Abstract

A three-image method to extract absorption, refraction and scattering information for hard x-ray grating interferometry is presented. The method comprises a post-processing approach alternative to the conventional phase stepping procedure and is inspired by a similar three-image technique developed for analyzer-based x-ray imaging. Results obtained with this algorithm are quantitatively comparable with phase-stepping. This method can be further extended to samples with negligible scattering, where only two images are needed to separate absorption and refraction signal. Thanks to the limited number of images required, this technique is a viable route to bio-compatible imaging with x-ray grating interferometer. In addition our method elucidates and strengthens the formal and practical analogies between grating interferometry and the (non-interferometric) diffraction enhanced imaging technique.

© 2013 OSA

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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]
  2. U. Bonse and M. Hart, “An x-ray interferometer,” Appl. Phys. Lett.6(8), 155–156 (1965).
    [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. 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]
  5. 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]
  6. 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]
  7. 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]
  8. L. Rigon, F. Arfelli, and R.-H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction and ultrasmall-angle scattering,” Appl. Phys. Lett.90(11), 114102 (2007).
    [CrossRef]
  9. L. Rigon, F. Arfelli, and R.-H. Menk, “Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects,” J. Phys. D Appl. Phys.40(10), 3077–3089 (2007).
    [CrossRef]
  10. 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]
  11. F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
    [CrossRef]
  12. L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys.36(10A), A107–A112 (2003).
    [CrossRef]
  13. P. C. Diemoz, P. Coan, I. Zanette, A. Bravin, S. Lang, C. Glaser, and T. Weitkamp, “A simplified approach for computed tomography with an X-ray grating interferometer,” Opt. Express19(3), 1691–1698 (2011).
    [CrossRef] [PubMed]
  14. 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]
  15. 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]
  16. 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]
  17. Ya. I. Nesterets, “On the origin of decoherence and extinction contrast in phase-contrast imaging,” Opt. Commun.281(4), 533–542 (2008).
    [CrossRef]
  18. Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett.95(9), 094105 (2009).
    [CrossRef]
  19. 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]
  20. F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. (2013), doi:.
    [CrossRef] [PubMed]
  21. W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express18(16), 16890–16901 (2010).
    [CrossRef] [PubMed]
  22. 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]
  23. S. K. Lynch, V. Pai, J. Auxier, A. F. Stein, E. E. Bennett, C. K. Kemble, X. Xiao, W.-K. Lee, N. Y. Morgan, and H. H. Wen, “Interpretation of dark-field contrast and particle-size selectivity in grating interferometers,” Appl. Opt.50(22), 4310–4319 (2011).
    [CrossRef] [PubMed]
  24. H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of x-ray scattering--initial results,” IEEE Trans. Med. Imaging27(8), 997–1002 (2008).
    [CrossRef] [PubMed]
  25. 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), 13576–13581 (2010).
    [CrossRef] [PubMed]
  26. 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]
  27. A. Momose, W. Yashiro, and Y. Takeda, “X-Ray Phase Imaging with Talbot Interferometry” in Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning, and Inverse Problems, Y. Censor, M. Jiang, G. Wang, ed. (Medical Physics Publishing, 2009).

2013

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]

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. (2013), doi:.
[CrossRef] [PubMed]

2012

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]

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]

2011

2010

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), 13576–13581 (2010).
[CrossRef] [PubMed]

W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express18(16), 16890–16901 (2010).
[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]

2009

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett.95(9), 094105 (2009).
[CrossRef]

2008

H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of x-ray scattering--initial results,” IEEE Trans. Med. Imaging27(8), 997–1002 (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]

Ya. I. Nesterets, “On the origin 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]

2007

L. Rigon, F. Arfelli, and R.-H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction and ultrasmall-angle scattering,” Appl. Phys. Lett.90(11), 114102 (2007).
[CrossRef]

L. Rigon, F. Arfelli, and R.-H. Menk, “Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects,” J. Phys. D Appl. Phys.40(10), 3077–3089 (2007).
[CrossRef]

2006

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]

2005

2003

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys.36(10A), A107–A112 (2003).
[CrossRef]

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]

1997

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]

1995

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

1965

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]

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.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

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]

L. Rigon, F. Arfelli, and R.-H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction and ultrasmall-angle scattering,” Appl. Phys. Lett.90(11), 114102 (2007).
[CrossRef]

L. Rigon, F. Arfelli, and R.-H. Menk, “Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects,” J. Phys. D Appl. Phys.40(10), 3077–3089 (2007).
[CrossRef]

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys.36(10A), A107–A112 (2003).
[CrossRef]

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.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

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]

Auxier, J.

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]

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.

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. (2013), doi:.
[CrossRef] [PubMed]

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]

Bennett, E. E.

Besch, H.-J.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys.36(10A), A107–A112 (2003).
[CrossRef]

Bonse, U.

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

Brankov, J. 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]

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.

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.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

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]

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]

Cardarelli, P.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

Carroll, S. C.

H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of x-ray scattering--initial results,” IEEE Trans. Med. Imaging27(8), 997–1002 (2008).
[CrossRef] [PubMed]

Cedola, A.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

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]

Chen, Z.-Q.

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett.95(9), 094105 (2009).
[CrossRef]

Cloetens, P.

Coan, P.

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]

De Caro, L.

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. (2013), doi:.
[CrossRef] [PubMed]

Diaz, A.

Diemoz, P. C.

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]

Dreossi, D.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

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]

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]

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]

Glaser, C.

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]

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]

Hegedus, M. M.

H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of x-ray scattering--initial results,” IEEE Trans. Med. Imaging27(8), 997–1002 (2008).
[CrossRef] [PubMed]

Heitner, G.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys.36(10A), A107–A112 (2003).
[CrossRef]

Huang, Z.-F.

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett.95(9), 094105 (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]

Kang, K.-J.

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett.95(9), 094105 (2009).
[CrossRef]

Kawabata, K.

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]

Kemble, C. K.

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]

Lagomarsino, S.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

Lang, S.

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]

Lee, W.-K.

Liu, X.

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), 13576–13581 (2010).
[CrossRef] [PubMed]

Liu, Y.

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), 13576–13581 (2010).
[CrossRef] [PubMed]

Longo, R.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

Lynch, S. K.

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), 13576–13581 (2010).
[CrossRef] [PubMed]

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), 13576–13581 (2010).
[CrossRef] [PubMed]

Menk, R. H.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

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]

Menk, R.-H.

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]

L. Rigon, F. Arfelli, and R.-H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction and ultrasmall-angle scattering,” Appl. Phys. Lett.90(11), 114102 (2007).
[CrossRef]

L. Rigon, F. Arfelli, and R.-H. Menk, “Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects,” J. Phys. D Appl. Phys.40(10), 3077–3089 (2007).
[CrossRef]

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys.36(10A), A107–A112 (2003).
[CrossRef]

Modregger, P.

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. (2013), doi:.
[CrossRef] [PubMed]

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.

W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express18(16), 16890–16901 (2010).
[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]

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

Morgan, N. Y.

Muehleman, C.

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]

Nesterets, Ya. I.

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

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]

Pai, V.

Pelliccia, D.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

Pfeiffer, F.

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]

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]

Plothow-Besch, H.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys.36(10A), A107–A112 (2003).
[CrossRef]

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]

Rigon, L.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

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]

L. Rigon, F. Arfelli, and R.-H. Menk, “Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects,” J. Phys. D Appl. Phys.40(10), 3077–3089 (2007).
[CrossRef]

L. Rigon, F. Arfelli, and R.-H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction and ultrasmall-angle scattering,” Appl. Phys. Lett.90(11), 114102 (2007).
[CrossRef]

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys.36(10A), A107–A112 (2003).
[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.

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. (2013), doi:.
[CrossRef] [PubMed]

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]

Sodini, N.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

Stampanoni, M.

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. (2013), doi:.
[CrossRef] [PubMed]

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. 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), 13576–13581 (2010).
[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]

Stein, A. F.

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]

Tangaro, S.

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. (2013), doi:.
[CrossRef] [PubMed]

Terui, Y.

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]

Wang, 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), 13576–13581 (2010).
[CrossRef] [PubMed]

Wang, Z.-T.

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett.95(9), 094105 (2009).
[CrossRef]

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.

Wen, H.

H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of x-ray scattering--initial results,” IEEE Trans. Med. Imaging27(8), 997–1002 (2008).
[CrossRef] [PubMed]

Wen, H. H.

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]

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]

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]

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), 13576–13581 (2010).
[CrossRef] [PubMed]

Xiao, X.

Yang, Y.

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]

Yashiro, W.

Zanette, I.

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]

P. C. Diemoz, P. Coan, I. Zanette, A. Bravin, S. Lang, C. Glaser, and T. Weitkamp, “A simplified approach for computed tomography with an X-ray grating interferometer,” Opt. Express19(3), 1691–1698 (2011).
[CrossRef] [PubMed]

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), 13576–13581 (2010).
[CrossRef] [PubMed]

Zhong, Z.

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]

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), 13576–13581 (2010).
[CrossRef] [PubMed]

Ziegler, E.

Appl. Opt.

Appl. Phys. Lett.

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

L. Rigon, F. Arfelli, and R.-H. Menk, “Three-image diffraction enhanced imaging algorithm to extract absorption, refraction and ultrasmall-angle scattering,” Appl. Phys. Lett.90(11), 114102 (2007).
[CrossRef]

Z.-T. Wang, K.-J. Kang, Z.-F. Huang, and Z.-Q. Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett.95(9), 094105 (2009).
[CrossRef]

Eur. J. Radiol.

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]

IEEE Trans. Med. Imaging

H. Wen, E. E. Bennett, M. M. Hegedus, and S. C. Carroll, “Spatial harmonic imaging of x-ray scattering--initial results,” IEEE Trans. Med. Imaging27(8), 997–1002 (2008).
[CrossRef] [PubMed]

J. Instrum.

F. Arfelli, D. Pelliccia, A. Cedola, A. Astolfo, I. Bukreeva, P. Cardarelli, D. Dreossi, S. Lagomarsino, R. Longo, L. Rigon, N. Sodini, and R. H. Menk, “Recent developments on techniques for differential phase imaging at the medical beamline of ELETTRA,” J. Instrum.8(06), 06001 (2013).
[CrossRef]

J. Phys. D Appl. Phys.

L. Rigon, H.-J. Besch, F. Arfelli, R.-H. Menk, G. Heitner, and H. Plothow-Besch, “A new DEI algorithm capable of investigating sub-pixel structures,” J. Phys. D Appl. Phys.36(10A), A107–A112 (2003).
[CrossRef]

L. Rigon, F. Arfelli, and R.-H. Menk, “Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects,” J. Phys. D Appl. Phys.40(10), 3077–3089 (2007).
[CrossRef]

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]

Nat. Mater.

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]

Nucl. Instrum. Meth. A

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

Opt. Commun.

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

Opt. Express

Phys. Med.

F. Scattarella, S. Tangaro, P. Modregger, M. Stampanoni, L. De Caro, and R. Bellotti, “Post-detection analysis for grating-based ultra-small angle X-ray scattering,” Phys. Med. (2013), doi:.
[CrossRef] [PubMed]

Phys. Med. Biol.

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]

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]

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]

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]

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]

Phys. Rev. Lett.

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]

Proc. Natl. Acad. Sci. U.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), 13576–13581 (2010).
[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]

Other

A. Momose, W. Yashiro, and Y. Takeda, “X-Ray Phase Imaging with Talbot Interferometry” in Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning, and Inverse Problems, Y. Censor, M. Jiang, G. Wang, ed. (Medical Physics Publishing, 2009).

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Figures (4)

Fig. 1
Fig. 1

Measured intensity after the absorption grating in a certain pixel of the detector with coordinate x0 and y0 as a function of the relative position ξ of the two gratins. The blue crosses indicate the position where the images used in Eq. (6) have been acquired. Open red circles indicate the positions used for the PS approach, Eqs. (8) and (9).

Fig. 2
Fig. 2

(a) Absorption and (b) refraction images obtained with PS and (c)-(d) with the novel algorithm. (e) Line profiles along the rows marked with arrows in (b) and (d), black and red line respectively. (f) Histogram of the refraction angle as obtained by both methods in a region within the sample and (g) in the background region.

Fig. 3
Fig. 3

Bovine bone sample. (a) Image of the variance standard deviation of the scattering distribution obtained by the phase stepping method with three steps. (b) Scatter image calculated with Eq. (6). (c) Difference obtained from the previous images. (d) Histograms of the maps in (a) and (b).

Fig. 4
Fig. 4

(a) Absorption and (b) refraction image of the bovine bone sample obtained with a two-image algorithm. (c) Absorption and (d) refraction images (in μrad) of the nylon wire obtained with the two-image method and (e), (f) corresponding images obtained by PS.

Equations (9)

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I(x,y,ξ)= I 0 (x,y) T(ξΔ x R Δ x s )f(Δ x S )dΔ x S .
I(x,y, ξ 0 )= I 0 (x,y)( T( ξ 0 ) T ˙ ( ξ 0 )Δ x R + 1 2 T ¨ ( ξ 0 )Δ x R 2 + 1 2 T ¨ ( ξ 0 ) σ X 2 ).
σ X 2 = Δ x S 2 f(Δ x S )dΔ x S ,
σ X = Δ x S f(Δ x S )dΔ x S =0.
I(x,y,ξ)= I 0 (x,y) T(η)f(ξΔ x R η)dη=T(ξ)g(ξ).
I 0 =( i,j,k=1 3 ε ijk I i T ˙ j T ¨ k ) ( i,j,k=1 3 ε ijk T i T ˙ j T ¨ k ) 1 , Δ θ R = 1 L ( i,j,k=1 3 ε ijk I i T j T ¨ k ) ( i,j,k=1 3 ε ijk T i T ˙ j T ¨ k ) 1 , σ S 2 = 2 L 2 ( i,j,k=1 3 ε ijk I i T j T ˙ k ) ( i,j,k=1 3 ε ijk T i T ˙ j T ¨ k ) 1 Δ θ R 2 .
2ln(V/ V 0 )= σ S 2 ,
I(x,y,ξ)= I 0 (x,y)+ m=1 a m (x,y)cos( 2π p ξ+ ϕ m (x,y) ) .
Δ θ R (x,y)= p 2πL ϕ 1 (x,y), V(x,y) V 0 (x,y) = a 1 (x,y) I 0 (x,y) .

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