Abstract

A multiple slices approach in ptychography, termed 3ePIE algorithm, solves the multiple scattering problems of thick samples, which is crucial to biomedical imaging and in situ studies. However, it is unclear how many slices need to be separated and what the distance is between each layer respectively, while these two parameters are sensitive and crucial to the recovery of thick samples. The traditional method is to separate the sample with the same interval for convenience and to test the number of sections for the best reconstructions, which is reasonable for continuous samples and has achieved great results. But this kind of segmentation approach may not be scientific enough for those discrete samples with an uneven spatial distribution. The two inaccurate parameters may yield the algorithm to diverge or generate artifacts, and the empty slices may decrease the reconstruction quality and increase computation time. In addition, repeatedly testing the number of slices is tedious work even for a continuous sample. To this end, a genetic algorithm-based 3ePIE approach, termed the GA-3ePIE method, is proposed to retrieve both the interval between each layer and the number of slices. The performance is verified by both simulations and experiments. The maximum number of sections that can be resolved is also investigated in numerical analysis, which is associated with the sampling and overlap rate in a spatial domain. Our method can be also promoted to image thick samples with coherent X-rays and in the electron regime. The limitations of our method are also discussed.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (1)

A. Pan, M. Zhou, Y. Zhang, J. Min, M. Lei, and B. Yao, “Adaptive-window angular spectrum algorithm for near-field ptychography,” Opt. Commun. 430, 73–82 (2019).
[Crossref]

2018 (4)

2017 (3)

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(9), 1–11 (2017).
[Crossref] [PubMed]

C. Wang, Z. Xu, H. Liu, Y. Wang, J. Wang, and R. Tai, “Background noise removal in x-ray ptychography,” Appl. Opt. 56(8), 2099–2111 (2017).
[Crossref] [PubMed]

Y. Zhang, A. Pan, M. Lei, and B. Yao, “Data preprocessing methods for robust Fourier ptychographic microscopy,” Opt. Eng. 56(12), 123107 (2017).
[Crossref]

2016 (5)

2015 (7)

P. Li, D. J. Batey, T. B. Edo, and J. M. Rodenburg, “Separation of three-dimensional scattering effects in tilt-series Fourier ptychography,” Ultramicroscopy 158, 1–7 (2015).
[Crossref] [PubMed]

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref] [PubMed]

L. Tian, Z. Liu, L. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2(10), 904–911 (2015).
[Crossref]

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(1), 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23(10), 12720–12731 (2015).
[Crossref] [PubMed]

R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (2015).
[Crossref] [PubMed]

D. Claus and J. M. Rodenburg, “Pixel size adjustment in coherent diffractive imaging within the Rayleigh-Sommerfeld regime,” Appl. Opt. 54(8), 1936–1944 (2015).
[Crossref] [PubMed]

2014 (1)

2013 (5)

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

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (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(1), 1927 (2013).
[Crossref] [PubMed]

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3(1), 2369 (2013).
[Crossref] [PubMed]

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

2012 (6)

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” Opt. Express 20(5), 4840–4849 (2012).
[Crossref] [PubMed]

K. Wang and Z. Shen, “A GPU-based parallel genetic algorithm for generating daily activity plans,” IEEE Trans. Intell. Transp. Syst. 13(3), 1474–1480 (2012).
[Crossref]

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 (2012).
[Crossref] [PubMed]

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

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, 64–72 (2012).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29(8), 1606–1614 (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]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref] [PubMed]

2009 (2)

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

2008 (2)

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]

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]

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]

2004 (2)

H. M. L. 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]

1998 (1)

G. M. Morris, D. S. Goodsell, R. S. Halliday, R. Huey, W. E. Hart, R. K. Belew, and A. J. Olson, “Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function,” J. Comput. Chem. 19(14), 1639–1662 (1998).
[Crossref]

1992 (1)

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. Lond. A 339(1655), 521–553 (1992).

Allner, S.

Bates, R. H. T.

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. Lond. A 339(1655), 521–553 (1992).

Batey, D.

P. Li, T. Edo, D. Batey, J. Rodenburg, and A. Maiden, “Breaking ambiguities in mixed state ptychography,” Opt. Express 24(8), 9038–9052 (2016).
[Crossref] [PubMed]

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

Batey, D. J.

P. Li, D. J. Batey, T. B. Edo, and J. M. Rodenburg, “Separation of three-dimensional scattering effects in tilt-series Fourier ptychography,” Ultramicroscopy 158, 1–7 (2015).
[Crossref] [PubMed]

Belew, R. K.

G. M. Morris, D. S. Goodsell, R. S. Halliday, R. Huey, W. E. Hart, R. K. Belew, and A. J. Olson, “Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function,” J. Comput. Chem. 19(14), 1639–1662 (1998).
[Crossref]

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(1), 014005 (2015).
[Crossref]

Brown, A. N.

Bunk, O.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[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]

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]

Caravaca-Aguirre, A. M.

Chen, M.

Chen, Q.

Chu, Y. S.

Clare, R.

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23(10), 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(1), 014005 (2015).
[Crossref]

Clare, R. M.

Claus, D.

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(1), 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23(10), 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(1), 1927 (2013).
[Crossref] [PubMed]

Conkey, D. B.

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]

Dan, D.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(9), 1–11 (2017).
[Crossref] [PubMed]

Daurer, B. J.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Cryst. 49(4), 1245–1252 (2016).
[Crossref]

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]

Diaz, A.

Dierolf, M.

R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (2015).
[Crossref] [PubMed]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23(10), 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(1), 014005 (2015).
[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(1), 1927 (2013).
[Crossref] [PubMed]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[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]

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]

Dong, X.

Dong, Z.

Edo, T.

P. Li, T. Edo, D. Batey, J. Rodenburg, and A. Maiden, “Breaking ambiguities in mixed state ptychography,” Opt. Express 24(8), 9038–9052 (2016).
[Crossref] [PubMed]

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

Edo, T. B.

P. Li, D. J. Batey, T. B. Edo, and J. M. Rodenburg, “Separation of three-dimensional scattering effects in tilt-series Fourier ptychography,” Ultramicroscopy 158, 1–7 (2015).
[Crossref] [PubMed]

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(1), 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23(10), 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(1), 1927 (2013).
[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]

Faulkner, H. M. L.

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

Fehringer, A.

Fienup, J. R.

Ge, M.

Godden, T. M.

Goodsell, D. S.

G. M. Morris, D. S. Goodsell, R. S. Halliday, R. Huey, W. E. Hart, R. K. Belew, and A. J. Olson, “Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function,” J. Comput. Chem. 19(14), 1639–1662 (1998).
[Crossref]

Guizar-Sicairos, M.

Halliday, R. S.

G. M. Morris, D. S. Goodsell, R. S. Halliday, R. Huey, W. E. Hart, R. K. Belew, and A. J. Olson, “Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function,” J. Comput. Chem. 19(14), 1639–1662 (1998).
[Crossref]

Hart, W. E.

G. M. Morris, D. S. Goodsell, R. S. Halliday, R. Huey, W. E. Hart, R. K. Belew, and A. J. Olson, “Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function,” J. Comput. Chem. 19(14), 1639–1662 (1998).
[Crossref]

He, Y.

Higashino, T.

Hirose, M.

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Huang, X.

Hubert, M.

Huey, R.

G. M. Morris, D. S. Goodsell, R. S. Halliday, R. Huey, W. E. Hart, R. K. Belew, and A. J. Olson, “Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function,” J. Comput. Chem. 19(14), 1639–1662 (1998).
[Crossref]

Humphry, M. J.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[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]

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29(8), 1606–1614 (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 (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, 64–72 (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 (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]

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]

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]

Kewish, C. M.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref] [PubMed]

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 (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, 64–72 (2012).
[Crossref] [PubMed]

Krishnan, H.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Cryst. 49(4), 1245–1252 (2016).
[Crossref]

Laurencin, J.

Lei, M.

A. Pan, M. Zhou, Y. Zhang, J. Min, M. Lei, and B. Yao, “Adaptive-window angular spectrum algorithm for near-field ptychography,” Opt. Commun. 430, 73–82 (2019).
[Crossref]

A. Pan, Y. Zhang, K. Wen, M. Zhou, J. Min, M. Lei, and B. Yao, “Subwavelength resolution Fourier ptychography with hemispherical digital condensers,” Opt. Express 26(18), 23119–23131 (2018).
[Crossref] [PubMed]

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(9), 1–11 (2017).
[Crossref] [PubMed]

Y. Zhang, A. Pan, M. Lei, and B. Yao, “Data preprocessing methods for robust Fourier ptychographic microscopy,” Opt. Eng. 56(12), 123107 (2017).
[Crossref]

Li, P.

P. Li, T. Edo, D. Batey, J. Rodenburg, and A. Maiden, “Breaking ambiguities in mixed state ptychography,” Opt. Express 24(8), 9038–9052 (2016).
[Crossref] [PubMed]

P. Li, D. J. Batey, T. B. Edo, and J. M. Rodenburg, “Separation of three-dimensional scattering effects in tilt-series Fourier ptychography,” Ultramicroscopy 158, 1–7 (2015).
[Crossref] [PubMed]

Lin, M.

Liu, C.

Liu, H.

Liu, Z.

Maia, F. R. N. C.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Cryst. 49(4), 1245–1252 (2016).
[Crossref]

Maiden, A.

P. Li, T. Edo, D. Batey, J. Rodenburg, and A. Maiden, “Breaking ambiguities in mixed state ptychography,” Opt. Express 24(8), 9038–9052 (2016).
[Crossref] [PubMed]

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

Maiden, A. M.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[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. 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 (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, 64–72 (2012).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29(8), 1606–1614 (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]

Marchesini, S.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Cryst. 49(4), 1245–1252 (2016).
[Crossref]

Marriott, P.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3(1), 2369 (2013).
[Crossref] [PubMed]

Marrison, J.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3(1), 2369 (2013).
[Crossref] [PubMed]

Menzel, A.

E. H. R. Tsai, I. Usov, A. Diaz, A. Menzel, and M. Guizar-Sicairos, “X-ray ptychography with extended depth of field,” Opt. Express 24(25), 29089–29108 (2016).
[Crossref] [PubMed]

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

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[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]

Min, J.

A. Pan, M. Zhou, Y. Zhang, J. Min, M. Lei, and B. Yao, “Adaptive-window angular spectrum algorithm for near-field ptychography,” Opt. Commun. 430, 73–82 (2019).
[Crossref]

A. Pan, Y. Zhang, K. Wen, M. Zhou, J. Min, M. Lei, and B. Yao, “Subwavelength resolution Fourier ptychography with hemispherical digital condensers,” Opt. Express 26(18), 23119–23131 (2018).
[Crossref] [PubMed]

Morris, G. M.

G. M. Morris, D. S. Goodsell, R. S. Halliday, R. Huey, W. E. Hart, R. K. Belew, and A. J. Olson, “Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function,” J. Comput. Chem. 19(14), 1639–1662 (1998).
[Crossref]

Nazaretski, E.

O’Toole, P.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3(1), 2369 (2013).
[Crossref] [PubMed]

Olson, A. J.

G. M. Morris, D. S. Goodsell, R. S. Halliday, R. Huey, W. E. Hart, R. K. Belew, and A. J. Olson, “Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function,” J. Comput. Chem. 19(14), 1639–1662 (1998).
[Crossref]

Öztürk, H.

Pan, A.

A. Pan, M. Zhou, Y. Zhang, J. Min, M. Lei, and B. Yao, “Adaptive-window angular spectrum algorithm for near-field ptychography,” Opt. Commun. 430, 73–82 (2019).
[Crossref]

A. Pan, Y. Zhang, K. Wen, M. Zhou, J. Min, M. Lei, and B. Yao, “Subwavelength resolution Fourier ptychography with hemispherical digital condensers,” Opt. Express 26(18), 23119–23131 (2018).
[Crossref] [PubMed]

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(9), 1–11 (2017).
[Crossref] [PubMed]

Y. Zhang, A. Pan, M. Lei, and B. Yao, “Data preprocessing methods for robust Fourier ptychographic microscopy,” Opt. Eng. 56(12), 123107 (2017).
[Crossref]

Pan, X.

Perciano, T.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Cryst. 49(4), 1245–1252 (2016).
[Crossref]

Pesic, Z.

T. Edo, D. Batey, A. Maiden, C. Rau, U. Wagner, Z. Pesic, T. Waigh, and J. Rodenburg, “Sampling in x-ray ptychography,” Phys. Rev. A 87(5), 053850 (2013).
[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(1), 014005 (2015).
[Crossref]

R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (2015).
[Crossref] [PubMed]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23(10), 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(1), 1927 (2013).
[Crossref] [PubMed]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[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]

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]

Piestun, R.

Räty, L.

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3(1), 2369 (2013).
[Crossref] [PubMed]

Rau, C.

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

Robinson, I. K.

Rodenburg, J.

P. Li, T. Edo, D. Batey, J. Rodenburg, and A. Maiden, “Breaking ambiguities in mixed state ptychography,” Opt. Express 24(8), 9038–9052 (2016).
[Crossref] [PubMed]

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

Rodenburg, J. M.

D. Claus and J. M. Rodenburg, “Pixel size adjustment in coherent diffractive imaging within the Rayleigh-Sommerfeld regime,” Appl. Opt. 54(8), 1936–1944 (2015).
[Crossref] [PubMed]

P. Li, D. J. Batey, T. B. Edo, and J. M. Rodenburg, “Separation of three-dimensional scattering effects in tilt-series Fourier ptychography,” Ultramicroscopy 158, 1–7 (2015).
[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]

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29(8), 1606–1614 (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, 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 (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. L. 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]

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. Lond. A 339(1655), 521–553 (1992).

Sarahan, M. C.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[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, 64–72 (2012).
[Crossref] [PubMed]

Schneider, P.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref] [PubMed]

Schramm, S. M.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref] [PubMed]

Sethian, J. A.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Cryst. 49(4), 1245–1252 (2016).
[Crossref]

Shapiro, D. A.

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Cryst. 49(4), 1245–1252 (2016).
[Crossref]

Shen, Z.

K. Wang and Z. Shen, “A GPU-based parallel genetic algorithm for generating daily activity plans,” IEEE Trans. Intell. Transp. Syst. 13(3), 1474–1480 (2012).
[Crossref]

Shimomura, K.

Stagg, M. D.

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (2015).
[Crossref] [PubMed]

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(1), 014005 (2015).
[Crossref]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23(10), 12720–12731 (2015).
[Crossref] [PubMed]

R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (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(1), 1927 (2013).
[Crossref] [PubMed]

Suman, R.

Sun, J.

Tai, R.

Takahashi, Y.

Thibault, P.

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23(10), 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(1), 014005 (2015).
[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(1), 1927 (2013).
[Crossref] [PubMed]

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 diffraction imaging,” New J. Phys. 14(6), 063004 (2012).
[Crossref]

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[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]

Tian, L.

Tsai, E. H. R.

Usov, I.

Villanova, J.

Wagner, U.

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

Waigh, T.

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

Waller, L.

Wang, C.

Wang, J.

Wang, K.

K. Wang and Z. Shen, “A GPU-based parallel genetic algorithm for generating daily activity plans,” IEEE Trans. Intell. Transp. Syst. 13(3), 1474–1480 (2012).
[Crossref]

Wang, Y.

Wang, Z.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(9), 1–11 (2017).
[Crossref] [PubMed]

Wen, K.

Wepf, R.

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref] [PubMed]

Xu, Z.

Yan, H.

Yang, C.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Yao, B.

A. Pan, M. Zhou, Y. Zhang, J. Min, M. Lei, and B. Yao, “Adaptive-window angular spectrum algorithm for near-field ptychography,” Opt. Commun. 430, 73–82 (2019).
[Crossref]

A. Pan, Y. Zhang, K. Wen, M. Zhou, J. Min, M. Lei, and B. Yao, “Subwavelength resolution Fourier ptychography with hemispherical digital condensers,” Opt. Express 26(18), 23119–23131 (2018).
[Crossref] [PubMed]

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(9), 1–11 (2017).
[Crossref] [PubMed]

Y. Zhang, A. Pan, M. Lei, and B. Yao, “Data preprocessing methods for robust Fourier ptychographic microscopy,” Opt. Eng. 56(12), 123107 (2017).
[Crossref]

Yeh, L.

Zanette, I.

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23(10), 12720–12731 (2015).
[Crossref] [PubMed]

R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (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(1), 014005 (2015).
[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(1), 1927 (2013).
[Crossref] [PubMed]

Zhang, Y.

A. Pan, M. Zhou, Y. Zhang, J. Min, M. Lei, and B. Yao, “Adaptive-window angular spectrum algorithm for near-field ptychography,” Opt. Commun. 430, 73–82 (2019).
[Crossref]

A. Pan, Y. Zhang, K. Wen, M. Zhou, J. Min, M. Lei, and B. Yao, “Subwavelength resolution Fourier ptychography with hemispherical digital condensers,” Opt. Express 26(18), 23119–23131 (2018).
[Crossref] [PubMed]

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(9), 1–11 (2017).
[Crossref] [PubMed]

Y. Zhang, A. Pan, M. Lei, and B. Yao, “Data preprocessing methods for robust Fourier ptychographic microscopy,” Opt. Eng. 56(12), 123107 (2017).
[Crossref]

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Sampling criteria for Fourier ptychographic microscopy in object space and frequency space,” Opt. Express 24(14), 15765–15781 (2016).
[Crossref] [PubMed]

Zhao, T.

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(9), 1–11 (2017).
[Crossref] [PubMed]

Zheng, G.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Zhong, J.

Zhou, M.

A. Pan, M. Zhou, Y. Zhang, J. Min, M. Lei, and B. Yao, “Adaptive-window angular spectrum algorithm for near-field ptychography,” Opt. Commun. 430, 73–82 (2019).
[Crossref]

A. Pan, Y. Zhang, K. Wen, M. Zhou, J. Min, M. Lei, and B. Yao, “Subwavelength resolution Fourier ptychography with hemispherical digital condensers,” Opt. Express 26(18), 23119–23131 (2018).
[Crossref] [PubMed]

Zhu, J.

Zuo, C.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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

IEEE Trans. Intell. Transp. Syst. (1)

K. Wang and Z. Shen, “A GPU-based parallel genetic algorithm for generating daily activity plans,” IEEE Trans. Intell. Transp. Syst. 13(3), 1474–1480 (2012).
[Crossref]

J. Appl. Cryst. (1)

S. Marchesini, H. Krishnan, B. J. Daurer, D. A. Shapiro, T. Perciano, J. A. Sethian, and F. R. N. C. Maia, “SHARP: a distributed GPU-based ptychographic solver,” J. Appl. Cryst. 49(4), 1245–1252 (2016).
[Crossref]

J. Biomed. Opt. (1)

A. Pan, Y. Zhang, T. Zhao, Z. Wang, D. Dan, M. Lei, and B. Yao, “System calibration method for Fourier ptychographic microscopy,” J. Biomed. Opt. 22(9), 1–11 (2017).
[Crossref] [PubMed]

J. Comput. Chem. (1)

G. M. Morris, D. S. Goodsell, R. S. Halliday, R. Huey, W. E. Hart, R. K. Belew, and A. J. Olson, “Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function,” J. Comput. Chem. 19(14), 1639–1662 (1998).
[Crossref]

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

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 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Nature (2)

M. Dierolf, A. Menzel, P. Thibault, P. Schneider, C. M. Kewish, R. Wepf, O. Bunk, and F. Pfeiffer, “Ptychographic X-ray computed tomography at the nanoscale,” Nature 467(7314), 436–439 (2010).
[Crossref] [PubMed]

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 diffraction imaging,” New J. Phys. 14(6), 063004 (2012).
[Crossref]

Opt. Commun. (1)

A. Pan, M. Zhou, Y. Zhang, J. Min, M. Lei, and B. Yao, “Adaptive-window angular spectrum algorithm for near-field ptychography,” Opt. Commun. 430, 73–82 (2019).
[Crossref]

Opt. Eng. (1)

Y. Zhang, A. Pan, M. Lei, and B. Yao, “Data preprocessing methods for robust Fourier ptychographic microscopy,” Opt. Eng. 56(12), 123107 (2017).
[Crossref]

Opt. Express (11)

J. Sun, Q. Chen, Y. Zhang, and C. Zuo, “Sampling criteria for Fourier ptychographic microscopy in object space and frequency space,” Opt. Express 24(14), 15765–15781 (2016).
[Crossref] [PubMed]

D. B. Conkey, A. N. Brown, A. M. Caravaca-Aguirre, and R. Piestun, “Genetic algorithm optimization for focusing through turbid media in noisy environments,” Opt. Express 20(5), 4840–4849 (2012).
[Crossref] [PubMed]

A. Pan, Y. Zhang, K. Wen, M. Zhou, J. Min, M. Lei, and B. Yao, “Subwavelength resolution Fourier ptychography with hemispherical digital condensers,” Opt. Express 26(18), 23119–23131 (2018).
[Crossref] [PubMed]

M. Stockmar, M. Hubert, M. Dierolf, B. Enders, R. Clare, S. Allner, A. Fehringer, I. Zanette, J. Villanova, J. Laurencin, P. Cloetens, F. Pfeiffer, and P. Thibault, “X-ray nanotomography using near-field ptychography,” Opt. Express 23(10), 12720–12731 (2015).
[Crossref] [PubMed]

R. M. Clare, M. Stockmar, M. Dierolf, I. Zanette, and F. Pfeiffer, “Characterization of near-field ptychography,” Opt. Express 23(15), 19728–19742 (2015).
[Crossref] [PubMed]

E. H. R. Tsai, I. Usov, A. Diaz, A. Menzel, and M. Guizar-Sicairos, “X-ray ptychography with extended depth of field,” Opt. Express 24(25), 29089–29108 (2016).
[Crossref] [PubMed]

K. Shimomura, M. Hirose, T. Higashino, and Y. Takahashi, “Three-dimensional iterative multislice reconstruction for ptychographic X-ray computed tomography,” Opt. Express 26(24), 31199–31208 (2018).
[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]

C. Zuo, J. Sun, and Q. Chen, “Adaptive step-size strategy for noise-robust Fourier ptychographic microscopy,” Opt. Express 24(18), 20724–20744 (2016).
[Crossref] [PubMed]

P. Li, T. Edo, D. Batey, J. Rodenburg, and A. Maiden, “Breaking ambiguities in mixed state ptychography,” Opt. Express 24(8), 9038–9052 (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]

Opt. Lett. (2)

Optica (2)

Phil. Trans. R. Soc. Lond. A (1)

J. M. Rodenburg and R. H. T. Bates, “The theory of super-resolution electron microscopy via Wigner-distribution deconvolution,” Phil. Trans. R. Soc. Lond. A 339(1655), 521–553 (1992).

Phys. Rev. A (1)

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

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(1), 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(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]

Sci. Rep. (3)

J. Marrison, L. Räty, P. Marriott, and P. O’Toole, “Ptychography--a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3(1), 2369 (2013).
[Crossref] [PubMed]

A. M. Maiden, M. C. Sarahan, M. D. Stagg, S. M. Schramm, and M. J. Humphry, “Quantitative electron phase imaging with high sensitivity and an unlimited field of view,” Sci. Rep. 5, 14690 (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(1), 1927 (2013).
[Crossref] [PubMed]

Science (1)

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]

Ultramicroscopy (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, 64–72 (2012).
[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 and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

P. Li, D. J. Batey, T. B. Edo, and J. M. Rodenburg, “Separation of three-dimensional scattering effects in tilt-series Fourier ptychography,” Ultramicroscopy 158, 1–7 (2015).
[Crossref] [PubMed]

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Figures (10)

Fig. 1
Fig. 1 Schematic of 3D near-field ptychography with thick specimen of uneven spatial distribution.
Fig. 2
Fig. 2 Reconstructions with different cases. (a1)-(a6) The simulated images served as the ground truth with d1 = 10mm, d2 = 20mm and d3 = 50mm. (b1)-(b6) The ideal reconstructions with precise parameters. (c1)-(c6), (d1)-(d6), (e1)-(e4) and (f1)-(f8) The reconstructions using 3ePIE algorithm with four typical and unknown cases. Case 1: d1 = 15mm, d2 = 15mm and d3 = 50mm; Case 2: d1 = 10mm, d2 = 10mm and d3 = 50mm; Case 3: d1 = 30mm and d2 = 50mm; Case 4: d1 = 10mm, d2 = 10mm, d3 = 10mm and d4 = 50mm. (g1)-(g6) The reconstructions with our GA-3ePIE approach. The numbers beneath each image: the MSE compared with the ground truth.
Fig. 3
Fig. 3 Results of three slices in simulations. (a) The cost function SSE versus the iterations with GA-3ePIE approach. (b) The SSEs versus the iterations with different cases.
Fig. 4
Fig. 4 Photograph of optical setup.
Fig. 5
Fig. 5 Intensity reconstructions of USAF target with different parameters. (a) Intensity reconstructions with only one slice. (b1)-(b2) and (c1)-(c2) Intensity reconstructions with two slices but with different distance between layers. (d1)-(d3) Intensity reconstructions with three slices including one empty slice. (e1)-(e2) and (f1)-(f2) Intensity reconstructions with GA-3ePIE approach and their close-ups. (g) A typical diffraction patterns.
Fig. 6
Fig. 6 Results of USAF target. (a) The cost function SSE versus the iterations with GA-3ePIE approach. (b) The SSEs versus the iterations with different cases.
Fig. 7
Fig. 7 Digital refocusing results.
Fig. 8
Fig. 8 Phase reconstructions of biological samples with different parameters. (a1) and (a2) Photographs of biological samples. (b1)-(b2) and (c1)-(c2) Phase reconstructions with two slices but with different distance between layers. (d1)-(d2) Phase reconstructions with GA-3ePIE approach. (e) A typical diffraction patterns.
Fig. 9
Fig. 9 Results of biological samples. (a) The cost function SSE versus the iterations with GA-3ePIE approach; (b) The SSEs versus the iterations with different cases.
Fig. 10
Fig. 10 (a) The average MSEs of phase of layers versus the deviations of the distance between layers. (b) The number of slices can be resolved versus the overlap rate and sampling in spatial domain.

Tables (2)

Tables Icon

Table 1 Summary of notations

Tables Icon

Table 2 Computation time with different number of individuals

Equations (18)

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

E e,1 (r)=P(r R c ) O 1 (r)
E i,2 (r)= ρ d 1 [ E e,1 (r)]
E e,2 (r)= E i,2 (r) O 2 (r)
E i,N ( r )= ρ d N1 [ E e,N1 (r) ] E e,N (r)= E i,N (r) O N (r)
E c ( u )= ρ d N [ E e,N (r) ]
E c ' (u)= I c (u) E c (u) | E c (u) |
O N ' = O N +α E i,N | E i,N | max 2 ( E e,N ' E e,N ) E i,N ' = E i,N +β O N | O N | max 2 ( E e,N ' E e,N )
SSE= c,u | | E c ( u ) | I c ( u ) | 2 I c ( u )
SSE=minf( N, d 1 , d 2 ,..., d N )
F= 1 f
P j = F j 1 M F j
a jv = a jv (1b)+ a lv b a lv = a lv (1b)+ a jv b
a hv ={ a hv +( a max a hv )g(k), r 1 0.5 a hv +( a min a hv )g(k), r 1 <0.5
g(k)= r 2 ( 1 k k max ) 2
MSE= [ G(x,y)Q(x,y) ] 2 mn
Δ x 1 = λ d N L
R overlap = 1 π ( 2arccos S t 2r S t r 2 r 2 S t 2 4 )
deviations= Δ d s d s ×100%

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