Abstract

X-ray ptychography, a scanning coherent diffraction imaging method, was used to reconstruct images of a “Siemens star” test pattern with amplitude and phase contrast. While studying how the use of illumination with an increased bandwidth results in clear improvements in the quality of image reconstructions, we found that an artificial change in the overall distance scale factor of the algorithm leads to a systematic response in the image, which is reproduced with an incorrect number of spokes. This pathology is explained by the conflict between the length scales set by the scan and by the diffraction patterns on the detector.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  20. X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2013 (3)

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. D. 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]

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

2012 (4)

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103 (2012).
[CrossRef]

A. Fannjiang, W. Liao, “Phase retrieval with random phase illumination,” J. Opt. Soc. Am. A 29, 1847–1859 (2012).
[CrossRef]

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

J. N. Clark, X. Huang, R. Harder, I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[CrossRef] [PubMed]

2011 (3)

F. J. Salgado-Remacha, L. M. Sanchez-Brea, E. Bernabeu, “Effect of fill-factor on the Talbot effect of diffraction gratings,” J. Europ. Opt. Soc. Rap. Public. 6, 11055 (2011).
[CrossRef]

P. Godard, M. Allain, V. Chamard, “Imaging of highly inhomogeneous strain field in nanocrystals using x-ray Bragg ptychography: A numerical study,” Phys. Rev. B 84, 144109 (2011).
[CrossRef]

J. N. Clark, C. T. Putkunz, E. K. Curwood, D. J. Vine, R. Scholten, I. McNulty, K. A. Nugent, A. G. Peele, “Dynamic sample imaging in coherent diffractive imaging,” Opt. Lett. 36, 1954–1956 (2011).
[CrossRef] [PubMed]

2010 (2)

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]

2009 (4)

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

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[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]

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

2008 (2)

J. N. Clark, G. J. Williams, H. M. Quiney, L. Whitehead, M. D. de Jonge, E. Hanssen, M. Altissimo, K. A. Nugent, A. G. Peele, “Quantitative phase measurement in coherent diffraction imaging,” Opt. Express 16, 3342–3348 (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 108, 481–487 (2008).
[CrossRef]

2004 (1)

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

1982 (2)

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

A. Oppenheim, M. Hayes, J. Lim, “Iterative procedures for signal reconstruction from fourier-transform phase,” Opt. Eng. 21, 122–127 (1982).
[CrossRef]

1836 (1)

H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Phil. Mag. Ser. 3 9, 401–407 (1836).

Allain, M.

P. Godard, M. Allain, V. Chamard, “Imaging of highly inhomogeneous strain field in nanocrystals using x-ray Bragg ptychography: A numerical study,” Phys. Rev. B 84, 144109 (2011).
[CrossRef]

Altissimo, M.

Balaur, E.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[CrossRef]

Bean, R.

Berenguer, A. D. F.

Bernabeu, E.

F. J. Salgado-Remacha, L. M. Sanchez-Brea, E. Bernabeu, “Effect of fill-factor on the Talbot effect of diffraction gratings,” J. Europ. Opt. Soc. Rap. Public. 6, 11055 (2011).
[CrossRef]

Bunk, O.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103 (2012).
[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, 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 108, 481–487 (2008).
[CrossRef]

Burdet, N.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

Burgess, A.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

Chamard, V.

P. Godard, M. Allain, V. Chamard, “Imaging of highly inhomogeneous strain field in nanocrystals using x-ray Bragg ptychography: A numerical study,” Phys. Rev. B 84, 144109 (2011).
[CrossRef]

Chen, B.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

F. Zhang, I. Peterson, J. Vila-Comamala, A. D. 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]

Chu, Y. S.

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

Clark, J. N.

Curwood, E. K.

de Jonge, M. D.

Diaz, A.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103 (2012).
[CrossRef]

Dierolf, M.

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, 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 108, 481–487 (2008).
[CrossRef]

Dilanian, R. A.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[CrossRef]

Fannjiang, A.

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]

Fienup, J. R.

Flewett, S.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[CrossRef]

Godard, P.

P. Godard, M. Allain, V. Chamard, “Imaging of highly inhomogeneous strain field in nanocrystals using x-ray Bragg ptychography: A numerical study,” Phys. Rev. B 84, 144109 (2011).
[CrossRef]

Guizar-Sicairos, M.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103 (2012).
[CrossRef]

Hanssen, E.

Harder, R.

J. N. Clark, X. Huang, R. Harder, I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[CrossRef] [PubMed]

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

Hayes, M.

A. Oppenheim, M. Hayes, J. Lim, “Iterative procedures for signal reconstruction from fourier-transform phase,” Opt. Eng. 21, 122–127 (1982).
[CrossRef]

Holler, M.

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103 (2012).
[CrossRef]

Huang, X.

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

J. N. Clark, X. Huang, R. Harder, I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[CrossRef] [PubMed]

Huo, S.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

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 108, 481–487 (2008).
[CrossRef]

Kewish, C. M.

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]

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 108, 481–487 (2008).
[CrossRef]

Legnini, D.

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

Liao, W.

Lim, J.

A. Oppenheim, M. Hayes, J. Lim, “Iterative procedures for signal reconstruction from fourier-transform phase,” Opt. Eng. 21, 122–127 (1982).
[CrossRef]

Maiden, A. M.

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

Mancuso, J.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

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 108, 481–487 (2008).
[CrossRef]

McNulty, I.

J. N. Clark, C. T. Putkunz, E. K. Curwood, D. J. Vine, R. Scholten, I. McNulty, K. A. Nugent, A. G. Peele, “Dynamic sample imaging in coherent diffractive imaging,” Opt. Lett. 36, 1954–1956 (2011).
[CrossRef] [PubMed]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[CrossRef]

Menzel, A.

F. Zhang, I. Peterson, J. Vila-Comamala, A. D. 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. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103 (2012).
[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, O. Bunk, A. Menzel, F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[CrossRef] [PubMed]

Monteith, A.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

Morrison, G. R.

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

Nugent, K. A.

Nutter, J.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

Oppenheim, A.

A. Oppenheim, M. Hayes, J. Lim, “Iterative procedures for signal reconstruction from fourier-transform phase,” Opt. Eng. 21, 122–127 (1982).
[CrossRef]

Peele, A. G.

Peterson, I.

F. Zhang, I. Peterson, J. Vila-Comamala, A. D. 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]

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

Pfeiffer, F.

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, 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 108, 481–487 (2008).
[CrossRef]

Putkunz, C. T.

Quiney, H. M.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[CrossRef]

J. N. Clark, G. J. Williams, H. M. Quiney, L. Whitehead, M. D. de Jonge, E. Hanssen, M. Altissimo, K. A. Nugent, A. G. Peele, “Quantitative phase measurement in coherent diffraction imaging,” Opt. Express 16, 3342–3348 (2008).
[CrossRef] [PubMed]

Robinson, I.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

Robinson, I. K.

F. Zhang, I. Peterson, J. Vila-Comamala, A. D. 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]

J. N. Clark, X. Huang, R. Harder, I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[CrossRef] [PubMed]

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

Rodenburg, J. M.

F. Zhang, I. Peterson, J. Vila-Comamala, A. D. 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. 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]

Salgado-Remacha, F. J.

F. J. Salgado-Remacha, L. M. Sanchez-Brea, E. Bernabeu, “Effect of fill-factor on the Talbot effect of diffraction gratings,” J. Europ. Opt. Soc. Rap. Public. 6, 11055 (2011).
[CrossRef]

Sanchez-Brea, L. M.

F. J. Salgado-Remacha, L. M. Sanchez-Brea, E. Bernabeu, “Effect of fill-factor on the Talbot effect of diffraction gratings,” J. Europ. Opt. Soc. Rap. Public. 6, 11055 (2011).
[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]

Scholten, R.

Shemilt, L.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

Talbot, H. F.

H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Phil. Mag. Ser. 3 9, 401–407 (1836).

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]

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

Vergeer, F.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

Vila-Comamala, J.

F. Zhang, I. Peterson, J. Vila-Comamala, A. D. 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]

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103 (2012).
[CrossRef]

Vine, D. J.

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

J. N. Clark, C. T. Putkunz, E. K. Curwood, D. J. Vine, R. Scholten, I. McNulty, K. A. Nugent, A. G. Peele, “Dynamic sample imaging in coherent diffractive imaging,” Opt. Lett. 36, 1954–1956 (2011).
[CrossRef] [PubMed]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[CrossRef]

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]

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]

Whitehead, L.

Whitehead, L. W.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[CrossRef]

Williams, G. J.

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[CrossRef]

J. N. Clark, G. J. Williams, H. M. Quiney, L. Whitehead, M. D. de Jonge, E. Hanssen, M. Altissimo, K. A. Nugent, A. G. Peele, “Quantitative phase measurement in coherent diffraction imaging,” Opt. Express 16, 3342–3348 (2008).
[CrossRef] [PubMed]

Wojcik, M.

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

Xiong, G.

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

Zhang, F.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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

J. Europ. Opt. Soc. Rap. Public. (1)

F. J. Salgado-Remacha, L. M. Sanchez-Brea, E. Bernabeu, “Effect of fill-factor on the Talbot effect of diffraction gratings,” J. Europ. Opt. Soc. Rap. Public. 6, 11055 (2011).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nat. Commun. (1)

J. N. Clark, X. Huang, R. Harder, I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[CrossRef] [PubMed]

Nature (2)

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. (1)

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 (1)

X. Huang, M. Wojcik, N. Burdet, I. Peterson, G. R. Morrison, D. J. Vine, D. Legnini, R. Harder, Y. S. Chu, I. K. Robinson, “Quantitative x-ray wavefront measurements of Fresnel zone plate and k-b mirrors using phase retrieval,” Opt. Express 20, 24038–24048 (2012).
[CrossRef] [PubMed]

Opt. Eng. (1)

A. Oppenheim, M. Hayes, J. Lim, “Iterative procedures for signal reconstruction from fourier-transform phase,” Opt. Eng. 21, 122–127 (1982).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phil. Mag. Ser. 3 (1)

H. F. Talbot, “LXXVI. Facts relating to optical science. No. IV,” Phil. Mag. Ser. 3 9, 401–407 (1836).

Phys. Rev. B (2)

M. Guizar-Sicairos, M. Holler, A. Diaz, J. Vila-Comamala, O. Bunk, A. Menzel, “Role of the illumination spatial-frequency spectrum for ptychography,” Phys. Rev. B 86, 100103 (2012).
[CrossRef]

P. Godard, M. Allain, V. Chamard, “Imaging of highly inhomogeneous strain field in nanocrystals using x-ray Bragg ptychography: A numerical study,” Phys. Rev. B 84, 144109 (2011).
[CrossRef]

Phys. Rev. Lett. (1)

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
[CrossRef]

Sci. Rep. (1)

B. Chen, M. Guizar-Sicairos, G. Xiong, L. Shemilt, A. Diaz, J. Nutter, N. Burdet, S. Huo, J. Mancuso, A. Monteith, F. Vergeer, A. Burgess, I. Robinson, “Three-dimensional structure analysis and percolation properties of a barrier marine coating,” Sci. Rep. 3, 1177 (2013).
[CrossRef] [PubMed]

Ultramicroscopy (4)

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 108, 481–487 (2008).
[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]

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

Other (1)

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Figures (6)

Fig. 1
Fig. 1

(a) Sketch of the experimental setup at 34-ID-C with entrance slits (1), KB mirrors (2), piezo-stage (3) and camera (4). A flight tube represented as a semi-transparent tube here is used only for distances above 1 m. (b) SEM image of the test pattern. Siemens star, diameter 11.4 μm. (c),(d) show reconstructed phase and amplitude images using data measured at z =2.184 m. Scale bars inside images, 2 μm.

Fig. 2
Fig. 2

From left to right: reconstructed objects and probes for detectors located at distance z = 0.55, 1.0 and 2.184 m from the sample. Top half: reconstructions for slit openings of 10 × 10 μm. Lower half: reconstructions for slit openings of 30 × 50 μm (note: the horizontal KB mirror has one half the focal length of the vertical). The probes are shown on a common scale but a white frame has been drawn to represent the original size of the CDI window. The probe amplitude is mapped to the image brightness, and the phase is mapped to hue. The probe sizes are in good agreement with values predicted from diffraction theory.

Fig. 3
Fig. 3

Reconstructed image phases (a)–(e) for different assumed distances z between sample and detector. The reconstructed object phase at the correct distance z0=0.55 m are shown in Fig. 2(d). The length of the closed bars (3 μm) is set by the real-space step size of the piezo scanner, while the open bars show the same 3 μm length as set by the CDI window size. The bars are of equal length when the distance z = z0 = 0.55m. A circular cut (see Fig. 3(c)) located 3 μm from the centre of each image was used to count the spokes in each reconstruction.

Fig. 4
Fig. 4

Number of spokes as a function of the assumed sample-to-camera distance z in the range 0.4 m to 0.8 m. The distance of reference, where the measured data were taken, is z0 = 0.55m (≈ 1.8m−1 in this plot) and the number of spokes for the reference object is 36. The red dotted line is the predicted number of spokes (see discussion). For each z value used, the corresponding R-factor is plotted (calculated at iteration 100 with all 460 frames).

Fig. 5
Fig. 5

Amplitude and phase of a reconstructed Siemens star at 0.5 m, showing 39 spokes. These results from a numerical simulation can be compared directly with the reconstruction based on experimental measurements that is shown in Figure 3(b). Scale bar, 2 μm.

Fig. 6
Fig. 6

Computed free-space propagation of the simulated Siemens star to planes situated at 5 mm intervals upstream from the reference position. The colour rendering shows complex valued data after histogram equalisation to stretch the contrast of the images.

Equations (3)

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

Δ x = λ z N Δ p .
R = j J q Q ( I obs j ( q ) | | I calc j ( q ) ) j J q Q | I obs j ( q ) |
O ( z ) = 1 [ exp ( i z q 2 2 k ) ( O ) ]

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