Abstract

Ptychography is a lensless phase imaging technique that obtains an image by scanning a specimen at several points with respect to a localized illumination beam. For larger specimens, it takes a longer time to complete scanning and hence higher stability is required in the setup which is often not guaranteed. An alternative technique is proposed here that reduces the sequential scanning time for such applications. A pinhole array is used to generate multiple tiny spatially separated beams to scan an object simultaneously at various points. The resulting diffraction patterns are recorded and processed in the Fresnel regime to obtain the images. Unlike other ptychographic methods using multiple beams, the proposed method does not require the use of a multimode ptychography algorithm or autocorrelation filtering of the diffraction patterns. The effectiveness of the method is studied through simulations and experiments. In contrast to conventional single-beam ptychography, the proposed method has the ability to achieve a larger field of view while leaving the number of scanned positions unchanged.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5(6), 843 (1952).
    [Crossref]
  2. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
    [Crossref]
  3. W. Hua, G. Zhou, Y. Wang, P. Zhou, S. Yang, C. Peng, F. Bian, X. Li, and J. Wang, “Measurement of the spatial coherence of hard synchrotron radiation using a pencil beam,” Chin. Opt. Lett. 15(3), 033401 (2017).
    [Crossref]
  4. J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities,” Science 300(5624), 1419–1421 (2003).
    [Crossref] [PubMed]
  5. J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O’Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89(15), 155502 (2002).
    [Crossref] [PubMed]
  6. K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
    [Crossref] [PubMed]
  7. R. Dronyak, K. S. Liang, Y. P. Stetsko, T. K. Lee, C. Feng, J. Tsai, and F. Chen, “Electron diffractive imaging of nano-objects using a guided method with a dynamic support,” Appl. Phys. Lett. 95(11), 111908 (2009).
    [Crossref]
  8. O. Kamimura, K. Kawahara, T. Doi, T. Dobashi, T. Abe, and K. Gohara, “Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes,” Appl. Phys. Lett. 92(2), 024106 (2008).
    [Crossref]
  9. J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
    [Crossref]
  10. H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
    [Crossref] [PubMed]
  11. J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
    [Crossref] [PubMed]
  12. A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
    [Crossref] [PubMed]
  13. X. Pan, S. P. Veetil, C. Liu, and J. Zhu, “High contrast imaging for weakly diffracting specimens with ptychographical iterative engine,” Opt. Lett. 37(16), 3348–3350 (2012).
    [Crossref] [PubMed]
  14. X. He, C. Liu, and J. Zhu, “On-line beam diagnostics based on single-shot beam splitting phase retrieval,” Chin. Opt. Lett. 16(9), 091001 (2018).
    [Crossref]
  15. A. Sun, X. He, Y. Kong, H. Cui, X. Song, L. Xue, S. Wang, and C. Liu, “Ultra-high speed digital micro-mirror device based ptychographic iterative engine method,” Biomed. Opt. Express 8(7), 3155–3162 (2017).
    [Crossref] [PubMed]
  16. M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730–737 (2012).
    [Crossref] [PubMed]
  17. J. Zhang, T. Xu, X. Wang, S. Chen, and G. Ni, “Fast gradational reconstruction for Fourier ptychographic microscopy,” Chin. Opt. Lett. 15(11), 111702 (2017).
    [Crossref]
  18. W. Yu, S. Wang, S. P. Veetil, S. Gao, C. Liu, and J. Zhu, “High-quality image reconstruction method for ptychography with partially coherent illumination,” Phys. Rev. B 93(24), 241105 (2016).
    [Crossref]
  19. P. Hessing, B. Pfau, E. Guehrs, M. Schneider, L. Shemilt, J. Geilhufe, and S. Eisebitt, “Holography-guided ptychography with soft X-rays,” Opt. Express 24(2), 1840–1851 (2016).
    [Crossref] [PubMed]
  20. T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, and A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22(10), 12513–12523 (2014).
    [Crossref] [PubMed]
  21. M. D. Seaberg, B. Zhang, D. F. Gardner, E. R. Shanblatt, M. M. Murnane, H. C. Kapteyn, and D. E. Adams, “Tabletop nanometer extreme ultraviolet imaging in an extended reflection mode using coherent Fresnel ptychography,” Optica 1(1), 39–44 (2014).
    [Crossref]
  22. L. Valzania, T. Feurer, P. Zolliker, and E. Hack, “Terahertz ptychography,” Opt. Lett. 43(3), 543–546 (2018).
    [Crossref] [PubMed]
  23. L. Valzania, E. Hack, P. Zolliker, R. Brönnimann, and T. Feurer, “Resolution limits of terahertz ptychography,” Proc. SPIE 10677, 1067720 (2018).
  24. M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16(10), 7264–7278 (2008).
    [Crossref] [PubMed]
  25. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
    [Crossref] [PubMed]
  26. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
    [Crossref] [PubMed]
  27. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109(4), 338–343 (2009).
    [Crossref] [PubMed]
  28. A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120(5), 64–72 (2012).
    [Crossref] [PubMed]
  29. F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21(11), 13592–13606 (2013).
    [Crossref] [PubMed]
  30. A. Tripathi, I. McNulty, and O. G. Shpyrko, “Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods,” Opt. Express 22(2), 1452–1466 (2014).
    [Crossref] [PubMed]
  31. P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494(7435), 68–71 (2013).
    [Crossref] [PubMed]
  32. D. J. Batey, D. Claus, and J. M. Rodenburg, “Information multiplexing in ptychography,” Ultramicroscopy 138, 13–21 (2014).
    [Crossref] [PubMed]
  33. T. B. Edo, D. J. Batey, A. Maiden, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
    [Crossref]
  34. D. J. Batey, T. B. Edo, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
    [Crossref]
  35. X. Pan, C. Liu, and J. Zhu, “Single shot ptychographical iterative engine based on multi-beam illumination,” Appl. Phys. Lett. 103(17), 171105 (2013).
    [Crossref]
  36. P. Sidorenko and O. Cohen, “Single-shot ptychography,” Optica 3(1), 9–14 (2016).
    [Crossref]
  37. R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
    [Crossref] [PubMed]
  38. C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
    [Crossref] [PubMed]
  39. D. R. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse Probl. 21(1), 37–50 (2005).
    [Crossref]
  40. P. Thibault and M. Guizar-Sicairos, “Maximum-likelihood refinement for coherent diffractive imaging,” New J. Phys. 14(6), 063004 (2012).
    [Crossref]
  41. Y. S. G. Nashed, D. J. Vine, T. Peterka, J. Deng, R. Ross, and C. Jacobsen, “Parallel ptychographic reconstruction,” Opt. Express 22(26), 32082–32097 (2014).
    [Crossref] [PubMed]
  42. J. C. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy 101(2-4), 149–152 (2004).
    [Crossref] [PubMed]
  43. S. Dong, Z. Bian, R. Shiradkar, and G. Zheng, “Sparsely sampled Fourier ptychography,” Opt. Express 22(5), 5455–5464 (2014).
    [Crossref] [PubMed]

2018 (4)

L. Valzania, E. Hack, P. Zolliker, R. Brönnimann, and T. Feurer, “Resolution limits of terahertz ptychography,” Proc. SPIE 10677, 1067720 (2018).

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

L. Valzania, T. Feurer, P. Zolliker, and E. Hack, “Terahertz ptychography,” Opt. Lett. 43(3), 543–546 (2018).
[Crossref] [PubMed]

X. He, C. Liu, and J. Zhu, “On-line beam diagnostics based on single-shot beam splitting phase retrieval,” Chin. Opt. Lett. 16(9), 091001 (2018).
[Crossref]

2017 (3)

2016 (3)

2015 (1)

2014 (7)

2013 (4)

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21(11), 13592–13606 (2013).
[Crossref] [PubMed]

X. Pan, C. Liu, and J. Zhu, “Single shot ptychographical iterative engine based on multi-beam illumination,” Appl. Phys. Lett. 103(17), 171105 (2013).
[Crossref]

T. B. Edo, D. J. Batey, A. Maiden, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

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

2012 (4)

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120(5), 64–72 (2012).
[Crossref] [PubMed]

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730–737 (2012).
[Crossref] [PubMed]

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

X. Pan, S. P. Veetil, C. Liu, and J. Zhu, “High contrast imaging for weakly diffracting specimens with ptychographical iterative engine,” Opt. Lett. 37(16), 3348–3350 (2012).
[Crossref] [PubMed]

2010 (2)

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

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
[Crossref] [PubMed]

2009 (3)

R. Dronyak, K. S. Liang, Y. P. Stetsko, T. K. Lee, C. Feng, J. Tsai, and F. Chen, “Electron diffractive imaging of nano-objects using a guided method with a dynamic support,” Appl. Phys. Lett. 95(11), 111908 (2009).
[Crossref]

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

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

2008 (3)

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

O. Kamimura, K. Kawahara, T. Doi, T. Dobashi, T. Abe, and K. Gohara, “Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes,” Appl. Phys. Lett. 92(2), 024106 (2008).
[Crossref]

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

2007 (1)

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

2005 (1)

D. R. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse Probl. 21(1), 37–50 (2005).
[Crossref]

2004 (3)

J. C. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy 101(2-4), 149–152 (2004).
[Crossref] [PubMed]

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

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

2003 (1)

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref] [PubMed]

2002 (1)

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O’Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89(15), 155502 (2002).
[Crossref] [PubMed]

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

1952 (1)

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5(6), 843 (1952).
[Crossref]

Abe, T.

O. Kamimura, K. Kawahara, T. Doi, T. Dobashi, T. Abe, and K. Gohara, “Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes,” Appl. Phys. Lett. 92(2), 024106 (2008).
[Crossref]

Adams, D.

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
[Crossref] [PubMed]

Adams, D. E.

Batey, D. J.

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

D. J. Batey, T. B. Edo, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. Maiden, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Bean, R.

Berenguer, F.

Bevis, C.

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
[Crossref] [PubMed]

Bian, F.

Bian, Z.

Brönnimann, R.

L. Valzania, E. Hack, P. Zolliker, R. Brönnimann, and T. Feurer, “Resolution limits of terahertz ptychography,” Proc. SPIE 10677, 1067720 (2018).

Bunk, O.

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

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

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

Chen, B.

Chen, F.

R. Dronyak, K. S. Liang, Y. P. Stetsko, T. K. Lee, C. Feng, J. Tsai, and F. Chen, “Electron diffractive imaging of nano-objects using a guided method with a dynamic support,” Appl. Phys. Lett. 95(11), 111908 (2009).
[Crossref]

Chen, S.

Claus, D.

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

Cohen, O.

Cui, H.

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

David, C.

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

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Deng, J.

Diaz, A.

Dierolf, M.

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

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

Dobashi, T.

O. Kamimura, K. Kawahara, T. Doi, T. Dobashi, T. Abe, and K. Gohara, “Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes,” Appl. Phys. Lett. 92(2), 024106 (2008).
[Crossref]

Dobson, B. R.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Doi, T.

O. Kamimura, K. Kawahara, T. Doi, T. Dobashi, T. Abe, and K. Gohara, “Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes,” Appl. Phys. Lett. 92(2), 024106 (2008).
[Crossref]

Dong, S.

Dronyak, R.

R. Dronyak, K. S. Liang, Y. P. Stetsko, T. K. Lee, C. Feng, J. Tsai, and F. Chen, “Electron diffractive imaging of nano-objects using a guided method with a dynamic support,” Appl. Phys. Lett. 95(11), 111908 (2009).
[Crossref]

Du, J.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
[Crossref] [PubMed]

Edo, T. B.

D. J. Batey, T. B. Edo, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. Maiden, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Eisebitt, S.

Fahimian, B. P.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
[Crossref] [PubMed]

Faulkner, H. M.

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

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

Feng, C.

R. Dronyak, K. S. Liang, Y. P. Stetsko, T. K. Lee, C. Feng, J. Tsai, and F. Chen, “Electron diffractive imaging of nano-objects using a guided method with a dynamic support,” Appl. Phys. Lett. 95(11), 111908 (2009).
[Crossref]

Feurer, T.

L. Valzania, E. Hack, P. Zolliker, R. Brönnimann, and T. Feurer, “Resolution limits of terahertz ptychography,” Proc. SPIE 10677, 1067720 (2018).

L. Valzania, T. Feurer, P. Zolliker, and E. Hack, “Terahertz ptychography,” Opt. Lett. 43(3), 543–546 (2018).
[Crossref] [PubMed]

Fienup, J. R.

Gao, M.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref] [PubMed]

Gao, S.

W. Yu, S. Wang, S. P. Veetil, S. Gao, C. Liu, and J. Zhu, “High-quality image reconstruction method for ptychography with partially coherent illumination,” Phys. Rev. B 93(24), 241105 (2016).
[Crossref]

Gardner, D.

Gardner, D. F.

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

M. D. Seaberg, B. Zhang, D. F. Gardner, E. R. Shanblatt, M. M. Murnane, H. C. Kapteyn, and D. E. Adams, “Tabletop nanometer extreme ultraviolet imaging in an extended reflection mode using coherent Fresnel ptychography,” Optica 1(1), 39–44 (2014).
[Crossref]

Geilhufe, J.

Godden, T. M.

Gohara, K.

O. Kamimura, K. Kawahara, T. Doi, T. Dobashi, T. Abe, and K. Gohara, “Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes,” Appl. Phys. Lett. 92(2), 024106 (2008).
[Crossref]

Guehrs, E.

Guizar-Sicairos, M.

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

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

Hack, E.

L. Valzania, E. Hack, P. Zolliker, R. Brönnimann, and T. Feurer, “Resolution limits of terahertz ptychography,” Proc. SPIE 10677, 1067720 (2018).

L. Valzania, T. Feurer, P. Zolliker, and E. Hack, “Terahertz ptychography,” Opt. Lett. 43(3), 543–546 (2018).
[Crossref] [PubMed]

He, X.

Hessing, P.

Hodgson, K. O.

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O’Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89(15), 155502 (2002).
[Crossref] [PubMed]

Howells, M.

J. C. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy 101(2-4), 149–152 (2004).
[Crossref] [PubMed]

Hua, W.

Humphry, M. J.

T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, and A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22(10), 12513–12523 (2014).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120(5), 64–72 (2012).
[Crossref] [PubMed]

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730–737 (2012).
[Crossref] [PubMed]

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

Hurst, A. C.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730–737 (2012).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Jacobsen, C.

Jefimovs, K.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Jiang, H.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
[Crossref] [PubMed]

Johnson, I.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Kamimura, O.

O. Kamimura, K. Kawahara, T. Doi, T. Dobashi, T. Abe, and K. Gohara, “Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes,” Appl. Phys. Lett. 92(2), 024106 (2008).
[Crossref]

Kapteyn, H.

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
[Crossref] [PubMed]

Kapteyn, H. C.

M. D. Seaberg, B. Zhang, D. F. Gardner, E. R. Shanblatt, M. M. Murnane, H. C. Kapteyn, and D. E. Adams, “Tabletop nanometer extreme ultraviolet imaging in an extended reflection mode using coherent Fresnel ptychography,” Optica 1(1), 39–44 (2014).
[Crossref]

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
[Crossref] [PubMed]

Karl, R.

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
[Crossref] [PubMed]

Kawahara, K.

O. Kamimura, K. Kawahara, T. Doi, T. Dobashi, T. Abe, and K. Gohara, “Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes,” Appl. Phys. Lett. 92(2), 024106 (2008).
[Crossref]

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

Kong, Y.

Kraus, B.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730–737 (2012).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120(5), 64–72 (2012).
[Crossref] [PubMed]

Lee, T. K.

R. Dronyak, K. S. Liang, Y. P. Stetsko, T. K. Lee, C. Feng, J. Tsai, and F. Chen, “Electron diffractive imaging of nano-objects using a guided method with a dynamic support,” Appl. Phys. Lett. 95(11), 111908 (2009).
[Crossref]

Li, X.

Liang, K. S.

R. Dronyak, K. S. Liang, Y. P. Stetsko, T. K. Lee, C. Feng, J. Tsai, and F. Chen, “Electron diffractive imaging of nano-objects using a guided method with a dynamic support,” Appl. Phys. Lett. 95(11), 111908 (2009).
[Crossref]

Liu, C.

Lopez-Rios, R.

Luke, D. R.

D. R. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse Probl. 21(1), 37–50 (2005).
[Crossref]

Maiden, A.

T. B. Edo, D. J. Batey, A. Maiden, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Maiden, A. M.

T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, and A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22(10), 12513–12523 (2014).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120(5), 64–72 (2012).
[Crossref] [PubMed]

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730–737 (2012).
[Crossref] [PubMed]

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

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

Mancini, G. F.

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
[Crossref] [PubMed]

McNulty, I.

Menzel, A.

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21(11), 13592–13606 (2013).
[Crossref] [PubMed]

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

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

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

Miao, J.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
[Crossref] [PubMed]

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O’Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89(15), 155502 (2002).
[Crossref] [PubMed]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

Murnane, M.

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
[Crossref] [PubMed]

Murnane, M. M.

Nagahara, L. A.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref] [PubMed]

Nashed, Y. S. G.

Ni, G.

O’Keefe, M. A.

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O’Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89(15), 155502 (2002).
[Crossref] [PubMed]

Ohsuna, T.

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O’Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89(15), 155502 (2002).
[Crossref] [PubMed]

Pan, X.

X. Pan, C. Liu, and J. Zhu, “Single shot ptychographical iterative engine based on multi-beam illumination,” Appl. Phys. Lett. 103(17), 171105 (2013).
[Crossref]

X. Pan, S. P. Veetil, C. Liu, and J. Zhu, “High contrast imaging for weakly diffracting specimens with ptychographical iterative engine,” Opt. Lett. 37(16), 3348–3350 (2012).
[Crossref] [PubMed]

Peng, C.

Pesic, Z.

D. J. Batey, T. B. Edo, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. Maiden, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Peterka, T.

Peterson, I.

Pfau, B.

Pfeiffer, F.

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

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

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Porter, C.

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
[Crossref] [PubMed]

Raines, K. S.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
[Crossref] [PubMed]

Rau, C. D.

D. J. Batey, T. B. Edo, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. Maiden, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Reichanadter, J.

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
[Crossref] [PubMed]

Robinson, I. K.

Rodenburg, J. M.

D. J. Batey, T. B. Edo, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

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

T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, and A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22(10), 12513–12523 (2014).
[Crossref] [PubMed]

T. B. Edo, D. J. Batey, A. Maiden, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21(11), 13592–13606 (2013).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120(5), 64–72 (2012).
[Crossref] [PubMed]

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730–737 (2012).
[Crossref] [PubMed]

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

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

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

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

Rodríguez, J. A.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
[Crossref] [PubMed]

Ross, R.

Salha, S.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
[Crossref] [PubMed]

Sandberg, R. L.

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
[Crossref] [PubMed]

Sarahan, M. C.

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120(5), 64–72 (2012).
[Crossref] [PubMed]

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5(6), 843 (1952).
[Crossref]

Schneider, M.

Seaberg, M. D.

Shanblatt, E.

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
[Crossref] [PubMed]

Shanblatt, E. R.

Shemilt, L.

Shiradkar, R.

Shpyrko, O. G.

Sidorenko, P.

Song, X.

Spence, J. C.

J. C. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy 101(2-4), 149–152 (2004).
[Crossref] [PubMed]

Stetsko, Y. P.

R. Dronyak, K. S. Liang, Y. P. Stetsko, T. K. Lee, C. Feng, J. Tsai, and F. Chen, “Electron diffractive imaging of nano-objects using a guided method with a dynamic support,” Appl. Phys. Lett. 95(11), 111908 (2009).
[Crossref]

Suman, R.

Sun, A.

Tanksalvala, M.

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
[Crossref] [PubMed]

Terasaki, O.

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O’Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89(15), 155502 (2002).
[Crossref] [PubMed]

Thibault, P.

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

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

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

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

Tripathi, A.

Tsai, J.

R. Dronyak, K. S. Liang, Y. P. Stetsko, T. K. Lee, C. Feng, J. Tsai, and F. Chen, “Electron diffractive imaging of nano-objects using a guided method with a dynamic support,” Appl. Phys. Lett. 95(11), 111908 (2009).
[Crossref]

Valzania, L.

L. Valzania, E. Hack, P. Zolliker, R. Brönnimann, and T. Feurer, “Resolution limits of terahertz ptychography,” Proc. SPIE 10677, 1067720 (2018).

L. Valzania, T. Feurer, P. Zolliker, and E. Hack, “Terahertz ptychography,” Opt. Lett. 43(3), 543–546 (2018).
[Crossref] [PubMed]

Vartanyants, I.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref] [PubMed]

Veetil, S. P.

W. Yu, S. Wang, S. P. Veetil, S. Gao, C. Liu, and J. Zhu, “High-quality image reconstruction method for ptychography with partially coherent illumination,” Phys. Rev. B 93(24), 241105 (2016).
[Crossref]

X. Pan, S. P. Veetil, C. Liu, and J. Zhu, “High contrast imaging for weakly diffracting specimens with ptychographical iterative engine,” Opt. Lett. 37(16), 3348–3350 (2012).
[Crossref] [PubMed]

Vila-Comamala, J.

Vine, D. J.

Wagner, U.

D. J. Batey, T. B. Edo, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. Maiden, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Waigh, T. A.

D. J. Batey, T. B. Edo, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

T. B. Edo, D. J. Batey, A. Maiden, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

Wang, J.

Wang, S.

A. Sun, X. He, Y. Kong, H. Cui, X. Song, L. Xue, S. Wang, and C. Liu, “Ultra-high speed digital micro-mirror device based ptychographic iterative engine method,” Biomed. Opt. Express 8(7), 3155–3162 (2017).
[Crossref] [PubMed]

W. Yu, S. Wang, S. P. Veetil, S. Gao, C. Liu, and J. Zhu, “High-quality image reconstruction method for ptychography with partially coherent illumination,” Phys. Rev. B 93(24), 241105 (2016).
[Crossref]

Wang, X.

Wang, Y.

Weierstall, U.

J. C. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy 101(2-4), 149–152 (2004).
[Crossref] [PubMed]

Xu, T.

Xue, L.

Yang, S.

Yu, W.

W. Yu, S. Wang, S. P. Veetil, S. Gao, C. Liu, and J. Zhu, “High-quality image reconstruction method for ptychography with partially coherent illumination,” Phys. Rev. B 93(24), 241105 (2016).
[Crossref]

Zhang, B.

Zhang, F.

Zhang, J.

Zhang, R.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref] [PubMed]

Zheng, G.

Zhou, G.

Zhou, P.

Zhu, J.

X. He, C. Liu, and J. Zhu, “On-line beam diagnostics based on single-shot beam splitting phase retrieval,” Chin. Opt. Lett. 16(9), 091001 (2018).
[Crossref]

W. Yu, S. Wang, S. P. Veetil, S. Gao, C. Liu, and J. Zhu, “High-quality image reconstruction method for ptychography with partially coherent illumination,” Phys. Rev. B 93(24), 241105 (2016).
[Crossref]

X. Pan, C. Liu, and J. Zhu, “Single shot ptychographical iterative engine based on multi-beam illumination,” Appl. Phys. Lett. 103(17), 171105 (2013).
[Crossref]

X. Pan, S. P. Veetil, C. Liu, and J. Zhu, “High contrast imaging for weakly diffracting specimens with ptychographical iterative engine,” Opt. Lett. 37(16), 3348–3350 (2012).
[Crossref] [PubMed]

Zolliker, P.

L. Valzania, E. Hack, P. Zolliker, R. Brönnimann, and T. Feurer, “Resolution limits of terahertz ptychography,” Proc. SPIE 10677, 1067720 (2018).

L. Valzania, T. Feurer, P. Zolliker, and E. Hack, “Terahertz ptychography,” Opt. Lett. 43(3), 543–546 (2018).
[Crossref] [PubMed]

Zuo, J. M.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref] [PubMed]

Acta Crystallogr. (1)

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5(6), 843 (1952).
[Crossref]

Appl. Phys. Lett. (4)

R. Dronyak, K. S. Liang, Y. P. Stetsko, T. K. Lee, C. Feng, J. Tsai, and F. Chen, “Electron diffractive imaging of nano-objects using a guided method with a dynamic support,” Appl. Phys. Lett. 95(11), 111908 (2009).
[Crossref]

O. Kamimura, K. Kawahara, T. Doi, T. Dobashi, T. Abe, and K. Gohara, “Diffraction microscopy using 20 kV electron beam for multiwall carbon nanotubes,” Appl. Phys. Lett. 92(2), 024106 (2008).
[Crossref]

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

X. Pan, C. Liu, and J. Zhu, “Single shot ptychographical iterative engine based on multi-beam illumination,” Appl. Phys. Lett. 103(17), 171105 (2013).
[Crossref]

Biomed. Opt. Express (1)

Chin. Opt. Lett. (3)

Inverse Probl. (1)

D. R. Luke, “Relaxed averaged alternating reflections for diffraction imaging,” Inverse Probl. 21(1), 37–50 (2005).
[Crossref]

Nat. Commun. (1)

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730–737 (2012).
[Crossref] [PubMed]

Nature (3)

K. S. Raines, S. Salha, R. L. Sandberg, H. Jiang, J. A. Rodríguez, B. P. Fahimian, H. C. Kapteyn, J. Du, and J. Miao, “Three-dimensional structure determination from a single view,” Nature 463(7278), 214–217 (2010).
[Crossref] [PubMed]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

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

New J. Phys. (1)

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

Opt. Express (8)

Y. S. G. Nashed, D. J. Vine, T. Peterka, J. Deng, R. Ross, and C. Jacobsen, “Parallel ptychographic reconstruction,” Opt. Express 22(26), 32082–32097 (2014).
[Crossref] [PubMed]

S. Dong, Z. Bian, R. Shiradkar, and G. Zheng, “Sparsely sampled Fourier ptychography,” Opt. Express 22(5), 5455–5464 (2014).
[Crossref] [PubMed]

R. Karl, C. Bevis, R. Lopez-Rios, J. Reichanadter, D. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, M. Murnane, H. Kapteyn, and D. Adams, “Spatial, spectral, and polarization multiplexed ptychography,” Opt. Express 23(23), 30250–30258 (2015).
[Crossref] [PubMed]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21(11), 13592–13606 (2013).
[Crossref] [PubMed]

A. Tripathi, I. McNulty, and O. G. Shpyrko, “Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods,” Opt. Express 22(2), 1452–1466 (2014).
[Crossref] [PubMed]

P. Hessing, B. Pfau, E. Guehrs, M. Schneider, L. Shemilt, J. Geilhufe, and S. Eisebitt, “Holography-guided ptychography with soft X-rays,” Opt. Express 24(2), 1840–1851 (2016).
[Crossref] [PubMed]

T. M. Godden, R. Suman, M. J. Humphry, J. M. Rodenburg, and A. M. Maiden, “Ptychographic microscope for three-dimensional imaging,” Opt. Express 22(10), 12513–12523 (2014).
[Crossref] [PubMed]

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

Opt. Lett. (3)

Optica (2)

Phys. Rev. A (2)

T. B. Edo, D. J. Batey, A. Maiden, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[Crossref]

D. J. Batey, T. B. Edo, C. D. Rau, U. Wagner, Z. Pesic, T. A. Waigh, and J. M. Rodenburg, “Reciprocal-space up-sampling from real-space oversampling in x-ray ptychography,” Phys. Rev. A 89(4), 043812 (2014).
[Crossref]

Phys. Rev. B (1)

W. Yu, S. Wang, S. P. Veetil, S. Gao, C. Liu, and J. Zhu, “High-quality image reconstruction method for ptychography with partially coherent illumination,” Phys. Rev. B 93(24), 241105 (2016).
[Crossref]

Phys. Rev. Lett. (3)

J. Miao, T. Ohsuna, O. Terasaki, K. O. Hodgson, and M. A. O’Keefe, “Atomic resolution three-dimensional electron diffraction microscopy,” Phys. Rev. Lett. 89(15), 155502 (2002).
[Crossref] [PubMed]

H. M. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Proc. SPIE (1)

L. Valzania, E. Hack, P. Zolliker, R. Brönnimann, and T. Feurer, “Resolution limits of terahertz ptychography,” Proc. SPIE 10677, 1067720 (2018).

Science (2)

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

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref] [PubMed]

Ultramicroscopy (6)

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

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

A. M. Maiden, M. J. Humphry, M. C. Sarahan, B. Kraus, and J. M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography,” Ultramicroscopy 120(5), 64–72 (2012).
[Crossref] [PubMed]

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

C. Bevis, R. Karl, J. Reichanadter, D. F. Gardner, C. Porter, E. Shanblatt, M. Tanksalvala, G. F. Mancini, H. Kapteyn, M. Murnane, and D. Adams, “Multiple beam ptychography for large field-of-view, high throughput, quantitative phase contrast imaging,” Ultramicroscopy 184(Pt A), 164–171 (2018).
[Crossref] [PubMed]

J. C. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy 101(2-4), 149–152 (2004).
[Crossref] [PubMed]

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Figures (9)

Fig. 1
Fig. 1 Setup of (a) mb-PIE and (b) conventional single-beam ptychography.
Fig. 2
Fig. 2 (a) Amplitude and (b) phase of complex specimen.
Fig. 3
Fig. 3 (a)–(d) Simulation results of mb-PIE: (a) 5 × 5 pinhole array used as a multiple-beam probe, where each pinhole has a 1 mm diameter, the distance between the centers of two adjacent pinholes is 2 mm, and the width of the pinhole array is 9 mm, which does not satisfy the sampling criteria; (b) one of the recorded diffraction patterns (shown at the log scale), the inset of which shows interference fringes between adjacent diffraction blocks; reconstructed (c) amplitude and (d) phase of the specimen, respectively; and (e)–(h) simulation results using a large probe: (e) the large probe, with a width of 9 mm [as large as the multiple-beam probe in (a)], (f) one of the recorded diffraction patterns, reconstructed (g) amplitude and (h) phase of the specimen, respectively.
Fig. 4
Fig. 4 Reconstructed (a) amplitude and (b) phase using fPIE; reconstructed (c) amplitude and (d) phase using sPIE.
Fig. 5
Fig. 5 Simulation results using mb-PIE and conventional ptychography: the true (a1) amplitude and (a2) phase of the specimen, reconstructed (b1) amplitude and (b2) phase using mb-PIE, and reconstructed (c1) amplitude and (c2) phase using conventional ptychography with a small probe that meets the sampling requirement.
Fig. 6
Fig. 6 Red circles show the convergence of mb-PIE, and blue squares show the convergence of conventional ptychography with a small probe. The error is calculated between the reconstructed and true specimens.
Fig. 7
Fig. 7 mb-PIE method: reconstructed (a1) amplitude and (b) phase, (a2) magnified image of the yellow box in (a1), (c) multiple-beam probe and (d) single view of the diffraction pattern (at the log scale). Conventional single-beam ptychography: reconstructed (e1) amplitude and (f) phase, (e2) magnified image of the yellow box in (e1), (g) probe, and (h) single view of the diffraction pattern (at the log scale).
Fig. 8
Fig. 8 Reconstructed (a) amplitude and (b) phase from the cropped central blocks at each scanning position, (c) magnified image of red box in (a), and (d) magnified image obtained from the mb-PIE method.
Fig. 9
Fig. 9 Single view of the diffraction pattern (at the log scale) for (a) mb-PIE and (e) conventional ptychography. Reconstructed resolution chart using (b) mb-PIE and (f) conventional ptychography. In addition, (c) and (g) are magnified images of the red square region in (b) and (f), and (d) and (h) are the distribution of the red line section in (c) and (g), respectively.

Equations (5)

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

φ jr = O r r j P r .
ψ ju =P( φ jr ).
ψ ju ' = I ju ψ ju /( | ψ ju |+σ ).
O r r j ' = O r r j +α P r * / | P r | max 2 [ P ( ψ ju ' ) φ jr ] P r ' = P r +β O r r j * / | O r r j | max 2 [ P ( ψ ju ' ) φ jr ],
E= [ 1/N x,y | | f( x,y ) || g( x,y ) | | 2 ] 1/2 .

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