Abstract

Near-field X-ray ptychography has recently been proposed and shown to be able to retrieve a sample’s complex-valued transmission function from multiple near-field diffraction images each with a lateral shift of the sample and with a structured (by a diffuser) illumination [Stockmar et al. Sci Rep. 3 (2013)]. In this paper, we undertake the first investigation - via numerical simulation - of the influence of the sampling and step size of the lateral shifts, the diffuser structure size, and the propagation distance on the reconstruction of the sample’s transmission function. We find that for a gold Siemens star of thickness 750 nm with typical experimental parameters, for a successful reconstruction - given a theoretical minimum of four required measurements per imaged pixel - at least six diffraction images are required.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
X-ray nanotomography using near-field ptychography

Marco Stockmar, Maxime Hubert, Martin Dierolf, Bjoern Enders, Richard Clare, Sebastian Allner, Andreas Fehringer, Irene Zanette, Julie Villanova, Jérôme Laurencin, Peter Cloetens, Franz Pfeiffer, and Pierre Thibault
Opt. Express 23(10) 12720-12731 (2015)

Near-field Fourier ptychography: super-resolution phase retrieval via speckle illumination

He Zhang, Shaowei Jiang, Jun Liao, Junjing Deng, Jian Liu, Yongbing Zhang, and Guoan Zheng
Opt. Express 27(5) 7498-7512 (2019)

Continuous motion scan ptychography: characterization for increased speed in coherent x-ray imaging

Junjing Deng, Youssef S. G. Nashed, Si Chen, Nicholas W. Phillips, Tom Peterka, Rob Ross, Stefan Vogt, Chris Jacobsen, and David J. Vine
Opt. Express 23(5) 5438-5451 (2015)

References

  • View by:
  • |
  • |
  • |

  1. A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
    [Crossref]
  2. R. Fitzgerald, “Phase-sensitive X-ray imaging,” Phys. Today 53, 23–26 (2000).
    [Crossref]
  3. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Phys. 2, 258–261 (2006).
    [Crossref]
  4. T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature,  373, 595–598 (1995).
    [Crossref]
  5. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
    [Crossref]
  6. P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys.,  29, 133–146 (1996).
    [Crossref]
  7. H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
    [Crossref] [PubMed]
  8. J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illimuination,” App. Phys. Lett. 85, 4795–4797 (2004).
    [Crossref]
  9. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
    [Crossref] [PubMed]
  10. M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
    [Crossref] [PubMed]
  11. M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
    [Crossref]
  12. M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
    [Crossref] [PubMed]
  13. D. M. Paganin, Coherent X-ray Optics (Oxford series on synchrotron radiation), (Oxford University, 2006).
    [Crossref]
  14. M. Born and E. Wolf, eds., Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).
    [Crossref]
  15. J. R. Fieunp, “Invariant error metrics for image reconstruction,” Appl. Opt. 36, 8352–8357 (1997).
    [Crossref]
  16. O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical engine,” Ultramicroscopy 108, 481–487 (2008).
    [Crossref]
  17. A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” Europhys. Lett. 99, 48001 (2012).
    [Crossref]
  18. J. Wolf, A. Malecki, J. Sperl, M. Chabior, M. Schüttler, D. Berqué, C. Cozzini, and P. Pfeiffer, “Fast one-dimensional wave-front propagation for x-ray differential phase-contrast imaging,” Biomed. Opt. Express 5, 3739–3747 (2014).
    [PubMed]
  19. M.-C Zdora, “X-ray multimodal imaging using near-field speckles,” Master’s Thesis, Technische Universität München (2014).
  20. Federation of European Producers of Abrasives, “FEPA P-grit sizes coated abrasives,” http://www.fepa-abrasives.org/Abrasiveproducts/Grains/Pgritsizescoated.aspx
  21. A. Hamed, “Recognition of direction of new apertures from the eloganted speckle images: simulation,” J. Opt. Photon. 3, 250–258 (2013).
    [Crossref]
  22. R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
    [Crossref]
  23. P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68 (2013).
    [Crossref] [PubMed]
  24. P. Thibault, M. Deirolf, A. Menzel, O. Bunk, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
    [Crossref] [PubMed]
  25. P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New. J. Phys. 14, 1256–1262 (2012).
    [Crossref]
  26. M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
    [Crossref]
  27. H. Huang, H. Yan, R. Harder, Y. Hwu, I. K. Robinson, and Y. S. Chu, “Optimization of overlap uniformness for ptychography,” Opt. Express 22, 12634–12644 (2014).
    [Crossref] [PubMed]
  28. I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Herz, “Speckle-base X-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
    [Crossref]
  29. S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
    [Crossref] [PubMed]

2015 (2)

M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref] [PubMed]

2014 (3)

2013 (3)

A. Hamed, “Recognition of direction of new apertures from the eloganted speckle images: simulation,” J. Opt. Photon. 3, 250–258 (2013).
[Crossref]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref] [PubMed]

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

2012 (2)

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New. J. Phys. 14, 1256–1262 (2012).
[Crossref]

A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” Europhys. Lett. 99, 48001 (2012).
[Crossref]

2010 (1)

M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
[Crossref]

2009 (2)

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

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

2008 (2)

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

2006 (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Phys. 2, 258–261 (2006).
[Crossref]

2004 (2)

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

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

2003 (1)

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

2002 (1)

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

2000 (1)

R. Fitzgerald, “Phase-sensitive X-ray imaging,” Phys. Today 53, 23–26 (2000).
[Crossref]

1997 (1)

1996 (2)

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys.,  29, 133–146 (1996).
[Crossref]

1995 (1)

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature,  373, 595–598 (1995).
[Crossref]

Allner, S.

Ando, M.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Barrett, R.

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys.,  29, 133–146 (1996).
[Crossref]

Baruchel, J.

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys.,  29, 133–146 (1996).
[Crossref]

Berqué, D.

Bonnin, A.

M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
[Crossref]

Bösecke, P.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Bunk, O.

M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
[Crossref]

P. Thibault, M. Deirolf, A. Menzel, O. Bunk, and 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, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Phys. 2, 258–261 (2006).
[Crossref]

Burvall, A.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Herz, “Speckle-base X-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref]

Cerbino, R.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Chabior, M.

Chu, Y. S.

Clare, R.

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref] [PubMed]

M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
[Crossref]

Cloetens, P.

M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref] [PubMed]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref] [PubMed]

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys.,  29, 133–146 (1996).
[Crossref]

Cookson, D. J.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Cozzini, C.

David, C.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Phys. 2, 258–261 (2006).
[Crossref]

Davis, T. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature,  373, 595–598 (1995).
[Crossref]

Deirolf, M.

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

Dierolf, M.

M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref] [PubMed]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref] [PubMed]

M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
[Crossref]

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Dolbnya, I. P.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Enders, B.

M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref] [PubMed]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref] [PubMed]

Faulkner, H. M. L.

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

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

Fieunp, J. R.

Fitzgerald, R.

R. Fitzgerald, “Phase-sensitive X-ray imaging,” Phys. Today 53, 23–26 (2000).
[Crossref]

Gao, D.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature,  373, 595–598 (1995).
[Crossref]

Garrett, R. F.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Giglio, M.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Guigay, J.-P.

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys.,  29, 133–146 (1996).
[Crossref]

Guizar-Sicairos, M.

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New. J. Phys. 14, 1256–1262 (2012).
[Crossref]

Gureyev, T. E.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature,  373, 595–598 (1995).
[Crossref]

Hamed, A.

A. Hamed, “Recognition of direction of new apertures from the eloganted speckle images: simulation,” J. Opt. Photon. 3, 250–258 (2013).
[Crossref]

Harder, R.

Herz, H. M.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Herz, “Speckle-base X-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref]

Huang, H.

Hubert, M.

Hwu, Y.

Hyodo, K.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Jefimovs, K.

M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
[Crossref]

Johnson, I.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Kewish, C.

M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
[Crossref]

Kynde, S.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Lai, B.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Larsson, D. H

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Herz, “Speckle-base X-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref]

Laurencin, J.

Lundström, U.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Herz, “Speckle-base X-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref]

Maiden, A. M.

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

Malecki, A.

J. Wolf, A. Malecki, J. Sperl, M. Chabior, M. Schüttler, D. Berqué, C. Cozzini, and P. Pfeiffer, “Fast one-dimensional wave-front propagation for x-ray differential phase-contrast imaging,” Biomed. Opt. Express 5, 3739–3747 (2014).
[PubMed]

A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” Europhys. Lett. 99, 48001 (2012).
[Crossref]

Marti, O.

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

Mayo, S. C.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

Menzel, A.

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

M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
[Crossref]

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

Miller, P. R.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

Paganin, D.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

Paganin, D. M.

D. M. Paganin, Coherent X-ray Optics (Oxford series on synchrotron radiation), (Oxford University, 2006).
[Crossref]

Parry, D. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

Peverini, L.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Pfeiffer, F.

M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref] [PubMed]

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Herz, “Speckle-base X-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” Europhys. Lett. 99, 48001 (2012).
[Crossref]

M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
[Crossref]

P. Thibault, M. Deirolf, A. Menzel, O. Bunk, and 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, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Phys. 2, 258–261 (2006).
[Crossref]

Pfeiffer, P.

Pogany, A.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

Potdevin, G.

A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” Europhys. Lett. 99, 48001 (2012).
[Crossref]

Potenza, M. A. C.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Rau, C.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Robert, A.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Robinson, I. K.

Rodenburg, J. M.

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

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

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

Schlenker, M.

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys.,  29, 133–146 (1996).
[Crossref]

Schlichting, I.

M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
[Crossref]

Schüttler, M.

Snigirev, A.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Snigireva, I.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Sperl, J.

Stevenson, A. W.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature,  373, 595–598 (1995).
[Crossref]

Stockmar, M.

M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref] [PubMed]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref] [PubMed]

Thibault, P.

M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref] [PubMed]

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Herz, “Speckle-base X-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref]

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

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref] [PubMed]

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New. J. Phys. 14, 1256–1262 (2012).
[Crossref]

M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
[Crossref]

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

Villanova, J.

von König, K.

M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
[Crossref]

Weitkamp, T.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Phys. 2, 258–261 (2006).
[Crossref]

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Wilkins, S. W.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature,  373, 595–598 (1995).
[Crossref]

Wolf, J.

Yan, H.

Youn, H. S.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Yun, W.

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Zanette, I.

M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23, 12720–12731 (2015).
[Crossref] [PubMed]

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Herz, “Speckle-base X-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref] [PubMed]

Zdora, M.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Herz, “Speckle-base X-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref]

Zdora, M.-C

M.-C Zdora, “X-ray multimodal imaging using near-field speckles,” Master’s Thesis, Technische Universität München (2014).

Zhou, T.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Herz, “Speckle-base X-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref]

App. Phys. Lett. (1)

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

Appl. Opt. (1)

Biomed. Opt. Express (1)

Europhys. Lett. (1)

A. Malecki, G. Potdevin, and F. Pfeiffer, “Quantitative wave-optical numerical analysis of the dark-field signal in grating-based X-ray interferometry,” Europhys. Lett. 99, 48001 (2012).
[Crossref]

J. Microsc. (1)

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2002).
[Crossref] [PubMed]

J. Opt. Photon. (1)

A. Hamed, “Recognition of direction of new apertures from the eloganted speckle images: simulation,” J. Opt. Photon. 3, 250–258 (2013).
[Crossref]

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

P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys.,  29, 133–146 (1996).
[Crossref]

Nat. Phys. (1)

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Nature (3)

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

T. J. Davis, D. Gao, T. E. Gureyev, A. W. Stevenson, and S. W. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature,  373, 595–598 (1995).
[Crossref]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard x-rays,” Nature 384, 335–338 (1996).
[Crossref]

Nature Phys. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Phys. 2, 258–261 (2006).
[Crossref]

New J. Phys. (1)

M. Dierolf, P. Thibault, A. Menzel, C. Kewish, K. Jefimovs, I. Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 35017 (2010).
[Crossref]

New. J. Phys. (1)

P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New. J. Phys. 14, 1256–1262 (2012).
[Crossref]

Nucl. Instrum. Meth. B (1)

A. W. Stevenson, T. E. Gureyev, D. Paganin, S. W. Wilkins, T. Weitkamp, A. Snigirev, C. Rau, I. Snigireva, H. S. Youn, I. P. Dolbnya, W. Yun, B. Lai, R. F. Garrett, D. J. Cookson, K. Hyodo, and M. Ando, “Phase-contrast X-ray imaging with synchrotron radiation for materials science applications,” Nucl. Instrum. Meth. B 199, 427–435 (2003).
[Crossref]

Opt. Express (2)

Phys. Rev. Appl. (1)

M. Stockmar, I. Zanette, M. Dierolf, B. Enders, R. Clare, F. Pfeiffer, P. Cloetens, A. Bonnin, and P. Thibault, “X-ray near-field ptychography for optically thick specimens,” Phys. Rev. Appl. 3, 014005 (2015).
[Crossref]

Phys. Rev. Lett. (2)

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

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Herz, “Speckle-base X-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 253903 (2014).
[Crossref]

Phys. Today (1)

R. Fitzgerald, “Phase-sensitive X-ray imaging,” Phys. Today 53, 23–26 (2000).
[Crossref]

Sci. Rep. (1)

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Sci. Rep. 3, 1927 (2013).
[Crossref] [PubMed]

Ultramicroscopy (3)

O. Bunk, M. Dierolf, S. Kynde, I. Johnson, O. Marti, and F. Pfeiffer, “Influence of the overlap parameter on the convergence of the ptychographical engine,” Ultramicroscopy 108, 481–487 (2008).
[Crossref]

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

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

Other (4)

M.-C Zdora, “X-ray multimodal imaging using near-field speckles,” Master’s Thesis, Technische Universität München (2014).

Federation of European Producers of Abrasives, “FEPA P-grit sizes coated abrasives,” http://www.fepa-abrasives.org/Abrasiveproducts/Grains/Pgritsizescoated.aspx

D. M. Paganin, Coherent X-ray Optics (Oxford series on synchrotron radiation), (Oxford University, 2006).
[Crossref]

M. Born and E. Wolf, eds., Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge University, 1999).
[Crossref]

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 (14)

Fig. 1
Fig. 1 The parallel beam near-field ptychography set-up considered in this paper.
Fig. 2
Fig. 2 Flat field diffraction images for the default case (the FOV is the full 154 μm × 154 μm) for grain radii of (a) 0.45 μm, (b) 3.5 μm (P3000), and (c) 10.9 μm (P800). The colorbar, which is for all three images, is in photons.
Fig. 3
Fig. 3 Diffraction images for the P3000 diffuser with the default parameters with sample as (a) the uranium sphere, and (b) the gold Siemens star. The FOV is 154 μm × 154 μm. The colorbar, which is for both images, is in photons.
Fig. 4
Fig. 4 The visibility of the flat field images measured at the detector plane versus (a) the propagation distance z and diffuser-sample distance zd−s, and (b) the grain radius of the sandpaper.
Fig. 5
Fig. 5 The sampling patterns of the diffraction images: (a) experimental (default), (b) raster, (c) round, (d) spiral, and (e) random.
Fig. 6
Fig. 6 Histogram of the distance between every pair of the 16 positions for the (a) experimental, (b) raster, (c) round, (d) spiral, and (e) random sampling patterns.
Fig. 7
Fig. 7 For the uranium sphere with the default parameters, the reconstructed (a) magnitude Â(x, y), and (b) phase ϕ̂(x, y) (in radians) of the sample transmission function, and (c) magnitude and (d) phase (radians) of the probe function. The error in the sample transmission function reconstruction for (e) the magnitude |A(x, y) − Â(x, y)|, and (f) the phase |ϕ(x, y) −ϕ̂(x, y)| (radians).
Fig. 8
Fig. 8 For the Siemens star with the default parameters, the reconstructed (a) magnitude Â(x, y), and (b) phase ϕ̂(x, y) (in radians) of the transmission function.
Fig. 9
Fig. 9 The rmse in phase, amplitude and quadrature sum versus the number of iterations of the DM algorithm for the Siemens star and with the default parameters. The first 1000 iterations are with one probe mode, and the subsequent 300 iterations are with three probe modes.
Fig. 10
Fig. 10 Reconstructed (a) magnitude Â(x, y), and (b) phase ϕ̂(x, y) (in radians) of the Siemens star with the default parameters but without the diffuser.
Fig. 11
Fig. 11 The rmse in phase, amplitude and quadrature sum versus the maximum step size (linear extent of the sampling pattern) of the random scan pattern for the Siemens star and with the default parameters.
Fig. 12
Fig. 12 The rmse in phase, amplitude and quadrature sum versus the number of diffraction images for the Siemens star with the default parameters. The numer of images is increased by alternating between each of the four quadrants in the experimental scan pattern.
Fig. 13
Fig. 13 The rmse E versus the total flux for the Siemens star with the default parameters. The different curves represent the relative flux per image compared to the default case. The first (leftmost) point in each curve is for two diffraction images and each subsequent point is an extra image.
Fig. 14
Fig. 14 For the Siemens star with the default parameters, (a) the rmse E versus the grain radius of the sandpaper diffuser. (b) The rmse E versus the propagation distance z with the P3000 diffuser (blue), P800 diffuser (green) and P240 diffuser (red). (c) The rmse in phase, amplitude and quadrature sum versus the diffuser-sample distance zd−s.

Tables (3)

Tables Icon

Table 1 Default (from experiment [11]) near-field ptychography parameters.

Tables Icon

Table 2 Designated grit sizes of sandpaper and their corresponding mean radii [20].

Tables Icon

Table 3 rmse in magnitude EA, phase Eϕ and quadrature sum E for the different scan patterns for the Siemens star and with the default parameters.

Equations (13)

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

ψ m ( x , y ) = p ( x , y ) T ( x x m , y y m ) ,
T ( x , y ) = A ( x , y ) exp [ j ϕ ( x , y ) ] ,
I m ( x , y ) = | D z { ψ m ( x , y ) } | 2 ,
D z { ψ ( x , y ) } = 1 { { ψ ( x , y ) } × exp [ j z ( u 2 + v 2 ) 2 k ] } ,
C ( x , y ) = 1 [ { T ( x , y ) } { T ^ ( x , y ) } * ] ,
α = C ( x 0 , y 0 ) | T ^ ( x , y ) | 2 ,
E A = | A ( x , y ) A ^ ( x , y ) | 2 | A ( x , y ) | 2 , E ϕ = | ϕ ( x , y ) ϕ ^ ( x , y ) | 2 | ϕ ( x , y ) | 2 .
E = E A 2 + E ϕ 2 .
M = z 1 + z 2 z 2 ,
z = z 2 M .
Δ x = Δ s M ,
v = σ I ¯ ( x , y ) ,
I m ( x , y ) = n | D z { p n ( x , y ) T ( x x m , y y m ) } | 2 .

Metrics