Abstract

We analyze the spatial resolution of edge illumination X-ray phase-contrast imaging and its dependence upon various experimental parameters such as source size, source-to-sample and sample-to-detector distances, X-ray energy and size of the beam-shaping aperture. Different propagation regimes, as well as the beam divergence and polychromaticity encountered with laboratory sources, are also considered. We show that spatial resolution in edge illumination phase-contrast imaging presents peculiar features compared to other X-ray phase-contrast techniques. In particular, in the direction orthogonal to the s or mask lines used to shape the beam, this can be better than both the pixel dimension and the projected source size. Numerical simulations based on Fresnel diffraction integrals are presented, which confirm the analytical predictions. The obtained results allow a simple estimation of the spatial resolution for edge-illumination phase imaging in both synchrotron and laboratory setups.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. M. Marenzana, C. K. Hagen, P. Das Neves Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based X-ray phase contrast imaging,” Phys. Med. Biol.57(24), 8173–8184 (2012).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  26. Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for X-ray in-line phase-contrast imaging,” Rev. Sci. Instrum.76(9), 093706 (2005).
    [CrossRef]
  27. T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line X-ray phase-contrast imaging,” Opt. Express16(5), 3223–3241 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]

2014

S. W. Wilkins, Y. I. Nesterets, T. E. Gureyev, S. C. Mayo, A. Pogany, and A. W. Stevenson, “On the evolution and relative merits of hard X-ray phase-contrast imaging methods,” Phil. Trans. R. Soc. A372(2010), 20130021 (2014).
[CrossRef] [PubMed]

P. C. Diemoz, M. Endrizzi, A. Bravin, I. K. Robinson, and A. Olivo, “Sensitivity of edge illumination X-ray phase-contrast imaging,” Phil. Trans. R. Soc. A372(2010), 20130128 (2014).
[CrossRef] [PubMed]

2013

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

P. C. Diemoz, C. K. Hagen, M. Endrizzi, and A. Olivo, “Sensitivity of laboratory based implementations of edge illumination X-ray phase-contrast imaging,” Appl. Phys. Lett.103(24), 244104 (2013).
[CrossRef]

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett.110(13), 138105 (2013).
[CrossRef] [PubMed]

F. A. Vittoria, P. C. Diemoz, M. Endrizzi, L. Rigon, F. C. Lopez, D. Dreossi, P. R. T. Munro, and A. Olivo, “Strategies for efficient and fast wave optics simulation of coded-aperture and other X-ray phase-contrast imaging methods,” Appl. Opt.52(28), 6940–6947 (2013).
[PubMed]

2012

P. C. Diemoz, A. Bravin, and P. Coan, “Theoretical comparison of three X-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry,” Opt. Express20(3), 2789–2805 (2012).
[CrossRef] [PubMed]

A. Olivo, P. C. Diemoz, and A. Bravin, “Amplification of the phase contrast signal at very high X-ray energies,” Opt. Lett.37(5), 915–917 (2012).
[CrossRef] [PubMed]

J. W. Miao, R. L. Sandberg, and C. Y. Song, “Coherent X-ray diffraction imaging,” IEEE J. Sel. Top. Quantum Electron.18(1), 399–410 (2012).
[CrossRef]

P. R. T. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U.S.A.109(35), 13922–13927 (2012).
[CrossRef] [PubMed]

M. Marenzana, C. K. Hagen, P. Das Neves Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based X-ray phase contrast imaging,” Phys. Med. Biol.57(24), 8173–8184 (2012).
[CrossRef] [PubMed]

2011

K. Ignatyev, P. R. T. Munro, R. D. Speller, and A. Olivo, “Effects of signal diffusion on X-ray phase contrast images,” Rev. Sci. Instrum.82(7), 073702 (2011).
[CrossRef] [PubMed]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “Quantitative single-exposure X-ray phase contrast imaging using a single attenuation grid,” Opt. Express19(20), 19781–19789 (2011).
[CrossRef] [PubMed]

2010

2009

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

2007

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

2006

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

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for X-ray in-line phase-contrast imaging,” Rev. Sci. Instrum.76(9), 093706 (2005).
[CrossRef]

2003

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]

2001

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

1997

A. Pogany, D. Gao, and S. Wilkins, “Contrast and resolution in imaging with a microfocus X-ray source,” Rev. Sci. Instrum.68(7), 2774–2782 (1997).
[CrossRef]

1996

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996).
[CrossRef]

1995

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

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibility of X-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum.66(12), 5486–5492 (1995).
[CrossRef]

1983

Arfelli, F.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

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]

Bravin, A.

P. C. Diemoz, M. Endrizzi, A. Bravin, I. K. Robinson, and A. Olivo, “Sensitivity of edge illumination X-ray phase-contrast imaging,” Phil. Trans. R. Soc. A372(2010), 20130128 (2014).
[CrossRef] [PubMed]

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett.110(13), 138105 (2013).
[CrossRef] [PubMed]

P. C. Diemoz, A. Bravin, and P. Coan, “Theoretical comparison of three X-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry,” Opt. Express20(3), 2789–2805 (2012).
[CrossRef] [PubMed]

A. Olivo, P. C. Diemoz, and A. Bravin, “Amplification of the phase contrast signal at very high X-ray energies,” Opt. Lett.37(5), 915–917 (2012).
[CrossRef] [PubMed]

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. H. 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]

Castelli, E.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

Coan, P.

Das Neves Borges, P.

M. Marenzana, C. K. Hagen, P. Das Neves Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based X-ray phase contrast imaging,” Phys. Med. Biol.57(24), 8173–8184 (2012).
[CrossRef] [PubMed]

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]

Davis, T.

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

Diemoz, P. C.

P. C. Diemoz, M. Endrizzi, A. Bravin, I. K. Robinson, and A. Olivo, “Sensitivity of edge illumination X-ray phase-contrast imaging,” Phil. Trans. R. Soc. A372(2010), 20130128 (2014).
[CrossRef] [PubMed]

F. A. Vittoria, P. C. Diemoz, M. Endrizzi, L. Rigon, F. C. Lopez, D. Dreossi, P. R. T. Munro, and A. Olivo, “Strategies for efficient and fast wave optics simulation of coded-aperture and other X-ray phase-contrast imaging methods,” Appl. Opt.52(28), 6940–6947 (2013).
[PubMed]

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett.110(13), 138105 (2013).
[CrossRef] [PubMed]

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

P. C. Diemoz, C. K. Hagen, M. Endrizzi, and A. Olivo, “Sensitivity of laboratory based implementations of edge illumination X-ray phase-contrast imaging,” Appl. Phys. Lett.103(24), 244104 (2013).
[CrossRef]

A. Olivo, P. C. Diemoz, and A. Bravin, “Amplification of the phase contrast signal at very high X-ray energies,” Opt. Lett.37(5), 915–917 (2012).
[CrossRef] [PubMed]

P. C. Diemoz, A. Bravin, and P. Coan, “Theoretical comparison of three X-ray phase-contrast imaging techniques: propagation-based imaging, analyzer-based imaging and grating interferometry,” Opt. Express20(3), 2789–2805 (2012).
[CrossRef] [PubMed]

Dreossi, D.

Endrizzi, M.

P. C. Diemoz, M. Endrizzi, A. Bravin, I. K. Robinson, and A. Olivo, “Sensitivity of edge illumination X-ray phase-contrast imaging,” Phil. Trans. R. Soc. A372(2010), 20130128 (2014).
[CrossRef] [PubMed]

F. A. Vittoria, P. C. Diemoz, M. Endrizzi, L. Rigon, F. C. Lopez, D. Dreossi, P. R. T. Munro, and A. Olivo, “Strategies for efficient and fast wave optics simulation of coded-aperture and other X-ray phase-contrast imaging methods,” Appl. Opt.52(28), 6940–6947 (2013).
[PubMed]

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett.110(13), 138105 (2013).
[CrossRef] [PubMed]

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

P. C. Diemoz, C. K. Hagen, M. Endrizzi, and A. Olivo, “Sensitivity of laboratory based implementations of edge illumination X-ray phase-contrast imaging,” Appl. Phys. Lett.103(24), 244104 (2013).
[CrossRef]

M. Marenzana, C. K. Hagen, P. Das Neves Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based X-ray phase contrast imaging,” Phys. Med. Biol.57(24), 8173–8184 (2012).
[CrossRef] [PubMed]

Gao, D.

A. Pogany, D. Gao, and S. Wilkins, “Contrast and resolution in imaging with a microfocus X-ray source,” Rev. Sci. Instrum.68(7), 2774–2782 (1997).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996).
[CrossRef]

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

Gkoumas, S.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

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]

Gureyev, T. E.

S. W. Wilkins, Y. I. Nesterets, T. E. Gureyev, S. C. Mayo, A. Pogany, and A. W. Stevenson, “On the evolution and relative merits of hard X-ray phase-contrast imaging methods,” Phil. Trans. R. Soc. A372(2010), 20130021 (2014).
[CrossRef] [PubMed]

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line X-ray phase-contrast imaging,” Opt. Express16(5), 3223–3241 (2008).
[CrossRef] [PubMed]

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for X-ray in-line phase-contrast imaging,” Rev. Sci. Instrum.76(9), 093706 (2005).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996).
[CrossRef]

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

Hagen, C. K.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

P. C. Diemoz, C. K. Hagen, M. Endrizzi, and A. Olivo, “Sensitivity of laboratory based implementations of edge illumination X-ray phase-contrast imaging,” Appl. Phys. Lett.103(24), 244104 (2013).
[CrossRef]

M. Marenzana, C. K. Hagen, P. Das Neves Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based X-ray phase contrast imaging,” Phys. Med. Biol.57(24), 8173–8184 (2012).
[CrossRef] [PubMed]

Hamaishi, Y.

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]

Horrocks, J. A.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

Ignatyev, K.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

P. R. T. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U.S.A.109(35), 13922–13927 (2012).
[CrossRef] [PubMed]

M. Marenzana, C. K. Hagen, P. Das Neves Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based X-ray phase contrast imaging,” Phys. Med. Biol.57(24), 8173–8184 (2012).
[CrossRef] [PubMed]

K. Ignatyev, P. R. T. Munro, R. D. Speller, and A. Olivo, “Effects of signal diffusion on X-ray phase contrast images,” Rev. Sci. Instrum.82(7), 073702 (2011).
[CrossRef] [PubMed]

P. R. T. Munro, K. Ignatyev, R. D. 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. R. T. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “Limitations imposed by specimen phase gradients on the design of grating based X-ray phase contrast imaging systems,” Appl. Opt.49(20), 3860–3863 (2010).
[CrossRef] [PubMed]

Jakubek, J.

F. Krejci, J. Jakubek, and M. Kroupa, “Hard X-ray phase contrast imaging using single absorption grating and hybrid semiconductor pixel detector,” Rev. Sci. Instrum.81(11), 113702 (2010).
[CrossRef] [PubMed]

Johnson, B.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

Jones, J. L.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

Kawamoto, S.

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]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibility of X-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum.66(12), 5486–5492 (1995).
[CrossRef]

Konstantinidis, 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]

Koyama, I.

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]

Krejci, F.

F. Krejci, J. Jakubek, and M. Kroupa, “Hard X-ray phase contrast imaging using single absorption grating and hybrid semiconductor pixel detector,” Rev. Sci. Instrum.81(11), 113702 (2010).
[CrossRef] [PubMed]

Kroupa, M.

F. Krejci, J. Jakubek, and M. Kroupa, “Hard X-ray phase contrast imaging using single absorption grating and hybrid semiconductor pixel detector,” Rev. Sci. Instrum.81(11), 113702 (2010).
[CrossRef] [PubMed]

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibility of X-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum.66(12), 5486–5492 (1995).
[CrossRef]

Longo, R.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

Lopez, F. C.

Marenzana, M.

M. Marenzana, C. K. Hagen, P. Das Neves Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based X-ray phase contrast imaging,” Phys. Med. Biol.57(24), 8173–8184 (2012).
[CrossRef] [PubMed]

Mayo, S. C.

S. W. Wilkins, Y. I. Nesterets, T. E. Gureyev, S. C. Mayo, A. Pogany, and A. W. Stevenson, “On the evolution and relative merits of hard X-ray phase-contrast imaging methods,” Phil. Trans. R. Soc. A372(2010), 20130021 (2014).
[CrossRef] [PubMed]

Menk, R. H.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

Miao, J. W.

J. W. Miao, R. L. Sandberg, and C. Y. Song, “Coherent X-ray diffraction imaging,” IEEE J. Sel. Top. Quantum Electron.18(1), 399–410 (2012).
[CrossRef]

Miller, P. R.

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]

Morgan, K. S.

Munro, P. R. T.

F. A. Vittoria, P. C. Diemoz, M. Endrizzi, L. Rigon, F. C. Lopez, D. Dreossi, P. R. T. Munro, and A. Olivo, “Strategies for efficient and fast wave optics simulation of coded-aperture and other X-ray phase-contrast imaging methods,” Appl. Opt.52(28), 6940–6947 (2013).
[PubMed]

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

P. R. T. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U.S.A.109(35), 13922–13927 (2012).
[CrossRef] [PubMed]

K. Ignatyev, P. R. T. Munro, R. D. Speller, and A. Olivo, “Effects of signal diffusion on X-ray phase contrast images,” Rev. Sci. Instrum.82(7), 073702 (2011).
[CrossRef] [PubMed]

P. R. T. Munro, K. Ignatyev, R. D. 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. R. T. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “Limitations imposed by specimen phase gradients on the design of grating based X-ray phase contrast imaging systems,” Appl. Opt.49(20), 3860–3863 (2010).
[CrossRef] [PubMed]

Nesterets, Y. I.

S. W. Wilkins, Y. I. Nesterets, T. E. Gureyev, S. C. Mayo, A. Pogany, and A. W. Stevenson, “On the evolution and relative merits of hard X-ray phase-contrast imaging methods,” Phil. Trans. R. Soc. A372(2010), 20130021 (2014).
[CrossRef] [PubMed]

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line X-ray phase-contrast imaging,” Opt. Express16(5), 3223–3241 (2008).
[CrossRef] [PubMed]

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for X-ray in-line phase-contrast imaging,” Rev. Sci. Instrum.76(9), 093706 (2005).
[CrossRef]

Olivo, A.

P. C. Diemoz, M. Endrizzi, A. Bravin, I. K. Robinson, and A. Olivo, “Sensitivity of edge illumination X-ray phase-contrast imaging,” Phil. Trans. R. Soc. A372(2010), 20130128 (2014).
[CrossRef] [PubMed]

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett.110(13), 138105 (2013).
[CrossRef] [PubMed]

F. A. Vittoria, P. C. Diemoz, M. Endrizzi, L. Rigon, F. C. Lopez, D. Dreossi, P. R. T. Munro, and A. Olivo, “Strategies for efficient and fast wave optics simulation of coded-aperture and other X-ray phase-contrast imaging methods,” Appl. Opt.52(28), 6940–6947 (2013).
[PubMed]

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

P. C. Diemoz, C. K. Hagen, M. Endrizzi, and A. Olivo, “Sensitivity of laboratory based implementations of edge illumination X-ray phase-contrast imaging,” Appl. Phys. Lett.103(24), 244104 (2013).
[CrossRef]

A. Olivo, P. C. Diemoz, and A. Bravin, “Amplification of the phase contrast signal at very high X-ray energies,” Opt. Lett.37(5), 915–917 (2012).
[CrossRef] [PubMed]

M. Marenzana, C. K. Hagen, P. Das Neves Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based X-ray phase contrast imaging,” Phys. Med. Biol.57(24), 8173–8184 (2012).
[CrossRef] [PubMed]

P. R. T. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U.S.A.109(35), 13922–13927 (2012).
[CrossRef] [PubMed]

K. Ignatyev, P. R. T. Munro, R. D. Speller, and A. Olivo, “Effects of signal diffusion on X-ray phase contrast images,” Rev. Sci. Instrum.82(7), 073702 (2011).
[CrossRef] [PubMed]

P. R. T. Munro, K. Ignatyev, R. D. 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. R. T. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “Limitations imposed by specimen phase gradients on the design of grating based X-ray phase contrast imaging systems,” Appl. Opt.49(20), 3860–3863 (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. D. 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. D. 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. Olivo and R. D. Speller, “A coded-aperture technique allowing X-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett.91(7), 074106 (2007).
[CrossRef]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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. M.

Pani, S.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

Pešic, Z. D.

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett.110(13), 138105 (2013).
[CrossRef] [PubMed]

Pfeiffer, F.

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]

Pogany, A.

S. W. Wilkins, Y. I. Nesterets, T. E. Gureyev, S. C. Mayo, A. Pogany, and A. W. Stevenson, “On the evolution and relative merits of hard X-ray phase-contrast imaging methods,” Phil. Trans. R. Soc. A372(2010), 20130021 (2014).
[CrossRef] [PubMed]

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line X-ray phase-contrast imaging,” Opt. Express16(5), 3223–3241 (2008).
[CrossRef] [PubMed]

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for X-ray in-line phase-contrast imaging,” Rev. Sci. Instrum.76(9), 093706 (2005).
[CrossRef]

A. Pogany, D. Gao, and S. Wilkins, “Contrast and resolution in imaging with a microfocus X-ray source,” Rev. Sci. Instrum.68(7), 2774–2782 (1997).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996).
[CrossRef]

Poropat, P.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

Prest, M.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

Rau, C.

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett.110(13), 138105 (2013).
[CrossRef] [PubMed]

Rigon, L.

F. A. Vittoria, P. C. Diemoz, M. Endrizzi, L. Rigon, F. C. Lopez, D. Dreossi, P. R. T. Munro, and A. Olivo, “Strategies for efficient and fast wave optics simulation of coded-aperture and other X-ray phase-contrast imaging methods,” Appl. Opt.52(28), 6940–6947 (2013).
[PubMed]

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

Robinson, I. K.

P. C. Diemoz, M. Endrizzi, A. Bravin, I. K. Robinson, and A. Olivo, “Sensitivity of edge illumination X-ray phase-contrast imaging,” Phil. Trans. R. Soc. A372(2010), 20130128 (2014).
[CrossRef] [PubMed]

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett.110(13), 138105 (2013).
[CrossRef] [PubMed]

Sandberg, R. L.

J. W. Miao, R. L. Sandberg, and C. Y. Song, “Coherent X-ray diffraction imaging,” IEEE J. Sel. Top. Quantum Electron.18(1), 399–410 (2012).
[CrossRef]

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibility of X-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum.66(12), 5486–5492 (1995).
[CrossRef]

Siu, K. K. W.

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibility of X-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum.66(12), 5486–5492 (1995).
[CrossRef]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibility of X-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum.66(12), 5486–5492 (1995).
[CrossRef]

Song, C. Y.

J. W. Miao, R. L. Sandberg, and C. Y. Song, “Coherent X-ray diffraction imaging,” IEEE J. Sel. Top. Quantum Electron.18(1), 399–410 (2012).
[CrossRef]

Speller, R. D.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

P. R. T. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U.S.A.109(35), 13922–13927 (2012).
[CrossRef] [PubMed]

K. Ignatyev, P. R. T. Munro, R. D. Speller, and A. Olivo, “Effects of signal diffusion on X-ray phase contrast images,” Rev. Sci. Instrum.82(7), 073702 (2011).
[CrossRef] [PubMed]

P. R. T. Munro, K. Ignatyev, R. D. 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. R. T. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “Limitations imposed by specimen phase gradients on the design of grating based X-ray phase contrast imaging systems,” Appl. Opt.49(20), 3860–3863 (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. D. 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. D. 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. Olivo and R. D. Speller, “A coded-aperture technique allowing X-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett.91(7), 074106 (2007).
[CrossRef]

Stevenson, A. W.

S. W. Wilkins, Y. I. Nesterets, T. E. Gureyev, S. C. Mayo, A. Pogany, and A. W. Stevenson, “On the evolution and relative merits of hard X-ray phase-contrast imaging methods,” Phil. Trans. R. Soc. A372(2010), 20130021 (2014).
[CrossRef] [PubMed]

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line X-ray phase-contrast imaging,” Opt. Express16(5), 3223–3241 (2008).
[CrossRef] [PubMed]

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for X-ray in-line phase-contrast imaging,” Rev. Sci. Instrum.76(9), 093706 (2005).
[CrossRef]

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996).
[CrossRef]

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

Suzuki, Y.

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]

Szafraniec, M. B.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

M. Marenzana, C. K. Hagen, P. Das Neves Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based X-ray phase contrast imaging,” Phys. Med. Biol.57(24), 8173–8184 (2012).
[CrossRef] [PubMed]

Takai, K.

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]

Teague, M. R.

Tromba, G.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

Vallazza, E.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

Vinnicombe, S. J.

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

Vittoria, F. A.

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]

Wilkins, S.

A. Pogany, D. Gao, and S. Wilkins, “Contrast and resolution in imaging with a microfocus X-ray source,” Rev. Sci. Instrum.68(7), 2774–2782 (1997).
[CrossRef]

Wilkins, S. W.

S. W. Wilkins, Y. I. Nesterets, T. E. Gureyev, S. C. Mayo, A. Pogany, and A. W. Stevenson, “On the evolution and relative merits of hard X-ray phase-contrast imaging methods,” Phil. Trans. R. Soc. A372(2010), 20130021 (2014).
[CrossRef] [PubMed]

T. E. Gureyev, Y. I. Nesterets, A. W. Stevenson, P. R. Miller, A. Pogany, and S. W. Wilkins, “Some simple rules for contrast, signal-to-noise and resolution in in-line X-ray phase-contrast imaging,” Opt. Express16(5), 3223–3241 (2008).
[CrossRef] [PubMed]

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for X-ray in-line phase-contrast imaging,” Rev. Sci. Instrum.76(9), 093706 (2005).
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[CrossRef]

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

Zapata, C. E.

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett.110(13), 138105 (2013).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

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).
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A. Olivo and R. D. Speller, “A coded-aperture technique allowing X-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett.91(7), 074106 (2007).
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P. C. Diemoz, C. K. Hagen, M. Endrizzi, and A. Olivo, “Sensitivity of laboratory based implementations of edge illumination X-ray phase-contrast imaging,” Appl. Phys. Lett.103(24), 244104 (2013).
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Jpn. J. Appl. Phys.

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]

Med. Phys.

A. Olivo, F. Arfelli, G. Cantatore, R. Longo, R. H. 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]

A. Olivo, S. Gkoumas, M. Endrizzi, C. K. Hagen, M. B. Szafraniec, P. C. Diemoz, P. R. T. Munro, K. Ignatyev, B. Johnson, J. A. Horrocks, S. J. Vinnicombe, J. L. Jones, and R. D. Speller, “Low-dose phase contrast mammography with conventional X-ray sources,” Med. Phys.40(9), 090701 (2013).
[CrossRef] [PubMed]

Nat. Phys.

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

S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature384(6607), 335–338 (1996).
[CrossRef]

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

Opt. Express

Opt. Lett.

Phil. Trans. R. Soc. A

P. C. Diemoz, M. Endrizzi, A. Bravin, I. K. Robinson, and A. Olivo, “Sensitivity of edge illumination X-ray phase-contrast imaging,” Phil. Trans. R. Soc. A372(2010), 20130128 (2014).
[CrossRef] [PubMed]

S. W. Wilkins, Y. I. Nesterets, T. E. Gureyev, S. C. Mayo, A. Pogany, and A. W. Stevenson, “On the evolution and relative merits of hard X-ray phase-contrast imaging methods,” Phil. Trans. R. Soc. A372(2010), 20130021 (2014).
[CrossRef] [PubMed]

Phys. Med. Biol.

M. Marenzana, C. K. Hagen, P. Das Neves Borges, M. Endrizzi, M. B. Szafraniec, K. Ignatyev, and A. Olivo, “Visualization of small lesions in rat cartilage by means of laboratory-based X-ray phase contrast imaging,” Phys. Med. Biol.57(24), 8173–8184 (2012).
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A. Olivo and R. D. Speller, “Modelling of a novel X-ray phase contrast imaging technique based on coded apertures,” Phys. Med. Biol.52(22), 6555–6573 (2007).
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A. Olivo and R. D. Speller, “Image formation principles in coded-aperture based X-ray phase contrast imaging,” Phys. Med. Biol.53(22), 6461–6474 (2008).
[CrossRef] [PubMed]

Phys. Rev. Lett.

P. C. Diemoz, M. Endrizzi, C. E. Zapata, Z. D. Pešić, C. Rau, A. Bravin, I. K. Robinson, and A. Olivo, “X-ray phase-contrast imaging with nanoradian angular resolution,” Phys. Rev. Lett.110(13), 138105 (2013).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

P. R. T. Munro, K. Ignatyev, R. D. Speller, and A. Olivo, “Phase and absorption retrieval using incoherent X-ray sources,” Proc. Natl. Acad. Sci. U.S.A.109(35), 13922–13927 (2012).
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[CrossRef]

K. Ignatyev, P. R. T. Munro, R. D. Speller, and A. Olivo, “Effects of signal diffusion on X-ray phase contrast images,” Rev. Sci. Instrum.82(7), 073702 (2011).
[CrossRef] [PubMed]

Y. I. Nesterets, S. W. Wilkins, T. E. Gureyev, A. Pogany, and A. W. Stevenson, “On the optimization of experimental parameters for X-ray in-line phase-contrast imaging,” Rev. Sci. Instrum.76(9), 093706 (2005).
[CrossRef]

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, “On the possibility of X-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum.66(12), 5486–5492 (1995).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Sketch of the EI experimental setup in the case of (a) a laminar beam and a single sample-detector aperture pair and (b) an extended beam and two sample and detector masks featuring a multitude of aperture pairs.

Fig. 2
Fig. 2

Examples of FSP intensity profiles produced by a phase edge, in the near-field and intermediate diffraction regimes.

Fig. 3
Fig. 3

Example illustrating the spatial resolution of the attenuation signal in EI. (a) Scheme of the considered experimental arrangement, with the edge of a lead slab being scanned through the beam. (b) Original absorption profile of the sample, compared to signals obtained at 50% and 25% illumination levels (see text for details on the considered experimental parameters).

Fig. 4
Fig. 4

Example illustrating the spatial resolution of EI in the near-field diffraction regime (special case of a large sample aperture): (a) a phase edge is scanned through a pair of sample and detector apertures, (b) plots of typical signals obtained with FSP (no masks are present, ideal detector with very small pixel size) and EI (very small dithering step).

Fig. 5
Fig. 5

Example illustrating the spatial resolution of the EI edge signal in the Fresnel (or intermediate) diffraction regime (special case of a large sample aperture): (a) a phase edge is scanned through a pair of sample and detector apertures, (b) plots of typical signals obtained with FSP (no masks are present, ideal detector with negligible pixel size) and EI (negligible dithering step).

Fig. 6
Fig. 6

Simulated intensity profiles for a lab-based EI system (z1 = 1.6 m, z2 = 0.4 m, a = 12 µm and d = 20 µm). The sample is a 10 µm thick Lucite slab, with an edge width of 1 µm standard deviation. Various source sizes are considered: 1 µm, 20 µm, 60 µm and 100 µm.

Fig. 7
Fig. 7

Simulated intensity profiles for a synchrotron EI system. Parameters for the setup are: z1 = 140 m, σsrc,y = 25 µm, E = 40 keV, a = 20 µm and d = 50 µm. The sample has a circular cross section with a radius of 2 µm. The following propagation distances z2 are considered: 1 m, 2 m, 3 m and 6 m.

Fig. 8
Fig. 8

Simulated intensity profile for a synchrotron EI setup, illustrating the case when both attenuation and edge signals are present. The setup parameters are: z1 = 140 m, σsrc,y = 25 µm, E = 30 keV, a = 30 µm, d = 50 µm, z2 = 0.1 m. The sample is made of lead and has a circular cross section of 3 µm radius.

Equations (23)

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q( x,y;λ )= T( x,y;λ ) exp[ iϕ( x,y;λ ) ]
m( y )=rec t a ( ya/2 )
E out ( x,y;p;λ )=q( x, y ;λ )m( y )
E det ( x,y;p;λ )= E out ( x,y;p;λ ) H z 2 ( x,y;λ )
E det ( Mx,My;p;λ )= 1 M [ q( x, y ;λ )m( y ) ] H z 2 /M ( x,y;λ )
I res ( x,y;p;λ )= | [ q( x, y ;λ )m( y ) ] H z 2 /M ( x,y;λ ) | 2 G( x,y )
S( n,p; y e ;λ )= ( n1 ) Δx /M n Δx /M dx y e /M ( y e +d ) /M dy I res ( x,y;p;λ )
I res ( x,y;λ )=[ | q( x;λ )* h z 2 /M ( x;λ ) | 2 g( x ) ][ | m( y )* h z 2 /M ( y;λ ) | 2 g( y ) ] k 1 ( x;λ ) k 2 ( y;λ )
S( n; y e ;λ )=[ (n1) Δx /M n Δx /M dx k 1 ( x;λ ) ][ y e /M ( y e +d ) /M dy k 2 ( y;λ ) ] K 1 ( n;λ ) K 2 ( y e ;λ )
I res ( y;p;λ )= | [ q( y ;λ )m( y ) ] h z 2 /M ( y;λ ) | 2 g( y )
S( p; y e ;λ )= Δx /M y e /M ( y e +d ) /M dy I res ( y;p;λ )
k 1 ( x;λ )=[ T( x;λ ) z 2 Mk ( T( x;λ ) 2 ϕ x 2 ( x;λ )+ T x ( x;λ ) ϕ x ( x;λ ) ) ]g( x ) T( x;λ )[ 1 z 2 Mk 2 ϕ x 2 ( x;λ ) ]g( x )
r near ( 4 σ x ) 2 + ( Δx M ) 2
r int ( 2max{ 2 σ x , λ z 2 /M } ) 2 + ( Δx M ) 2
S( p; y e ;λ )= Δx /M y e /M a dyT( ypΔy;λ ) = = Δx /M [ Trec t a y e /M ]( a/2 + y e / 2M pΔy )
S( p; y e ;λ )= Δx /M y e /M ( y e +d ) /M dy[ T( ypΔy;λ )rec t a ( ya /2 ) ] g( y )= = Δx /M [ T*PSF ]( pΔy )
PSF( y )=rec t a ( y+a /2 )[ [ grec t d/M ]( y+ y e /M +d / 2M ) ]
S( p; y e ;λ )= Δx /M ( y e z 2 Δ θ y ) /M ( y e +d z 2 Δ θ y ) /M dy[ T( ypΔy;λ )rec t a ( ya /2 ) ] g( y )
PSF( y )=rec t a ( y+a /2 )[ grec t d/M ]( y+ y e /M +d/ 2M z 2 Δ θ y /M )
I res ( y;p;λ )=[ | m( y ) | 2 z 2 Mk ( | m( y ) | 2 2 ϕ y 2 ( ypΔy;λ )+ y ( | m( y ) | 2 ) ϕ y ( ypΔy;λ ) ) ]g( y )
S( p; y e ;λ )= Δx /M y e /M ( y e +d ) /M dy[ rec t a ( ya /2 )g( y ) ] + + Δx /M z 2 /M Δ θ y ( ypΔy;λ ){ [ g( y y e /M )g( y y e /M d/M ) ]rec t a ( y+a/2 ) }
S( p; y e ;λ )= Δx /M ( a y e /M )+ Δx /M z 2 /M [ Δ θ y g ]( y e /M pΔy )
if 2 σ F <min[ y e /M ,a y e /M ] r=4 σ F if a y e /M <2 σ F < y e /M r=2 σ F +a y e /M if y e /M <2 σ F <a y e /M r= 2 σ F + y e /M if 2 σ F >max[ y e /M ,a y e /M ] r=a

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