Abstract

Multi-modal hard x-ray imaging sensitive to absorption, refraction, phase and scattering contrast is demonstrated using a simple setup implemented with a laboratory source. The method is based on selective reflection at the edge of a mirror, aligned to partially reflect a pencil x-ray beam after its interaction with a sample. Quantitative scattering contrast from a test sample is experimentally demonstrated using this method. Multi-modal imaging of a house fly (Musca domestica) is shown as proof of principle of the technique for biological samples.

© 2014 Optical Society of America

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  1. A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol.58(1), R1–R35 (2013).
    [CrossRef] [PubMed]
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    [CrossRef]
  3. 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]
  4. A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Meth. A352(3), 622–628 (1995).
    [CrossRef]
  5. T. J. 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]
  6. D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmür, Z. Zhong, R. H. Menk, F. Arfelli, and D. Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol.42(11), 2015–2025 (1997).
    [CrossRef] [PubMed]
  7. 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]
  8. 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]
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    [CrossRef]
  10. M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol.48(23), 3875–3895 (2003).
    [CrossRef] [PubMed]
  11. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater.7(2), 134–137 (2008).
    [CrossRef] [PubMed]
  12. M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett.104(2), 024106 (2014).
    [CrossRef]
  13. I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A.109(26), 10199–10204 (2012).
    [CrossRef] [PubMed]
  14. O. Bunk, M. Bech, T. H. Jensen, R. Feidenhans’l, T. Binderup, A. Menzel, and F. Pfeiffer, “Multimodal x-ray scatter imaging,” New J. Phys.11(12), 123016 (2009).
    [CrossRef]
  15. G. Wang, H. Yu, and B. De Man, “An outlook on x-ray CT research and development,” Med. Phys.35(3), 1051–1064 (2008).
    [CrossRef] [PubMed]
  16. F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based X-ray phase contrast for biomedical imaging applications,” Z. Med. Phys.23(3), 176–185 (2013).
    [CrossRef] [PubMed]
  17. 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]
  18. D. Pelliccia and D. M. Paganin, “X-ray phase imaging with a laboratory source using selective reflection from a mirror,” Opt. Express21(8), 9308–9314 (2013).
    [CrossRef] [PubMed]
  19. 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]
  20. G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol.51(2), 221–236 (2006).
    [CrossRef] [PubMed]
  21. J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys.33(2), 278–289 (2006).
    [CrossRef] [PubMed]
  22. L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol.68(3Suppl), S3–S7 (2008).
    [CrossRef] [PubMed]
  23. M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol.55(18), 5529–5539 (2010).
    [CrossRef] [PubMed]
  24. Ya. I. Nesterets, “On the origins of decoherence and extinction contrast in phase-contrast imaging,” Opt. Commun.281(4), 533–542 (2008).
    [CrossRef]
  25. P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett.108(4), 048101 (2012).
    [CrossRef] [PubMed]
  26. D. Pelliccia, L. Rigon, F. Arfelli, R. H. Menk, I. Bukreeva, and A. Cedola, “A three-image algorithm for hard x-ray grating interferometry,” Opt. Express21(16), 19401–19411 (2013).
    [CrossRef] [PubMed]

2014 (1)

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett.104(2), 024106 (2014).
[CrossRef]

2013 (4)

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based X-ray phase contrast for biomedical imaging applications,” Z. Med. Phys.23(3), 176–185 (2013).
[CrossRef] [PubMed]

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol.58(1), R1–R35 (2013).
[CrossRef] [PubMed]

D. Pelliccia and D. M. Paganin, “X-ray phase imaging with a laboratory source using selective reflection from a mirror,” Opt. Express21(8), 9308–9314 (2013).
[CrossRef] [PubMed]

D. Pelliccia, L. Rigon, F. Arfelli, R. H. Menk, I. Bukreeva, and A. Cedola, “A three-image algorithm for hard x-ray grating interferometry,” Opt. Express21(16), 19401–19411 (2013).
[CrossRef] [PubMed]

2012 (3)

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett.108(4), 048101 (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]

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A.109(26), 10199–10204 (2012).
[CrossRef] [PubMed]

2010 (1)

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol.55(18), 5529–5539 (2010).
[CrossRef] [PubMed]

2009 (1)

O. Bunk, M. Bech, T. H. Jensen, R. Feidenhans’l, T. Binderup, A. Menzel, and F. Pfeiffer, “Multimodal x-ray scatter imaging,” New J. Phys.11(12), 123016 (2009).
[CrossRef]

2008 (4)

G. Wang, H. Yu, and B. De Man, “An outlook on x-ray CT research and development,” Med. Phys.35(3), 1051–1064 (2008).
[CrossRef] [PubMed]

Ya. I. Nesterets, “On the origins of decoherence and extinction contrast in phase-contrast imaging,” Opt. Commun.281(4), 533–542 (2008).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater.7(2), 134–137 (2008).
[CrossRef] [PubMed]

L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol.68(3Suppl), S3–S7 (2008).
[CrossRef] [PubMed]

2007 (1)

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]

2006 (2)

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol.51(2), 221–236 (2006).
[CrossRef] [PubMed]

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys.33(2), 278–289 (2006).
[CrossRef] [PubMed]

2005 (1)

2003 (2)

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol.48(23), 3875–3895 (2003).
[CrossRef] [PubMed]

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 (1)

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 (1)

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

1996 (1)

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 (2)

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

T. J. 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]

1965 (1)

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

Anastasio, M. A.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol.51(2), 221–236 (2006).
[CrossRef] [PubMed]

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys.33(2), 278–289 (2006).
[CrossRef] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol.48(23), 3875–3895 (2003).
[CrossRef] [PubMed]

Arfelli, F.

D. Pelliccia, L. Rigon, F. Arfelli, R. H. Menk, I. Bukreeva, and A. Cedola, “A three-image algorithm for hard x-ray grating interferometry,” Opt. Express21(16), 19401–19411 (2013).
[CrossRef] [PubMed]

L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol.68(3Suppl), S3–S7 (2008).
[CrossRef] [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]

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

Astolfo, A.

L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol.68(3Suppl), S3–S7 (2008).
[CrossRef] [PubMed]

Auweter, S.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based X-ray phase contrast for biomedical imaging applications,” Z. Med. Phys.23(3), 176–185 (2013).
[CrossRef] [PubMed]

Bamberg, F.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based X-ray phase contrast for biomedical imaging applications,” Z. Med. Phys.23(3), 176–185 (2013).
[CrossRef] [PubMed]

Bech, M.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A.109(26), 10199–10204 (2012).
[CrossRef] [PubMed]

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol.55(18), 5529–5539 (2010).
[CrossRef] [PubMed]

O. Bunk, M. Bech, T. H. Jensen, R. Feidenhans’l, T. Binderup, A. Menzel, and F. Pfeiffer, “Multimodal x-ray scatter imaging,” New J. Phys.11(12), 123016 (2009).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater.7(2), 134–137 (2008).
[CrossRef] [PubMed]

Bellotti, R.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett.108(4), 048101 (2012).
[CrossRef] [PubMed]

Binderup, T.

O. Bunk, M. Bech, T. H. Jensen, R. Feidenhans’l, T. Binderup, A. Menzel, and F. Pfeiffer, “Multimodal x-ray scatter imaging,” New J. Phys.11(12), 123016 (2009).
[CrossRef]

Bonse, U.

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

Brankov, J. G.

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys.33(2), 278–289 (2006).
[CrossRef] [PubMed]

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol.51(2), 221–236 (2006).
[CrossRef] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol.48(23), 3875–3895 (2003).
[CrossRef] [PubMed]

Bravin, A.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol.58(1), R1–R35 (2013).
[CrossRef] [PubMed]

Brönnimann, Ch.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater.7(2), 134–137 (2008).
[CrossRef] [PubMed]

Bukreeva, I.

Bunk, O.

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol.55(18), 5529–5539 (2010).
[CrossRef] [PubMed]

O. Bunk, M. Bech, T. H. Jensen, R. Feidenhans’l, T. Binderup, A. Menzel, and F. Pfeiffer, “Multimodal x-ray scatter imaging,” New J. Phys.11(12), 123016 (2009).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater.7(2), 134–137 (2008).
[CrossRef] [PubMed]

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]

Cedola, A.

Chabior, M.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based X-ray phase contrast for biomedical imaging applications,” Z. Med. Phys.23(3), 176–185 (2013).
[CrossRef] [PubMed]

Chapman, D.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol.51(2), 221–236 (2006).
[CrossRef] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol.48(23), 3875–3895 (2003).
[CrossRef] [PubMed]

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

Cloetens, P.

Coan, P.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol.58(1), R1–R35 (2013).
[CrossRef] [PubMed]

David, C.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett.108(4), 048101 (2012).
[CrossRef] [PubMed]

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A.109(26), 10199–10204 (2012).
[CrossRef] [PubMed]

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol.55(18), 5529–5539 (2010).
[CrossRef] [PubMed]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater.7(2), 134–137 (2008).
[CrossRef] [PubMed]

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, T. J.

T. J. 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]

De Man, B.

G. Wang, H. Yu, and B. De Man, “An outlook on x-ray CT research and development,” Med. Phys.35(3), 1051–1064 (2008).
[CrossRef] [PubMed]

Diaz, A.

Diemoz, P. C.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett.104(2), 024106 (2014).
[CrossRef]

Donath, T.

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol.55(18), 5529–5539 (2010).
[CrossRef] [PubMed]

Eikenberry, E. F.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater.7(2), 134–137 (2008).
[CrossRef] [PubMed]

Endrizzi, M.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett.104(2), 024106 (2014).
[CrossRef]

Feidenhans’l, R.

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol.55(18), 5529–5539 (2010).
[CrossRef] [PubMed]

O. Bunk, M. Bech, T. H. Jensen, R. Feidenhans’l, T. Binderup, A. Menzel, and F. Pfeiffer, “Multimodal x-ray scatter imaging,” New J. Phys.11(12), 123016 (2009).
[CrossRef]

Galatsanos, N. P.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol.48(23), 3875–3895 (2003).
[CrossRef] [PubMed]

Gao, D.

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. J. 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]

Gmür, N.

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

Grünzweig, C.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater.7(2), 134–137 (2008).
[CrossRef] [PubMed]

Gureyev, T. E.

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. J. 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]

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]

Hart, M.

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

Herzen, J.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based X-ray phase contrast for biomedical imaging applications,” Z. Med. Phys.23(3), 176–185 (2013).
[CrossRef] [PubMed]

Ignatyev, K.

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]

Jensen, T. H.

O. Bunk, M. Bech, T. H. Jensen, R. Feidenhans’l, T. Binderup, A. Menzel, and F. Pfeiffer, “Multimodal x-ray scatter imaging,” New J. Phys.11(12), 123016 (2009).
[CrossRef]

Johnston, R. E.

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

Jones, J. L.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett.104(2), 024106 (2014).
[CrossRef]

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]

Khelashvili, G.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol.51(2), 221–236 (2006).
[CrossRef] [PubMed]

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]

Kraft, P.

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater.7(2), 134–137 (2008).
[CrossRef] [PubMed]

Le Duc, G.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A.109(26), 10199–10204 (2012).
[CrossRef] [PubMed]

Li, J.

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys.33(2), 278–289 (2006).
[CrossRef] [PubMed]

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]

Menk, R. H.

D. Pelliccia, L. Rigon, F. Arfelli, R. H. Menk, I. Bukreeva, and A. Cedola, “A three-image algorithm for hard x-ray grating interferometry,” Opt. Express21(16), 19401–19411 (2013).
[CrossRef] [PubMed]

L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol.68(3Suppl), S3–S7 (2008).
[CrossRef] [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]

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

Menzel, A.

O. Bunk, M. Bech, T. H. Jensen, R. Feidenhans’l, T. Binderup, A. Menzel, and F. Pfeiffer, “Multimodal x-ray scatter imaging,” New J. Phys.11(12), 123016 (2009).
[CrossRef]

Millard, T. P.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett.104(2), 024106 (2014).
[CrossRef]

Modregger, P.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett.108(4), 048101 (2012).
[CrossRef] [PubMed]

Mohr, J.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A.109(26), 10199–10204 (2012).
[CrossRef] [PubMed]

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]

Muehleman, C.

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys.33(2), 278–289 (2006).
[CrossRef] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol.48(23), 3875–3895 (2003).
[CrossRef] [PubMed]

Munro, P. R. T.

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]

Nesterets, Ya. I.

Ya. I. Nesterets, “On the origins of decoherence and extinction contrast in phase-contrast imaging,” Opt. Commun.281(4), 533–542 (2008).
[CrossRef]

Olivo, A.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett.104(2), 024106 (2014).
[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]

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, 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]

Oltulu, O.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol.48(23), 3875–3895 (2003).
[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]

Pelliccia, D.

Pfeiffer, F.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based X-ray phase contrast for biomedical imaging applications,” Z. Med. Phys.23(3), 176–185 (2013).
[CrossRef] [PubMed]

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A.109(26), 10199–10204 (2012).
[CrossRef] [PubMed]

M. Bech, O. Bunk, T. Donath, R. Feidenhans’l, C. David, and F. Pfeiffer, “Quantitative x-ray dark-field computed tomography,” Phys. Med. Biol.55(18), 5529–5539 (2010).
[CrossRef] [PubMed]

O. Bunk, M. Bech, T. H. Jensen, R. Feidenhans’l, T. Binderup, A. Menzel, and F. Pfeiffer, “Multimodal x-ray scatter imaging,” New J. Phys.11(12), 123016 (2009).
[CrossRef]

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater.7(2), 134–137 (2008).
[CrossRef] [PubMed]

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]

Pinzer, B. R.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett.108(4), 048101 (2012).
[CrossRef] [PubMed]

Pisano, E.

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

Pogany, A.

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]

Rack, A.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A.109(26), 10199–10204 (2012).
[CrossRef] [PubMed]

Reiser, M.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based X-ray phase contrast for biomedical imaging applications,” Z. Med. Phys.23(3), 176–185 (2013).
[CrossRef] [PubMed]

Rigon, L.

D. Pelliccia, L. Rigon, F. Arfelli, R. H. Menk, I. Bukreeva, and A. Cedola, “A three-image algorithm for hard x-ray grating interferometry,” Opt. Express21(16), 19401–19411 (2013).
[CrossRef] [PubMed]

L. Rigon, A. Astolfo, F. Arfelli, and R. H. Menk, “Generalized diffraction enhanced imaging: application to tomography,” Eur. J. Radiol.68(3Suppl), S3–S7 (2008).
[CrossRef] [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.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett.104(2), 024106 (2014).
[CrossRef]

Sayers, D.

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

Scattarella, F.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett.108(4), 048101 (2012).
[CrossRef] [PubMed]

Speller, R.

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]

Speller, R. D.

M. Endrizzi, P. C. Diemoz, T. P. Millard, J. L. Jones, R. D. Speller, I. K. Robinson, and A. Olivo, “Hard X-ray dark-field imaging with incoherent sample illumination,” Appl. Phys. Lett.104(2), 024106 (2014).
[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]

Stampanoni, M.

P. Modregger, F. Scattarella, B. R. Pinzer, C. David, R. Bellotti, and M. Stampanoni, “Imaging the ultrasmall-angle x-ray scattering distribution with grating interferometry,” Phys. Rev. Lett.108(4), 048101 (2012).
[CrossRef] [PubMed]

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]

Stevenson, A. W.

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. J. 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]

Suortti, P.

A. Bravin, P. Coan, and P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol.58(1), R1–R35 (2013).
[CrossRef] [PubMed]

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]

Tafforeau, P.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A.109(26), 10199–10204 (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]

Thomlinson, W.

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

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]

Wang, G.

G. Wang, H. Yu, and B. De Man, “An outlook on x-ray CT research and development,” Med. Phys.35(3), 1051–1064 (2008).
[CrossRef] [PubMed]

Washburn, D.

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

Weitkamp, T.

I. Zanette, M. Bech, A. Rack, G. Le Duc, P. Tafforeau, C. David, J. Mohr, F. Pfeiffer, and T. Weitkamp, “Trimodal low-dose X-ray tomography,” Proc. Natl. Acad. Sci. U.S.A.109(26), 10199–10204 (2012).
[CrossRef] [PubMed]

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]

Wernick, M. N.

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol.51(2), 221–236 (2006).
[CrossRef] [PubMed]

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys.33(2), 278–289 (2006).
[CrossRef] [PubMed]

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol.48(23), 3875–3895 (2003).
[CrossRef] [PubMed]

Wilkins, S. W.

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. J. 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]

Willner, M.

F. Pfeiffer, J. Herzen, M. Willner, M. Chabior, S. Auweter, M. Reiser, and F. Bamberg, “Grating-based X-ray phase contrast for biomedical imaging applications,” Z. Med. Phys.23(3), 176–185 (2013).
[CrossRef] [PubMed]

Wirjadi, O.

M. N. Wernick, O. Wirjadi, D. Chapman, Z. Zhong, N. P. Galatsanos, Y. Yang, J. G. Brankov, O. Oltulu, M. A. Anastasio, and C. Muehleman, “Multiple-image radiography,” Phys. Med. Biol.48(23), 3875–3895 (2003).
[CrossRef] [PubMed]

Yang, Y.

J. G. Brankov, M. N. Wernick, Y. Yang, J. Li, C. Muehleman, Z. Zhong, and M. A. Anastasio, “A computed tomography implementation of multiple-image radiography,” Med. Phys.33(2), 278–289 (2006).
[CrossRef] [PubMed]

G. Khelashvili, J. G. Brankov, D. Chapman, M. A. Anastasio, Y. Yang, Z. Zhong, and M. N. Wernick, “A physical model of multiple-image radiography,” Phys. Med. Biol.51(2), 221–236 (2006).
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Figures (3)

Fig. 1
Fig. 1

Schematic of the experimental setup (not to scale). X-rays, after interacting with the sample, illuminate the mirror edge, aligned to partially obscure a given pixel row of the detector (Id). Photons that strike the mirror are reflected onto a different pixel row (Ir). Weak scattering occurring at the sample may be detected around the direct beam direction, especially in a pixel row that is covered by the mirror shadow (Is), generating a dark field image. For the data shown in this paper we used z1 = 100 mm and z2 = 210 mm. The mirror tilt angle was 3.3 mrad from the optic axis producing a transverse displacement of the reflected beam of about 1.5 mm at the detector position.

Fig. 2
Fig. 2

(a) Dark field x-ray image of a stack of optical paper tissues with variable thickness. The leftmost region corresponds to one paper sheet while the rightmost region corresponds to scattering from a stack of 6 optical paper sheets. Image data have been background subtracted, the said background corresponding to the intensity image measured in the absence of the paper. (b) Plot of the average counts in regions of equal thickness against the paper stack thickness (filled diamonds). The red solid line gives the linear fit to the data.

Fig. 3
Fig. 3

Multi-modal x-ray imaging of the abdomen of a house fly. (a) Attenuation image, (b) Refraction angle image, (c) Phase image, (d) Scatter (dark-field) image and (e) Absorption-free image (see text for details). The linear structures on both sides of the sample are the edges of a kapton foil, rolled to form a conical shape, used to hold the sample in place during the scan.

Equations (2)

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A= e μt e εt ,
S=a ( 1 e εt ) e μt .

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