Abstract

We study by numerical simulation how spatial coherence affects the reconstruction quality of images in coherent diffractive x-ray imaging. Using a conceptually simple, but computationally demanding approach, we have simulated diffraction data recorded under partial coherence, and then use the data for iterative reconstruction algorithms using a support constraint. By comparison of experimental regimes and parameters, we observe a significantly higher robustness against partially coherent illumination in the near-field compared to the far-field setting.

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

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References

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    [Crossref] [PubMed]

2017 (4)

J. Hagemann and T. Salditt, “Reconstructing mode mixtures in the optical near-field,” Opt. Express 25, 13973–13969 (2017).
[Crossref] [PubMed]

G. N. Tran, G. A. van Riessen, and A. G. Peele, “Modal approach for partially coherent diffractive imaging with simultaneous sample and coherence recovery,” Opt. Express 25, 10757–10764 (2017).
[Crossref] [PubMed]

J. Hagemann and T. Salditt, “The fluence–resolution relationship in holographic and coherent diffractive imaging,” J. Appl. Crystallogr. 50, 531–538 (2017).
[Crossref] [PubMed]

M. Töpperwien, M. Krenkel, D. Vincenz, F. Stöber, A. M. Oelschlegel, J. Goldschmidt, and T. Salditt, “Three-dimensional mouse brain cytoarchitecture revealed by laboratory-based x-ray phase-contrast tomography,” Sci. Rep. 7, 42847 (2017).
[Crossref] [PubMed]

2016 (4)

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
[Crossref] [PubMed]

M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6, 035007 (2016).
[Crossref]

M. Odstrcil, P. Baksh, S. A. Boden, R. Card, J. E. Chad, J. G. Frey, and W. S. Brocklesby, “Ptychographic coherent diffractive imaging with orthogonal probe relaxation,” Opt. Express 24, 8360 (2016).
[Crossref] [PubMed]

M. Lyubomirskiy, I. Snigireva, and A. Snigirev, “Lens coupled tunable Young’s double pinhole system for hard X-ray spatial coherence characterization,” Opt. Express 24, 13679–13686 (2016).
[Crossref] [PubMed]

2015 (1)

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5, 09973 (2015).
[Crossref]

2014 (2)

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

2013 (1)

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

2012 (1)

B. Chen, B. Abbey, R. Dilanian, E. Balaur, G. van Riessen, M. Junker, C. Q. Tran, M. W. M. Jones, A. G. Peele, I. McNulty, D. J. Vine, C. T. Putkunz, H. M. Quiney, and K. A. Nugent, “Diffraction imaging: The limits of partial coherence,” Phys. Rev. B 86, 235401 (2012).
[Crossref]

2011 (4)

M. Osterhoff and T. Salditt, “Coherence filtering of x-ray waveguides: analytical and numerical approach,” New J. Phys. 13, 103026 (2011).
[Crossref]

T. Salditt, S. Kalbfleisch, M. Osterhoff, S. P. Krüger, M. Bartels, K. Giewekemeyer, H. Neubauer, and M. Sprung, “Partially coherent nano-focused x-ray radiation characterized by Talbot interferometry,” Opt. Express 19, 9656–9675 (2011).
[Crossref] [PubMed]

K. A. Nugent, “The measurement of phase through the propagation of intensity: an introduction,” Contemp. Phys. 52, 55–69 (2011).
[Crossref]

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. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

2010 (2)

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat Photon 4, 833–839 (2010).
[Crossref]

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

2009 (1)

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

2008 (1)

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, 254801 (2008).
[Crossref] [PubMed]

2007 (1)

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, “Effectiveness of iterative algorithms in recovering phase in the presence of noise,” Acta Crystallogr. A 63, 36–42 (2007).
[Crossref]

2006 (1)

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel Coherent Diffractive Imaging,” Phys. Rev. Lett. 97, 025506 (2006).
[Crossref] [PubMed]

2005 (4)

K. A. Nugent, A. G. Peele, H. M. Quiney, and H. N. Chapman, “Diffraction with wavefront curvature: a path to unique phase recovery,” Acta Crystallogr. Sect. A 61, 373–381 (2005).
[Crossref]

D. R. Luke, “Relaxed Averaged Alternating Reflections for Diffraction Imaging,” Inverse Prob. 21, 37 (2005).
[Crossref]

S. Zabler, P. Cloetens, J.-P. Guigay, J. Baruchel, and M. Schlenker, “Optimization of phase contrast imaging using hard x rays,” Rev. Sci. Instrum. 76, 073705 (2005).
[Crossref]

M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” J. Struct. Biol. 151, 250–262 (2005).
[Crossref] [PubMed]

2004 (1)

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

2002 (1)

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, “Propagation of a partially coherent focused X-ray beam within a planar X-ray waveguide,” J. Synchrotron Rad. 9, 383–393 (2002).
[Crossref]

1999 (2)

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

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

1998 (1)

S. K. Sinha, M. Tolan, and A. Gibaud, “Effects of partial coherence on the scattering of x rays by matter,” Phys. Rev. B 57, 2740 (1998).
[Crossref]

1995 (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[Crossref]

1994 (2)

G. Grübel, J. Als-Nielsen, and A. Freund, “The TROIKA beamline at ESRF,” Le J. de Physique IV 4, 9–27 (1994).

T. Salditt, H. Rhan, T. H. Metzger, J. Peisl, R. Schuster, and J. P. Kotthaus, “X-ray coherence and ultra small angle resolution at grazing incidence and exit angles,” Z. Phys. B 96, 227–230 (1994).
[Crossref]

1987 (1)

M. V. Heel, “Angular reconstitution: A posteriori assignment of projection directions for 3d reconstruction,” Ultramicroscopy. 21, 111–123 (1987).
[Crossref] [PubMed]

1982 (1)

Abbey, B.

B. Chen, B. Abbey, R. Dilanian, E. Balaur, G. van Riessen, M. Junker, C. Q. Tran, M. W. M. Jones, A. G. Peele, I. McNulty, D. J. Vine, C. T. Putkunz, H. M. Quiney, and K. A. Nugent, “Diffraction imaging: The limits of partial coherence,” Phys. Rev. B 86, 235401 (2012).
[Crossref]

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. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Als-Nielsen, J.

G. Grübel, J. Als-Nielsen, and A. Freund, “The TROIKA beamline at ESRF,” Le J. de Physique IV 4, 9–27 (1994).

Alves, F.

M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6, 035007 (2016).
[Crossref]

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5, 09973 (2015).
[Crossref]

Baksh, P.

Balaur, E.

B. Chen, B. Abbey, R. Dilanian, E. Balaur, G. van Riessen, M. Junker, C. Q. Tran, M. W. M. Jones, A. G. Peele, I. McNulty, D. J. Vine, C. T. Putkunz, H. M. Quiney, and K. A. Nugent, “Diffraction imaging: The limits of partial coherence,” Phys. Rev. B 86, 235401 (2012).
[Crossref]

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. 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]

Bartels, M.

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5, 09973 (2015).
[Crossref]

T. Salditt, S. Kalbfleisch, M. Osterhoff, S. P. Krüger, M. Bartels, K. Giewekemeyer, H. Neubauer, and M. Sprung, “Partially coherent nano-focused x-ray radiation characterized by Talbot interferometry,” Opt. Express 19, 9656–9675 (2011).
[Crossref] [PubMed]

Baruchel, J.

S. Zabler, P. Cloetens, J.-P. Guigay, J. Baruchel, and M. Schlenker, “Optimization of phase contrast imaging using hard x rays,” Rev. Sci. Instrum. 76, 073705 (2005).
[Crossref]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

Boden, S. A.

Bongaerts, J. H. H.

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, “Propagation of a partially coherent focused X-ray beam within a planar X-ray waveguide,” J. Synchrotron Rad. 9, 383–393 (2002).
[Crossref]

Brocklesby, W. S.

Burvall, A.

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

Butz, T.

T. Butz, Fourier transformation for pedestrians (Springer, 2006).

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. Peele, G. J. Williams, and I. McNulty, “Lensless imaging using broadband X-ray sources,” Nat. Photonics 5, 420–424 (2011).
[Crossref]

Card, R.

Chad, J. E.

Chapman, H. N.

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat Photon 4, 833–839 (2010).
[Crossref]

K. A. Nugent, A. G. Peele, H. M. Quiney, and H. N. Chapman, “Diffraction with wavefront curvature: a path to unique phase recovery,” Acta Crystallogr. Sect. A 61, 373–381 (2005).
[Crossref]

Charalambous, P.

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

Chen, B.

B. Chen, B. Abbey, R. Dilanian, E. Balaur, G. van Riessen, M. Junker, C. Q. Tran, M. W. M. Jones, A. G. Peele, I. McNulty, D. J. Vine, C. T. Putkunz, H. M. Quiney, and K. A. Nugent, “Diffraction imaging: The limits of partial coherence,” Phys. Rev. B 86, 235401 (2012).
[Crossref]

Cloetens, P.

S. Zabler, P. Cloetens, J.-P. Guigay, J. Baruchel, and M. Schlenker, “Optimization of phase contrast imaging using hard x rays,” Rev. Sci. Instrum. 76, 073705 (2005).
[Crossref]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
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A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[Crossref]

Schlenker, M.

S. Zabler, P. Cloetens, J.-P. Guigay, J. Baruchel, and M. Schlenker, “Optimization of phase contrast imaging using hard x rays,” Rev. Sci. Instrum. 76, 073705 (2005).
[Crossref]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

Schuster, R.

T. Salditt, H. Rhan, T. H. Metzger, J. Peisl, R. Schuster, and J. P. Kotthaus, “X-ray coherence and ultra small angle resolution at grazing incidence and exit angles,” Z. Phys. B 96, 227–230 (1994).
[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]

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, 254801 (2008).
[Crossref] [PubMed]

Sinha, S. K.

S. K. Sinha, M. Tolan, and A. Gibaud, “Effects of partial coherence on the scattering of x rays by matter,” Phys. Rev. B 57, 2740 (1998).
[Crossref]

Snigirev, A.

M. Lyubomirskiy, I. Snigireva, and A. Snigirev, “Lens coupled tunable Young’s double pinhole system for hard X-ray spatial coherence characterization,” Opt. Express 24, 13679–13686 (2016).
[Crossref] [PubMed]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[Crossref]

Snigireva, I.

M. Lyubomirskiy, I. Snigireva, and A. Snigirev, “Lens coupled tunable Young’s double pinhole system for hard X-ray spatial coherence characterization,” Opt. Express 24, 13679–13686 (2016).
[Crossref] [PubMed]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[Crossref]

Spence, J. C. H.

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

J. C. H. Spence, High-Resolution Electron Microscopy (Oxford University, 2013).
[Crossref]

Sprung, M.

Starikov, A.

Stöber, F.

M. Töpperwien, M. Krenkel, D. Vincenz, F. Stöber, A. M. Oelschlegel, J. Goldschmidt, and T. Salditt, “Three-dimensional mouse brain cytoarchitecture revealed by laboratory-based x-ray phase-contrast tomography,” Sci. Rep. 7, 42847 (2017).
[Crossref] [PubMed]

Thibault, P.

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

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

Tolan, M.

S. K. Sinha, M. Tolan, and A. Gibaud, “Effects of partial coherence on the scattering of x rays by matter,” Phys. Rev. B 57, 2740 (1998).
[Crossref]

Töpperwien, M.

M. Töpperwien, M. Krenkel, D. Vincenz, F. Stöber, A. M. Oelschlegel, J. Goldschmidt, and T. Salditt, “Three-dimensional mouse brain cytoarchitecture revealed by laboratory-based x-ray phase-contrast tomography,” Sci. Rep. 7, 42847 (2017).
[Crossref] [PubMed]

M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6, 035007 (2016).
[Crossref]

Tran, C. Q.

B. Chen, B. Abbey, R. Dilanian, E. Balaur, G. van Riessen, M. Junker, C. Q. Tran, M. W. M. Jones, A. G. Peele, I. McNulty, D. J. Vine, C. T. Putkunz, H. M. Quiney, and K. A. Nugent, “Diffraction imaging: The limits of partial coherence,” Phys. Rev. B 86, 235401 (2012).
[Crossref]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel Coherent Diffractive Imaging,” Phys. Rev. Lett. 97, 025506 (2006).
[Crossref] [PubMed]

Tran, G. N.

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, 254801 (2008).
[Crossref] [PubMed]

Vågberg, W.

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
[Crossref] [PubMed]

van der Veen, J. F.

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, “Propagation of a partially coherent focused X-ray beam within a planar X-ray waveguide,” J. Synchrotron Rad. 9, 383–393 (2002).
[Crossref]

Van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

van Heel, M.

M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” J. Struct. Biol. 151, 250–262 (2005).
[Crossref] [PubMed]

Van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
[Crossref]

van Riessen, G.

B. Chen, B. Abbey, R. Dilanian, E. Balaur, G. van Riessen, M. Junker, C. Q. Tran, M. W. M. Jones, A. G. Peele, I. McNulty, D. J. Vine, C. T. Putkunz, H. M. Quiney, and K. A. Nugent, “Diffraction imaging: The limits of partial coherence,” Phys. Rev. B 86, 235401 (2012).
[Crossref]

van Riessen, G. A.

Vartanyants, I.

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, “Effectiveness of iterative algorithms in recovering phase in the presence of noise,” Acta Crystallogr. A 63, 36–42 (2007).
[Crossref]

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, 254801 (2008).
[Crossref] [PubMed]

Vincenz, D.

M. Töpperwien, M. Krenkel, D. Vincenz, F. Stöber, A. M. Oelschlegel, J. Goldschmidt, and T. Salditt, “Three-dimensional mouse brain cytoarchitecture revealed by laboratory-based x-ray phase-contrast tomography,” Sci. Rep. 7, 42847 (2017).
[Crossref] [PubMed]

Vine, D. J.

B. Chen, B. Abbey, R. Dilanian, E. Balaur, G. van Riessen, M. Junker, C. Q. Tran, M. W. M. Jones, A. G. Peele, I. McNulty, D. J. Vine, C. T. Putkunz, H. M. Quiney, and K. A. Nugent, “Diffraction imaging: The limits of partial coherence,” Phys. Rev. B 86, 235401 (2012).
[Crossref]

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. 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]

Wegdam, G. H.

J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, “Propagation of a partially coherent focused X-ray beam within a planar X-ray waveguide,” J. Synchrotron Rad. 9, 383–393 (2002).
[Crossref]

Weierstall, U.

J. C. H. Spence, U. Weierstall, and M. Howells, “Coherence and sampling requirements for diffractive imaging,” Ultramicroscopy. 101, 149–152 (2004).
[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. 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.

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, “Effectiveness of iterative algorithms in recovering phase in the presence of noise,” Acta Crystallogr. A 63, 36–42 (2007).
[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. 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]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel Coherent Diffractive Imaging,” Phys. Rev. Lett. 97, 025506 (2006).
[Crossref] [PubMed]

Wolf, E.

Yaroshenko, A.

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
[Crossref] [PubMed]

Yildirim, A. Ö.

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
[Crossref] [PubMed]

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S. Zabler, P. Cloetens, J.-P. Guigay, J. Baruchel, and M. Schlenker, “Optimization of phase contrast imaging using hard x rays,” Rev. Sci. Instrum. 76, 073705 (2005).
[Crossref]

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

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

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

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J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, “Propagation of a partially coherent focused X-ray beam within a planar X-ray waveguide,” J. Synchrotron Rad. 9, 383–393 (2002).
[Crossref]

Acta Crystallogr. A (1)

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, “Effectiveness of iterative algorithms in recovering phase in the presence of noise,” Acta Crystallogr. A 63, 36–42 (2007).
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M. Krenkel, M. Töpperwien, C. Dullin, F. Alves, and T. Salditt, “Propagation-based phase-contrast tomography for high-resolution lung imaging with laboratory sources,” AIP Adv. 6, 035007 (2016).
[Crossref]

Appl. Phys. Lett. (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett. 75, 2912–2914 (1999).
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M. van Heel and M. Schatz, “Fourier shell correlation threshold criteria,” J. Struct. Biol. 151, 250–262 (2005).
[Crossref] [PubMed]

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J. H. H. Bongaerts, C. David, M. Drakopoulos, M. J. Zwanenburg, G. H. Wegdam, T. Lackner, H. Keymeulen, and J. F. van der Veen, “Propagation of a partially coherent focused X-ray beam within a planar X-ray waveguide,” J. Synchrotron Rad. 9, 383–393 (2002).
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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. 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).
[Crossref] [PubMed]

Nature. (1)

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Phys. Rev. A (1)

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]

Phys. Rev. B (2)

B. Chen, B. Abbey, R. Dilanian, E. Balaur, G. van Riessen, M. Junker, C. Q. Tran, M. W. M. Jones, A. G. Peele, I. McNulty, D. J. Vine, C. T. Putkunz, H. M. Quiney, and K. A. Nugent, “Diffraction imaging: The limits of partial coherence,” Phys. Rev. B 86, 235401 (2012).
[Crossref]

S. K. Sinha, M. Tolan, and A. Gibaud, “Effects of partial coherence on the scattering of x rays by matter,” Phys. Rev. B 57, 2740 (1998).
[Crossref]

Phys. Rev. Lett. (4)

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, 254801 (2008).
[Crossref] [PubMed]

L. W. Whitehead, G. J. Williams, H. M. Quiney, D. J. Vine, R. A. Dilanian, S. Flewett, K. A. Nugent, A. G. Peele, E. Balaur, and I. McNulty, “Diffractive Imaging Using Partially Coherent X Rays,” Phys. Rev. Lett. 103, 243902 (2009).
[Crossref]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel Coherent Diffractive Imaging,” Phys. Rev. Lett. 97, 025506 (2006).
[Crossref] [PubMed]

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

Rev. Sci. Instrum. (2)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[Crossref]

S. Zabler, P. Cloetens, J.-P. Guigay, J. Baruchel, and M. Schlenker, “Optimization of phase contrast imaging using hard x rays,” Rev. Sci. Instrum. 76, 073705 (2005).
[Crossref]

Sci. Rep. (3)

M. Krenkel, A. Markus, M. Bartels, C. Dullin, F. Alves, and T. Salditt, “Phase-contrast zoom tomography reveals precise locations of macrophages in mouse lungs,” Sci. Rep. 5, 09973 (2015).
[Crossref]

M. Töpperwien, M. Krenkel, D. Vincenz, F. Stöber, A. M. Oelschlegel, J. Goldschmidt, and T. Salditt, “Three-dimensional mouse brain cytoarchitecture revealed by laboratory-based x-ray phase-contrast tomography,” Sci. Rep. 7, 42847 (2017).
[Crossref] [PubMed]

D. H. Larsson, W. Vågberg, A. Yaroshenko, A. Ö. Yildirim, and H. M. Hertz, “High-resolution short-exposure small-animal laboratory x-ray phase-contrast tomography,” Sci. Rep. 6, 39074 (2016).
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Figures (7)

Fig. 1
Fig. 1 Schematic and notation for the coherence model. Plane waves are emitted by an incoherent source with extension d. An object is placed at distance R behind the source. This setting defines the lateral coherence length ξ = λR/(2d) in the object plane, expressed in pixel units for the simulation. Plane waves are then simulated to impinge on the object with random wave vectors out of a cone with opening angle θc. For each realisation, the diffraction pattern of the phantom object (see Fig. 2) is calculated both for the near- and far-field, i.e. for NFH and CDI, respectively. The diffraction patterns are then added up incoherently, providing the input data for the reconstruction. Note that this model of partial coherence essentially corresponds to a convolution of the diffraction pattern with an effective point-spread function in the detection plane. In the simulation however, the data is not generated by a convolution but by different stochastic realisations.
Fig. 2
Fig. 2 Setup for the simulation: limit of full coherence. (a) The pure phase phantom of a cell with maximum phase shift of −1 rad. The red line indicates the support used in the reconstruction. (b) The corresponding ideal near-field hologram for Fr = 10−3. (c) The corresponding ideal far-field measurement. The diffraction pattern simulated under partially settings are presented in Fig. 3. Scalebar: 50 px.
Fig. 3
Fig. 3 Reconstructions from measurements with finite coherence length ξ. The measurements are presented for (a) NFH and (c) CDI, with each panel showing on the left half the fully coherent measurement and on the right half the measurement obtained for the finite ξ as given in the title of the panel. The partially coherent CDI measurements have a virtual beam stop covering the zeroth order. The NFH measurement are shown on linear scale and the CDI measurement on logarithmic scale. The corresponding reconstructions are shown in (b) for NFH and (d) for CDI. The number in the upper right corner of each panel denotes the resolution Δr in 1/px. The scalebar indicates 50 px in all panels.
Fig. 4
Fig. 4 CDI reconstruction without the virtual beam stop. (a) The simulated measurement for ξ = 500 px (a) and (b) the corresponding reconstructed objet.
Fig. 5
Fig. 5 Image quality as a function of coherence length ξ. (a) Resolution as a function of ξ. (b) The 2 error (Eq. (14)) with respect to the original phantom, as a function of ξ. Curves are shown for NFH (blue) and CDI (red). ξ was varied between 20 to 900 px. Results were obtained by averaging of 20 reconstructions for each ξ. Each reconstruction started from a new measurement generated from 5000 source realizations.
Fig. 6
Fig. 6 ξ-resolution relationship for different setup parameters, namely (a) Fresnel number Fr and (b) object size L, for (a) NFH and (b) CDI, respectively The NFH results in (a) show that a smaller Fr requires a larger ξ for a high resolution reconstruction. The CDI result in (b) show that objects with larger size L require a higher degree of coherence in the illumination to reach high resolution in the reconstruction. In both settings, NR = 5000 and 20 realizations per ξ have been used.
Fig. 7
Fig. 7 Resolution as function of ξ at varied fluence μ (photons per pixel). (a) results for NFH and (b) for CDI. Note that (a) and (b) do not show exactly the same choice of μ. Also the sampling of ξ’s was adapted to the respective method. The dashed lines indicate the noise free result for comparison, from Fig. 5(a).

Tables (1)

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Algorithm 1 Generation of of partially coherent measurements using sub-pixel shifts.

Equations (14)

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ξ = λ 2 R d = λ 2 1 θ c ,
q ( α ) = 2 π λ sin ( α ) .
q = π ζ 2 ξ ,
Ψ α = P α O ,
M = n R = 1 N R 𝒳 ( Ψ α ) 2 .
𝒟 Fr ( Ψ ) = 1 [ [ Ψ ] exp ( ( i π ) / ( 2 Fr ) ( k x 2 + k y 2 ) ) ] ,
P α = exp ( i ( α x r x + α y r y ) ) ,
Δ s FF = α x , y N x , y ( pixels ) .
Δ s NF = α x , y 1 Fr ( pixels ) .
Ψ n + 1 = β n 2 ( R S ( R M ( Ψ n ) ) + Ψ n ) + ( 1 β n ) P M ( Ψ n ) ,
β n = exp ( ( n / β s ) 3 ) β 0 + [ 1 exp ( ( n / β s ) 3 ) ] β max ,
P M ( Ψ ) 𝒳 1 { M 1 / 2 exp ( i arg [ 𝒳 ( Ψ m ) ] ) } ,
P S ( Ψ n ) = { exp ( i arg ( Ψ n ) ) for pixel S exp ( i 0 ) for pixel S
Δ = pixels S arg ( phantom ) arg ( reconstruction ) 2 .

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