Abstract

In this article, we report on a novel acquisition scheme for time- and dose-saving retrieval of dark-field data in grating-based phase-contrast imaging. In comparison to currently available techniques, the proposed approach only requires two phase steps. More importantly, our method is capable of accurately retrieving the dark-field signal where conventional approaches fail, for instance in the case of very low photon statistics. Finally, we successfully extend two-shot dark-field imaging to tomographic investigations, by implementing an iterative reconstruction with appropriate weights. Our results indicate an important progression towards the clinical feasibility of dark-field tomography.

© 2016 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref]
  23. A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  26. T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011).
    [Crossref] [PubMed]
  27. D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5, 10452 (2015).
    [Crossref] [PubMed]
  28. S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 23, 282–332 (1944).
    [Crossref]
  29. P. Li, K. Zhang, Y. Bao, Y. Ren, Z. Ju, Y. Wang, Q. He, Z. Zhu, W. Huang, Q. Yuan, and P. Zhu, “Angular signal radiography,” Opt. Express 24, 5829–5845 (2016).
    [Crossref] [PubMed]
  30. 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, A107–A112 (2003).
    [Crossref]
  31. 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. Express 21, 19401–11 (2013).
    [Crossref] [PubMed]
  32. Y. Bao, Y. Wang, K. Gao, Z.-L. Wang, P.-P. Zhu, and Z.-Y. Wu, “Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method,” Chin. Phys. B 24, 108702 (2015).
    [Crossref]
  33. L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
    [Crossref] [PubMed]
  34. A. Hipp, M. Willner, J. Herzen, S. D. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic X-ray sources,” Opt. Express 22, 30394 (2014).
    [Crossref]
  35. M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
    [Crossref] [PubMed]
  36. V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010).
    [Crossref] [PubMed]
  37. H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Biol. 44, 1064–1068 (2002).
  38. 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, 10–13 (2009).
  39. 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, 5529–5539 (2010).
    [Crossref] [PubMed]

2016 (3)

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in X-ray phase-contrast imaging,” Nat. Phys. 12, 830–834 (2016).
[Crossref]

P. Li, K. Zhang, Y. Bao, Y. Ren, Z. Ju, Y. Wang, Q. He, Z. Zhu, W. Huang, Q. Yuan, and P. Zhu, “Angular signal radiography,” Opt. Express 24, 5829–5845 (2016).
[Crossref] [PubMed]

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

2015 (5)

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5, 10452 (2015).
[Crossref] [PubMed]

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
[Crossref] [PubMed]

Y. Bao, Y. Wang, K. Gao, Z.-L. Wang, P.-P. Zhu, and Z.-Y. Wu, “Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method,” Chin. Phys. B 24, 108702 (2015).
[Crossref]

2014 (3)

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

A. Hipp, M. Willner, J. Herzen, S. D. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic X-ray sources,” Opt. Express 22, 30394 (2014).
[Crossref]

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 1–5 (2014).
[Crossref]

2013 (3)

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

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, 176–185 (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. Express 21, 19401–11 (2013).
[Crossref] [PubMed]

2012 (2)

S. Berujon, H. Wang, and K. Sawhney, “X-ray multimodal imaging using a random-phase object,” Phys. Rev. A 86, 1–9 (2012).
[Crossref]

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100, 124102 (2012).
[Crossref]

2011 (4)

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, 4310–4319 (2011).
[Crossref] [PubMed]

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011).
[Crossref] [PubMed]

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

2010 (3)

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref] [PubMed]

W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express 18, 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, 5529–5539 (2010).
[Crossref] [PubMed]

2009 (1)

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, 10–13 (2009).

2008 (3)

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

R. Cerbino, L. Peverini, M. a. C. Potenza, a. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

2007 (2)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007).
[Crossref] [PubMed]

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91, 1–3 (2007).
[Crossref]

2006 (1)

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

2005 (1)

2003 (1)

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, A107–A112 (2003).
[Crossref]

2002 (2)

H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Biol. 44, 1064–1068 (2002).

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287 (2002).
[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, 1610 (2001).
[Crossref] [PubMed]

1995 (2)

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,” Nature 373, 595–598 (1995).
[Crossref]

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

1965 (1)

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

1944 (1)

S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 23, 282–332 (1944).
[Crossref]

Achterhold, K.

Anton, G.

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011).
[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. Express 21, 19401–11 (2013).
[Crossref] [PubMed]

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, A107–A112 (2003).
[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, 1610 (2001).
[Crossref] [PubMed]

Auweter, S.

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

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, 176–185 (2013).
[Crossref] [PubMed]

Auweter, S. D.

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

A. Hipp, M. Willner, J. Herzen, S. D. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic X-ray sources,” Opt. Express 22, 30394 (2014).
[Crossref]

Auxier, J.

Bamberg, F.

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

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, 176–185 (2013).
[Crossref] [PubMed]

Bao, Y.

P. Li, K. Zhang, Y. Bao, Y. Ren, Z. Ju, Y. Wang, Q. He, Z. Zhu, W. Huang, Q. Yuan, and P. Zhu, “Angular signal radiography,” Opt. Express 24, 5829–5845 (2016).
[Crossref] [PubMed]

Y. Bao, Y. Wang, K. Gao, Z.-L. Wang, P.-P. Zhu, and Z.-Y. Wu, “Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method,” Chin. Phys. B 24, 108702 (2015).
[Crossref]

Bartl, P.

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011).
[Crossref] [PubMed]

Bayer, F.

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011).
[Crossref] [PubMed]

Bech, M.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5, 10452 (2015).
[Crossref] [PubMed]

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

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, 5529–5539 (2010).
[Crossref] [PubMed]

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

Bennett, E. E.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in X-ray phase-contrast imaging,” Nat. Phys. 12, 830–834 (2016).
[Crossref]

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
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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, 4310–4319 (2011).
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Berujon, S.

S. Berujon, H. Wang, and K. Sawhney, “X-ray multimodal imaging using a random-phase object,” Phys. Rev. A 86, 1–9 (2012).
[Crossref]

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, A107–A112 (2003).
[Crossref]

Bhandarkar, P.

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
[Crossref] [PubMed]

Biernath, T.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

Birnbacher, L.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

Bonse, U.

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

Bösecke, P.

R. Cerbino, L. Peverini, M. a. C. Potenza, a. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Bravin, A.

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

Brönnimann, C.

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

Bukreeva, I.

Bunk, O.

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[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, 5529–5539 (2010).
[Crossref] [PubMed]

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

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007).
[Crossref] [PubMed]

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, 258–261 (2006).
[Crossref]

Burvall, A.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 1–5 (2014).
[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, 1610 (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, 1610 (2001).
[Crossref] [PubMed]

Cedola, A.

Cerbino, R.

R. Cerbino, L. Peverini, M. a. C. Potenza, a. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Chabior, M.

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

A. Hipp, M. Willner, J. Herzen, S. D. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic X-ray sources,” Opt. Express 22, 30394 (2014).
[Crossref]

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, 176–185 (2013).
[Crossref] [PubMed]

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

Chedid, N.

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
[Crossref] [PubMed]

Chen, L.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in X-ray phase-contrast imaging,” Nat. Phys. 12, 830–834 (2016).
[Crossref]

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, 10–13 (2009).

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, R1 (2013).
[Crossref]

Conlon, T. M.

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

David, C.

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[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, 5529–5539 (2010).
[Crossref] [PubMed]

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

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

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007).
[Crossref] [PubMed]

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, 258–261 (2006).
[Crossref]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287 (2002).
[Crossref]

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,” Nature 373, 595–598 (1995).
[Crossref]

Diaz, A.

Dierolf, M.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

Donath, T.

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[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, 5529–5539 (2010).
[Crossref] [PubMed]

Durst, J.

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011).
[Crossref] [PubMed]

Eggl, E.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

Eickelberg, O.

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

Eikenberry, E. F.

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

Erdogan, H.

H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Biol. 44, 1064–1068 (2002).

Fehringer, A.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5, 10452 (2015).
[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, 5529–5539 (2010).
[Crossref] [PubMed]

Fessler, J. A.

H. Erdogan and J. A. Fessler, “Ordered subsets algorithms for transmission tomography,” Phys. Med. Biol. 44, 1064–1068 (2002).

Foster, B. A.

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
[Crossref] [PubMed]

Frei, G.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

Gao, D.

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,” Nature 373, 595–598 (1995).
[Crossref]

Gao, K.

Y. Bao, Y. Wang, K. Gao, Z.-L. Wang, P.-P. Zhu, and Z.-Y. Wu, “Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method,” Chin. Phys. B 24, 108702 (2015).
[Crossref]

Gibmeier, J.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

Giglio, M.

R. Cerbino, L. Peverini, M. a. C. Potenza, a. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Gomella, A. A.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in X-ray phase-contrast imaging,” Nat. Phys. 12, 830–834 (2016).
[Crossref]

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
[Crossref] [PubMed]

Grandl, S.

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

Grünzweig, C.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

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

Gureyev, T. E.

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,” Nature 373, 595–598 (1995).
[Crossref]

Haas, W.

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011).
[Crossref] [PubMed]

Hahn, D.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5, 10452 (2015).
[Crossref] [PubMed]

Harmon, K. J.

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
[Crossref] [PubMed]

Hart, M.

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

He, Q.

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, A107–A112 (2003).
[Crossref]

Hellbach, K.

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

Hellerhoff, K.

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

Hertz, H. M.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 1–5 (2014).
[Crossref]

Herzen, J.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

A. Hipp, M. Willner, J. Herzen, S. D. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic X-ray sources,” Opt. Express 22, 30394 (2014).
[Crossref]

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, 176–185 (2013).
[Crossref] [PubMed]

Hipp, A.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

A. Hipp, M. Willner, J. Herzen, S. D. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic X-ray sources,” Opt. Express 22, 30394 (2014).
[Crossref]

Huang, W.

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, 10–13 (2009).

Ju, Z.

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, 10–13 (2009).

Kaufmann, R.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref] [PubMed]

Kawabata, K.

Kemble, C. K.

Koch, F.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

Koehler, T.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5, 10452 (2015).
[Crossref] [PubMed]

Kohlbrecher, J.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

Kohn, V.

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

Kottler, C.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007).
[Crossref] [PubMed]

Kraft, P.

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

Kühne, G.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

Kunka, D.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

Kuznetsov, S.

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

Larsson, D. H.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 1–5 (2014).
[Crossref]

Lasser, T.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

Lee, W.-K.

Lejcek, P.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

Li, P.

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, 1610 (2001).
[Crossref] [PubMed]

Lundström, U.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 1–5 (2014).
[Crossref]

Lynch, S. K.

Maisenbacher, J.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

Malecki, A.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

Marschner, M.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

Mayr, D.

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

Meinel, F. G.

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

Meiser, J.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

A. Hipp, M. Willner, J. Herzen, S. D. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic X-ray sources,” Opt. Express 22, 30394 (2014).
[Crossref]

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, 1610 (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. Express 21, 19401–11 (2013).
[Crossref] [PubMed]

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, A107–A112 (2003).
[Crossref]

Miao, H.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in X-ray phase-contrast imaging,” Nat. Phys. 12, 830–834 (2016).
[Crossref]

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
[Crossref] [PubMed]

Michel, T.

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011).
[Crossref] [PubMed]

Mohr, J.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

A. Hipp, M. Willner, J. Herzen, S. D. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic X-ray sources,” Opt. Express 22, 30394 (2014).
[Crossref]

Momose, A.

Morgan, K. S.

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100, 124102 (2012).
[Crossref]

Morgan, N. Y.

Mueller, M.

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

Noël, P. B.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5, 10452 (2015).
[Crossref] [PubMed]

Nöhammer, B.

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287 (2002).
[Crossref]

Notohamiprodjo, M.

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

Olivo, A.

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91, 1–3 (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, 1610 (2001).
[Crossref] [PubMed]

Paganin, D. M.

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100, 124102 (2012).
[Crossref]

Pai, V.

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, 1610 (2001).
[Crossref] [PubMed]

Panna, A.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in X-ray phase-contrast imaging,” Nat. Phys. 12, 830–834 (2016).
[Crossref]

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
[Crossref] [PubMed]

Pelliccia, D.

Peverini, L.

R. Cerbino, L. Peverini, M. a. C. Potenza, a. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Pfeiffer, F.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5, 10452 (2015).
[Crossref] [PubMed]

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 1–5 (2014).
[Crossref]

A. Hipp, M. Willner, J. Herzen, S. D. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic X-ray sources,” Opt. Express 22, 30394 (2014).
[Crossref]

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, 176–185 (2013).
[Crossref] [PubMed]

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[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, 5529–5539 (2010).
[Crossref] [PubMed]

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

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007).
[Crossref] [PubMed]

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, 258–261 (2006).
[Crossref]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[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, A107–A112 (2003).
[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, 1610 (2001).
[Crossref] [PubMed]

Potdevin, G.

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

Potenza, M. a. C.

R. Cerbino, L. Peverini, M. a. C. Potenza, a. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

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, 1610 (2001).
[Crossref] [PubMed]

Reiser, M.

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

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, 176–185 (2013).
[Crossref] [PubMed]

Ren, Y.

Revol, V.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref] [PubMed]

Rice, S. O.

S. O. Rice, “Mathematical analysis of random noise,” Bell Syst. Tech. J. 23, 282–332 (1944).
[Crossref]

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. Express 21, 19401–11 (2013).
[Crossref] [PubMed]

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, A107–A112 (2003).
[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, 1610 (2001).
[Crossref] [PubMed]

Ritter, A.

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011).
[Crossref] [PubMed]

Robert, a.

R. Cerbino, L. Peverini, M. a. C. Potenza, a. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Rønnow, H.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

Sawhney, K.

S. Berujon, H. Wang, and K. Sawhney, “X-ray multimodal imaging using a random-phase object,” Phys. Rev. A 86, 1–9 (2012).
[Crossref]

Schäfer, R.

C. Grünzweig, C. David, O. Bunk, M. Dierolf, G. Frei, G. Kühne, J. Kohlbrecher, R. Schäfer, P. Lejcek, H. Rønnow, and F. Pfeiffer, “Neutron decoherence imaging for visualizing bulk magnetic domain structures,” Phys. Rev. Lett. 101, 025504 (2008).
[Crossref] [PubMed]

Schelokov, I.

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

Scherer, K.

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

Schroer, C.

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

Schröter, T.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

Schuster, M.

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
[Crossref]

Siu, K. K. W.

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100, 124102 (2012).
[Crossref]

Snigirev, A.

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

Snigireva, I.

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

Solak, H. H.

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287 (2002).
[Crossref]

Speller, R.

A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91, 1–3 (2007).
[Crossref]

Stampanoni, M.

Stein, A. F.

Stevenson, a. W.

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,” Nature 373, 595–598 (1995).
[Crossref]

Straumann, U.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref] [PubMed]

Suortti, P.

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

Sztrókay-Gaul, A.

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

Terui, Y.

Thibault, P.

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5, 10452 (2015).
[Crossref] [PubMed]

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 1–5 (2014).
[Crossref]

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, 1610 (2001).
[Crossref] [PubMed]

Urban, C.

V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010).
[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, 1610 (2001).
[Crossref] [PubMed]

Velroyen, A.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

Wang, H.

S. Berujon, H. Wang, and K. Sawhney, “X-ray multimodal imaging using a random-phase object,” Phys. Rev. A 86, 1–9 (2012).
[Crossref]

Wang, Y.

P. Li, K. Zhang, Y. Bao, Y. Ren, Z. Ju, Y. Wang, Q. He, Z. Zhu, W. Huang, Q. Yuan, and P. Zhu, “Angular signal radiography,” Opt. Express 24, 5829–5845 (2016).
[Crossref] [PubMed]

Y. Bao, Y. Wang, K. Gao, Z.-L. Wang, P.-P. Zhu, and Z.-Y. Wu, “Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method,” Chin. Phys. B 24, 108702 (2015).
[Crossref]

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, 10–13 (2009).

Wang, Z.-L.

Y. Bao, Y. Wang, K. Gao, Z.-L. Wang, P.-P. Zhu, and Z.-Y. Wu, “Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method,” Chin. Phys. B 24, 108702 (2015).
[Crossref]

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A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

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T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011).
[Crossref] [PubMed]

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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, 258–261 (2006).
[Crossref]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

Wen, H.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in X-ray phase-contrast imaging,” Nat. Phys. 12, 830–834 (2016).
[Crossref]

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
[Crossref] [PubMed]

Wen, H. H.

Wilkins, S. W.

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,” Nature 373, 595–598 (1995).
[Crossref]

Willer, K.

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

Willner, M.

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

A. Hipp, M. Willner, J. Herzen, S. D. Auweter, M. Chabior, J. Meiser, K. Achterhold, J. Mohr, and F. Pfeiffer, “Energy-resolved visibility analysis of grating interferometers operated at polychromatic X-ray sources,” Opt. Express 22, 30394 (2014).
[Crossref]

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, 176–185 (2013).
[Crossref] [PubMed]

Wu, Z.-Y.

Y. Bao, Y. Wang, K. Gao, Z.-L. Wang, P.-P. Zhu, and Z.-Y. Wu, “Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method,” Chin. Phys. B 24, 108702 (2015).
[Crossref]

Xiao, X.

Yaroshenko, A.

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

Yashiro, W.

Yildirim, A. Ö.

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
[Crossref]

Yuan, Q.

Zanette, I.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 1–5 (2014).
[Crossref]

Zdora, M.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 1–5 (2014).
[Crossref]

Zhang, K.

Zhou, T.

I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 1–5 (2014).
[Crossref]

Zhu, P.

Zhu, P.-P.

Y. Bao, Y. Wang, K. Gao, Z.-L. Wang, P.-P. Zhu, and Z.-Y. Wu, “Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method,” Chin. Phys. B 24, 108702 (2015).
[Crossref]

Zhu, Z.

Ziegler, E.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[Crossref] [PubMed]

C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287 (2002).
[Crossref]

Znati, S.

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in X-ray phase-contrast imaging,” Nat. Phys. 12, 830–834 (2016).
[Crossref]

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

K. S. Morgan, D. M. Paganin, and K. K. W. Siu, “X-ray phase imaging with a paper analyzer,” Appl. Phys. Lett. 100, 124102 (2012).
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A. Olivo and R. Speller, “A coded-aperture technique allowing x-ray phase contrast imaging with conventional sources,” Appl. Phys. Lett. 91, 1–3 (2007).
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C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287 (2002).
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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, 10–13 (2009).

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Y. Bao, Y. Wang, K. Gao, Z.-L. Wang, P.-P. Zhu, and Z.-Y. Wu, “Investigation of noise properties in grating-based x-ray phase tomography with reverse projection method,” Chin. Phys. B 24, 108702 (2015).
[Crossref]

Eur. Radiol. (1)

S. Grandl, K. Scherer, A. Sztrókay-Gaul, L. Birnbacher, K. Willer, M. Chabior, J. Herzen, D. Mayr, S. D. Auweter, F. Pfeiffer, F. Bamberg, and K. Hellerhoff, “Improved visualization of breast cancer features in multifocal carcinoma using phase-contrast and dark-field mammography: an ex vivo study,” Eur. Radiol. 25, 3659–3668 (2015).
[Crossref] [PubMed]

Europhys. Lett. (1)

A. Malecki, G. Potdevin, T. Biernath, E. Eggl, K. Willer, T. Lasser, J. Maisenbacher, J. Gibmeier, A. Wanner, and F. Pfeiffer, “X-ray tensor tomography,” Europhys. Lett. 105, 38002 (2014).
[Crossref]

Invest. Radiol. (1)

K. Hellbach, A. Yaroshenko, F. G. Meinel, A. Ö. Yildirim, T. M. Conlon, M. Bech, M. Mueller, A. Velroyen, M. Notohamiprodjo, F. Bamberg, S. Auweter, M. Reiser, O. Eickelberg, and F. Pfeiffer, “In vivo dark-field radiography for early diagnosis and staging of pulmonary emphysema,” Invest. Radiol. 50, 1–6 (2015).
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J. Appl. Phys. (1)

M. Chabior, T. Donath, C. David, M. Schuster, C. Schroer, and F. Pfeiffer, “Signal-to-noise ratio in x ray dark-field imaging using a grating interferometer,” J. Appl. Phys. 110, 053105 (2011).
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J. Phys. D. Appl. Phys. (1)

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, A107–A112 (2003).
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Med. Phys. (3)

M. Chabior, T. Donath, C. David, O. Bunk, M. Schuster, C. Schroer, and F. Pfeiffer, “Beam hardening effects in grating-based x-ray phase-contrast imaging,” Med. Phys. 38, 1189–1195 (2011).
[Crossref] [PubMed]

T. Weber, P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, and G. Anton, “Noise in x-ray grating-based phase-contrast imaging,” Med. Phys. 38, 4133–4140 (2011).
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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, 1610 (2001).
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Nat. Mater. (1)

F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, C. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7, 134–137 (2008).
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Nat. Phys. (3)

R. Cerbino, L. Peverini, M. a. C. Potenza, a. Robert, P. Bösecke, and M. Giglio, “X-ray-scattering information obtained from near-field speckle,” Nat. Phys. 4, 238–243 (2008).
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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, 258–261 (2006).
[Crossref]

H. Miao, A. Panna, A. A. Gomella, E. E. Bennett, S. Znati, L. Chen, and H. Wen, “A universal moiré effect and application in X-ray phase-contrast imaging,” Nat. Phys. 12, 830–834 (2016).
[Crossref]

Nature (1)

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,” Nature 373, 595–598 (1995).
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Phys. Rev. A (1)

S. Berujon, H. Wang, and K. Sawhney, “X-ray multimodal imaging using a random-phase object,” Phys. Rev. A 86, 1–9 (2012).
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F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98, 108105 (2007).
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I. Zanette, T. Zhou, A. Burvall, U. Lundström, D. H. Larsson, M. Zdora, P. Thibault, F. Pfeiffer, and H. M. Hertz, “Speckle-based x-ray phase-contrast and dark-field imaging with a laboratory source,” Phys. Rev. Lett. 112, 1–5 (2014).
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V. Revol, C. Kottler, R. Kaufmann, U. Straumann, and C. Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010).
[Crossref] [PubMed]

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[Crossref]

Sci. Rep. (3)

H. Miao, A. a. Gomella, K. J. Harmon, E. E. Bennett, N. Chedid, S. Znati, A. Panna, B. A. Foster, P. Bhandarkar, and H. Wen, “Enhancing tabletop x-ray phase contrast imaging with nano-fabrication,” Sci. Rep. 5, 13581 (2015).
[Crossref] [PubMed]

L. Birnbacher, M. Willner, A. Velroyen, M. Marschner, A. Hipp, J. Meiser, F. Koch, T. Schröter, D. Kunka, J. Mohr, F. Pfeiffer, and J. Herzen, “Experimental Realisation of High-sensitivity Laboratory X-ray Grating-based Phase-contrast Computed Tomography,” Sci. Rep. 6, 24022 (2016).
[Crossref] [PubMed]

D. Hahn, P. Thibault, A. Fehringer, M. Bech, T. Koehler, F. Pfeiffer, and P. B. Noël, “Statistical iterative reconstruction algorithm for X-ray phase-contrast CT,” Sci. Rep. 5, 10452 (2015).
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Z. Med. Phys. (1)

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, 176–185 (2013).
[Crossref] [PubMed]

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Figures (10)

Fig. 1
Fig. 1 Principle of the two-shot dark-field acquisition scheme. The reference stepping curve is recorded with high statistics and a sufficient number of phase steps. The dark-field signal is directly retrieved from the two measured intensities I1,2, rather than by performing a fitting procedure.
Fig. 2
Fig. 2 Transmission and dark-field projections of air and stacks of paper (number of layers: 1, 3, 5, and 11) with high and low SNR obtained using the conventional and the novel two-shot method. Using the phase-stepping approach, the dark-field values rise in all areas of the sample when the exposure time is decreased. In comparison, when using the two-shot method the correct values are maintained even for low statistics. The mean count numbers refer to the number of photons per pixel and were measured in a sample free area.
Fig. 3
Fig. 3 Dependency of the measured mean dark-field values on the noise levels in the attenuation channel for the three ROIs marked in Fig. 2. In the case of least-squares fitting (lsq-fit), which is the conventional signal extraction method, the measured values deviate from the correct values for high noise levels, indicating a failure of signal retrieval. In contrast, using the novel two-shot approach the image results remain still consistent for highly increased noise levels.
Fig. 4
Fig. 4 Transmission and dark-field projections of air and aluminum (thickness 1.95mm, 4.95mm and 8.95mm) with high and low SNR obtained using the conventional and the novel two-shot method. Visibility hardening was corrected, which results in a mean dark-field of unity for all materials in the high-SNR scan. Using the phase-stepping approach, regions with lower transmission exhibit a dark-field signal exceeding the correct value of unity with decreasing exposure time. In comparison, when using the two-shot method the correct value is maintained even for low staticsts. The dark-field images were scaled from [0 − 2σ, 2+2σ], with σ being the standard deviation in a region of interest in the dark-field projection of 8.95mm aluminum.
Fig. 5
Fig. 5 Dependency of the measured mean dark-field values on the noise levels in the attenuation channel for two materials with vastly differing attenuation properties. In the case of least-squares fitting, which is the conventional signal extraction method, the measured values deviate from the expected value of unity for high noise levels, indicating a failure of signal retrieval. Using the novel two-shot approach, the image results remain still consistent for highly increased noise levels. The mean values were measured in the regions of interest as displayed in Fig. 4
Fig. 6
Fig. 6 Transmission, differential phase-contrast and dark-field projections of the foam ear plug. The attenuation of the sample is very weak, leading to transmission values close to unity. The sample has a very noisy differential phase-contrast signal, due to its strong scattering (dark-field) signal. The arrow marks the rotation axis of the tomographic measurement.
Fig. 7
Fig. 7 Axial slices of the reconstructed dark-field tomography of a foam earplug. The count numbers correspond to one projection and pixel. The reconstructions of the phase-stepping projections show a vanishing signal for scans with low counts. In contrast, the two-shot method is able to visualize the sample even in low-SNR scenarios.
Fig. 8
Fig. 8 Results of two-shot dark-field tomography with globally fixed steps. (a) two-shot dark-field projection showing areas of unsuccessful signal extraction, (b) corresponding weights used for reconstruction, (c) reconstruction without weights showing severe artifacts, (d) artifact-free reconstruction of the same projections using the weights shown above, (e) successful reconstruction of low-SNR scan (59 counts) using weights.
Fig. 9
Fig. 9 Additional slices of the two-shot dark-field tomography with globally fixed steps shown in Fig. 8(d–e). The top two rows (a–f) show the high statistics scan that was previously displayed in Fig. 8(d). The bottom row shows the low statistics scan (59 photons per pixel and projection) of Fig. 8(e). All slices through the volumes are 50 pixels apart. The slices are in (a–c) axial and (d–i) coronal direction. The image quality is consistent in all slices, which illustrates the effectiveness of the weighted reconstruction scheme.
Fig. 10
Fig. 10 Differential phase-contrast projection of the paper sample, obtained using the phase-stepping approach with subsequent least-squares fitting and an exposure time of 26.2s.

Equations (10)

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I ( x ) = a 0 + a 1 cos ( 2 π x p + φ ) ,
I ( x 1 , 2 ) = a 0 + a 1 a 1 φ 2 2 +
a 0 = 1 2 ( I ( x 1 ) + I ( x 2 ) )
v = a 1 a 0 = I ( x 1 ) I ( x 2 ) I ( x 1 ) + I ( x 2 ) .
c 0 = a 1 2 [ cos ( 2 π Δ x 1 p ) cos ( 2 π Δ x 2 p ) ]
c 1 = 1 2 [ cos ( 2 π Δ x 1 p ) + cos ( 2 π Δ x 2 p ) ] ,
a 1 = 1 2 ( I 1 I 2 ) = 1 2 { [ a 0 + a 1 cos ( 2 π Δ x 1 ) ] [ a 0 a 1 cos ( 2 π Δ x 2 ) ] } =
= a 1 2 [ cos ( 2 π Δ x 1 ) + cos ( 2 π Δ x 2 ) ] a 1 c 1
a 0 = 1 2 ( I 1 + I 2 ) = 1 2 { [ a 0 + a 1 cos ( 2 π Δ x 1 ) ] + [ a 0 a 1 cos ( 2 π Δ x 2 ) ] } =
= a 0 + a 1 2 [ cos ( 2 π Δ x 1 ) cos ( 2 π Δ x 2 ) ] a 0 + c 0

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