Abstract

We present a quantitative, non-interferometric, X-ray differential phase contrast imaging technique based on the edge illumination principle. We derive a novel phase retrieval algorithm which requires only two images to be acquired and verify the technique experimentally using synchrotron radiation. The technique is useful for planar imaging but is expected to be important for quantitative phase tomography also. The properties and limitations of the technique are studied in detail.

© 2012 OSA

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  1. U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett.6(8), 155–156 (1965).
    [CrossRef]
  2. T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature373(6515), 595–598 (1995).
    [CrossRef]
  3. A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Meth. A352(3), 622 – 628 (1995).
    [CrossRef]
  4. 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(12), 5486–5492 (1995).
    [CrossRef]
  5. D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).
  6. P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, “Phase objects in synchrotron radiation hard X-ray imaging,” J. Phys. D Appl. Phys.29, 133–146 (1996).
    [CrossRef]
  7. D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
    [CrossRef] [PubMed]
  8. D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun.234, 87 – 105 (2004).
    [CrossRef]
  9. Y. I. Nesterets, T. Gureyev, D. Paganin, K. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D Appl. Phys.37(8), 1262–1274 (2004).
    [CrossRef]
  10. M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper, and K. M. Pavlov, “X-ray phase, absorption and scatter retrieval using two or more phase contrast images,” Opt. Express18(19), 19,994–20,012 (2010).
    [CrossRef]
  11. P. C. Diemoz, P. Coan, C. Glaser, and A. Bravin, “Absorption, refraction and scattering in analyzer-based imaging: comparison of different algorithms,” Opt. Express18, 3494–3509 (2010).
    [CrossRef] [PubMed]
  12. D. J. Vine, D. M. Paganin, K. M. Pavlov, J. Kraeusslich, O. Wehrhan, I. Uschmann, and E. Foerster, “Analyzer-based phase contrast imaging and phase retrieval using a rotating anode X-ray source,” Appl. Phys. Lett.91(25), 254110 (2007).
    [CrossRef]
  13. S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384, 335–338 (1996).
    [CrossRef]
  14. K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett.77, 2961–2964 (1996).
    [CrossRef] [PubMed]
  15. P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett.75(19), 2912–2914 (1999).
    [CrossRef]
  16. T. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. Wilkins, “Hard X-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys.32(5), 563–567 (1999).
    [CrossRef]
  17. D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc.-Oxford206, 33–40 (2002).
    [CrossRef]
  18. T. Gureyev, A. Pogany, D. Paganin, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region,” Opt. Commun.231, 53–70 (2004).
    [CrossRef]
  19. T. Gureyev, Y. Ne, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun.259, 569–580 (2005).
    [CrossRef]
  20. K. Nugent, “The measurement of phase through the propagation of intensity: an introduction,” Contemp. Phys.52, 55–69 (2011).
    [CrossRef]
  21. K. Creath, “Phase-measurement interferometry techniques,” Prog. OpticsXXVI, 349–393 (1988).
    [CrossRef]
  22. A. Lohmann and D. Silva, “An interferometer based on the Talbot effect,” Opt. Commun.2(9), 413–415 (1971).
    [CrossRef]
  23. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005).
    [CrossRef] [PubMed]
  24. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys.42(Part 2, No. 7B), L866–L868 (2003).
    [CrossRef]
  25. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
    [CrossRef]
  26. P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010).
    [CrossRef]
  27. T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009).
    [CrossRef]
  28. A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
    [CrossRef] [PubMed]
  29. P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Source size and temporal coherence requirements of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(19), 19681–19692 (2010).
    [CrossRef]
  30. Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard X-rays,” Phys. Rev. A79(1), 013815 (2009).
    [CrossRef]
  31. A. Olivo and R. Speller, “A coded-aperture technique allowing X-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett.91(7), 074106 (2007).
    [CrossRef]
  32. A. Olivo and R. Speller, “Modelling of a novel X-ray phase contrast imaging technique based on coded apertures,” Phys. Med. Biol.52(22), 6555–6573 (2007).
    [CrossRef] [PubMed]
  33. P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U. S. A.109, 13,922–13,927 (2012).
    [CrossRef]
  34. A. Olivo and R. Speller, “Image formation principles in coded-aperture based X-ray phase contrast imaging,” Phys. Med. Biol.53(22), 6461–6474 (2008).
    [CrossRef] [PubMed]
  35. A. Olivo, S. E. Bohndiek, J. A. Griffiths, A. Konstantinidis, and R. D. Speller, “A non-free-space propagation X-ray phase contrast imaging method sensitive to phase effects in two directions simultaneously,” Appl. Phys. Lett.94(4), 044108 (2009).
    [CrossRef]
  36. P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Design of a novel phase contrast X-ray imaging system for mammography,” Phys. Med. Biol.55(14), 4169–4185 (2010).
    [CrossRef] [PubMed]
  37. G. James, Geometrical theory of diffraction for electromagnetic waves (Peter Peregrinus Ltd., 1976).
  38. P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “The relationship between wave and geometrical optics models of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(5), 4103–4117 (2010).
    [CrossRef] [PubMed]
  39. F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
    [CrossRef]
  40. A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
    [CrossRef]
  41. L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
    [CrossRef]
  42. L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
    [CrossRef]
  43. F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011).
    [CrossRef]
  44. B. Henke, E. Gullikson, and J. Davis, “X-Ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” Atom. Data Nucl. Data54(2), 181 – 342 (1993).
    [CrossRef]

2012 (1)

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U. S. A.109, 13,922–13,927 (2012).
[CrossRef]

2011 (2)

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

F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011).
[CrossRef]

2010 (7)

L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
[CrossRef]

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010).
[CrossRef]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Design of a novel phase contrast X-ray imaging system for mammography,” Phys. Med. Biol.55(14), 4169–4185 (2010).
[CrossRef] [PubMed]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “The relationship between wave and geometrical optics models of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(5), 4103–4117 (2010).
[CrossRef] [PubMed]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Source size and temporal coherence requirements of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(19), 19681–19692 (2010).
[CrossRef]

M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper, and K. M. Pavlov, “X-ray phase, absorption and scatter retrieval using two or more phase contrast images,” Opt. Express18(19), 19,994–20,012 (2010).
[CrossRef]

P. C. Diemoz, P. Coan, C. Glaser, and A. Bravin, “Absorption, refraction and scattering in analyzer-based imaging: comparison of different algorithms,” Opt. Express18, 3494–3509 (2010).
[CrossRef] [PubMed]

2009 (4)

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard X-rays,” Phys. Rev. A79(1), 013815 (2009).
[CrossRef]

T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009).
[CrossRef]

L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
[CrossRef]

A. Olivo, S. E. Bohndiek, J. A. Griffiths, A. Konstantinidis, and R. D. Speller, “A non-free-space propagation X-ray phase contrast imaging method sensitive to phase effects in two directions simultaneously,” Appl. Phys. Lett.94(4), 044108 (2009).
[CrossRef]

2008 (1)

A. Olivo and R. Speller, “Image formation principles in coded-aperture based X-ray phase contrast imaging,” Phys. Med. Biol.53(22), 6461–6474 (2008).
[CrossRef] [PubMed]

2007 (3)

A. Olivo and R. Speller, “A coded-aperture technique allowing X-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett.91(7), 074106 (2007).
[CrossRef]

A. Olivo and R. Speller, “Modelling of a novel X-ray phase contrast imaging technique based on coded apertures,” Phys. Med. Biol.52(22), 6555–6573 (2007).
[CrossRef] [PubMed]

D. J. Vine, D. M. Paganin, K. M. Pavlov, J. Kraeusslich, O. Wehrhan, I. Uschmann, and E. Foerster, “Analyzer-based phase contrast imaging and phase retrieval using a rotating anode X-ray source,” Appl. Phys. Lett.91(25), 254110 (2007).
[CrossRef]

2006 (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
[CrossRef]

2005 (3)

T. Gureyev, Y. Ne, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun.259, 569–580 (2005).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

2004 (3)

T. Gureyev, A. Pogany, D. Paganin, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region,” Opt. Commun.231, 53–70 (2004).
[CrossRef]

D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun.234, 87 – 105 (2004).
[CrossRef]

Y. I. Nesterets, T. Gureyev, D. Paganin, K. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D Appl. Phys.37(8), 1262–1274 (2004).
[CrossRef]

2003 (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys.42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

2002 (1)

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc.-Oxford206, 33–40 (2002).
[CrossRef]

2001 (1)

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
[CrossRef] [PubMed]

1999 (2)

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett.75(19), 2912–2914 (1999).
[CrossRef]

T. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. Wilkins, “Hard X-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys.32(5), 563–567 (1999).
[CrossRef]

1997 (1)

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

1996 (4)

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).

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

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384, 335–338 (1996).
[CrossRef]

K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett.77, 2961–2964 (1996).
[CrossRef] [PubMed]

1995 (4)

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature373(6515), 595–598 (1995).
[CrossRef]

A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Meth. A352(3), 622 – 628 (1995).
[CrossRef]

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(12), 5486–5492 (1995).
[CrossRef]

F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
[CrossRef]

1993 (1)

B. Henke, E. Gullikson, and J. Davis, “X-Ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” Atom. Data Nucl. Data54(2), 181 – 342 (1993).
[CrossRef]

1988 (1)

K. Creath, “Phase-measurement interferometry techniques,” Prog. OpticsXXVI, 349–393 (1988).
[CrossRef]

1971 (1)

A. Lohmann and D. Silva, “An interferometer based on the Talbot effect,” Opt. Commun.2(9), 413–415 (1971).
[CrossRef]

1965 (1)

U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett.6(8), 155–156 (1965).
[CrossRef]

Abrami, A.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Allison, B. J.

M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper, and K. M. Pavlov, “X-ray phase, absorption and scatter retrieval using two or more phase contrast images,” Opt. Express18(19), 19,994–20,012 (2010).
[CrossRef]

Arfelli, F.

F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011).
[CrossRef]

L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
[CrossRef]

L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
[CrossRef]

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).

F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
[CrossRef]

Astolfo, A.

L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
[CrossRef]

Barbiellini, G.

F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
[CrossRef]

Barnea, Z.

K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett.77, 2961–2964 (1996).
[CrossRef] [PubMed]

Barrett, R.

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

Barroso, R.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett.75(19), 2912–2914 (1999).
[CrossRef]

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

Bergamaschi, A.

F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011).
[CrossRef]

L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
[CrossRef]

L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
[CrossRef]

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Bernstorff, S.

F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
[CrossRef]

Bille, F.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Bohndiek, S. E.

A. Olivo, S. E. Bohndiek, J. A. Griffiths, A. Konstantinidis, and R. D. Speller, “A non-free-space propagation X-ray phase contrast imaging method sensitive to phase effects in two directions simultaneously,” Appl. Phys. Lett.94(4), 044108 (2009).
[CrossRef]

Bonse, U.

U. Bonse and M. Hart, “An X-ray interferometer,” Appl. Phys. Lett.6(8), 155–156 (1965).
[CrossRef]

Bravin, A.

P. C. Diemoz, P. Coan, C. Glaser, and A. Bravin, “Absorption, refraction and scattering in analyzer-based imaging: comparison of different algorithms,” Opt. Express18, 3494–3509 (2010).
[CrossRef] [PubMed]

F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
[CrossRef]

Bregant, P.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Brizzi, F.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Bunk, O.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
[CrossRef]

Cantatore, G.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
[CrossRef] [PubMed]

F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
[CrossRef]

Casarin, K.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Castelli, E.

F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011).
[CrossRef]

L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
[CrossRef]

L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
[CrossRef]

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
[CrossRef] [PubMed]

F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
[CrossRef]

Chapman, D.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).

Chen, R. C.

F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011).
[CrossRef]

L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
[CrossRef]

Chen, Z.-Q.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard X-rays,” Phys. Rev. A79(1), 013815 (2009).
[CrossRef]

Chenda, V.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Cloetens, P.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett.75(19), 2912–2914 (1999).
[CrossRef]

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

Coan, P.

Cookson, D.

K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett.77, 2961–2964 (1996).
[CrossRef] [PubMed]

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” Prog. OpticsXXVI, 349–393 (1988).
[CrossRef]

David, C.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Davis, J.

B. Henke, E. Gullikson, and J. Davis, “X-Ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” Atom. Data Nucl. Data54(2), 181 – 342 (1993).
[CrossRef]

Davis, T.

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature373(6515), 595–598 (1995).
[CrossRef]

Diaz, A.

Diemoz, P. C.

Ding, F.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard X-rays,” Phys. Rev. A79(1), 013815 (2009).
[CrossRef]

Dreossi, D.

F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011).
[CrossRef]

L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
[CrossRef]

L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
[CrossRef]

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Fang, Q.-G.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard X-rays,” Phys. Rev. A79(1), 013815 (2009).
[CrossRef]

Fava, A.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
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Foerster, E.

D. J. Vine, D. M. Paganin, K. M. Pavlov, J. Kraeusslich, O. Wehrhan, I. Uschmann, and E. Foerster, “Analyzer-based phase contrast imaging and phase retrieval using a rotating anode X-ray source,” Appl. Phys. Lett.91(25), 254110 (2007).
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Gao, D.

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384, 335–338 (1996).
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T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature373(6515), 595–598 (1995).
[CrossRef]

Glaser, C.

Gmür, N.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).

Griffiths, J. A.

A. Olivo, S. E. Bohndiek, J. A. Griffiths, A. Konstantinidis, and R. D. Speller, “A non-free-space propagation X-ray phase contrast imaging method sensitive to phase effects in two directions simultaneously,” Appl. Phys. Lett.94(4), 044108 (2009).
[CrossRef]

Guigay, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett.75(19), 2912–2914 (1999).
[CrossRef]

Guigay, J.-P.

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

Gullikson, E.

B. Henke, E. Gullikson, and J. Davis, “X-Ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” Atom. Data Nucl. Data54(2), 181 – 342 (1993).
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Gureyev, T.

T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009).
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T. Gureyev, Y. Ne, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun.259, 569–580 (2005).
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T. Gureyev, A. Pogany, D. Paganin, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region,” Opt. Commun.231, 53–70 (2004).
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Y. I. Nesterets, T. Gureyev, D. Paganin, K. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D Appl. Phys.37(8), 1262–1274 (2004).
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D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc.-Oxford206, 33–40 (2002).
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T. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. Wilkins, “Hard X-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys.32(5), 563–567 (1999).
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K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett.77, 2961–2964 (1996).
[CrossRef] [PubMed]

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384, 335–338 (1996).
[CrossRef]

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature373(6515), 595–598 (1995).
[CrossRef]

Gureyev, T. E.

D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun.234, 87 – 105 (2004).
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A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys.42(Part 2, No. 7B), L866–L868 (2003).
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M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper, and K. M. Pavlov, “X-ray phase, absorption and scatter retrieval using two or more phase contrast images,” Opt. Express18(19), 19,994–20,012 (2010).
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A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys.42(Part 2, No. 7B), L866–L868 (2003).
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D. J. Vine, D. M. Paganin, K. M. Pavlov, J. Kraeusslich, O. Wehrhan, I. Uschmann, and E. Foerster, “Analyzer-based phase contrast imaging and phase retrieval using a rotating anode X-ray source,” Appl. Phys. Lett.91(25), 254110 (2007).
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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(12), 5486–5492 (1995).
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M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper, and K. M. Pavlov, “X-ray phase, absorption and scatter retrieval using two or more phase contrast images,” Opt. Express18(19), 19,994–20,012 (2010).
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D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun.234, 87 – 105 (2004).
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P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010).
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L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
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L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
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A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
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A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
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F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
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Lopez, F. C.

F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011).
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P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett.75(19), 2912–2914 (1999).
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A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Marone, F.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010).
[CrossRef]

Mayo, S.

T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009).
[CrossRef]

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc.-Oxford206, 33–40 (2002).
[CrossRef]

McDonald, S. A.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010).
[CrossRef]

Menk, R.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).

Menk, R. H.

L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
[CrossRef]

Menk, R.-H.

L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
[CrossRef]

Michiel, M. D.

F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
[CrossRef]

Miller, P.

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc.-Oxford206, 33–40 (2002).
[CrossRef]

Momose, A.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys.42(Part 2, No. 7B), L866–L868 (2003).
[CrossRef]

A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Meth. A352(3), 622 – 628 (1995).
[CrossRef]

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A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Munro, P.

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U. S. A.109, 13,922–13,927 (2012).
[CrossRef]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Design of a novel phase contrast X-ray imaging system for mammography,” Phys. Med. Biol.55(14), 4169–4185 (2010).
[CrossRef] [PubMed]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Source size and temporal coherence requirements of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(19), 19681–19692 (2010).
[CrossRef]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “The relationship between wave and geometrical optics models of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(5), 4103–4117 (2010).
[CrossRef] [PubMed]

Myers, D.

T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009).
[CrossRef]

Ne, Y.

T. Gureyev, Y. Ne, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun.259, 569–580 (2005).
[CrossRef]

Nesterets, Y.

T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009).
[CrossRef]

Nesterets, Y. I.

Y. I. Nesterets, T. Gureyev, D. Paganin, K. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D Appl. Phys.37(8), 1262–1274 (2004).
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K. Nugent, “The measurement of phase through the propagation of intensity: an introduction,” Contemp. Phys.52, 55–69 (2011).
[CrossRef]

K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett.77, 2961–2964 (1996).
[CrossRef] [PubMed]

Olivo, A.

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U. S. A.109, 13,922–13,927 (2012).
[CrossRef]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Source size and temporal coherence requirements of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(19), 19681–19692 (2010).
[CrossRef]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Design of a novel phase contrast X-ray imaging system for mammography,” Phys. Med. Biol.55(14), 4169–4185 (2010).
[CrossRef] [PubMed]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “The relationship between wave and geometrical optics models of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(5), 4103–4117 (2010).
[CrossRef] [PubMed]

A. Olivo, S. E. Bohndiek, J. A. Griffiths, A. Konstantinidis, and R. D. Speller, “A non-free-space propagation X-ray phase contrast imaging method sensitive to phase effects in two directions simultaneously,” Appl. Phys. Lett.94(4), 044108 (2009).
[CrossRef]

A. Olivo and R. Speller, “Image formation principles in coded-aperture based X-ray phase contrast imaging,” Phys. Med. Biol.53(22), 6461–6474 (2008).
[CrossRef] [PubMed]

A. Olivo and R. Speller, “A coded-aperture technique allowing X-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett.91(7), 074106 (2007).
[CrossRef]

A. Olivo and R. Speller, “Modelling of a novel X-ray phase contrast imaging technique based on coded apertures,” Phys. Med. Biol.52(22), 6555–6573 (2007).
[CrossRef] [PubMed]

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
[CrossRef] [PubMed]

Paganin, D.

T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009).
[CrossRef]

T. Gureyev, Y. Ne, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun.259, 569–580 (2005).
[CrossRef]

T. Gureyev, A. Pogany, D. Paganin, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region,” Opt. Commun.231, 53–70 (2004).
[CrossRef]

D. Paganin, T. E. Gureyev, K. M. Pavlov, R. A. Lewis, and M. Kitchen, “Phase retrieval using coherent imaging systems with linear transfer functions,” Opt. Commun.234, 87 – 105 (2004).
[CrossRef]

Y. I. Nesterets, T. Gureyev, D. Paganin, K. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D Appl. Phys.37(8), 1262–1274 (2004).
[CrossRef]

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc.-Oxford206, 33–40 (2002).
[CrossRef]

K. Nugent, T. Gureyev, D. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Phys. Rev. Lett.77, 2961–2964 (1996).
[CrossRef] [PubMed]

Paganin, D. M.

M. J. Kitchen, D. M. Paganin, K. Uesugi, B. J. Allison, R. A. Lewis, S. B. Hooper, and K. M. Pavlov, “X-ray phase, absorption and scatter retrieval using two or more phase contrast images,” Opt. Express18(19), 19,994–20,012 (2010).
[CrossRef]

D. J. Vine, D. M. Paganin, K. M. Pavlov, J. Kraeusslich, O. Wehrhan, I. Uschmann, and E. Foerster, “Analyzer-based phase contrast imaging and phase retrieval using a rotating anode X-ray source,” Appl. Phys. Lett.91(25), 254110 (2007).
[CrossRef]

Palma, L.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Palma, L. D.

F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
[CrossRef]

Pani, S.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
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A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
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A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
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L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
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L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
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A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
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F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
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F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
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D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
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D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).

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T. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. Wilkins, “Hard X-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys.32(5), 563–567 (1999).
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T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009).
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A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
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A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
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D. J. Vine, D. M. Paganin, K. M. Pavlov, J. Kraeusslich, O. Wehrhan, I. Uschmann, and E. Foerster, “Analyzer-based phase contrast imaging and phase retrieval using a rotating anode X-ray source,” Appl. Phys. Lett.91(25), 254110 (2007).
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F. Arfelli, A. Bravin, G. Barbiellini, G. Cantatore, E. Castelli, M. D. Michiel, P. Poropat, R. Rosei, M. Sessa, A. Vacchi, L. D. Palma, R. Longo, S. Bernstorff, A. Savoia, and G. Tromba, “Digital mammography with synchrotron radiation,” Rev. Sci. Instrum.66(2), 1325–1328 (1995).
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F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011).
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L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
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L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
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A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
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A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
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D. J. Vine, D. M. Paganin, K. M. Pavlov, J. Kraeusslich, O. Wehrhan, I. Uschmann, and E. Foerster, “Analyzer-based phase contrast imaging and phase retrieval using a rotating anode X-ray source,” Appl. Phys. Lett.91(25), 254110 (2007).
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P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010).
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Washburn, D.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).

Wehrhan, O.

D. J. Vine, D. M. Paganin, K. M. Pavlov, J. Kraeusslich, O. Wehrhan, I. Uschmann, and E. Foerster, “Analyzer-based phase contrast imaging and phase retrieval using a rotating anode X-ray source,” Appl. Phys. Lett.91(25), 254110 (2007).
[CrossRef]

Weitkamp, T.

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Wilkins, S.

T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009).
[CrossRef]

T. Gureyev, Y. Ne, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun.259, 569–580 (2005).
[CrossRef]

T. Gureyev, A. Pogany, D. Paganin, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region,” Opt. Commun.231, 53–70 (2004).
[CrossRef]

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc.-Oxford206, 33–40 (2002).
[CrossRef]

T. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. Wilkins, “Hard X-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys.32(5), 563–567 (1999).
[CrossRef]

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384, 335–338 (1996).
[CrossRef]

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature373(6515), 595–598 (1995).
[CrossRef]

Wilkins, S. W.

Y. I. Nesterets, T. Gureyev, D. Paganin, K. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D Appl. Phys.37(8), 1262–1274 (2004).
[CrossRef]

Wu, Z.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010).
[CrossRef]

Zanconati, F.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Zanetti, A.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Zanini, F.

A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

Zhang, K.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010).
[CrossRef]

Zhang, L.

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard X-rays,” Phys. Rev. A79(1), 013815 (2009).
[CrossRef]

Zhong, Z.

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).

Zhu, P.

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010).
[CrossRef]

Ziegler, E.

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[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. Van Dyck, J. Van Landuyt, J. Guigay, and M. Schlenker, “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett.75(19), 2912–2914 (1999).
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B. Henke, E. Gullikson, and J. Davis, “X-Ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92,” Atom. Data Nucl. Data54(2), 181 – 342 (1993).
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Contemp. Phys. (1)

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

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T. Gureyev, S. Mayo, D. Myers, Y. Nesterets, D. Paganin, A. Pogany, A. Stevenson, and S. Wilkins, “Refracting Rontgen’s rays: propagation-based X-ray phase contrast for biomedical imaging,” J. Appl. Phys.105(10), 102005 (2009).
[CrossRef]

J. Instrum. (1)

F. C. Lopez, L. Rigon, R. Longo, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, B. Schmitt, E. Vallazza, and E. Castelli, “Development of a fast read-out system of a single photon counting detector for mammography with synchrotron radiation,” J. Instrum.6, C12031 (2011).
[CrossRef]

J. Microsc.-Oxford (1)

D. Paganin, S. Mayo, T. Gureyev, P. Miller, and S. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc.-Oxford206, 33–40 (2002).
[CrossRef]

J. Phys. D Appl. Phys. (3)

T. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. Wilkins, “Hard X-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D Appl. Phys.32(5), 563–567 (1999).
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Y. I. Nesterets, T. Gureyev, D. Paganin, K. Pavlov, and S. W. Wilkins, “Quantitative diffraction-enhanced X-ray imaging of weak objects,” J. Phys. D Appl. Phys.37(8), 1262–1274 (2004).
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Jpn. J. Appl. Phys. (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Jpn. J. Appl. Phys.42(Part 2, No. 7B), L866–L868 (2003).
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Med. Phys. (1)

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. Menk, S. Pani, M. Prest, P. Poropat, L. Rigon, G. Tromba, E. Vallazza, and E. Castelli, “An innovative digital imaging set-up allowing a low-dose approach to phase contrast applications in the medical field,” Med. Phys.28(8), 1610–1619 (2001).
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Nat. Phys. (1)

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys.2(4), 258–261 (2006).
[CrossRef]

Nature (2)

T. Davis, D. Gao, T. Gureyev, A. Stevenson, and S. Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature373(6515), 595–598 (1995).
[CrossRef]

S. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384, 335–338 (1996).
[CrossRef]

Nucl. Instrum. Meth. A (4)

A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Meth. A352(3), 622 – 628 (1995).
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A. Abrami, F. Arfelli, R. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Palma, D. Dreossi, A. Fava, R. Longo, L. Mancini, R. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vaseotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of Elettra,” Nucl. Instrum. Meth. A548, 221–227 (2005).
[CrossRef]

L. Rigon, F. Arfelli, A. Astolfo, A. Bergamaschi, D. Dreossi, R. Longo, R.-H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “A single-photon counting edge-on silicon detector for synchrotron radiation mammography,” Nucl. Instrum. Meth. A608(1, Supplement 1), S62 – S65 (2009).
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L. Rigon, F. Arfelli, A. Bergamaschi, R. C. Chen, D. Dreossi, R. Longo, R. H. Menk, B. Schmitt, E. Vallazza, and E. Castelli, “Evaluation of charge -sharing effects on the spatial resolution of the PICASSO detector,” Nucl. Instrum. Meth. A617(1–3), 244–245 (2010).
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Opt. Express (1)

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Source size and temporal coherence requirements of coded aperture type X-ray phase contrast imaging systems,” Opt. Express18(19), 19681–19692 (2010).
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T. Gureyev, A. Pogany, D. Paganin, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region,” Opt. Commun.231, 53–70 (2004).
[CrossRef]

T. Gureyev, Y. Ne, D. Paganin, A. Pogany, and S. Wilkins, “Linear algorithms for phase retrieval in the fresnel region. 2. partially coherent illumination,” Opt. Commun.259, 569–580 (2005).
[CrossRef]

Opt. Express (4)

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[CrossRef] [PubMed]

D. Chapman, W. Thomlinson, R. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced X-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
[CrossRef] [PubMed]

Phys. Rev. A (1)

Z.-F. Huang, K.-J. Kang, L. Zhang, Z.-Q. Chen, F. Ding, Z.-T. Wang, and Q.-G. Fang, “Alternative method for differential phase-contrast imaging with weakly coherent hard X-rays,” Phys. Rev. A79(1), 013815 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

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Proc. Natl. Acad. Sci. U. S. A. (2)

P. Zhu, K. Zhang, Z. Wang, Y. Liu, X. Liu, Z. Wu, S. A. McDonald, F. Marone, and M. Stampanoni, “Low-dose, simple, and fast grating-based X-ray phase-contrast imaging,” Proc. Natl. Acad. Sci. U. S. A.107(31), 576–581 (2010).
[CrossRef]

P. Munro, K. Ignatyev, R. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U. S. A.109, 13,922–13,927 (2012).
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The 9th National Conference on Synchrotron Radiation Instrumentation (1)

D. Chapman, W. Thomlinson, F. Arfelli, N. Gmür, Z. Zhong, R. Menk, R. E. Johnson, D. Washburn, E. Pisano, and D. Sayers, “Mammography imaging studies using a Laue crystal analyzer,” The 9th National Conference on Synchrotron Radiation Instrumentation67(9), 3360–3360 (1996).

Other (1)

G. James, Geometrical theory of diffraction for electromagnetic waves (Peter Peregrinus Ltd., 1976).

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Figures (12)

Fig. 1
Fig. 1

(a) Demonstration of the edge illumination principle whereby pre-sample apertures, located a distance zso from the source, shape a beam which is incident upon detector apertures and detector, placed a distance zod from the pre-sample apertures. The centre of the detector apertures is offset from the centre of the beam by a distance ΔP. (b) A CAXPCI system made by tiling the setup used in (a). A1 and A2 are apertures with the same projected pitch which also matches the detector pixel width P. All parameters have the same meaning as in (a). A1 creates X-ray beams which are incident upon A2 which is used to achieve the partial pixel illumination condition.The imaging system continues uniformly out of the page.

Fig. 2
Fig. 2

The two complementary aperture configurations used to perform quantitative EIX-PCI. W is the width of the pre-sample apertures, A1, M = (zso + zod)/zso is the magnification, ξ is the spatial coordinate within the open region of the pre-sample aperture and Iand I+ represent the signals measured by the detector pixels in the left and right configurations respectively. A2 represents the detector aperture.

Fig. 3
Fig. 3

Plot of the error, ε, introduced into the ratio (I+I)/(I+ + I) by the SPA as β varies for a wedge-like object.

Fig. 4
Fig. 4

Plot of the value of (1/k) (∂ϕ/∂ξ)|ξs calculated for the example wedge-like object for a range of values of β. The value is calculated by simulating the values of I+ and I by evaluating the diffraction integrals of Eq. (4). The actual value of (1/k) (∂ϕ/∂ξ|ξs is 5 × 10−6.

Fig. 5
Fig. 5

Plot of (1 − I/I+)/((1/k) (∂μ/∂ξ)|ξs) for the wedge-like object for a range of values of β.

Fig. 6
Fig. 6

Plot of how (∂ϕ/∂ξ)|ξs varies with the source photon energy for the wedge-like object example considered in this section with β = 10−8.

Fig. 7
Fig. 7

Schematic, side-on view of the experimental system employed to verify the phase extraction algorithm. The diagram is not to scale.

Fig. 8
Fig. 8

Photograph of the sample used in the experiment.

Fig. 9
Fig. 9

Images of the sample taken in the I+ and I configurations. Note that some vertical scan positions, in between filaments, were omitted to reduce the total number of acquisitions. The image shows 16mm of the sample in the horizontal direction. Each row of pixels was normalised by the mean of the rows within the boxed region in each image. The filaments are arranged in the same order as in Fig. 8.

Fig. 10
Fig. 10

Profile plots for a single pixel column for the absorption image ((I + I+)/2), I+ and I.

Fig. 11
Fig. 11

Images of μ (left) and (1/k)∂ϕ/∂ξ (right) derived from Fig. 9 according to Eqs. (14) and (15) respectively.

Fig. 12
Fig. 12

Plots comparing the extracted value (broken line) for (1/k)∂ϕ/∂ξ for each wire and the theoretical value (solid line). The dots superimposed on the broken line represent the experimentally determined values of (1/k)∂ϕ/∂ξ. The wires are labeled with a letter which corresponds to a row in Table 1.

Tables (1)

Tables Icon

Table 1 Properties of wires making up the sample. PEEK stands for polyetheretherketone. The boron is supplied on a 5μm diameter tungsten core. The filaments were sourced from Goodfellow (Goodfellow Cambridge Ltd., Huntingdon, UK) and the nominal diameters were obtained from data sheets provided by Goodfellow.

Equations (19)

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ϕ ( x , y ) = k 𝒪 δ ( x , y , z ) d z μ ( x , y ) = k 𝒪 β ( x , y , z ) d z
I = 0 P M W 0 | U ( x ) | 2 d x d y I + = 0 P 0 M W | U ( x ) | 2 d x d y
T ( ξ + ξ s ; ξ i ) = exp ( i ϕ ( ξ s ) i ϕ ξ | ξ s ( ξ ξ i ) μ ( ξ s ) μ ξ | ξ s ( ξ ξ i ) )
U ( x ) = C W / 2 W / 2 T ( ξ ξ s ; ξ i ) exp ( i k ξ 2 z s o + z o d 2 z s o z o d ) exp ( i k ξ x z o d ) d ξ = C exp ( i ( ϕ ξ | ξ s ξ i ϕ ( ξ s ) ) ) exp ( μ ξ | ξ s ξ i μ ( ξ s ) ) W / 2 W / 2 exp ( μ ξ | ξ s ξ ) exp ( i k ξ 2 z s o + z o d 2 z s o z o d i k ξ ( x z o d + 1 k ϕ ξ | ξ s ) ) d ξ
C = U 0 i λ z s o z o d ( z s o + z o d ) exp ( i k ( z s o + z o d ) ) exp ( i k ( x 2 2 z o d ) ) .
U 0 ~ C exp ( i ( ϕ ξ | ξ s ξ i ϕ ( ξ s ) ) ) exp ( μ ξ | ξ s ξ i μ ( ξ s ) ) i λ z s o z o d z s o + z o d exp [ μ ξ | ξ s z s o z o d z s o + z o d ( x z o d + 1 k ϕ ξ | ξ s ) ] exp [ i k 2 z s o z o d z s o + z o d ( x z o d + 1 k ϕ ξ | ξ s ) 2 ]
I = 𝒜 [ exp ( μ ξ | ξ s W ) ] I + = 𝒜 [ exp ( μ ξ | ξ s W ) + ]
I + + I = 2 𝒜 sinh ( μ ξ | ξ s W )
I + I _ = 2 𝒜 [ cosh ( μ ξ | ξ s W ) ]
I 0 = | U 0 | 2 M W P ( z s o + z o d ) 2
μ ξ | ξ s = 1 4 Δ ξ log ( ( I + + I ) | ξ i = Δ ξ ( I + + I ) | ξ i = Δ ξ )
μ ξ | ξ s = 1 2 Δ ξ log ( ( I + + I ) | ξ i = 0 ( I + + I ) | ξ i = Δ ξ )
μ ( ξ s ) = 1 2 log [ I 0 ( I + + I ) | ξ i = 0 sinh ( μ ξ | ξ s W ) μ ξ | ξ s W ]
1 2 log [ I 0 ( I + + I ) | ξ i = 0 ]
( 1 / k ) ϕ ξ | ξ s = log [ I + I I + + I | ξ i = 0 sinh ( μ ξ | ξ s W ) + cosh ( μ ξ | ξ s W ) ] ( z s o + z o d ) 2 μ ξ | ξ s z s o z o d
( 1 / k ) ϕ ξ | ξ s = [ I + I I + + I | ξ i = 0 + 1 2 μ ξ | ξ s W ] W ( z s o + z o d ) 2 z s o z o d
( 1 / k ) ϕ ξ | ξ s = I + I I + + I | ξ i = 0 W ( z s o + z o d ) 2 z s o z o d
( 1 / k ) | ϕ ξ | ξ s M W 2 z o d .
ϕ ξ | ξ s ϕ ξ | ξ s ˜ ε ( z s o + z o d ) 4 z s o z o d ( 1 I I + ) ( 1 / k ) μ ξ | ξ s

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