Abstract

Over the recent years X-ray differential phase-contrast imaging was developed for the hard X-ray regime as produced from laboratory X-ray sources. The technique uses a grating-based Talbot-Lau interferometer and was shown to yield image contrast gain, which makes it very interesting to the fields of medical imaging and non-destructive testing, respectively. In addition to X-ray attenuation contrast, the differential phase-contrast and dark-field images provide different structural information about a specimen. For the dark-field even at length scales much smaller than the spatial resolution of the imaging system. Physical interpretation of the dark-field information as present in radiographic and tomographic (CT) images requires a detailed look onto the geometric orientation between specimen and the setup. During phase-stepping the drop in intensity modulation, due to local scattering effects within the specimen is reproduced in the dark-field signal. This signal shows strong dependencies on micro-porosity and micro-fibers if these are numerous enough in the object. Since a grating-interferometer using a common unidirectional line grating is sensitive to X-ray scattering in one plane only, the dark-field image is influenced by the fiber orientations with respect to the grating bars, which can be exploited to obtain anisotropic structural information. With this contribution, we attempt to extend existing models for 2D projections to 3D data by analyzing dark-field contrast tomography of anisotropically structured materials such as carbon fiber reinforced carbon (CFRC).

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  1. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase Tomography by X-ray Talbot Interferometry for Biological Imaging,” Japanese Journal of Applied Physics45, 5254–5262 (2006).
    [CrossRef]
  2. 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, 6296–304 (2005).
    [CrossRef] [PubMed]
  3. P. Cloetens, W. Ludwig, J. Baruchel, D. VanDyck, J. Van Landuyt, J.-P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett.75, 2912–14 (1999).
    [CrossRef]
  4. F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
    [CrossRef]
  5. 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,” Nature materials7, 134–137 (2008).
    [CrossRef] [PubMed]
  6. H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of X-ray scatteringInitial Results,” IEEE Trans. Med. Imaging27, 997–1002 (2008).
    [CrossRef] [PubMed]
  7. V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
    [CrossRef]
  8. W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express18, 16890–901 (2010).
    [CrossRef] [PubMed]
  9. V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys.112, 114903 (2012).
    [CrossRef]
  10. 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, 5529–39 (2010).
    [CrossRef] [PubMed]
  11. T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol.55, 3317–3323 (2010).
    [CrossRef] [PubMed]
  12. H. Wen, E. Bennett, M. Hegedus, and S. Rapacci, “Fourier X-ray scattering radiography yields bone structural information,” Radiology252, 910–918 (2009).
    [CrossRef]
  13. G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
    [CrossRef] [PubMed]
  14. T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
    [CrossRef]
  15. E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures,” Microsyst. Technol.14, 1683–1688 (2008).
    [CrossRef]
  16. J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Syncrotron Rad.11, 476–482 (2004).
    [CrossRef]
  17. V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
    [CrossRef]

2012 (3)

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys.112, 114903 (2012).
[CrossRef]

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[CrossRef]

2011 (1)

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
[CrossRef]

2010 (4)

W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express18, 16890–901 (2010).
[CrossRef] [PubMed]

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[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, 5529–39 (2010).
[CrossRef] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol.55, 3317–3323 (2010).
[CrossRef] [PubMed]

2009 (1)

H. Wen, E. Bennett, M. Hegedus, and S. Rapacci, “Fourier X-ray scattering radiography yields bone structural information,” Radiology252, 910–918 (2009).
[CrossRef]

2008 (3)

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures,” Microsyst. Technol.14, 1683–1688 (2008).
[CrossRef]

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,” Nature materials7, 134–137 (2008).
[CrossRef] [PubMed]

H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of X-ray scatteringInitial Results,” IEEE Trans. Med. Imaging27, 997–1002 (2008).
[CrossRef] [PubMed]

2006 (1)

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase Tomography by X-ray Talbot Interferometry for Biological Imaging,” Japanese Journal of Applied Physics45, 5254–5262 (2006).
[CrossRef]

2005 (1)

2004 (1)

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Syncrotron Rad.11, 476–482 (2004).
[CrossRef]

1999 (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. VanDyck, J. Van Landuyt, J.-P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett.75, 2912–14 (1999).
[CrossRef]

Anton, G.

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[CrossRef]

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. VanDyck, J. Van Landuyt, J.-P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett.75, 2912–14 (1999).
[CrossRef]

Bayer, F.

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[CrossRef]

Bech, M.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol.55, 3317–3323 (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, 5529–39 (2010).
[CrossRef] [PubMed]

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

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,” Nature materials7, 134–137 (2008).
[CrossRef] [PubMed]

Bennett, E.

H. Wen, E. Bennett, M. Hegedus, and S. Rapacci, “Fourier X-ray scattering radiography yields bone structural information,” Radiology252, 910–918 (2009).
[CrossRef]

H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of X-ray scatteringInitial Results,” IEEE Trans. Med. Imaging27, 997–1002 (2008).
[CrossRef] [PubMed]

Biernath, T.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

Boerner, M.

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures,” Microsyst. Technol.14, 1683–1688 (2008).
[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,” Nature materials7, 134–137 (2008).
[CrossRef] [PubMed]

Bunk, O.

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol.55, 3317–3323 (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, 5529–39 (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,” Nature materials7, 134–137 (2008).
[CrossRef] [PubMed]

Cardot, F.

V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
[CrossRef]

Carroll, S.

H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of X-ray scatteringInitial Results,” IEEE Trans. Med. Imaging27, 997–1002 (2008).
[CrossRef] [PubMed]

Cloetens, P.

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13, 6296–304 (2005).
[CrossRef] [PubMed]

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Syncrotron Rad.11, 476–482 (2004).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. VanDyck, J. Van Landuyt, J.-P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett.75, 2912–14 (1999).
[CrossRef]

David, C.

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, 5529–39 (2010).
[CrossRef] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol.55, 3317–3323 (2010).
[CrossRef] [PubMed]

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

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,” Nature materials7, 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, 6296–304 (2005).
[CrossRef] [PubMed]

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Syncrotron Rad.11, 476–482 (2004).
[CrossRef]

Deyhle, H.

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

Diaz, A.

Dommann, A.

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys.112, 114903 (2012).
[CrossRef]

Donath, T.

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol.55, 3317–3323 (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, 5529–39 (2010).
[CrossRef] [PubMed]

Durst, J.

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[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,” Nature materials7, 134–137 (2008).
[CrossRef] [PubMed]

Feidenhans’l, R.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol.55, 3317–3323 (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, 5529–39 (2010).
[CrossRef] [PubMed]

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

Fratzl, P.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

Gödel, K.

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[CrossRef]

Grünzweig, 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,” Nature materials7, 134–137 (2008).
[CrossRef] [PubMed]

Guigay, J.-P.

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Syncrotron Rad.11, 476–482 (2004).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. VanDyck, J. Van Landuyt, J.-P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett.75, 2912–14 (1999).
[CrossRef]

Haas, W.

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[CrossRef]

Hattori, T.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase Tomography by X-ray Talbot Interferometry for Biological Imaging,” Japanese Journal of Applied Physics45, 5254–5262 (2006).
[CrossRef]

Hegedus, M.

H. Wen, E. Bennett, M. Hegedus, and S. Rapacci, “Fourier X-ray scattering radiography yields bone structural information,” Radiology252, 910–918 (2009).
[CrossRef]

H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of X-ray scatteringInitial Results,” IEEE Trans. Med. Imaging27, 997–1002 (2008).
[CrossRef] [PubMed]

Jakobs, P.-J.

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures,” Microsyst. Technol.14, 1683–1688 (2008).
[CrossRef]

Jensen, T.

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

Jensen, T. H.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol.55, 3317–3323 (2010).
[CrossRef] [PubMed]

Jerjen, I.

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
[CrossRef]

V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
[CrossRef]

Kaufmann, R.

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys.112, 114903 (2012).
[CrossRef]

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
[CrossRef]

V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
[CrossRef]

Kawabata, K.

Kenntner, J.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

Kerschnitzki, M.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

Klaushofer, K.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

Kottler, C.

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys.112, 114903 (2012).
[CrossRef]

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
[CrossRef]

V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
[CrossRef]

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,” Nature materials7, 134–137 (2008).
[CrossRef] [PubMed]

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, D. VanDyck, J. Van Landuyt, J.-P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett.75, 2912–14 (1999).
[CrossRef]

Lüthi, T.

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
[CrossRef]

V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
[CrossRef]

Malecki, A.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

Michel, T.

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[CrossRef]

Mohr, J.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures,” Microsyst. Technol.14, 1683–1688 (2008).
[CrossRef]

Mokso, R.

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Syncrotron Rad.11, 476–482 (2004).
[CrossRef]

Momose, A.

W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express18, 16890–901 (2010).
[CrossRef] [PubMed]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase Tomography by X-ray Talbot Interferometry for Biological Imaging,” Japanese Journal of Applied Physics45, 5254–5262 (2006).
[CrossRef]

Nazmov, V.

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures,” Microsyst. Technol.14, 1683–1688 (2008).
[CrossRef]

Neels, A.

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys.112, 114903 (2012).
[CrossRef]

Niedermann, P.

V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
[CrossRef]

Pfeiffer, F.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol.55, 3317–3323 (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, 5529–39 (2010).
[CrossRef] [PubMed]

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

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,” Nature materials7, 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, 6296–304 (2005).
[CrossRef] [PubMed]

Potdevin, G.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

Rapacci, S.

H. Wen, E. Bennett, M. Hegedus, and S. Rapacci, “Fourier X-ray scattering radiography yields bone structural information,” Radiology252, 910–918 (2009).
[CrossRef]

Revol, V.

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys.112, 114903 (2012).
[CrossRef]

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
[CrossRef]

V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
[CrossRef]

Reznikova, E.

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures,” Microsyst. Technol.14, 1683–1688 (2008).
[CrossRef]

Rieger, J.

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[CrossRef]

Ritter, A.

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[CrossRef]

Roschger, P.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

Rutishauser, S.

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

Schlenker, M.

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Syncrotron Rad.11, 476–482 (2004).
[CrossRef]

P. Cloetens, W. Ludwig, J. Baruchel, D. VanDyck, J. Van Landuyt, J.-P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett.75, 2912–14 (1999).
[CrossRef]

Schütz, P.

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
[CrossRef]

Sennhauser, U.

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
[CrossRef]

V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
[CrossRef]

Stampanoni, M.

Straumann, U.

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
[CrossRef]

V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
[CrossRef]

Suzuki, Y.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase Tomography by X-ray Talbot Interferometry for Biological Imaging,” Japanese Journal of Applied Physics45, 5254–5262 (2006).
[CrossRef]

Takeda, Y.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase Tomography by X-ray Talbot Interferometry for Biological Imaging,” Japanese Journal of Applied Physics45, 5254–5262 (2006).
[CrossRef]

Terui, Y.

Urban, C.

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
[CrossRef]

V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
[CrossRef]

Van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. VanDyck, J. Van Landuyt, J.-P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett.75, 2912–14 (1999).
[CrossRef]

VanDyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. VanDyck, J. Van Landuyt, J.-P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett.75, 2912–14 (1999).
[CrossRef]

Wagermaier, W.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

Weber, T.

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[CrossRef]

Weitkamp, T.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13, 6296–304 (2005).
[CrossRef] [PubMed]

Wen, H.

H. Wen, E. Bennett, M. Hegedus, and S. Rapacci, “Fourier X-ray scattering radiography yields bone structural information,” Radiology252, 910–918 (2009).
[CrossRef]

H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of X-ray scatteringInitial Results,” IEEE Trans. Med. Imaging27, 997–1002 (2008).
[CrossRef] [PubMed]

Wucherer, L.

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[CrossRef]

Yashiro, W.

W. Yashiro, Y. Terui, K. Kawabata, and A. Momose, “On the origin of visibility contrast in x-ray Talbot interferometry,” Opt. Express18, 16890–901 (2010).
[CrossRef] [PubMed]

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase Tomography by X-ray Talbot Interferometry for Biological Imaging,” Japanese Journal of Applied Physics45, 5254–5262 (2006).
[CrossRef]

Zabler, S.

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Syncrotron Rad.11, 476–482 (2004).
[CrossRef]

Zanette, I.

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

Ziegler, E.

Appl. Phys. Lett. (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. VanDyck, J. Van Landuyt, J.-P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays,” Appl. Phys. Lett.75, 2912–14 (1999).
[CrossRef]

IEEE Trans. Med. Imaging (1)

H. Wen, E. Bennett, M. Hegedus, and S. Carroll, “Spatial harmonic imaging of X-ray scatteringInitial Results,” IEEE Trans. Med. Imaging27, 997–1002 (2008).
[CrossRef] [PubMed]

J. Appl. Phys. (2)

V. Revol, I. Jerjen, C. Kottler, P. Schütz, R. Kaufmann, T. Lüthi, U. Sennhauser, U. Straumann, and C. Urban, “Sub-pixel porosity revealed by x-ray scatter dark field imaging,” J. Appl. Phys.110, 044912 (2011).
[CrossRef]

V. Revol, C. Kottler, R. Kaufmann, A. Neels, and A. Dommann, “Orientation-selective X-ray dark field imaging of ordered systems,” J. Appl. Phys.112, 114903 (2012).
[CrossRef]

J. Syncrotron Rad. (1)

J.-P. Guigay, S. Zabler, P. Cloetens, C. David, R. Mokso, and M. Schlenker, “The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays,” J. Syncrotron Rad.11, 476–482 (2004).
[CrossRef]

Japanese Journal of Applied Physics (1)

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase Tomography by X-ray Talbot Interferometry for Biological Imaging,” Japanese Journal of Applied Physics45, 5254–5262 (2006).
[CrossRef]

Microsyst. Technol. (1)

E. Reznikova, J. Mohr, M. Boerner, V. Nazmov, and P.-J. Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures,” Microsyst. Technol.14, 1683–1688 (2008).
[CrossRef]

Nature materials (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,” Nature materials7, 134–137 (2008).
[CrossRef] [PubMed]

Opt. Express (2)

Phys. Med. Biol. (3)

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, 5529–39 (2010).
[CrossRef] [PubMed]

T. H. Jensen, M. Bech, O. Bunk, T. Donath, C. David, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging,” Phys. Med. Biol.55, 3317–3323 (2010).
[CrossRef] [PubMed]

G. Potdevin, A. Malecki, T. Biernath, M. Bech, T. H. Jensen, R. Feidenhans’l, I. Zanette, T. Weitkamp, J. Kenntner, J. Mohr, P. Roschger, M. Kerschnitzki, W. Wagermaier, K. Klaushofer, P. Fratzl, and F. Pfeiffer, “X-ray vector radiography for bone micro-architecture diagnostics,” Phys. Med. Biol.57, 3451–3461 (2012).
[CrossRef] [PubMed]

Phys. Rev. B (1)

T. Jensen, M. Bech, I. Zanette, T. Weitkamp, C. David, H. Deyhle, S. Rutishauser, E. Reznikova, J. Mohr, R. Feidenhans’l, and F. Pfeiffer, “Directional x-ray dark-field imaging of strongly ordered systems,” Phys. Rev. B82, 214103 (2010).
[CrossRef]

Proc. SPIE (1)

F. Bayer, K. Gödel, W. Haas, J. Rieger, A. Ritter, T. Weber, L. Wucherer, J. Durst, T. Michel, and G. Anton, “Spectroscopic dark-field imaging using a grating-based Talbot-Lau interferometer,” in Physics of Medical Imaging,Proc. SPIE8313, 83135 (2012).
[CrossRef]

Radiology (1)

H. Wen, E. Bennett, M. Hegedus, and S. Rapacci, “Fourier X-ray scattering radiography yields bone structural information,” Radiology252, 910–918 (2009).
[CrossRef]

Other (1)

V. Revol, C. Kottler, R. Kaufmann, F. Cardot, P. Niedermann, I. Jerjen, T. Lüthi, U. Straumann, U. Sennhauser, and C. Urban, “Sensing Small Angle Scattering with an X-ray Grating Interferometer,” in Proceedings of IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 2010), pp. 892–895.
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Sketch of the Talbot-Lau interferometer setup. The investigated test sample, for this case a parallel aligned fiber stack, is placed in front of the phase-grating G1. The definition of the coordinate angles θ and ϕ is shown.

Fig. 2
Fig. 2

Photography of the CFRC sample investigated in a dark-field computed tomography scan.

Fig. 3
Fig. 3

Photography of the fiber sample in the holder: The glass capillary filled with the carbon fiber bundle can be mounted at different angles of elevation, i.e. 0°, 15°, 30°, 45°, 60°. The holder is mounted onto a rotation axis which permits additional azimuthal rotation for CT imaging.

Fig. 4
Fig. 4

Sketch of the stacked fiber bundle sample, showing azimuthal scanning positions for an elevation of θ = 45° for several azimuthal angles ϕ. The dark-field signal of the depicted ROI intersection was averaged for evaluation.

Fig. 5
Fig. 5

Three representative DFC images from the CT scan of the CFRC sample in axial scan: ϕ = 0° (a), ϕ = 41.4° (b) and ϕ = 66.6° (c). The inset on the right side shows schematically the different orientations of the cross-woven fiber sheets in blocks (1) and (3) with respect to the coordinate axes defined in Fig. 1.

Fig. 6
Fig. 6

Dark-field sinograms of the CFRC block, corresponding to the horizontal image line indicated by the white arrows in Fig. 5(b): (a) refers to the upper, (b) to the lower image line. The vertical axis represents the projection angle ϕ. “Dark spots” correspond to maximum alignment of the fiber bundles with the grating bars. (c, d) Reconstructed slices from the sinograms in (a,b). Bright intensities correspond to carbon fiber bundles, black corresponds to the carbon matrix in between the bundles. Note the clear difference in fiber bundle orientation in different slices.

Fig. 7
Fig. 7

DFC images of the fiber capillary for elevation angles θ = 15° (a) and θ = 60° (b). Each column shows a series of six dark-field images obtained at the azimuthal angles ϕ = 0°, 18°, 36°, 54°, 72° and 90° (from top to bottom). Minor Moiré patterns are visible in the images.

Fig. 8
Fig. 8

Dark-field signal of the stacked fiber bundle, averaged over a region of interest as exemplary shown in Fig. 4. Each curve corresponds to a different sample elevation θ = 30°, 45°, 60° and 90° with respect to the grating bars. The azimuthal angle varies between 0° and 360° (18° steps).

Tables (1)

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Table 1 Results of the sin2(ϕ)-fit to the corrected logarithmic dark-field values according to Eq. (5), taking into account the effective thickness of the sample.

Equations (5)

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I ( k ) = a + b cos ( 2 π k τ p 2 + Φ )
D F C ˜ ( ϕ ) = ln ( D F C ( ϕ ) ) = α + β sin 2 ( ϕ )
d eff ( ϕ ) = r min r max r min 2 cos 2 ( ϕ ) + r max 2 sin 2 ( ϕ ) .
d eff ( ϕ , θ ) = r min sin 2 ( ϕ ) + cos 2 ( ϕ ) cos 2 ( θ ) .
ln ( D F C measured ( ϕ , θ ) ) sin 2 ( ϕ ) + cos 2 ( ϕ ) cos 2 ( θ ) = α corr + β corr sin 2 ( ϕ )

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