Abstract

Coherent X-ray Diffraction Imaging (CDI) and X-ray ptychography both heavily rely on the high degree of spatial coherence of the X-ray illumination for sufficient experimental data quality for reconstruction convergence. Nevertheless, the majority of the available synchrotron undulator sources have a limited degree of partial coherence, leading to reduced data quality and a lower speckle contrast in the coherent diffraction patterns. It is still an open question whether experimentalists should compromise the coherence properties of an X-ray source in exchange for a higher flux density at a sample, especially when some materials of scientific interest are relatively weak scatterers. A previous study has suggested that in CDI, the best strategy for the study of strong phase objects is to maintain a high degree of coherence of the illuminating X-rays because of the broadening of solution space resulting from the strong phase structures. In this article, we demonstrate the first systematic analysis of the effectiveness of partial coherence correction in ptychography as a function of the coherence properties, degree of complexity of illumination (degree of phase diversity of the probe) and sample phase complexity. We have also performed analysis of how well ptychographic algorithms refine X-ray probe and complex coherence functions when those variables are unknown at the start of reconstructions, for noise-free simulated data, in the case of both real-valued and highly-complex objects.

© 2015 Optical Society of America

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References

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    [Crossref]

2014 (5)

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

J.N. Clark, X. Huang, R.J. Harder, and I.K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112, 113901 (2014).
[Crossref] [PubMed]

D.H. Parks, X. Shi, and S.D. Kevan, “Partially coherent x-ray diffractive imaging of complex objects,” Phys. Rev. A 89, 063824 (2014).
[Crossref]

C.G. Schroera and G. Falkenberg, “Hard X-ray nanofocusing at low-emittance synchrotron radiation sources”, J. Synchrotron Radiat. 21, 996–1005 (2014).
[Crossref]

N. Burdet, G.R. Morrison, X. Huang, X. Shi, J.N. Clark, F. Zhang, M. Civita, R. Harder, and I.K. Robinson, “Observations of artefacts in the x-ray ptychography method,” Optics Express 22, 10294–10303 (2014).
[Crossref] [PubMed]

2013 (5)

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

J.R. Fienup, “Phase retrieval algorithms: a personal tour,” Appl. Opt. 52, 45–56 (2013).
[Crossref] [PubMed]

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

T.B. Edo, D.J. Batey, A.M. Maiden, C. Rau, U. Wagner, Z.D. Pesic, T.A. Waigh, and J.M. Rodenburg, “Sampling in x-ray ptychography”, Phys. Rev. A 87053850 (2013).
[Crossref]

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

2012 (2)

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

A. Fannjiang and W. Liao, “Phase retrieval with random phase illumination,” JOSA A-Optics Image Science and Vision 29, 1847–1859 (2012).
[Crossref]

2011 (2)

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

W. Chen and X. Chen, “Quantitative phase retrieval of complex-valued specimens based on noninterferometric imaging,” Appl. Opt. 50, 2008–2015(2011).
[Crossref] [PubMed]

2010 (2)

2009 (4)

B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
[Crossref]

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

R.A. Dilanian, B. Chen, G.J. Williams, H.M. Quiney, K.A. Nugent, S. Teichmann, P. Hannaford, L.V. Dao, and A.G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106, 023110 (2009).
[Crossref]

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

2008 (2)

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

A. Singer, I.A. Vartanyants, M. Kuhlmann, S. Duesterer, R. Treusch, and J. Feldhaus, “Transverse-coherence properties of the free-electron-laser flash at desy,” Phys. Rev. Lett. 101, 053850 (2008).
[Crossref] [PubMed]

2006 (1)

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
[Crossref]

2005 (1)

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J.F. Vander Veen, I. Vartanyants, and I.K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

2004 (1)

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

2003 (1)

2000 (1)

V. Kohn, I. Snigireva, and A. Snigirev, “Direct Measurement of Transverse Coherence Length of Hard X Rays from Interference Fringes,” Phys. Rev. Lett. 85, 2745 (2000).
[Crossref] [PubMed]

1999 (1)

P.A. Lemieux and D.J. Durian, “Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions”, J. Opt. Soc. Am. A 16, 7 (1999).
[Crossref]

1998 (1)

J. Miao, D. Sayre, and H.N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects”, J. Opt. Soc. Am. A 15, 16621669 (1998).
[Crossref]

Abbey, B.

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
[Crossref]

Attwood, D.

Balaur, E.

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

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

Barty, A.

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
[Crossref]

Batey, D.J.

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

T.B. Edo, D.J. Batey, A.M. Maiden, C. Rau, U. Wagner, Z.D. Pesic, T.A. Waigh, and J.M. Rodenburg, “Sampling in x-ray ptychography”, Phys. Rev. A 87053850 (2013).
[Crossref]

Bean, R.

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

Beetz, T.

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
[Crossref]

Berenguer, A.D.F.

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

Bunk, O.

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

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J.F. Vander Veen, I. Vartanyants, and I.K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Burdet, N.

N. Burdet, G.R. Morrison, X. Huang, X. Shi, J.N. Clark, F. Zhang, M. Civita, R. Harder, and I.K. Robinson, “Observations of artefacts in the x-ray ptychography method,” Optics Express 22, 10294–10303 (2014).
[Crossref] [PubMed]

Cadenazzi, G.A.

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Chang, C.

Chapman, H.N.

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
[Crossref]

J. Miao, D. Sayre, and H.N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects”, J. Opt. Soc. Am. A 15, 16621669 (1998).
[Crossref]

Chen, B.

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

R.A. Dilanian, B. Chen, G.J. Williams, H.M. Quiney, K.A. Nugent, S. Teichmann, P. Hannaford, L.V. Dao, and A.G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106, 023110 (2009).
[Crossref]

B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
[Crossref]

Chen, W.

Chen, X.

Civita, M.

N. Burdet, G.R. Morrison, X. Huang, X. Shi, J.N. Clark, F. Zhang, M. Civita, R. Harder, and I.K. Robinson, “Observations of artefacts in the x-ray ptychography method,” Optics Express 22, 10294–10303 (2014).
[Crossref] [PubMed]

Clark, J.N.

N. Burdet, G.R. Morrison, X. Huang, X. Shi, J.N. Clark, F. Zhang, M. Civita, R. Harder, and I.K. Robinson, “Observations of artefacts in the x-ray ptychography method,” Optics Express 22, 10294–10303 (2014).
[Crossref] [PubMed]

J.N. Clark, X. Huang, R.J. Harder, and I.K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112, 113901 (2014).
[Crossref] [PubMed]

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

Claus, D.

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

Cui, C.

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
[Crossref]

Dao, L.V.

R.A. Dilanian, B. Chen, G.J. Williams, H.M. Quiney, K.A. Nugent, S. Teichmann, P. Hannaford, L.V. Dao, and A.G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106, 023110 (2009).
[Crossref]

David, C.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J.F. Vander Veen, I. Vartanyants, and I.K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Diaz, A.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J.F. Vander Veen, I. Vartanyants, and I.K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Dierolf, M.

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

Dilanian, R.A.

R.A. Dilanian, B. Chen, G.J. Williams, H.M. Quiney, K.A. Nugent, S. Teichmann, P. Hannaford, L.V. Dao, and A.G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106, 023110 (2009).
[Crossref]

B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
[Crossref]

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

Duesterer, S.

A. Singer, I.A. Vartanyants, M. Kuhlmann, S. Duesterer, R. Treusch, and J. Feldhaus, “Transverse-coherence properties of the free-electron-laser flash at desy,” Phys. Rev. Lett. 101, 053850 (2008).
[Crossref] [PubMed]

Durian, D.J.

P.A. Lemieux and D.J. Durian, “Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions”, J. Opt. Soc. Am. A 16, 7 (1999).
[Crossref]

Edo, T.B.

T.B. Edo, D.J. Batey, A.M. Maiden, C. Rau, U. Wagner, Z.D. Pesic, T.A. Waigh, and J.M. Rodenburg, “Sampling in x-ray ptychography”, Phys. Rev. A 87053850 (2013).
[Crossref]

Falkenberg, G.

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L.W. Whitehead, G.J. Williams, H.M. Quiney, D.J. Vine, R.A. Dilanian, S. Flewett, K.A. Nugent, A.G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
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B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
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R.A. Dilanian, B. Chen, G.J. Williams, H.M. Quiney, K.A. Nugent, S. Teichmann, P. Hannaford, L.V. Dao, and A.G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106, 023110 (2009).
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N. Burdet, G.R. Morrison, X. Huang, X. Shi, J.N. Clark, F. Zhang, M. Civita, R. Harder, and I.K. Robinson, “Observations of artefacts in the x-ray ptychography method,” Optics Express 22, 10294–10303 (2014).
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J.N. Clark, X. Huang, R.J. Harder, and I.K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112, 113901 (2014).
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H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
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He, H.

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
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B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
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H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
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N. Burdet, G.R. Morrison, X. Huang, X. Shi, J.N. Clark, F. Zhang, M. Civita, R. Harder, and I.K. Robinson, “Observations of artefacts in the x-ray ptychography method,” Optics Express 22, 10294–10303 (2014).
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J.N. Clark, X. Huang, R.J. Harder, and I.K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112, 113901 (2014).
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J.N. Clark, X. Huang, R. Harder, and I.K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
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H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
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A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
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D.H. Parks, X. Shi, and S.D. Kevan, “Partially coherent x-ray diffractive imaging of complex objects,” Phys. Rev. A 89, 063824 (2014).
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V. Kohn, I. Snigireva, and A. Snigirev, “Direct Measurement of Transverse Coherence Length of Hard X Rays from Interference Fringes,” Phys. Rev. Lett. 85, 2745 (2000).
[Crossref] [PubMed]

Kuhlmann, M.

A. Singer, I.A. Vartanyants, M. Kuhlmann, S. Duesterer, R. Treusch, and J. Feldhaus, “Transverse-coherence properties of the free-electron-laser flash at desy,” Phys. Rev. Lett. 101, 053850 (2008).
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Liao, W.

A. Fannjiang and W. Liao, “Phase retrieval with random phase illumination,” JOSA A-Optics Image Science and Vision 29, 1847–1859 (2012).
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Maiden, A.M.

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
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T.B. Edo, D.J. Batey, A.M. Maiden, C. Rau, U. Wagner, Z.D. Pesic, T.A. Waigh, and J.M. Rodenburg, “Sampling in x-ray ptychography”, Phys. Rev. A 87053850 (2013).
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Marchesini, S.

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
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B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

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

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

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

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

J. Miao, D. Sayre, and H.N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects”, J. Opt. Soc. Am. A 15, 16621669 (1998).
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Morrison, G.R.

N. Burdet, G.R. Morrison, X. Huang, X. Shi, J.N. Clark, F. Zhang, M. Civita, R. Harder, and I.K. Robinson, “Observations of artefacts in the x-ray ptychography method,” Optics Express 22, 10294–10303 (2014).
[Crossref] [PubMed]

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Naulleau, P.

Noy, A.

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
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Nugent, K.A.

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
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K.A. Nugent, “Coherent methods in the X-ray sciences”, Advances in Physics,  59(1), 1–99 (2010).
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R.A. Dilanian, B. Chen, G.J. Williams, H.M. Quiney, K.A. Nugent, S. Teichmann, P. Hannaford, L.V. Dao, and A.G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106, 023110 (2009).
[Crossref]

B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
[Crossref]

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

Parks, D.H.

D.H. Parks, X. Shi, and S.D. Kevan, “Partially coherent x-ray diffractive imaging of complex objects,” Phys. Rev. A 89, 063824 (2014).
[Crossref]

Peele, A.G.

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
[Crossref]

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

R.A. Dilanian, B. Chen, G.J. Williams, H.M. Quiney, K.A. Nugent, S. Teichmann, P. Hannaford, L.V. Dao, and A.G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106, 023110 (2009).
[Crossref]

Pesic, Z.D.

T.B. Edo, D.J. Batey, A.M. Maiden, C. Rau, U. Wagner, Z.D. Pesic, T.A. Waigh, and J.M. Rodenburg, “Sampling in x-ray ptychography”, Phys. Rev. A 87053850 (2013).
[Crossref]

Peterson, I.

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

Pfeiffer, F.

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

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J.F. Vander Veen, I. Vartanyants, and I.K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Putkunz, C.T.

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Quiney, H.M.

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

R.A. Dilanian, B. Chen, G.J. Williams, H.M. Quiney, K.A. Nugent, S. Teichmann, P. Hannaford, L.V. Dao, and A.G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106, 023110 (2009).
[Crossref]

B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
[Crossref]

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

Rau, C.

T.B. Edo, D.J. Batey, A.M. Maiden, C. Rau, U. Wagner, Z.D. Pesic, T.A. Waigh, and J.M. Rodenburg, “Sampling in x-ray ptychography”, Phys. Rev. A 87053850 (2013).
[Crossref]

Robinson, I.K.

N. Burdet, G.R. Morrison, X. Huang, X. Shi, J.N. Clark, F. Zhang, M. Civita, R. Harder, and I.K. Robinson, “Observations of artefacts in the x-ray ptychography method,” Optics Express 22, 10294–10303 (2014).
[Crossref] [PubMed]

J.N. Clark, X. Huang, R.J. Harder, and I.K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112, 113901 (2014).
[Crossref] [PubMed]

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

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

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J.F. Vander Veen, I. Vartanyants, and I.K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Rodenburg, J.M.

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

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

T.B. Edo, D.J. Batey, A.M. Maiden, C. Rau, U. Wagner, Z.D. Pesic, T.A. Waigh, and J.M. Rodenburg, “Sampling in x-ray ptychography”, Phys. Rev. A 87053850 (2013).
[Crossref]

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

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

Rosen, R.

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
[Crossref]

Sayre, D.

J. Miao, D. Sayre, and H.N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects”, J. Opt. Soc. Am. A 15, 16621669 (1998).
[Crossref]

Schroera, C.G.

C.G. Schroera and G. Falkenberg, “Hard X-ray nanofocusing at low-emittance synchrotron radiation sources”, J. Synchrotron Radiat. 21, 996–1005 (2014).
[Crossref]

Schulze-Briese, C.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J.F. Vander Veen, I. Vartanyants, and I.K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Shapiro, D.

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
[Crossref]

Shi, X.

D.H. Parks, X. Shi, and S.D. Kevan, “Partially coherent x-ray diffractive imaging of complex objects,” Phys. Rev. A 89, 063824 (2014).
[Crossref]

N. Burdet, G.R. Morrison, X. Huang, X. Shi, J.N. Clark, F. Zhang, M. Civita, R. Harder, and I.K. Robinson, “Observations of artefacts in the x-ray ptychography method,” Optics Express 22, 10294–10303 (2014).
[Crossref] [PubMed]

Singer, A.

A. Singer, I.A. Vartanyants, M. Kuhlmann, S. Duesterer, R. Treusch, and J. Feldhaus, “Transverse-coherence properties of the free-electron-laser flash at desy,” Phys. Rev. Lett. 101, 053850 (2008).
[Crossref] [PubMed]

Snigirev, A.

V. Kohn, I. Snigireva, and A. Snigirev, “Direct Measurement of Transverse Coherence Length of Hard X Rays from Interference Fringes,” Phys. Rev. Lett. 85, 2745 (2000).
[Crossref] [PubMed]

Snigireva, I.

V. Kohn, I. Snigireva, and A. Snigirev, “Direct Measurement of Transverse Coherence Length of Hard X Rays from Interference Fringes,” Phys. Rev. Lett. 85, 2745 (2000).
[Crossref] [PubMed]

Spence, J.C.H.

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
[Crossref]

Teichmann, S.

R.A. Dilanian, B. Chen, G.J. Williams, H.M. Quiney, K.A. Nugent, S. Teichmann, P. Hannaford, L.V. Dao, and A.G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106, 023110 (2009).
[Crossref]

B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
[Crossref]

Thibault, P.

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 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, 338–343 (2009).
[Crossref] [PubMed]

Treusch, R.

A. Singer, I.A. Vartanyants, M. Kuhlmann, S. Duesterer, R. Treusch, and J. Feldhaus, “Transverse-coherence properties of the free-electron-laser flash at desy,” Phys. Rev. Lett. 101, 053850 (2008).
[Crossref] [PubMed]

VanDao, L.

B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
[Crossref]

Vander Veen, J.F.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J.F. Vander Veen, I. Vartanyants, and I.K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Vartanyants, I.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J.F. Vander Veen, I. Vartanyants, and I.K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Vartanyants, I.A.

A. Singer, I.A. Vartanyants, M. Kuhlmann, S. Duesterer, R. Treusch, and J. Feldhaus, “Transverse-coherence properties of the free-electron-laser flash at desy,” Phys. Rev. Lett. 101, 053850 (2008).
[Crossref] [PubMed]

Vila-Comamala, J.

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

Vine, D.J.

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

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

Wagner, U.

T.B. Edo, D.J. Batey, A.M. Maiden, C. Rau, U. Wagner, Z.D. Pesic, T.A. Waigh, and J.M. Rodenburg, “Sampling in x-ray ptychography”, Phys. Rev. A 87053850 (2013).
[Crossref]

Waigh, T.A.

T.B. Edo, D.J. Batey, A.M. Maiden, C. Rau, U. Wagner, Z.D. Pesic, T.A. Waigh, and J.M. Rodenburg, “Sampling in x-ray ptychography”, Phys. Rev. A 87053850 (2013).
[Crossref]

Weierstall, U.

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
[Crossref]

Weitkamp, T.

F. Pfeiffer, O. Bunk, C. Schulze-Briese, A. Diaz, T. Weitkamp, C. David, J.F. Vander Veen, I. Vartanyants, and I.K. Robinson, “Shearing interferometer for quantifying the coherence of hard x-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[Crossref] [PubMed]

Whitehead, L.W.

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

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

Williams, G.J.

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
[Crossref]

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

R.A. Dilanian, B. Chen, G.J. Williams, H.M. Quiney, K.A. Nugent, S. Teichmann, P. Hannaford, L.V. Dao, and A.G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106, 023110 (2009).
[Crossref]

Zhang, F.

N. Burdet, G.R. Morrison, X. Huang, X. Shi, J.N. Clark, F. Zhang, M. Civita, R. Harder, and I.K. Robinson, “Observations of artefacts in the x-ray ptychography method,” Optics Express 22, 10294–10303 (2014).
[Crossref] [PubMed]

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

Advances in Physics (1)

K.A. Nugent, “Coherent methods in the X-ray sciences”, Advances in Physics,  59(1), 1–99 (2010).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

J.M. Rodenburg and H.M.L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
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J. Appl. Phys. (1)

R.A. Dilanian, B. Chen, G.J. Williams, H.M. Quiney, K.A. Nugent, S. Teichmann, P. Hannaford, L.V. Dao, and A.G. Peele, “Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source,” J. Appl. Phys. 106, 023110 (2009).
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J. Opt. Soc. Am. A (2)

J. Miao, D. Sayre, and H.N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects”, J. Opt. Soc. Am. A 15, 16621669 (1998).
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J. Synchrotron Radiat. (1)

C.G. Schroera and G. Falkenberg, “Hard X-ray nanofocusing at low-emittance synchrotron radiation sources”, J. Synchrotron Radiat. 21, 996–1005 (2014).
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JOSA A (1)

H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High-resolution ab initio three-dimensional x-ray diffraction microscopy”, JOSA A 23, 5 (2006).
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JOSA A-Optics Image Science and Vision (1)

A. Fannjiang and W. Liao, “Phase retrieval with random phase illumination,” JOSA A-Optics Image Science and Vision 29, 1847–1859 (2012).
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Nat. Commun. (2)

A.M. Maiden, G.R. Morrison, B. Kaulich, A. Gianoncelli, and J.M. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
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J.N. Clark, X. Huang, R. Harder, and I.K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

B. Abbey, L.W. Whitehead, H.M. Quiney, D.J. Vine, G.A. Cadenazzi, C.A. Henderson, K.A. Nugent, E. Balaur, C.T. Putkunz, A.G. Peele, G.J. Williams, and I. McNulty, “Lensless imaging using broadband x-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Nature (1)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
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Opt. Express (1)

Optics Express (3)

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

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

N. Burdet, G.R. Morrison, X. Huang, X. Shi, J.N. Clark, F. Zhang, M. Civita, R. Harder, and I.K. Robinson, “Observations of artefacts in the x-ray ptychography method,” Optics Express 22, 10294–10303 (2014).
[Crossref] [PubMed]

Phys. Rev. A (3)

T.B. Edo, D.J. Batey, A.M. Maiden, C. Rau, U. Wagner, Z.D. Pesic, T.A. Waigh, and J.M. Rodenburg, “Sampling in x-ray ptychography”, Phys. Rev. A 87053850 (2013).
[Crossref]

B. Chen, R.A. Dilanian, S. Teichmann, B. Abbey, A.G. Peele, G.J. Williams, P. Hannaford, L. VanDao, H.M. Quiney, and K.A. Nugent, “Multiple wavelength diffractive imaging,” Phys. Rev. A 79, 023809 (2009).
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D.H. Parks, X. Shi, and S.D. Kevan, “Partially coherent x-ray diffractive imaging of complex objects,” Phys. Rev. A 89, 063824 (2014).
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J.N. Clark, X. Huang, R.J. Harder, and I.K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112, 113901 (2014).
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L.W. Whitehead, G.J. Williams, H.M. Quiney, D.J. Vine, R.A. Dilanian, S. Flewett, K.A. Nugent, A.G. Peele, E. Balaur, and I. McNulty, “Diffractive imaging using partially coherent x rays,” Phys. Rev. Lett. 103, 243902 (2009).
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Ultramicroscopy (2)

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

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

Other (1)

J.W. Goodman, Statistical Optics ISBN: 978-0-471-39916-2, 572 (The Wiley Classics Library, 2000).

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Figures (5)

Fig. 1
Fig. 1 Types of objects used in reconstruction simulations. (a) a real- valued object with max phase = 0; (b) a complex- valued object with max phase = 2π; (d) a real-valued probe with max phase = 0; (e) complex -valued probe with = 0.5π; the amplitude is flat ; (f) complex -valued probe with max phase = 2π; the amplitude is flat (c) magnitude/phase colormap for (a), (b), (d),(e) and (f) is illustrated in top right image (c). (g) diffraction patterns with complex Lena probe with maximum phase = 0.5 π when object maximum phase = 2 π (h) diffraction patterns with complex Lena probe with maximum phase = 2 π when object maximum phase = 2 π; (k) line-cut profile of amplitude of complex Lena probe as presented in (e), the Lena probe has smooth profile throughout, including the edges.
Fig. 2
Fig. 2 Results of reconstructions using both the PC and FC projections for complex valued (max phase= 2π and max phase= 0.5π and) samples at 7 degrees of coherence = σ/L. The reconstruction of the weakly-complex sample has better reconstruction results from the PC projection vis-a-vis the FC projection, but the strongly-complex sample needs higher degree of coherence σ/L for successful convergence. All reconstructions were performed with overlap of 70% in ptychographic simulations. We used a soft-edged square-shape probe for this part of study.
Fig. 3
Fig. 3 Rreal (FC/PC) Vs. σ/L for 9 σ/L used in simulations, for object maximum phase = 2π and 0.5 π. Two sets of results are done with soft-edged square-shape probe in simulations. This figure is for investigation of cut-off σ/L for maximum phase = 2π and maximum phase = 0.5 π of objects. Our results show that the cut-off σ/L for good reconstructions is higher for max object phase = 2π than for max object phase = 0.5π. In other words, better coherence is needed for highly complex objects. All simulation were performed with 70 % overlap. The horizontal lines drawn here are the cut-off degree of coherence σ/L, above which successful data reconstructions are obtained for both object cases, in the same colour scheme.
Fig. 4
Fig. 4 Top: real-space R-factor log-scale FC/PC bonus plots for high phase-diversity (maximum probe phase = 2π) and real-valued probe as a function of degree of coherence σ/L for both object maximum phase = 0 and 2π for 0.3, 0.5 and 0.7 overlap ratios. The horizontal lines in all the graphs in the top panel are cut-off lines for acceptable reconstructions with correctly converged images. Above the cut-off lines the reconstructions are acceptable, while below the lines the reconstructions fail to converge. The performance of a high phase diversity probe is slightly worse than a real probe when overlap ratio is very low (30 % overlap ratio), with 50 % and 70 % overlap ratios the high phase diversity probe always produce better reconstructions results. Bottom: Comparison of real-space R-factors of reconstruction results of high-phase and real-valued probes ratio as a function of degree of coherence σ/L for both object maximum phase = 0 and 2π. Reconstructions are performed with simulated data of 50 % overlap ratio.
Fig. 5
Fig. 5 Results of reconstructed coherence function, parametrized by σ/L, the results are plotted as ratio of reconstructed σ to simulated σ 0 for various degree of coherence, sample complexity and probe phase diversity. Left: with 30% overlap; Right: with 70% overlap in simulated dataset.

Equations (13)

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ψ ^ ( q ) = ψ ^ ( q ) I m ( q ) | ψ ^ ( q ) |
I m ( q ) = J ( r 1 , r 2 ) ψ ( r 1 ) ψ * ( r 2 ) exp [ i q . ( r 1 r 2 ) ] d r 1 d r 2
μ ( Δ x , Δ y ) = μ ( r ) = exp [ ( ( Δ x ) 2 + ( Δ y ) 2 ) / 2 σ 2 ]
I pc ( q ) = I fc ( q ) γ ^ ( q )
ψ ^ ( q ) = ψ ^ ( q ) I m ( q ) | ψ ^ ( q ) | 2 γ ^ ( q )
ψ j k + 1 ( r ) = ψ j k ( r ) + Π pc [ 2 Π o ( ψ j k ( r ) ) ψ j k ( r ) ] Π o ( ψ j k ( r ) )
Π pc = 1 [ ( 2 Π o [ ψ j k ( r ) ] ψ j k ( r ) ) . ( I m j ( q ) | ( 2 Π o [ ψ j k ( r ) ] ψ j k ( r ) ) | 2 γ ^ ( q ) ) ] .
O 0 = L max ( L ) . exp ( i L ϕ max max ( L ) )
R real = Δ n j , Δ m j | O O 0 | 2 Δ n j , Δ m j | O 0 |
P j ( r ) = P ( x + Δ n j Δ ( Θ ) , y + Δ m j Δ ( Θ ) )
γ ^ k , i + 1 ( q ) = γ ^ k , i ( q ) . ( I Δ k ( q ) I m ( q ) I Δ k ( q ) γ ^ k , i ( q ) )
I Δ k ( q ) = 2 | ( 2 Π o [ ψ j k ( r ) ] ψ j k ( r ) ) | 2 | ( 2 Π o [ ψ j k 1 ( r ) ] ψ j k 1 ( r ) ) | 2
E j = | I m j ( q ) | ψ ^ j k ( q ) | 2 γ ^ k , j ( q , σ ^ ) | 2 d q

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