Abstract

Ptychographic coherent x-ray diffractive imaging is a form of scanning microscopy that does not require optics to image a sample. A series of scanned coherent diffraction patterns recorded from multiple overlapping illuminated regions on the sample are inverted numerically to retrieve its image. The technique recovers the phase lost by detecting the diffraction patterns by using experimentally known constraints, in this case the measured diffraction intensities and the assumed scan positions on the sample. The spatial resolution of the recovered image of the sample is limited by the angular extent over which the diffraction patterns are recorded and how well these constraints are known. Here, we explore how reconstruction quality degrades with uncertainties in the scan positions. We show experimentally that large errors in the assumed scan positions on the sample can be numerically determined and corrected using conjugate gradient descent methods. We also explore in simulations the limits, based on the signal to noise of the diffraction patterns and amount of overlap between adjacent scan positions, of just how large these errors can be and still be rendered tractable by this method.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Sayre, “Some implications of a theorem due to Shannon,” Acta Cryst. 5, 843 (1952).
    [CrossRef]
  2. J. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978).
    [CrossRef] [PubMed]
  3. J.M. Rodenburg, H.M.L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
    [CrossRef]
  4. R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. I. Underlying theory,” Optik 61, 247–262 (1982).
  5. J. Miao, P. Charalambous, J. Kirz, D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
    [CrossRef]
  6. P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
    [CrossRef]
  7. K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C.M. Kewish, M. Dierolf, F. Pfeiffer, T. Salditt, “Quantitative biological imaging by ptychographic X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 107, 529–534 (2010).
    [CrossRef]
  8. A. Tripathi, J. Mohanty, S.H. Dietze, O.G. Shpyrko, E. Shipton, E.E. Fullerton, S.S. Kim, I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. USA 108, 13393–13398 (2011).
    [CrossRef] [PubMed]
  9. B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Physics 4, 394–398 (2008).
    [CrossRef]
  10. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C.M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
    [CrossRef] [PubMed]
  11. Image of sample modified from an original courtesy of Invitrogen: http://www.biovis.com/carv-ii.htm .
  12. O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108481–487 (2008).
    [CrossRef]
  13. H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
    [CrossRef]
  14. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321, 379–382 (2008).
    [CrossRef] [PubMed]
  15. A.M. Maiden, J.M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
    [CrossRef] [PubMed]
  16. C.M. Kewish, M. Guizar-Sicairos, C. Liu, J. Qian, B. Shi, C. Benson, A.M. Khounsary, J. Vila-Comamala, O. Bunk, J.R. Fienup, A.T. Macrander, L. Assoufid, “Reconstruction of an astigmatic hard X-ray beam and alignment of K-B mirrors from ptychographic coherent diffraction data,” Opt. Express 18, 23420–23427 (2010).
    [CrossRef] [PubMed]
  17. J. R. Fienup, “Phase retrieval algorithms: a comparison,” App. Opt. 21, 2758–2769 (1982).
    [CrossRef]
  18. S. Marchesini, “A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78, 011301 (2007).
    [CrossRef]
  19. M. Guizar-Sicairos, J.R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16, 7264–7278 (2008).
    [CrossRef] [PubMed]
  20. V. Elser, I. Rankenburg, P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. USA 104, 418–423 (2007).
    [CrossRef] [PubMed]
  21. F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
    [CrossRef] [PubMed]
  22. A. Shenfield, J. M. Rodenburg, “Evolutionary determination of experimental parameters for ptychographical imaging,” J. Appl. Phys. 109, 124510 (2011).
    [CrossRef]
  23. M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
    [CrossRef] [PubMed]
  24. Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
    [CrossRef]
  25. A.M. Maiden, M.J. Humphry, M.C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 164–172 (2012).
    [CrossRef]
  26. P. Thibault, A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71(2013).
    [CrossRef] [PubMed]
  27. E. Polak, G. Ribière, “Note sur la convergence de méthodes de directions conjuguées,” Rev. Fr. Inform. Rech. Oper. 16, 35–43 (1969).
  28. I. McNulty, A.M. Khounsary, Y.P. Feng, Y. Qian, J. Barraza, C. Benson, D. Shu, “A beamline for 1–4 keV microscopy and coherence experiments at the Advanced Photon Source,” Rev. Sci. Instrum. 67, 3372 (1996).
    [CrossRef]
  29. C. Kittel, “Physical theory of ferromagnetic domains,” Rev. Mod. Phys. 21, 541–583 (1949).
    [CrossRef]
  30. C. Kooy, U. Enz, “Experimental and theoretical study of the domain configuration in thin layers of BaFe12O9,” Philips Res. Rep. 15, 7–29 (1960).
  31. M. Seul, D. Andelman, “Domain shapes and patterns: The phenomenology of modulated phases,” Science 267, 476–483 (1995).
    [CrossRef] [PubMed]
  32. M.T. Johnson, P.J.H. Bloemen, F.J.A. den Broeder, J.J. de Vries, “Magnetic anisotropy in metallic multilayers,” Rep. Prog. Phys. 59, 1409–1458 (1996).
    [CrossRef]
  33. O. Hellwig, G. Denbeau, B. Kortright, E.E. Fullerton, “X-ray studies of aligned magnetic stripe domains in perpendicular multilayers,” Physica B 336, 136–144 (2003).
    [CrossRef]
  34. D. Raasch, J. Reck, C. Mathieu, B. Hillebrands, “Exchange stiffness constant and wall energy density of amorphous GdTb-FeCo thin films,” J. Appl. Phys. 76, 1145–1149 (1994).
    [CrossRef]
  35. Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic properties of amorphous alloy films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208–1215 (1978).
    [CrossRef]
  36. C. Mathieu, B. Hillebrands, D. Raasch, “Exchange stiffness constant and effective gyromagnetic factor of Gd, Tb, and Nd containing, amorphous rare earth-transition metal film,” IEEE Trans. Magn. 30, 4434–4436 (1994).
    [CrossRef]
  37. E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
    [CrossRef]
  38. A. C. Hurst, T. B. Edo, T. Walther, F. Sweeney, J. M. Rodenburg, “Probe position recovery for ptychographical imaging,” J. Phys. Conf. Ser. 241, 012004 (2010).
    [CrossRef]
  39. M. Guizar-Sicairos, S. T. Thurman, J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156–158 (2008).
    [CrossRef] [PubMed]
  40. M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467, 436–439 (2010).
    [CrossRef] [PubMed]
  41. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
    [CrossRef] [PubMed]
  42. M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
    [CrossRef]

2013

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

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

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[CrossRef] [PubMed]

2012

A.M. Maiden, M.J. Humphry, M.C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 164–172 (2012).
[CrossRef]

2011

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

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[CrossRef]

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

A. Tripathi, J. Mohanty, S.H. Dietze, O.G. Shpyrko, E. Shipton, E.E. Fullerton, S.S. Kim, I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. USA 108, 13393–13398 (2011).
[CrossRef] [PubMed]

2010

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

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

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

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

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
[CrossRef]

C.M. Kewish, M. Guizar-Sicairos, C. Liu, J. Qian, B. Shi, C. Benson, A.M. Khounsary, J. Vila-Comamala, O. Bunk, J.R. Fienup, A.T. Macrander, L. Assoufid, “Reconstruction of an astigmatic hard X-ray beam and alignment of K-B mirrors from ptychographic coherent diffraction data,” Opt. Express 18, 23420–23427 (2010).
[CrossRef] [PubMed]

2009

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

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

2008

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108481–487 (2008).
[CrossRef]

B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Physics 4, 394–398 (2008).
[CrossRef]

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

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

2007

S. Marchesini, “A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78, 011301 (2007).
[CrossRef]

V. Elser, I. Rankenburg, P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. USA 104, 418–423 (2007).
[CrossRef] [PubMed]

2006

2004

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

2003

O. Hellwig, G. Denbeau, B. Kortright, E.E. Fullerton, “X-ray studies of aligned magnetic stripe domains in perpendicular multilayers,” Physica B 336, 136–144 (2003).
[CrossRef]

2000

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

1999

J. Miao, P. Charalambous, J. Kirz, D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

1996

M.T. Johnson, P.J.H. Bloemen, F.J.A. den Broeder, J.J. de Vries, “Magnetic anisotropy in metallic multilayers,” Rep. Prog. Phys. 59, 1409–1458 (1996).
[CrossRef]

I. McNulty, A.M. Khounsary, Y.P. Feng, Y. Qian, J. Barraza, C. Benson, D. Shu, “A beamline for 1–4 keV microscopy and coherence experiments at the Advanced Photon Source,” Rev. Sci. Instrum. 67, 3372 (1996).
[CrossRef]

1995

M. Seul, D. Andelman, “Domain shapes and patterns: The phenomenology of modulated phases,” Science 267, 476–483 (1995).
[CrossRef] [PubMed]

1994

C. Mathieu, B. Hillebrands, D. Raasch, “Exchange stiffness constant and effective gyromagnetic factor of Gd, Tb, and Nd containing, amorphous rare earth-transition metal film,” IEEE Trans. Magn. 30, 4434–4436 (1994).
[CrossRef]

D. Raasch, J. Reck, C. Mathieu, B. Hillebrands, “Exchange stiffness constant and wall energy density of amorphous GdTb-FeCo thin films,” J. Appl. Phys. 76, 1145–1149 (1994).
[CrossRef]

1982

J. R. Fienup, “Phase retrieval algorithms: a comparison,” App. Opt. 21, 2758–2769 (1982).
[CrossRef]

R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. I. Underlying theory,” Optik 61, 247–262 (1982).

1978

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic properties of amorphous alloy films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208–1215 (1978).
[CrossRef]

J. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978).
[CrossRef] [PubMed]

1969

E. Polak, G. Ribière, “Note sur la convergence de méthodes de directions conjuguées,” Rev. Fr. Inform. Rech. Oper. 16, 35–43 (1969).

1960

C. Kooy, U. Enz, “Experimental and theoretical study of the domain configuration in thin layers of BaFe12O9,” Philips Res. Rep. 15, 7–29 (1960).

1952

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Cryst. 5, 843 (1952).
[CrossRef]

1949

C. Kittel, “Physical theory of ferromagnetic domains,” Rev. Mod. Phys. 21, 541–583 (1949).
[CrossRef]

Abbey, B.

B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Physics 4, 394–398 (2008).
[CrossRef]

Allain, M.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

Andelman, D.

M. Seul, D. Andelman, “Domain shapes and patterns: The phenomenology of modulated phases,” Science 267, 476–483 (1995).
[CrossRef] [PubMed]

Assoufid, L.

Barraza, J.

I. McNulty, A.M. Khounsary, Y.P. Feng, Y. Qian, J. Barraza, C. Benson, D. Shu, “A beamline for 1–4 keV microscopy and coherence experiments at the Advanced Photon Source,” Rev. Sci. Instrum. 67, 3372 (1996).
[CrossRef]

Barty, A.

Bates, R. H. T.

R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. I. Underlying theory,” Optik 61, 247–262 (1982).

Bean, R.

Beckers, M.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

Beerlink, A.

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

Beetz, T.

Belakhovsky, M.

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

Benson, C.

Berenguer, F.

Bloemen, P.J.H.

M.T. Johnson, P.J.H. Bloemen, F.J.A. den Broeder, J.J. de Vries, “Magnetic anisotropy in metallic multilayers,” Rep. Prog. Phys. 59, 1409–1458 (1996).
[CrossRef]

Bunk, O.

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

C.M. Kewish, M. Guizar-Sicairos, C. Liu, J. Qian, B. Shi, C. Benson, A.M. Khounsary, J. Vila-Comamala, O. Bunk, J.R. Fienup, A.T. Macrander, L. Assoufid, “Reconstruction of an astigmatic hard X-ray beam and alignment of K-B mirrors from ptychographic coherent diffraction data,” Opt. Express 18, 23420–23427 (2010).
[CrossRef] [PubMed]

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

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
[CrossRef]

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

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108481–487 (2008).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

Capello, L.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

Carbone, G.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

Chamard, V.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

Chapman, H.N.

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Chen, B.

Chen, G.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

Chesnel, K.

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

Clark, J.N.

B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Physics 4, 394–398 (2008).
[CrossRef]

Collins, S. P.

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

Cui, C.

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

de Jonge, M.

B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Physics 4, 394–398 (2008).
[CrossRef]

de Vries, J.J.

M.T. Johnson, P.J.H. Bloemen, F.J.A. den Broeder, J.J. de Vries, “Magnetic anisotropy in metallic multilayers,” Rep. Prog. Phys. 59, 1409–1458 (1996).
[CrossRef]

den Broeder, F.J.A.

M.T. Johnson, P.J.H. Bloemen, F.J.A. den Broeder, J.J. de Vries, “Magnetic anisotropy in metallic multilayers,” Rep. Prog. Phys. 59, 1409–1458 (1996).
[CrossRef]

Denbeau, G.

O. Hellwig, G. Denbeau, B. Kortright, E.E. Fullerton, “X-ray studies of aligned magnetic stripe domains in perpendicular multilayers,” Physica B 336, 136–144 (2003).
[CrossRef]

Dhesi, S. S.

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

Diaz, A.

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[CrossRef] [PubMed]

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

Dierolf, M.

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

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
[CrossRef]

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

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

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

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108481–487 (2008).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

Dietze, S.H.

A. Tripathi, J. Mohanty, S.H. Dietze, O.G. Shpyrko, E. Shipton, E.E. Fullerton, S.S. Kim, I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. USA 108, 13393–13398 (2011).
[CrossRef] [PubMed]

Dudzik, E.

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

Dürr, H. A.

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

Edo, T. B.

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

Elser, V.

V. Elser, I. Rankenburg, P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. USA 104, 418–423 (2007).
[CrossRef] [PubMed]

Enz, U.

C. Kooy, U. Enz, “Experimental and theoretical study of the domain configuration in thin layers of BaFe12O9,” Philips Res. Rep. 15, 7–29 (1960).

Faulkner, H.M.L.

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

Feng, Y.P.

I. McNulty, A.M. Khounsary, Y.P. Feng, Y. Qian, J. Barraza, C. Benson, D. Shu, “A beamline for 1–4 keV microscopy and coherence experiments at the Advanced Photon Source,” Rev. Sci. Instrum. 67, 3372 (1996).
[CrossRef]

Fienup, J.

Fienup, J. R.

Fienup, J.R.

Fullerton, E.E.

A. Tripathi, J. Mohanty, S.H. Dietze, O.G. Shpyrko, E. Shipton, E.E. Fullerton, S.S. Kim, I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. USA 108, 13393–13398 (2011).
[CrossRef] [PubMed]

O. Hellwig, G. Denbeau, B. Kortright, E.E. Fullerton, “X-ray studies of aligned magnetic stripe domains in perpendicular multilayers,” Physica B 336, 136–144 (2003).
[CrossRef]

Giewekemeyer, K.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

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

Godard, P.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

Goedkoop, J. B.

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

Gorniak, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

Guizar-Sicairos, M.

Hau-Riege, S.P.

He, H.

Hellwig, O.

O. Hellwig, G. Denbeau, B. Kortright, E.E. Fullerton, “X-ray studies of aligned magnetic stripe domains in perpendicular multilayers,” Physica B 336, 136–144 (2003).
[CrossRef]

Hillebrands, B.

D. Raasch, J. Reck, C. Mathieu, B. Hillebrands, “Exchange stiffness constant and wall energy density of amorphous GdTb-FeCo thin films,” J. Appl. Phys. 76, 1145–1149 (1994).
[CrossRef]

C. Mathieu, B. Hillebrands, D. Raasch, “Exchange stiffness constant and effective gyromagnetic factor of Gd, Tb, and Nd containing, amorphous rare earth-transition metal film,” IEEE Trans. Magn. 30, 4434–4436 (1994).
[CrossRef]

Howells, M.R.

Humphry, M.J.

A.M. Maiden, M.J. Humphry, M.C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 164–172 (2012).
[CrossRef]

Hurst, A. C.

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

Imamura, N.

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic properties of amorphous alloy films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208–1215 (1978).
[CrossRef]

Ishikawa, T.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[CrossRef]

Jacobsen, C.

Jefimovs, K.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
[CrossRef]

Johnson, I.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108481–487 (2008).
[CrossRef]

Johnson, M.T.

M.T. Johnson, P.J.H. Bloemen, F.J.A. den Broeder, J.J. de Vries, “Magnetic anisotropy in metallic multilayers,” Rep. Prog. Phys. 59, 1409–1458 (1996).
[CrossRef]

Kalbfleisch, S.

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

Kewish, C. M.

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

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
[CrossRef]

Kewish, C.M.

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

C.M. Kewish, M. Guizar-Sicairos, C. Liu, J. Qian, B. Shi, C. Benson, A.M. Khounsary, J. Vila-Comamala, O. Bunk, J.R. Fienup, A.T. Macrander, L. Assoufid, “Reconstruction of an astigmatic hard X-ray beam and alignment of K-B mirrors from ptychographic coherent diffraction data,” Opt. Express 18, 23420–23427 (2010).
[CrossRef] [PubMed]

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

Khounsary, A.M.

Kim, S.S.

A. Tripathi, J. Mohanty, S.H. Dietze, O.G. Shpyrko, E. Shipton, E.E. Fullerton, S.S. Kim, I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. USA 108, 13393–13398 (2011).
[CrossRef] [PubMed]

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Kittel, C.

C. Kittel, “Physical theory of ferromagnetic domains,” Rev. Mod. Phys. 21, 541–583 (1949).
[CrossRef]

Kobayashi, T.

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic properties of amorphous alloy films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208–1215 (1978).
[CrossRef]

Kohmura, Y.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[CrossRef]

Kooy, C.

C. Kooy, U. Enz, “Experimental and theoretical study of the domain configuration in thin layers of BaFe12O9,” Philips Res. Rep. 15, 7–29 (1960).

Kortright, B.

O. Hellwig, G. Denbeau, B. Kortright, E.E. Fullerton, “X-ray studies of aligned magnetic stripe domains in perpendicular multilayers,” Physica B 336, 136–144 (2003).
[CrossRef]

Kraus, B.

A.M. Maiden, M.J. Humphry, M.C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 164–172 (2012).
[CrossRef]

Kushiro, Y.

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic properties of amorphous alloy films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208–1215 (1978).
[CrossRef]

Kynde, S.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108481–487 (2008).
[CrossRef]

Liu, C.

Macrander, A.T.

Maiden, A.M.

A.M. Maiden, M.J. Humphry, M.C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 164–172 (2012).
[CrossRef]

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

Marchesini, S.

Marti, O.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108481–487 (2008).
[CrossRef]

Marty, A.

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

Mastropietro, F.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

Mathieu, C.

D. Raasch, J. Reck, C. Mathieu, B. Hillebrands, “Exchange stiffness constant and wall energy density of amorphous GdTb-FeCo thin films,” J. Appl. Phys. 76, 1145–1149 (1994).
[CrossRef]

C. Mathieu, B. Hillebrands, D. Raasch, “Exchange stiffness constant and effective gyromagnetic factor of Gd, Tb, and Nd containing, amorphous rare earth-transition metal film,” IEEE Trans. Magn. 30, 4434–4436 (1994).
[CrossRef]

McNulty, I.

A. Tripathi, J. Mohanty, S.H. Dietze, O.G. Shpyrko, E. Shipton, E.E. Fullerton, S.S. Kim, I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. USA 108, 13393–13398 (2011).
[CrossRef] [PubMed]

B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Physics 4, 394–398 (2008).
[CrossRef]

I. McNulty, A.M. Khounsary, Y.P. Feng, Y. Qian, J. Barraza, C. Benson, D. Shu, “A beamline for 1–4 keV microscopy and coherence experiments at the Advanced Photon Source,” Rev. Sci. Instrum. 67, 3372 (1996).
[CrossRef]

Menzel, A.

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[CrossRef] [PubMed]

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

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

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

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
[CrossRef]

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

Metzger, T. H.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

Miao, J.

J. Miao, P. Charalambous, J. Kirz, D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Mimura, Y.

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic properties of amorphous alloy films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208–1215 (1978).
[CrossRef]

Mohanty, J.

A. Tripathi, J. Mohanty, S.H. Dietze, O.G. Shpyrko, E. Shipton, E.E. Fullerton, S.S. Kim, I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. USA 108, 13393–13398 (2011).
[CrossRef] [PubMed]

Noy, A.

Nugent, K.A.

B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Physics 4, 394–398 (2008).
[CrossRef]

Ohashi, H.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[CrossRef]

Okada, A.

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic properties of amorphous alloy films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208–1215 (1978).
[CrossRef]

Peele, A.G.

B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Physics 4, 394–398 (2008).
[CrossRef]

Peterson, I.

Pfeifer, M.A.

B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Physics 4, 394–398 (2008).
[CrossRef]

Pfeiffer, F.

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

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
[CrossRef]

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

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

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

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108481–487 (2008).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

Polak, E.

E. Polak, G. Ribière, “Note sur la convergence de méthodes de directions conjuguées,” Rev. Fr. Inform. Rech. Oper. 16, 35–43 (1969).

Qian, J.

Qian, Y.

I. McNulty, A.M. Khounsary, Y.P. Feng, Y. Qian, J. Barraza, C. Benson, D. Shu, “A beamline for 1–4 keV microscopy and coherence experiments at the Advanced Photon Source,” Rev. Sci. Instrum. 67, 3372 (1996).
[CrossRef]

Raasch, D.

D. Raasch, J. Reck, C. Mathieu, B. Hillebrands, “Exchange stiffness constant and wall energy density of amorphous GdTb-FeCo thin films,” J. Appl. Phys. 76, 1145–1149 (1994).
[CrossRef]

C. Mathieu, B. Hillebrands, D. Raasch, “Exchange stiffness constant and effective gyromagnetic factor of Gd, Tb, and Nd containing, amorphous rare earth-transition metal film,” IEEE Trans. Magn. 30, 4434–4436 (1994).
[CrossRef]

Rankenburg, I.

V. Elser, I. Rankenburg, P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. USA 104, 418–423 (2007).
[CrossRef] [PubMed]

Reck, J.

D. Raasch, J. Reck, C. Mathieu, B. Hillebrands, “Exchange stiffness constant and wall energy density of amorphous GdTb-FeCo thin films,” J. Appl. Phys. 76, 1145–1149 (1994).
[CrossRef]

Ribière, G.

E. Polak, G. Ribière, “Note sur la convergence de méthodes de directions conjuguées,” Rev. Fr. Inform. Rech. Oper. 16, 35–43 (1969).

Robinson, I. K.

Rodenburg, J. M.

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[CrossRef] [PubMed]

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

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

Rodenburg, J.M.

A.M. Maiden, M.J. Humphry, M.C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 164–172 (2012).
[CrossRef]

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

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

Rosen, R.

Rosenhahn, A.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

Salditt, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

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

Samson, Y.

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

Sarahan, M.C.

A.M. Maiden, M.J. Humphry, M.C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 164–172 (2012).
[CrossRef]

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Cryst. 5, 843 (1952).
[CrossRef]

Schlichting, I.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
[CrossRef]

Schneider, P.

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

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

Senba, Y.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[CrossRef]

Senkbeil, T.

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

Seul, M.

M. Seul, D. Andelman, “Domain shapes and patterns: The phenomenology of modulated phases,” Science 267, 476–483 (1995).
[CrossRef] [PubMed]

Shapiro, D.

Shenfield, A.

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

Shi, B.

Shipton, E.

A. Tripathi, J. Mohanty, S.H. Dietze, O.G. Shpyrko, E. Shipton, E.E. Fullerton, S.S. Kim, I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. USA 108, 13393–13398 (2011).
[CrossRef] [PubMed]

Shpyrko, O.G.

A. Tripathi, J. Mohanty, S.H. Dietze, O.G. Shpyrko, E. Shipton, E.E. Fullerton, S.S. Kim, I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. USA 108, 13393–13398 (2011).
[CrossRef] [PubMed]

Shu, D.

I. McNulty, A.M. Khounsary, Y.P. Feng, Y. Qian, J. Barraza, C. Benson, D. Shu, “A beamline for 1–4 keV microscopy and coherence experiments at the Advanced Photon Source,” Rev. Sci. Instrum. 67, 3372 (1996).
[CrossRef]

Spence, J.C.H.

Stangl, J.

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

Suzuki, A.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[CrossRef]

Sweeney, F.

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

Takahashi, Y.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[CrossRef]

Thibault, P.

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

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

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

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
[CrossRef]

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

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

V. Elser, I. Rankenburg, P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. USA 104, 418–423 (2007).
[CrossRef] [PubMed]

Thurman, S. T.

Tripathi, A.

A. Tripathi, J. Mohanty, S.H. Dietze, O.G. Shpyrko, E. Shipton, E.E. Fullerton, S.S. Kim, I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. USA 108, 13393–13398 (2011).
[CrossRef] [PubMed]

van der Laan, G.

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

Vila-Comamala, J.

von König, K.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
[CrossRef]

Walther, T.

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

Weierstall, U.

Wepf, R.

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

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

Williams, G.J.

B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Physics 4, 394–398 (2008).
[CrossRef]

Yamauchi, K.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[CrossRef]

Zettsu, N.

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[CrossRef]

Zhang, F.

Acta Cryst.

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Cryst. 5, 843 (1952).
[CrossRef]

App. Opt.

J. R. Fienup, “Phase retrieval algorithms: a comparison,” App. Opt. 21, 2758–2769 (1982).
[CrossRef]

Appl. Phys. Lett.

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

IEEE Trans. Magn.

C. Mathieu, B. Hillebrands, D. Raasch, “Exchange stiffness constant and effective gyromagnetic factor of Gd, Tb, and Nd containing, amorphous rare earth-transition metal film,” IEEE Trans. Magn. 30, 4434–4436 (1994).
[CrossRef]

J. Appl. Phys.

E. Dudzik, S. S. Dhesi, S. P. Collins, H. A. Dürr, G. van der Laan, K. Chesnel, M. Belakhovsky, A. Marty, Y. Samson, J. B. Goedkoop, “X-ray resonant magnetic scattering from FePd thin films,” J. Appl. Phys. 87, 5469–5471 (2000).
[CrossRef]

D. Raasch, J. Reck, C. Mathieu, B. Hillebrands, “Exchange stiffness constant and wall energy density of amorphous GdTb-FeCo thin films,” J. Appl. Phys. 76, 1145–1149 (1994).
[CrossRef]

Y. Mimura, N. Imamura, T. Kobayashi, A. Okada, Y. Kushiro, “Magnetic properties of amorphous alloy films of Fe with Gd, Tb, Dy, Ho, or Er,” J. Appl. Phys. 49, 1208–1215 (1978).
[CrossRef]

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

J. Opt. Soc. Am. A

J. Phys. Conf. Ser.

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

Nat. Communications

P. Godard, G. Carbone, M. Allain, F. Mastropietro, G. Chen, L. Capello, A. Diaz, T. H. Metzger, J. Stangl, V. Chamard, “Three-dimensional high-resolution quantitative microscopy of extended crystals,” Nat. Communications 2, 568 (2011).
[CrossRef]

Nat. Physics

B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Physics 4, 394–398 (2008).
[CrossRef]

Nature

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

J. Miao, P. Charalambous, J. Kirz, D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

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

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

New J. Phys.

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12035017 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

R. H. T. Bates, “Fourier phase problems are uniquely solvable in more than one dimension. I. Underlying theory,” Optik 61, 247–262 (1982).

Philips Res. Rep.

C. Kooy, U. Enz, “Experimental and theoretical study of the domain configuration in thin layers of BaFe12O9,” Philips Res. Rep. 15, 7–29 (1960).

Phys. Rev. B

Y. Takahashi, A. Suzuki, N. Zettsu, Y. Kohmura, Y. Senba, H. Ohashi, K. Yamauchi, T. Ishikawa, “Towards high-resolution ptychographic x-ray diffraction microscopy,” Phys. Rev. B 83, 214109 (2011).
[CrossRef]

Physica B

O. Hellwig, G. Denbeau, B. Kortright, E.E. Fullerton, “X-ray studies of aligned magnetic stripe domains in perpendicular multilayers,” Physica B 336, 136–144 (2003).
[CrossRef]

Proc. Natl. Acad. Sci. USA

V. Elser, I. Rankenburg, P. Thibault, “Searching with iterated maps,” Proc. Natl. Acad. Sci. USA 104, 418–423 (2007).
[CrossRef] [PubMed]

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

A. Tripathi, J. Mohanty, S.H. Dietze, O.G. Shpyrko, E. Shipton, E.E. Fullerton, S.S. Kim, I. McNulty, “Dichroic coherent diffractive imaging,” Proc. Natl. Acad. Sci. USA 108, 13393–13398 (2011).
[CrossRef] [PubMed]

Rep. Prog. Phys.

M.T. Johnson, P.J.H. Bloemen, F.J.A. den Broeder, J.J. de Vries, “Magnetic anisotropy in metallic multilayers,” Rep. Prog. Phys. 59, 1409–1458 (1996).
[CrossRef]

Rev. Fr. Inform. Rech. Oper.

E. Polak, G. Ribière, “Note sur la convergence de méthodes de directions conjuguées,” Rev. Fr. Inform. Rech. Oper. 16, 35–43 (1969).

Rev. Mod. Phys.

C. Kittel, “Physical theory of ferromagnetic domains,” Rev. Mod. Phys. 21, 541–583 (1949).
[CrossRef]

Rev. Sci. Instrum.

I. McNulty, A.M. Khounsary, Y.P. Feng, Y. Qian, J. Barraza, C. Benson, D. Shu, “A beamline for 1–4 keV microscopy and coherence experiments at the Advanced Photon Source,” Rev. Sci. Instrum. 67, 3372 (1996).
[CrossRef]

S. Marchesini, “A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78, 011301 (2007).
[CrossRef]

Science

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

M. Seul, D. Andelman, “Domain shapes and patterns: The phenomenology of modulated phases,” Science 267, 476–483 (1995).
[CrossRef] [PubMed]

Ultramicroscopy

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

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

A.M. Maiden, M.J. Humphry, M.C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120, 164–172 (2012).
[CrossRef]

M. Beckers, T. Senkbeil, T. Gorniak, K. Giewekemeyer, T. Salditt, A. Rosenhahn, “Drift correction in ptychographic diffractive imaging,” Ultramicroscopy 126, 44–47 (2013).
[CrossRef] [PubMed]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical iterative engine,” Ultramicroscopy 108481–487 (2008).
[CrossRef]

Other

Image of sample modified from an original courtesy of Invitrogen: http://www.biovis.com/carv-ii.htm .

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 (7)

Fig. 1
Fig. 1

Schematic of an X-ray scanning CDI measurement in the forward-scattering geometry. X-rays, defined by an illumination function p(r) are incident on a sample with a transmission function T(r). A ptychographic data set is acquired by recording a series of diffraction patterns by an X-ray area detector while scanning the sample with overlapping illumination regions, depicted here by the overlapping circles.

Fig. 2
Fig. 2

(a–b) Reconstructions of p(r) and T(r) for when there is no error in scan position constraint. (c–d) Reconstructions of p(r) and T(r) for when random errors up to 10ΔxS are added to the x and y components of each of the scan locations. (e–f) Line cuts of T(r) along the red line in (b); (e) is the magnitude of T(r) along this line while (f) is the phase. (g–h) Line cuts of p(r) along the red line in (a); (g) is the magnitude of p(r) along this line while (h) is the phase. In Fig. 2(e) to 2(h), the solid green line is the true T(r) or p(r), the solid black line is the line cut from reconstructions for T(r) or p(r) assuming no scan position errors, while the dotted red line is the line cut from reconstructions for T(r) or p(r) with scan position errors. The white horizontal scale bars in frames (a) and (b) are both 100ΔxS.

Fig. 3
Fig. 3

(a) Reconstructed T(r) and (b) p(r) when incorrect scan positions are used from experimentally collected diffraction at the Advanced Photon Source. (c) Improved reconstructions for T(r) and (d) p(r) after application of the scan position correction method presented in Section 2. (e) The recovered scan positions rj (green dots) starting from the incorrect scan positions (black dots). The distance between the black dots on the square scanning grid is 3 μm.

Fig. 4
Fig. 4

To explore the limits of recoverable scan position error we look at two parameters: the photon fluence, and correspondingly the SNR of a diffraction pattern, and the amount of overlap, which determines the degree to which regions on the sample are overdetermined by information in the diffraction. (a) A simulated diffraction pattern. A beamstop, used in experiments to prevent damage to the area detector, is also assumed to be present in all cases. (b) A relatively low amount of overlap, and (c) a relatively high amount of overlap. (d) The different average diffraction intensities I(q) integrated azimuthally versus spatial frequency used for the simulations in this letter, and (e) the SNR of the diffraction intensities in (d). Here, SNR = 10 log 10 ( I ( q ) / I ( q ) ).

Fig. 5
Fig. 5

The dependence on the maximum recoverable scan position error ej,max (and corresponding average error over all scan positions Δ r avg initial) on the diffraction SNR and overlap. Here, we look at when a square 7 × 7 grid is scanned with 65%, 75%, and 85% overlap between adjacent scan positions, and then scan position errors ej, up to some maximum given by ej,max, are added to each of the j scan positions. The procedure given in Section 2 is performed and we determine final scan position configurations with average error Δ r avg final. The results shown here are those with the lowest final error metric value averaged over all j scan positions, as defined by Eq. (2), out of a total of twenty independent reconstruction trials. The maximum average scan position error Δ r avg initial the CG method is able to handle is determined by where Δ r avg final stops being roughly flat with increasing Δ r avg initial and begins to increase with increasing Δ r avg initial. For the 65% case, this cutoff is Δ r avg initial 30.6 Δ x S with e j , max 40 2 Δ x S, for the 75% case, this cutoff is Δ r avg initial 45.9 Δ x S with e j , max 60 2 Δ x S, while for the 85% case, this cutoff is Δ r avg initial 68.9 Δ x S with e j , max 90 2 Δ x S. Also included are results for perfect data when there is no simulated beamstop or Poisson noise, to establish a baseline for the performance of the method presented in Sec. 2. The primary differences for these perfect data baseline cases are greatly decreased total computation times (about a factor of 2–3), in addition to a modest increase in tolerable Δ r avg initial.

Fig. 6
Fig. 6

Recovered T(r), p(r), scan positions rj and reconstructions for three values of ej,max. (a) e j , max 90 2 Δ x S, (b) e j , max 110 2 Δ x S, and (c) e j , max 120 2 Δ x S. All reconstructions correspond to an integrated intensity of 109, corresponding to the blue curves in Fig. 4(d) and 4(e) and Fig. 5, and the 85% overlap square 7 × 7 grid (the black circles with distance between them of 40ΔxS), with the red dots corresponding to the true scan positions, and the green dots corresponding to the recovered scan positions.

Fig. 7
Fig. 7

When below the critical maximum scan position error ej,max, it is possible to further refine incorrectly recovered peripheral scan positions shown in (a). By keeping the previously recovered probe p(r) and scan positions rj but resetting T(r) to be initially consisting of complex valued random numbers, we perform the method given in Section 2 a number of subsequent times, here twenty, and average the results for all the recovered rj. This gives almost perfectly recovered scan positions, as seen in (b), with a Δ r avg final 0.1 Δ x S. All values for Δr are in units of ΔxS.

Equations (9)

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

[ ψ ( r ) ] = Ψ ( q ) = 1 N x , y ψ ( x , y ) exp [ 2 π i ( x q x + y q y N ) ] 1 [ Ψ ( q ) ] = ψ ( r ) = 1 N q x , q y Ψ ( q x , q y ) exp [ + 2 π i ( x q x + y q y N ) ] ,
ε j = q { | Ψ j , n ( q ) | I j ( q ) } 2 ,
r j , n + 1 = r j , n α n r j , n ε j .
Λ j , 0 = r j , 0 ε j Λ j , n = β n Λ j , n 1 r j , n ε j r j , n + 1 = r j , n + α n Λ j , n ,
β n P R = Δ j , n T ( Δ j , n Δ j , n 1 ) Δ j , n 1 T Δ j , n 1 ,
ε j x j , n = 4 π N q { ( 1 I j ( q ) | Ψ j , n ( q ) | ) Im [ Ψ j , n * ( q ) × ( p ( r ) 1 { q x T ^ ( q ) exp [ 2 π i ( q x x j , n + q y y j , n N ) ] } ) ] } ,
ε j x j , n = 4 π N q { ( 1 I j ( q ) | Ψ j , n ( q ) | ) Im [ Ψ j , n * ( q ) × ( p ( r ) 1 { q y T ^ ( q ) exp [ 2 π i ( q x x j , n + q y y j , n N ) ] } ) ] } ,
ε j ( α n ) = q { | [ p ( r ) T ( r r j , n α n Λ j , n ) ] | I j ( q ) } 2 .
Δ r avg final = j | r j true r j final | / 7 × 7 ,

Metrics