Abstract

Accurate knowledge of translation positions is essential in ptychography to achieve a good image quality and the diffraction limited resolution. We propose a method to retrieve and correct position errors during the image reconstruction iterations. Sub-pixel position accuracy after refinement is shown to be achievable within several tens of iterations. Simulation and experimental results for both optical and X-ray wavelengths are given. The method improves both the quality of the retrieved object image and relaxes the position accuracy requirement while acquiring the diffraction patterns.

© 2013 OSA

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  1. H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscope: a novel phase retrieval algorithm,” Phys. Rev. Lett.93, 023903 (2004)
  2. J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett.85(20), 4795–4797 (2004).
    [CrossRef]
  3. J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imag. Elec. Phys.150, 87–184 (2008).
    [CrossRef]
  4. 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]
  5. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science321(5887), 379–382 (2008).
    [CrossRef] [PubMed]
  6. 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]
  7. 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,” Nature467(7314), 436–439 (2010).
    [CrossRef] [PubMed]
  8. C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110(4), 325–329 (2010).
    [CrossRef] [PubMed]
  9. E. Lima, A. Diaz, M. Guizar-Sicairos, S. Gorelick, P. Pernot, T. Schleier, and A. Menzel, “Cryo-scanning x-ray diffraction microscopy of frozen-hydrated yeast,” J. Microsc.249(1), 1–7 (2013).
    [CrossRef]
  10. C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
    [CrossRef] [PubMed]
  11. F. Hüe, J. M. Rodenburg, A. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B82(12), 121415 (2010).
    [CrossRef]
  12. 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 Commun3, 730 (2012).
    [CrossRef] [PubMed]
  13. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009).
    [CrossRef] [PubMed]
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  15. M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express16(10), 7264–7278 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
    [CrossRef] [PubMed]
  18. A. C. Hurst, T. B. Edo, T. Walther, F. Sweeney, and J. M. Rodenburg, “Probe position recovery for ptychographical imaging,” J. Phys. Conf. Ser.241, 012004 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  22. M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett.33(2), 156–158 (2008).
    [CrossRef] [PubMed]
  23. M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
    [CrossRef]
  24. F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B82(12), 121104 (2010).
    [CrossRef]
  25. S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salomé, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Radiat.18(3), 442–446 (2011).
    [CrossRef] [PubMed]
  26. F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A75(4), 043805 (2007).
    [CrossRef]
  27. X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, and I. K. Robinson, “Quantitative X-ray wavefront measurements of Fresnel zone plate and K-B mirrors using phase retrieval,” Opt. Express20(21), 24038–24048 (2012).
    [CrossRef] [PubMed]
  28. P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature494(7435), 68–71 (2013).
    [CrossRef] [PubMed]

2013 (3)

E. Lima, A. Diaz, M. Guizar-Sicairos, S. Gorelick, P. Pernot, T. Schleier, and A. Menzel, “Cryo-scanning x-ray diffraction microscopy of frozen-hydrated yeast,” J. Microsc.249(1), 1–7 (2013).
[CrossRef]

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[CrossRef] [PubMed]

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature494(7435), 68–71 (2013).
[CrossRef] [PubMed]

2012 (5)

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy120, 64–72 (2012).
[CrossRef] [PubMed]

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, and I. K. Robinson, “Quantitative X-ray wavefront measurements of Fresnel zone plate and K-B mirrors using phase retrieval,” Opt. Express20(21), 24038–24048 (2012).
[CrossRef] [PubMed]

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[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 Commun3, 730 (2012).
[CrossRef] [PubMed]

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys.14(6), 063004 (2012).
[CrossRef]

2011 (3)

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys.109(12), 124510 (2011).
[CrossRef]

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salomé, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Radiat.18(3), 442–446 (2011).
[CrossRef] [PubMed]

2010 (7)

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B82(12), 121104 (2010).
[CrossRef]

A. C. Hurst, T. B. Edo, T. Walther, F. Sweeney, and J. M. Rodenburg, “Probe position recovery for ptychographical imaging,” J. Phys. Conf. Ser.241, 012004 (2010).
[CrossRef]

F. Hüe, J. M. Rodenburg, A. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B82(12), 121415 (2010).
[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,” Nature467(7314), 436–439 (2010).
[CrossRef] [PubMed]

C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110(4), 325–329 (2010).
[CrossRef] [PubMed]

2009 (2)

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009).
[CrossRef] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy109(10), 1256–1262 (2009).
[CrossRef] [PubMed]

2008 (4)

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express16(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,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imag. Elec. Phys.150, 87–184 (2008).
[CrossRef]

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett.33(2), 156–158 (2008).
[CrossRef] [PubMed]

2007 (2)

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A75(4), 043805 (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(3), 034801 (2007).
[CrossRef] [PubMed]

2004 (2)

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

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

Allen, L. J.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

Barrett, R.

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salomé, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Radiat.18(3), 442–446 (2011).
[CrossRef] [PubMed]

Beckers, M.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[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]

Bourgeois, L.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

Bunk, O.

C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110(4), 325–329 (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,” Nature467(7314), 436–439 (2010).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(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,” Science321(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]

Burdet, N.

Chu, Y. S.

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]

D’Alfonso, A. J.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

David, C.

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salomé, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Radiat.18(3), 442–446 (2011).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science321(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]

Diaz, A.

E. Lima, A. Diaz, M. Guizar-Sicairos, S. Gorelick, P. Pernot, T. Schleier, and A. Menzel, “Cryo-scanning x-ray diffraction microscopy of frozen-hydrated yeast,” J. Microsc.249(1), 1–7 (2013).
[CrossRef]

Dierolf, 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,” Nature467(7314), 436–439 (2010).
[CrossRef] [PubMed]

C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110(4), 325–329 (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]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(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,” Science321(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]

Dwyer, C.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

Edo, T. B.

A. C. Hurst, T. B. Edo, T. Walther, F. Sweeney, and J. M. Rodenburg, “Probe position recovery for ptychographical imaging,” J. Phys. Conf. Ser.241, 012004 (2010).
[CrossRef]

Etheridge, J.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

Faulkner, H. M. L.

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

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

Fienup, J. R.

Giewekemeyer, K.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[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]

Gorelick, S.

E. Lima, A. Diaz, M. Guizar-Sicairos, S. Gorelick, P. Pernot, T. Schleier, and A. Menzel, “Cryo-scanning x-ray diffraction microscopy of frozen-hydrated yeast,” J. Microsc.249(1), 1–7 (2013).
[CrossRef]

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salomé, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Radiat.18(3), 442–446 (2011).
[CrossRef] [PubMed]

Gorniak, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[CrossRef] [PubMed]

Guizar-Sicairos, M.

E. Lima, A. Diaz, M. Guizar-Sicairos, S. Gorelick, P. Pernot, T. Schleier, and A. Menzel, “Cryo-scanning x-ray diffraction microscopy of frozen-hydrated yeast,” J. Microsc.249(1), 1–7 (2013).
[CrossRef]

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys.14(6), 063004 (2012).
[CrossRef]

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express16(10), 7264–7278 (2008).
[CrossRef] [PubMed]

M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett.33(2), 156–158 (2008).
[CrossRef] [PubMed]

Guzenko, V. A.

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salomé, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Radiat.18(3), 442–446 (2011).
[CrossRef] [PubMed]

Harder, R.

Huang, X.

Hüe, F.

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

F. Hüe, J. M. Rodenburg, A. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B82(12), 121415 (2010).
[CrossRef]

Humphry, M. J.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy120, 64–72 (2012).
[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 Commun3, 730 (2012).
[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 Commun3, 730 (2012).
[CrossRef] [PubMed]

A. C. Hurst, T. B. Edo, T. Walther, F. Sweeney, and J. M. Rodenburg, “Probe position recovery for ptychographical imaging,” J. Phys. Conf. Ser.241, 012004 (2010).
[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(3), 034801 (2007).
[CrossRef] [PubMed]

Jefimovs, K.

C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110(4), 325–329 (2010).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[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(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]

Kewish, C. M.

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,” Nature467(7314), 436–439 (2010).
[CrossRef] [PubMed]

C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110(4), 325–329 (2010).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

König, K.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

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 Commun3, 730 (2012).
[CrossRef] [PubMed]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy120, 64–72 (2012).
[CrossRef] [PubMed]

Legnini, D.

Lima, E.

E. Lima, A. Diaz, M. Guizar-Sicairos, S. Gorelick, P. Pernot, T. Schleier, and A. Menzel, “Cryo-scanning x-ray diffraction microscopy of frozen-hydrated yeast,” J. Microsc.249(1), 1–7 (2013).
[CrossRef]

Maiden, A.

F. Hüe, J. M. Rodenburg, A. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B82(12), 121415 (2010).
[CrossRef]

Maiden, A. M.

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 Commun3, 730 (2012).
[CrossRef] [PubMed]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy120, 64–72 (2012).
[CrossRef] [PubMed]

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy109(10), 1256–1262 (2009).
[CrossRef] [PubMed]

Menzel, A.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature494(7435), 68–71 (2013).
[CrossRef] [PubMed]

E. Lima, A. Diaz, M. Guizar-Sicairos, S. Gorelick, P. Pernot, T. Schleier, and A. Menzel, “Cryo-scanning x-ray diffraction microscopy of frozen-hydrated yeast,” J. Microsc.249(1), 1–7 (2013).
[CrossRef]

C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110(4), 325–329 (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,” Nature467(7314), 436–439 (2010).
[CrossRef] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(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,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Midgley, P. A.

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

F. Hüe, J. M. Rodenburg, A. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B82(12), 121415 (2010).
[CrossRef]

Morgan, A. J.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

Morrison, G. R.

Nugent, K. A.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

Osten, W.

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A75(4), 043805 (2007).
[CrossRef]

Pedrini, G.

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A75(4), 043805 (2007).
[CrossRef]

Pernot, P.

E. Lima, A. Diaz, M. Guizar-Sicairos, S. Gorelick, P. Pernot, T. Schleier, and A. Menzel, “Cryo-scanning x-ray diffraction microscopy of frozen-hydrated yeast,” J. Microsc.249(1), 1–7 (2013).
[CrossRef]

Peterson, I.

Pfeiffer, F.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110(4), 325–329 (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,” Nature467(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,” Ultramicroscopy109(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,” Science321(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]

Putkunz, C. T.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

Roberts, A.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

Robinson, I. K.

Rodenburg, J. M.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy120, 64–72 (2012).
[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 Commun3, 730 (2012).
[CrossRef] [PubMed]

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys.109(12), 124510 (2011).
[CrossRef]

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

A. C. Hurst, T. B. Edo, T. Walther, F. Sweeney, and J. M. Rodenburg, “Probe position recovery for ptychographical imaging,” J. Phys. Conf. Ser.241, 012004 (2010).
[CrossRef]

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B82(12), 121104 (2010).
[CrossRef]

F. Hüe, J. M. Rodenburg, A. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B82(12), 121415 (2010).
[CrossRef]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy109(10), 1256–1262 (2009).
[CrossRef] [PubMed]

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imag. Elec. Phys.150, 87–184 (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, “Hard X-ray lensless imaging of extended objects,” Phys. Rev. Lett.98(3), 034801 (2007).
[CrossRef] [PubMed]

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

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

Rosenhahn, A.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[CrossRef] [PubMed]

Salditt, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[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]

Salomé, M.

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salomé, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Radiat.18(3), 442–446 (2011).
[CrossRef] [PubMed]

Sarahan, M. C.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy120, 64–72 (2012).
[CrossRef] [PubMed]

Schleier, T.

E. Lima, A. Diaz, M. Guizar-Sicairos, S. Gorelick, P. Pernot, T. Schleier, and A. Menzel, “Cryo-scanning x-ray diffraction microscopy of frozen-hydrated yeast,” J. Microsc.249(1), 1–7 (2013).
[CrossRef]

Schlichting, I.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

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,” Nature467(7314), 436–439 (2010).
[CrossRef] [PubMed]

Scholten, R. E.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

Senkbeil, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[CrossRef] [PubMed]

Shenfield, A.

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys.109(12), 124510 (2011).
[CrossRef]

Sweeney, F.

A. C. Hurst, T. B. Edo, T. Walther, F. Sweeney, and J. M. Rodenburg, “Probe position recovery for ptychographical imaging,” J. Phys. Conf. Ser.241, 012004 (2010).
[CrossRef]

F. Hüe, J. M. Rodenburg, A. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B82(12), 121415 (2010).
[CrossRef]

Thibault, P.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature494(7435), 68–71 (2013).
[CrossRef] [PubMed]

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys.14(6), 063004 (2012).
[CrossRef]

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[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,” Nature467(7314), 436–439 (2010).
[CrossRef] [PubMed]

C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110(4), 325–329 (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,” Ultramicroscopy109(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,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Thurman, S. T.

Vila-Comamala, J.

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salomé, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Radiat.18(3), 442–446 (2011).
[CrossRef] [PubMed]

C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110(4), 325–329 (2010).
[CrossRef] [PubMed]

Vine, D. J.

Walther, T.

A. C. Hurst, T. B. Edo, T. Walther, F. Sweeney, and J. M. Rodenburg, “Probe position recovery for ptychographical imaging,” J. Phys. Conf. Ser.241, 012004 (2010).
[CrossRef]

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,” Nature467(7314), 436–439 (2010).
[CrossRef] [PubMed]

Weyland, M.

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

Wojcik, M.

Zhang, F.

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B82(12), 121104 (2010).
[CrossRef]

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A75(4), 043805 (2007).
[CrossRef]

Adv. Imag. Elec. Phys. (1)

J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” Adv. Imag. Elec. Phys.150, 87–184 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

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

J. Appl. Phys. (1)

A. Shenfield and J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys.109(12), 124510 (2011).
[CrossRef]

J. Microsc. (1)

E. Lima, A. Diaz, M. Guizar-Sicairos, S. Gorelick, P. Pernot, T. Schleier, and A. Menzel, “Cryo-scanning x-ray diffraction microscopy of frozen-hydrated yeast,” J. Microsc.249(1), 1–7 (2013).
[CrossRef]

J. Phys. Conf. Ser. (1)

A. C. Hurst, T. B. Edo, T. Walther, F. Sweeney, and J. M. Rodenburg, “Probe position recovery for ptychographical imaging,” J. Phys. Conf. Ser.241, 012004 (2010).
[CrossRef]

J. Synchrotron Radiat. (1)

S. Gorelick, J. Vila-Comamala, V. A. Guzenko, R. Barrett, M. Salomé, and C. David, “High-efficiency Fresnel zone plates for hard X-rays by 100 keV e-beam lithography and electroplating,” J. Synchrotron Radiat.18(3), 442–446 (2011).
[CrossRef] [PubMed]

Nat Commun (1)

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 Commun3, 730 (2012).
[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,” Nature467(7314), 436–439 (2010).
[CrossRef] [PubMed]

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature494(7435), 68–71 (2013).
[CrossRef] [PubMed]

New J. Phys. (2)

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys.12(3), 035017 (2010).
[CrossRef]

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys.14(6), 063004 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (1)

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A75(4), 043805 (2007).
[CrossRef]

Phys. Rev. B (2)

F. Zhang and J. M. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B82(12), 121104 (2010).
[CrossRef]

F. Hüe, J. M. Rodenburg, A. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B82(12), 121415 (2010).
[CrossRef]

Phys. Rev. Lett. (3)

C. T. Putkunz, A. J. D’Alfonso, A. J. Morgan, M. Weyland, C. Dwyer, L. Bourgeois, J. Etheridge, A. Roberts, R. E. Scholten, K. A. Nugent, and L. J. Allen, “Atom-scale ptychographic electron diffractive imaging of boron nitride cones,” Phys. Rev. Lett.108(7), 073901 (2012).
[CrossRef] [PubMed]

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

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]

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]

Science (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science321(5887), 379–382 (2008).
[CrossRef] [PubMed]

Ultramicroscopy (6)

C. M. Kewish, P. Thibault, M. Dierolf, O. Bunk, A. Menzel, J. Vila-Comamala, K. Jefimovs, and F. Pfeiffer, “Ptychographic characterization of the wavefield in the focus of reflective hard x-ray optics,” Ultramicroscopy110(4), 325–329 (2010).
[CrossRef] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009).
[CrossRef] [PubMed]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy109(10), 1256–1262 (2009).
[CrossRef] [PubMed]

F. Hüe, J. M. Rodenburg, A. M. Maiden, and P. A. Midgley, “Extended ptychography in the transmission electron microscope: possibilities and limitations,” Ultramicroscopy111(8), 1117–1123 (2011).
[CrossRef] [PubMed]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy120, 64–72 (2012).
[CrossRef] [PubMed]

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, and A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy126, 44–47 (2013).
[CrossRef] [PubMed]

Supplementary Material (8)

» Media 1: MOV (2856 KB)     
» Media 2: MOV (11641 KB)     
» Media 3: MOV (2546 KB)     
» Media 4: MOV (2856 KB)     
» Media 5: MOV (11641 KB)     
» Media 6: MOV (2546 KB)     
» Media 7: AVI (11264 KB)     
» Media 8: AVI (2022 KB)     

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Figures (9)

Fig. 1
Fig. 1

Comparison of reconstruction quality with or without position refinement. (a) and (b) Test object modulus [0.3, 1] and phase [-π, π]. Insets are the probe amplitude and phase respectively. The highlighted areas indicate the measured region of object. (c) and (d) Reconstructed images with probe function update only. (e) and (f) Reconstructed images with position update only. (g) and (h) Reconstructed images with both probe function and translation position update. A movie, Media 1, showing the reconstruction process is available online.

Fig. 2
Fig. 2

Position maps used in the simulation. The green circles indicate the actual positions used in generating the diffraction data. The red dots and red pluses indicate the positions before and after position refinement, respectively. The blue lines illustrate the traces retrieved at each iteration step. The mean initial translation error is 17.7 pixels. A movie is available online, Media 2.

Fig. 3
Fig. 3

(a) Evolution of position error for various β settings with (blue solid lines) and without (red dashed lines) probe update. The probe update started at the iteration 60. (b) Evolution of feedback parameter β value with the iteration number in the case of automatic adjustment of β.

Fig. 4
Fig. 4

Dependence of residual position error on the magnitude of initial position error. (a) Mean residual error versus the initial position error. (b) Residual error at each scan positions for the three magnitudes of initial position errors: 19.28 pixels (green line); 21.6 pixels (circle headed blue line); and 26.6 pixels (square headed red line).

Fig. 5
Fig. 5

Effect of Poisson noise on the accuracy of retrieved position. The red line (9 pixels) indicates the mean error of initial position guesses.

Fig. 6
Fig. 6

Reconstructed images of a USAF 1951 target (a) without and (b) with position refinement.

Fig. 7
Fig. 7

Reconstructed images of a nano-fabricated random phase plate using X-ray data (cut-out of central region). (a) and (b) Reconstructed modulus of modulator without and with position refinement. (c) and (d) Reconstructed phase of modulator without and with positions refinement. (e) and (f) Reconstructed probe amplitude (cutout of central region) without and with position refinement.

Fig. 8
Fig. 8

(a) Retrieved translation position errors at each scan positions; (b) Position maps before (red crosses) and after (green circles) position refinement; a pixel is 35.2 nm wide.

Fig. 9
Fig. 9

(a) and (b) Reconstructed object phase without and with position refinement (unwrapped). (c) Retrieved errors at each scan positions, values for y-axis offset by 7 pixels for clarity. (d) Reconstructed probe amplitude with position refinement.

Equations (8)

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ψ j (r)=P(r)O(r, s j )
I j (u)= | F ψ j (r) | 2 , j=1, 2, ..., J
Ψ ˜ m j (u)= Ψ m j (u) / | Ψ m j (u)| I j (u) .
ψ ˜ m j (r)= F 1 Ψ ˜ m j (u) .
O m+1 (r, s j )= O m (r, s j )+ α 1 P m * (r) | P m (r) | max 2 [ ψ ˜ m j (r) ψ m j (r) ]
P m+1 (r)= P m (r)+ α 2 O m * (r, s j ) | O m (r, s j ) | max 2 [ ψ ˜ m j (r) ψ m j (r) ]
s j,m+1 = s j,m +β e j,m
C(t)= r O m+1 (r, s j;m ) Π m (r) O m * (rt, s j;m ) Π m * (rt)

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