]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104(17), 171104 (2014).
[Crossref]

2013 (3)

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref] [PubMed]

A. M. Maiden, G. R. Morrison, B. Kaulich, A. Gianoncelli, and J. M. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[Crossref] [PubMed]

2012 (3)

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[Crossref] [PubMed]

S. M. Solís, F. M. Santoyo, and M. S. Hernández-Montes, “3D displacement measurements of the tympanic membrane with digital holographic interferometry,” Opt. Express 20(5), 5613–5621 (2012).
[Crossref] [PubMed]

D. Boss, A. Hoffmann, B. Rappaz, C. Depeursinge, P. J. Magistretti, D. Van de Ville, and P. Marquet, “Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering,” PLoS One 7(8), e40667 (2012).
[Crossref] [PubMed]

2010 (3)

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(2), 529–534 (2010).
[Crossref] [PubMed]

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

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
[Crossref] [PubMed]

2009 (2)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

2008 (3)

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16(10), 7264–7278 (2008).
[Crossref] [PubMed]

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

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

2007 (1)

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(3), 034801 (2007).
[Crossref] [PubMed]

2004 (2)

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]

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

1997 (2)

J. R. Fienup, “Invariant error metrics for image reconstruction,” Appl. Opt. 36(32), 8352–8357 (1997).
[Crossref] [PubMed]

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774 (1997).
[Crossref]

1992 (2)

H. Yoshimura, T. Asakura, and N. Takai, “Spatial coherence properties of light from optical fibres,” Opt. Quantum Electron. 24(6), 631–646 (1992).
[Crossref]

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. A 339(1655), 521–553 (1992).
[Crossref]

1982 (1)

1976 (1)

D. L. Misell, “On the validity of the weak-phase and other approximations in the analysis of electron microscope images,” J. Phys. D Appl. Phys. 9(13), 1849–1866 (1976).
[Crossref]

Asakura, T.

H. Yoshimura, T. Asakura, and N. Takai, “Spatial coherence properties of light from optical fibres,” Opt. Quantum Electron. 24(6), 631–646 (1992).
[Crossref]

Bates, R. H. T.

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. A 339(1655), 521–553 (1992).
[Crossref]

Batey, D. J.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

Beerlink, A.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(2), 529–534 (2010).
[Crossref] [PubMed]

Boss, D.

D. Boss, A. Hoffmann, B. Rappaz, C. Depeursinge, P. J. Magistretti, D. Van de Ville, and P. Marquet, “Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering,” PLoS One 7(8), e40667 (2012).
[Crossref] [PubMed]

Bunk, O.

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

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and 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, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Clark, J. N.

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112(11), 113901 (2014).
[Crossref] [PubMed]

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Continuous scanning mode for ptychography,” Opt. Lett. 39(20), 6066–6069 (2014).
[Crossref] [PubMed]

Claus, D.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

Cloetens, P.

B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104(17), 171104 (2014).
[Crossref]

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(3), 034801 (2007).
[Crossref] [PubMed]

David, C.

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and 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, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Depeursinge, C.

D. Boss, A. Hoffmann, B. Rappaz, C. Depeursinge, P. J. Magistretti, D. Van de Ville, and P. Marquet, “Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering,” PLoS One 7(8), e40667 (2012).
[Crossref] [PubMed]

Dierolf, M.

B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104(17), 171104 (2014).
[Crossref]

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(2), 529–534 (2010).
[Crossref] [PubMed]

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

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and 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, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Enders, B.

B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104(17), 171104 (2014).
[Crossref]

Faulkner, H. M.

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

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(2), 023903 (2004).
[Crossref] [PubMed]

Fienup, J. R.

Gao, D.

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774 (1997).
[Crossref]

Gianoncelli, A.

A. M. Maiden, G. R. Morrison, B. Kaulich, A. Gianoncelli, and J. M. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Giewekemeyer, K.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(2), 529–534 (2010).
[Crossref] [PubMed]

Guizar-Sicairos, M.

Harder, R. J.

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Continuous scanning mode for ptychography,” Opt. Lett. 39(20), 6066–6069 (2014).
[Crossref] [PubMed]

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112(11), 113901 (2014).
[Crossref] [PubMed]

Hernández-Montes, M. S.

Hoffmann, A.

D. Boss, A. Hoffmann, B. Rappaz, C. Depeursinge, P. J. Magistretti, D. Van de Ville, and P. Marquet, “Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering,” PLoS One 7(8), e40667 (2012).
[Crossref] [PubMed]

Huang, X.

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112(11), 113901 (2014).
[Crossref] [PubMed]

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Continuous scanning mode for ptychography,” Opt. Lett. 39(20), 6066–6069 (2014).
[Crossref] [PubMed]

Humphry, M. J.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref] [PubMed]

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[Crossref] [PubMed]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
[Crossref] [PubMed]

Hurst, A. C.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[Crossref] [PubMed]

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(3), 034801 (2007).
[Crossref] [PubMed]

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

Kalbfleisch, S.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(2), 529–534 (2010).
[Crossref] [PubMed]

Kaulich, B.

A. M. Maiden, G. R. Morrison, B. Kaulich, A. Gianoncelli, and J. M. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Kewish, C. M.

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

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(2), 529–534 (2010).
[Crossref] [PubMed]

Kraus, B.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[Crossref] [PubMed]

Magistretti, P. J.

D. Boss, A. Hoffmann, B. Rappaz, C. Depeursinge, P. J. Magistretti, D. Van de Ville, and P. Marquet, “Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering,” PLoS One 7(8), e40667 (2012).
[Crossref] [PubMed]

Maiden, A. M.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref] [PubMed]

A. M. Maiden, G. R. Morrison, B. Kaulich, A. Gianoncelli, and J. M. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[Crossref] [PubMed]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

Marquet, P.

D. Boss, A. Hoffmann, B. Rappaz, C. Depeursinge, P. J. Magistretti, D. Van de Ville, and P. Marquet, “Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering,” PLoS One 7(8), e40667 (2012).
[Crossref] [PubMed]

Marriott, P.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref] [PubMed]

Marrison, J.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref] [PubMed]

Menzel, A.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[Crossref] [PubMed]

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

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

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

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

Misell, D. L.

D. L. Misell, “On the validity of the weak-phase and other approximations in the analysis of electron microscope images,” J. Phys. D Appl. Phys. 9(13), 1849–1866 (1976).
[Crossref]

Morrison, G. R.

A. M. Maiden, G. R. Morrison, B. Kaulich, A. Gianoncelli, and J. M. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

O’Toole, P.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref] [PubMed]

Pfeiffer, F.

B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104(17), 171104 (2014).
[Crossref]

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

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(2), 529–534 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and 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, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Pogany, A.

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774 (1997).
[Crossref]

Rappaz, B.

D. Boss, A. Hoffmann, B. Rappaz, C. Depeursinge, P. J. Magistretti, D. Van de Ville, and P. Marquet, “Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering,” PLoS One 7(8), e40667 (2012).
[Crossref] [PubMed]

Räty, L.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref] [PubMed]

Robinson, I. K.

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112(11), 113901 (2014).
[Crossref] [PubMed]

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Continuous scanning mode for ptychography,” Opt. Lett. 39(20), 6066–6069 (2014).
[Crossref] [PubMed]

Rodenburg, J. M.

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

A. M. Maiden, G. R. Morrison, B. Kaulich, A. Gianoncelli, and J. M. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[Crossref] [PubMed]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

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(3), 034801 (2007).
[Crossref] [PubMed]

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]

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. A 339(1655), 521–553 (1992).
[Crossref]

Salditt, T.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(2), 529–534 (2010).
[Crossref] [PubMed]

Santoyo, F. M.

Sarahan, M. C.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref] [PubMed]

Schneider, P.

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

Schramm, S. M.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref] [PubMed]

Solís, S. M.

Stagg, M. D.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref] [PubMed]

Stockmar, M.

B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104(17), 171104 (2014).
[Crossref]

Takai, N.

H. Yoshimura, T. Asakura, and N. Takai, “Spatial coherence properties of light from optical fibres,” Opt. Quantum Electron. 24(6), 631–646 (1992).
[Crossref]

Thibault, P.

B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104(17), 171104 (2014).
[Crossref]

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[Crossref] [PubMed]

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

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(2), 529–534 (2010).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

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

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

Van de Ville, D.

D. Boss, A. Hoffmann, B. Rappaz, C. Depeursinge, P. J. Magistretti, D. Van de Ville, and P. Marquet, “Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering,” PLoS One 7(8), e40667 (2012).
[Crossref] [PubMed]

Wepf, R.

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

Wilkins, S. W.

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774 (1997).
[Crossref]

Wolf, E.

Yoshimura, H.

H. Yoshimura, T. Asakura, and N. Takai, “Spatial coherence properties of light from optical fibres,” Opt. Quantum Electron. 24(6), 631–646 (1992).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

B. Enders, M. Dierolf, P. Cloetens, M. Stockmar, F. Pfeiffer, and P. Thibault, “Ptychography with broad-bandwidth radiation,” Appl. Phys. Lett. 104(17), 171104 (2014).
[Crossref]

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. D Appl. Phys. (1)

D. L. Misell, “On the validity of the weak-phase and other approximations in the analysis of electron microscope images,” J. Phys. D Appl. Phys. 9(13), 1849–1866 (1976).
[Crossref]

Nat. Commun. (2)

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3, 730 (2012).
[Crossref] [PubMed]

A. M. Maiden, G. R. Morrison, B. Kaulich, A. Gianoncelli, and J. M. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Nature (2)

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

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

H. Yoshimura, T. Asakura, and N. Takai, “Spatial coherence properties of light from optical fibres,” Opt. Quantum Electron. 24(6), 631–646 (1992).
[Crossref]

Phil. Trans. R. Soc. A (1)

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. A 339(1655), 521–553 (1992).
[Crossref]

Phys. Rev. Lett. (3)

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(3), 034801 (2007).
[Crossref] [PubMed]

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112(11), 113901 (2014).
[Crossref] [PubMed]

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]

PLoS One (1)

D. Boss, A. Hoffmann, B. Rappaz, C. Depeursinge, P. J. Magistretti, D. Van de Ville, and P. Marquet, “Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering,” PLoS One 7(8), e40667 (2012).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107(2), 529–534 (2010).
[Crossref] [PubMed]

Rev. Sci. Instrum. (1)

A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774 (1997).
[Crossref]

Sci. Rep. (2)

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref] [PubMed]

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref] [PubMed]

Science (2)

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

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

Ultramicroscopy (3)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
[Crossref] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
[Crossref] [PubMed]

Other (1)

D. B. Williams and C. B. Carter, Transmission Electron Microscopy: A Textbook for Materials Science (New York: Plenum Press, 1949).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1 The experimental setup of ptychography operating in the reflection mode. OF stands for the optical fiber, P for polarizer, L for the lens, A for aperture, BS for the beam splitter, D for the detector and SLM for the spatial light modulator. The focal length of L1 is 100mm and that of L2 is 45mm.
Fig. 2
Fig. 2 The modulus parts of the probe modes reconstructions after orthogonalisation assigning different numbers of modes, from 1(a) to 7(g), in the algorithm. The first mode, containing most of the power in the illumination, looked similar for all the reconstructions; the lower power modes evolved as the number of modes included in the reconstruction was increased, until five modes were included, after which the first five modes remained more or less constant; modes 6 and 7 varied randomly and contained very little power (totaling less than 3% of the incident beam), which account for the imperfection the data sets. Therefore we conclude that there are 5 modes in the illumination. The scale bars indicate a length of 300µm.
Fig. 3
Fig. 3 The reconstructions from the calibration experiments. (a) The dog pattern reconstruction. (b) The horse pattern reconstruction. (c) The probe states reconstructions. (d) The probe states reconstructions with the phase curvature removed. The scale bars indicate a length of 300µm. The color wheel applies to all the images.
Fig. 4
Fig. 4 Two different sets of reconstructions from the same data set using different initial guesses. (a) The first set of raw reconstructions. (b) The second set of raw reconstructions. The scale bars indicate a length of 300µm. The color wheel applies to all the images. To aid in display, the curvature of the probe phases has been removed.
Fig. 5
Fig. 5 Schematic demonstration of state-wise Kronecker product (denoted by ⊗) and the formation of exit waves (denoted by ψ) and diffraction waves (denoted by Ψ). P and O denote the probe state vector and the object state vector respectively. ℱ denotes the Fourier transform. The diffraction patterns are displayed at logarithm scale. The shown exit waves and diffraction patterns are simulated calculations, not related to the optical experiment.
Fig. 6
Fig. 6 Comparison of the normalised summations of the intensities of the states. (a) The normalised summations of the intensities of the calibrated probe modes (inset) and the calibrated object states (main figure). (b) The normalised summations of the intensities of the probe states and the object states from the first reconstruction. (c) The normalised summations of the intensities of the probe states and the object states from the second reconstruction. The scale bars indicate a length of 300µm.
Fig. 7
Fig. 7 Reconstructions of the two object states with applying the phase-only constraint. (a) The two object states reconstructions with the phase-only constraint through the whole reconstruction process. (b) The two object states reconstructions using (a) as the initial guesses respectively without the phase-only constraint. The scale bars indicate a length of 300µm. The scale bar and the color wheel apply to all the images.
Fig. 8
Fig. 8 The simulation and the reconstructions. (a) The phase parts of the four object states. The amplitudes are all set to 1. (b) The phase parts of the four states reconstructions without applying the phase only constraint. (c) The phase parts of the four states reconstructions with applying the phase only constraint. Clearly the phase-only constraint beaks the ambiguity of the linear combinations of the states, although the ordering of the reconstructed states remain ambiguous.
Fig. 9
Fig. 9 Comparison of the probe modes from the two different sets of reconstructions after orthogonalisation. (a) Orthogonal probe modes from the first set of reconstructions. (b) Orthogonal probe modes from the second set of reconstructions. (c) The power distributions of the original probe modes (reference as shown in Fig. 3(d)) and the two sets of reconstructed probe modes. The scale bars indicate a length of 300µm.

Equations (34)

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

Ψ q (m,n) =[ P x (m) O x (n) ],
Ψ=[ ( PO ) ],
Ψ ˜ =[ ( P ˜ O ˜ ) ].
P ˜ =P U P ,
O ˜ =O U O ,
U P U P =c I M ,
U O U O = I N /c,
P ˜ P ˜ =cP P ,
O ˜ O ˜ =O O /c.
O ˜ x (1) = u 11 O x (1) + u 21 O x (2) ,
O ˜ x (2) = u 12 O x (1) + u 22 O x (2) .
| O ˜ x (1) |= | u 11 Α x (1) | 2 + | u 21 Α x (2) | 2 +2 u 11 Α x (1) u 21 Α x (2) cos[ Φ x (1) Φ x (2) ] ,
| O ˜ x (2) |= | u 12 Α x (1) | 2 + | u 22 Α x (2) | 2 +2 u 12 Α x (1) u 22 Α x (2) cos[ Φ x (1) Φ x (2) ] .
u 11 u 21 =0,
u 12 u 22 =0.
| u 11 | 2 + | u 12 | 2 =1,
| u 21 | 2 + | u 22 | 2 =1.
s (m) s (n) ={ 0,mn η,m=n ,
S=[ s (1) , s (2) ,, s (M) ]=[ p x 1 (1) p x 1 (2) p x 1 (M) p x 2 (1) p x 2 (2) p x 2 (M) p x k (1) p x k (2) p x k (M) ],
D= S S=[ s (1) s (1) s (1) s (2) s (1) s (M) s (2) s (1) s (2) s (2) s (2) s (M) s (M) s (1) s (M) s (2) s (M) s (M) ]=[ η 1 0 0 0 η 2 0 0 0 η M ].
D ˜ = S ˜ S ˜ = U P D U P .
S= S ˜ U P .
S ˜ S ˜ =S U P U P S = S N D S N ,
S N =[ s 1 / η 1 , s 2 / η 2 ,, s M / η M ].
Ψ Ψ = m=1 M n=1 N Ψ q (m,n) Ψ q (m,n) = m=1 M n=1 N | [ P x (m) O x (n) ] | 2 .
Ψ ˜ Ψ ˜ =[ ( P ˜ O ˜ ) ] [ ( P ˜ O ˜ ) ] =[ ( P U P O U O ) ] [ ( P U P O U O ) ] .
P ˜ x (m) = i P x (i) u im ,
O ˜ x (n) = j O x (j) v jn ,
[ P ˜ x (m) O ˜ x (n) ]= i j [ P x (i) O x (j) ] u im v jn .
Ψ ˜ Ψ ˜ =[ ( PO ) ][ U P U O ] [ U P U O ] [ ( PO ) ] .
[ ( PO ) ][ U P U O ] [ U P U O ] [ ( PO ) ] =[ ( PO ) ] [ ( PO ) ] .
[ U P U O ] [ U P U O ] = U P U P U O U O = I MN ,
U P U P =c I M ,
U O U O = I N /c,

Metrics