Abstract

Over the last few years, differential phase-contrast x-ray computed tomography (PC-CT) using a hard x-ray grating interferometer and polychromatic x-ray tube sources has been developed. The method allows for simultaneous determination of the attenuation coefficient and the refractive index decrement distribution inside an object in three dimensions. Here we report experimental results of our investigation on the quantita-tiveness and accuracy of this method. For this study, a phantom consisting of several tubes filled with chemically well-defined liquids was built and measured in PC-CT. We find, that the measured attenuation coefficients and refractive index decrements closely match calculated, theoretical values. Moreover, the study demonstrates, how substances with similar attenuation coefficient or refractive index decrement, can be uniquely distinguished by the simultaneous, quantitative measurement of both quantities.

©2009 Optical Society of America

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    [Crossref] [PubMed]
  4. P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, 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, 2912–2914 (1999).
    [Crossref]
  5. T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D 32, 563–567 (1999).
    [Crossref]
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    [Crossref]
  7. U. Bonse, F. Busch, O. Günnewig, F. Beckmann, R. Pahl, G. Delling, M. Hahn, and W. Graeff, “3D computed X-ray tomography of human cancellous bone at 8 µm,” Bone and Miner. 25, 25–38 (1994).
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  17. F. Pfeiffer, O. Bunk, C. Kottler, and C. David, “Tomographic reconstruction of three-dimensional objects from hard X-ray differential phase contrast projection images,” Nucl. Instrum. Methods Phys. Res. A 580, 925–928 (2007).
    [Crossref]
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    [Crossref]
  19. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Phys. 2, 258 (2006).
    [Crossref]
  20. C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
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  25. C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84, 1172–1177 (2007).
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  26. D. R. Lide, “CRC Handbook of Chemistry and Physics (60th Edition),” Taylor and Francis, Boca Raton, FL (1980).
  27. For the calculation of δ c the tabulated values of f 1 from L. Kissel for elastic photon-atom scattering, anomalous scattering factors were taken from the file f1f2 asf Kissel.dat of the DABAX library [28].
  28. DABAX library, http://ftp.esrf.eu/pub/scisoft/xop2.3/DabaxFiles.
  29. E. F. Plechaty, D. E. Cullen, and R. J. Howerton, “Tables and graphs of photon-interaction cross sections from 0.1 keV to 100 MeV derived from the LLL evaluated-nuclear-data library,” Lawrence Livermore National Laboratory (1981).
  30. B. D. Arhatari, K. Hannah, E. Balaur, and A. G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16 (24), 19950–19956 (2008).
    [Crossref]
  31. M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232 (1), 145–157 (2008).
    [Crossref]

2008 (2)

B. D. Arhatari, K. Hannah, E. Balaur, and A. G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16 (24), 19950–19956 (2008).
[Crossref]

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232 (1), 145–157 (2008).
[Crossref]

2007 (7)

G. R. Myers, S. C. Mayo, T. E. Gureyev, D. M. Paganin, and S. W. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A (Atomic, Molecular, and Optical Physics) 76, 045804 (2007).
[Crossref]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84, 1172–1177 (2007).
[Crossref]

T. Koyama, H. Takano, Y. Tsusaka, and Y. Kagoshima, “Tomographic quantitative phase measurement by hard X-ray micro-interferometer with 250 nm spatial resolution,” Spectrochim. Acta Part B 62, 603–607 (2007).
[Crossref]

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, O. Bunk, C. Kottler, and C. David, “Tomographic reconstruction of three-dimensional objects from hard X-ray differential phase contrast projection images,” Nucl. Instrum. Methods Phys. Res. A 580, 925–928 (2007).
[Crossref]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (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,” Nature Phys. 2, 258 (2006).
[Crossref]

2005 (2)

A. Momose, “Recent advances in X-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
[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 12, 6296–6304 (2005).
[Crossref]

2003 (3)

2001 (1)

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2001).
[Crossref]

2000 (1)

F.A. Dilmanian, Z. Zhong, B. Ren, X.Y. Wu, L.D. Chapman, I. Orion, and W.C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45, 933–946 (2000).
[Crossref] [PubMed]

1999 (3)

F. Beckmann, K. Heise, B. Kölsch, U. Bonse, M. F. Rajewsky, M. Bartscher, and T. Biermann, “Three-Dimensional Imaging of Nerve Tissue by X-Ray Phase-Contrast Microtomography,” Biophys. J. 76, 98–102 (1999).
[Crossref] [PubMed]

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, 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, 2912–2914 (1999).
[Crossref]

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D 32, 563–567 (1999).
[Crossref]

1996 (1)

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

1995 (1)

A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Method A 352, 622–628 (1995).
[Crossref]

1994 (1)

U. Bonse, F. Busch, O. Günnewig, F. Beckmann, R. Pahl, G. Delling, M. Hahn, and W. Graeff, “3D computed X-ray tomography of human cancellous bone at 8 µm,” Bone and Miner. 25, 25–38 (1994).
[Crossref]

1980 (1)

D. R. Lide, “CRC Handbook of Chemistry and Physics (60th Edition),” Taylor and Francis, Boca Raton, FL (1980).

Als-Nielsen, J.

J. Als-Nielsen, “Elements of Modern x-ray Physics,” John Wiley & Sons, Chichester (2008).

Arhatari, B. D.

B. D. Arhatari, K. Hannah, E. Balaur, and A. G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16 (24), 19950–19956 (2008).
[Crossref]

Balaur, E.

B. D. Arhatari, K. Hannah, E. Balaur, and A. G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16 (24), 19950–19956 (2008).
[Crossref]

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Bartscher, M.

F. Beckmann, K. Heise, B. Kölsch, U. Bonse, M. F. Rajewsky, M. Bartscher, and T. Biermann, “Three-Dimensional Imaging of Nerve Tissue by X-Ray Phase-Contrast Microtomography,” Biophys. J. 76, 98–102 (1999).
[Crossref] [PubMed]

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, 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, 2912–2914 (1999).
[Crossref]

Baumann, J.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232 (1), 145–157 (2008).
[Crossref]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[Crossref]

Beckmann, F.

F. Beckmann, K. Heise, B. Kölsch, U. Bonse, M. F. Rajewsky, M. Bartscher, and T. Biermann, “Three-Dimensional Imaging of Nerve Tissue by X-Ray Phase-Contrast Microtomography,” Biophys. J. 76, 98–102 (1999).
[Crossref] [PubMed]

U. Bonse, F. Busch, O. Günnewig, F. Beckmann, R. Pahl, G. Delling, M. Hahn, and W. Graeff, “3D computed X-ray tomography of human cancellous bone at 8 µm,” Bone and Miner. 25, 25–38 (1994).
[Crossref]

Biermann, T.

F. Beckmann, K. Heise, B. Kölsch, U. Bonse, M. F. Rajewsky, M. Bartscher, and T. Biermann, “Three-Dimensional Imaging of Nerve Tissue by X-Ray Phase-Contrast Microtomography,” Biophys. J. 76, 98–102 (1999).
[Crossref] [PubMed]

Bonse, U.

F. Beckmann, K. Heise, B. Kölsch, U. Bonse, M. F. Rajewsky, M. Bartscher, and T. Biermann, “Three-Dimensional Imaging of Nerve Tissue by X-Ray Phase-Contrast Microtomography,” Biophys. J. 76, 98–102 (1999).
[Crossref] [PubMed]

U. Bonse, F. Busch, O. Günnewig, F. Beckmann, R. Pahl, G. Delling, M. Hahn, and W. Graeff, “3D computed X-ray tomography of human cancellous bone at 8 µm,” Bone and Miner. 25, 25–38 (1994).
[Crossref]

Briod, I.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

Bruder, J.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84, 1172–1177 (2007).
[Crossref]

Bunk, O.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232 (1), 145–157 (2008).
[Crossref]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84, 1172–1177 (2007).
[Crossref]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

F. Pfeiffer, O. Bunk, C. Kottler, and C. David, “Tomographic reconstruction of three-dimensional objects from hard X-ray differential phase contrast projection images,” Nucl. Instrum. Methods Phys. Res. A 580, 925–928 (2007).
[Crossref]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[Crossref]

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,” Nature Phys. 2, 258 (2006).
[Crossref]

Busch, F.

U. Bonse, F. Busch, O. Günnewig, F. Beckmann, R. Pahl, G. Delling, M. Hahn, and W. Graeff, “3D computed X-ray tomography of human cancellous bone at 8 µm,” Bone and Miner. 25, 25–38 (1994).
[Crossref]

Chapman, L.D.

F.A. Dilmanian, Z. Zhong, B. Ren, X.Y. Wu, L.D. Chapman, I. Orion, and W.C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45, 933–946 (2000).
[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. Express 12, 6296–6304 (2005).
[Crossref]

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, 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, 2912–2914 (1999).
[Crossref]

Cookson, D. F.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Cullen, D. E.

E. F. Plechaty, D. E. Cullen, and R. J. Howerton, “Tables and graphs of photon-interaction cross sections from 0.1 keV to 100 MeV derived from the LLL evaluated-nuclear-data library,” Lawrence Livermore National Laboratory (1981).

David, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232 (1), 145–157 (2008).
[Crossref]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84, 1172–1177 (2007).
[Crossref]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[Crossref]

F. Pfeiffer, O. Bunk, C. Kottler, and C. David, “Tomographic reconstruction of three-dimensional objects from hard X-ray differential phase contrast projection images,” Nucl. Instrum. Methods Phys. Res. A 580, 925–928 (2007).
[Crossref]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

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,” Nature Phys. 2, 258 (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 12, 6296–6304 (2005).
[Crossref]

Davis, T. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2001).
[Crossref]

Davis, T.J.

Delling, G.

U. Bonse, F. Busch, O. Günnewig, F. Beckmann, R. Pahl, G. Delling, M. Hahn, and W. Graeff, “3D computed X-ray tomography of human cancellous bone at 8 µm,” Bone and Miner. 25, 25–38 (1994).
[Crossref]

Diaz, A.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84, 1172–1177 (2007).
[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 12, 6296–6304 (2005).
[Crossref]

Dilmanian, F.A.

F.A. Dilmanian, Z. Zhong, B. Ren, X.Y. Wu, L.D. Chapman, I. Orion, and W.C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45, 933–946 (2000).
[Crossref] [PubMed]

Engelhardt, M.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232 (1), 145–157 (2008).
[Crossref]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[Crossref]

Gao, D.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2001).
[Crossref]

Graeff, W.

U. Bonse, F. Busch, O. Günnewig, F. Beckmann, R. Pahl, G. Delling, M. Hahn, and W. Graeff, “3D computed X-ray tomography of human cancellous bone at 8 µm,” Bone and Miner. 25, 25–38 (1994).
[Crossref]

Grünzweig, C.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84, 1172–1177 (2007).
[Crossref]

Guigay, J. P.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, 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, 2912–2914 (1999).
[Crossref]

Günnewig, O.

U. Bonse, F. Busch, O. Günnewig, F. Beckmann, R. Pahl, G. Delling, M. Hahn, and W. Graeff, “3D computed X-ray tomography of human cancellous bone at 8 µm,” Bone and Miner. 25, 25–38 (1994).
[Crossref]

Gureyev, T. E.

G. R. Myers, S. C. Mayo, T. E. Gureyev, D. M. Paganin, and S. W. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A (Atomic, Molecular, and Optical Physics) 76, 045804 (2007).
[Crossref]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2001).
[Crossref]

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D 32, 563–567 (1999).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Gureyev, T.E.

Hahn, M.

U. Bonse, F. Busch, O. Günnewig, F. Beckmann, R. Pahl, G. Delling, M. Hahn, and W. Graeff, “3D computed X-ray tomography of human cancellous bone at 8 µm,” Bone and Miner. 25, 25–38 (1994).
[Crossref]

Hannah, K.

B. D. Arhatari, K. Hannah, E. Balaur, and A. G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16 (24), 19950–19956 (2008).
[Crossref]

Heise, K.

F. Beckmann, K. Heise, B. Kölsch, U. Bonse, M. F. Rajewsky, M. Bartscher, and T. Biermann, “Three-Dimensional Imaging of Nerve Tissue by X-Ray Phase-Contrast Microtomography,” Biophys. J. 76, 98–102 (1999).
[Crossref] [PubMed]

Howerton, R. J.

E. F. Plechaty, D. E. Cullen, and R. J. Howerton, “Tables and graphs of photon-interaction cross sections from 0.1 keV to 100 MeV derived from the LLL evaluated-nuclear-data library,” Lawrence Livermore National Laboratory (1981).

Irving, T. H. K.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative X-ray phase tomography with sub-micron resolution,” Optics Communications 217, 53–58 (2003).
[Crossref]

James, R. W.

R. W. James, “The optical principles of the diffraction of x-rays,” (1962).

Kagoshima, Y.

T. Koyama, H. Takano, Y. Tsusaka, and Y. Kagoshima, “Tomographic quantitative phase measurement by hard X-ray micro-interferometer with 250 nm spatial resolution,” Spectrochim. Acta Part B 62, 603–607 (2007).
[Crossref]

Kak, A. C.

A. C. Kak and M. Slaney, “Principles of Computerized Tomography,” IEEE Press, New York (1987).

Kaufmann, R.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

Kölsch, B.

F. Beckmann, K. Heise, B. Kölsch, U. Bonse, M. F. Rajewsky, M. Bartscher, and T. Biermann, “Three-Dimensional Imaging of Nerve Tissue by X-Ray Phase-Contrast Microtomography,” Biophys. J. 76, 98–102 (1999).
[Crossref] [PubMed]

Kottler, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232 (1), 145–157 (2008).
[Crossref]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84, 1172–1177 (2007).
[Crossref]

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, O. Bunk, C. Kottler, and C. David, “Tomographic reconstruction of three-dimensional objects from hard X-ray differential phase contrast projection images,” Nucl. Instrum. Methods Phys. Res. A 580, 925–928 (2007).
[Crossref]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[Crossref]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

Koyama, T.

T. Koyama, H. Takano, Y. Tsusaka, and Y. Kagoshima, “Tomographic quantitative phase measurement by hard X-ray micro-interferometer with 250 nm spatial resolution,” Spectrochim. Acta Part B 62, 603–607 (2007).
[Crossref]

Lide, D. R.

D. R. Lide, “CRC Handbook of Chemistry and Physics (60th Edition),” Taylor and Francis, Boca Raton, FL (1980).

Lin, J. J. A.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative X-ray phase tomography with sub-micron resolution,” Optics Communications 217, 53–58 (2003).
[Crossref]

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, 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, 2912–2914 (1999).
[Crossref]

Mayo, S. C.

G. R. Myers, S. C. Mayo, T. E. Gureyev, D. M. Paganin, and S. W. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A (Atomic, Molecular, and Optical Physics) 76, 045804 (2007).
[Crossref]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2001).
[Crossref]

Mayo, S.C.

McMahon, P. J.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative X-ray phase tomography with sub-micron resolution,” Optics Communications 217, 53–58 (2003).
[Crossref]

McNulty, I.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative X-ray phase tomography with sub-micron resolution,” Optics Communications 217, 53–58 (2003).
[Crossref]

Miller, P. R.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2001).
[Crossref]

Miller, P.R.

Momose, A.

A. Momose, “Recent advances in X-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
[Crossref]

A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express 11, 2303–2314 (2003).
[Crossref] [PubMed]

A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instrum. Method A 352, 622–628 (1995).
[Crossref]

Myers, G. R.

G. R. Myers, S. C. Mayo, T. E. Gureyev, D. M. Paganin, and S. W. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A (Atomic, Molecular, and Optical Physics) 76, 045804 (2007).
[Crossref]

Nugent, K. A.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative X-ray phase tomography with sub-micron resolution,” Optics Communications 217, 53–58 (2003).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Orion, I.

F.A. Dilmanian, Z. Zhong, B. Ren, X.Y. Wu, L.D. Chapman, I. Orion, and W.C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45, 933–946 (2000).
[Crossref] [PubMed]

Paganin, D.

S.C. Mayo, T.J. Davis, T.E. Gureyev, P.R. Miller, D. Paganin, A. Pogany, A.W. Stevenson, and S.W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003).
[Crossref] [PubMed]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2001).
[Crossref]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, “Quantitative phase imaging using hard X rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).
[Crossref] [PubMed]

Paganin, D. M.

G. R. Myers, S. C. Mayo, T. E. Gureyev, D. M. Paganin, and S. W. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A (Atomic, Molecular, and Optical Physics) 76, 045804 (2007).
[Crossref]

D. M. Paganin, “Coherent x-ray Optics,” Oxford University Press, New York (2006).

Pahl, R.

U. Bonse, F. Busch, O. Günnewig, F. Beckmann, R. Pahl, G. Delling, M. Hahn, and W. Graeff, “3D computed X-ray tomography of human cancellous bone at 8 µm,” Bone and Miner. 25, 25–38 (1994).
[Crossref]

Parry, D. J.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2001).
[Crossref]

Paterson, D.

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative X-ray phase tomography with sub-micron resolution,” Optics Communications 217, 53–58 (2003).
[Crossref]

Peele, A. G.

B. D. Arhatari, K. Hannah, E. Balaur, and A. G. Peele, “Phase imaging using a polychromatic X-ray laboratory source,” Opt. Express 16 (24), 19950–19956 (2008).
[Crossref]

P. J. McMahon, A. G. Peele, D. Paterson, J. J. A. Lin, T. H. K. Irving, I. McNulty, and K. A. Nugent, “Quantitative X-ray phase tomography with sub-micron resolution,” Optics Communications 217, 53–58 (2003).
[Crossref]

Pfeiffer, F.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232 (1), 145–157 (2008).
[Crossref]

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84, 1172–1177 (2007).
[Crossref]

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[Crossref]

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, O. Bunk, C. Kottler, and C. David, “Tomographic reconstruction of three-dimensional objects from hard X-ray differential phase contrast projection images,” Nucl. Instrum. Methods Phys. Res. A 580, 925–928 (2007).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Phys. 2, 258 (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 12, 6296–6304 (2005).
[Crossref]

Plechaty, E. F.

E. F. Plechaty, D. E. Cullen, and R. J. Howerton, “Tables and graphs of photon-interaction cross sections from 0.1 keV to 100 MeV derived from the LLL evaluated-nuclear-data library,” Lawrence Livermore National Laboratory (1981).

Pogany, A.

S.C. Mayo, T.J. Davis, T.E. Gureyev, P.R. Miller, D. Paganin, A. Pogany, A.W. Stevenson, and S.W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003).
[Crossref] [PubMed]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2001).
[Crossref]

Rajewsky, M. F.

F. Beckmann, K. Heise, B. Kölsch, U. Bonse, M. F. Rajewsky, M. Bartscher, and T. Biermann, “Three-Dimensional Imaging of Nerve Tissue by X-Ray Phase-Contrast Microtomography,” Biophys. J. 76, 98–102 (1999).
[Crossref] [PubMed]

Raven, C.

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D 32, 563–567 (1999).
[Crossref]

Ren, B.

F.A. Dilmanian, Z. Zhong, B. Ren, X.Y. Wu, L.D. Chapman, I. Orion, and W.C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45, 933–946 (2000).
[Crossref] [PubMed]

Rohbeck, T.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84, 1172–1177 (2007).
[Crossref]

Schlenker, M.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, 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, 2912–2914 (1999).
[Crossref]

Schroer, C.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232 (1), 145–157 (2008).
[Crossref]

Schuster, M.

M. Engelhardt, C. Kottler, O. Bunk, C. David, C. Schroer, J. Baumann, M. Schuster, and F. Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232 (1), 145–157 (2008).
[Crossref]

M. Engelhardt, J. Baumann, M. Schuster, C. Kottler, F. Pfeiffer, O. Bunk, and C. David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
[Crossref]

Slaney, M.

A. C. Kak and M. Slaney, “Principles of Computerized Tomography,” IEEE Press, New York (1987).

Snigirev, A.

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D 32, 563–567 (1999).
[Crossref]

Snigireva, I.

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D 32, 563–567 (1999).
[Crossref]

Stampanoni, M.

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 12, 6296–6304 (2005).
[Crossref]

Stevenson, A. W.

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2001).
[Crossref]

Stevenson, A.W.

Takano, H.

T. Koyama, H. Takano, Y. Tsusaka, and Y. Kagoshima, “Tomographic quantitative phase measurement by hard X-ray micro-interferometer with 250 nm spatial resolution,” Spectrochim. Acta Part B 62, 603–607 (2007).
[Crossref]

Thomlinson, W.C.

F.A. Dilmanian, Z. Zhong, B. Ren, X.Y. Wu, L.D. Chapman, I. Orion, and W.C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45, 933–946 (2000).
[Crossref] [PubMed]

Tlustos, T.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

Tsusaka, Y.

T. Koyama, H. Takano, Y. Tsusaka, and Y. Kagoshima, “Tomographic quantitative phase measurement by hard X-ray micro-interferometer with 250 nm spatial resolution,” Spectrochim. Acta Part B 62, 603–607 (2007).
[Crossref]

van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, 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, 2912–2914 (1999).
[Crossref]

van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, 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, 2912–2914 (1999).
[Crossref]

Walt, H.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

Weitkamp, T.

C. Kottler, F. Pfeiffer, O. Bunk, C. Grünzweig, J. Bruder, R. Kaufmann, T. Tlustos, H. Walt, I. Briod, T. Weitkamp, and C. David, “Phase contrast X-ray imaging of large samples using an incoherent laboratory source,” Phys. Status Solidi A 204, 2728–2733 (2007).
[Crossref]

F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Phys. 2, 258 (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 12, 6296–6304 (2005).
[Crossref]

Wilkins, S. W.

G. R. Myers, S. C. Mayo, T. E. Gureyev, D. M. Paganin, and S. W. Wilkins, “Polychromatic cone-beam phase-contrast tomography,” Phys. Rev. A (Atomic, Molecular, and Optical Physics) 76, 045804 (2007).
[Crossref]

S. C. Mayo, P. R. Miller, S. W. Wilkins, T. J. Davis, D. Gao, T. E. Gureyev, D. Paganin, D. J. Parry, A. Pogany, and A. W. Stevenson, “Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging,” J. Microsc. 207, 79–96 (2001).
[Crossref]

T. E. Gureyev, C. Raven, A. Snigirev, I. Snigireva, and S. W. Wilkins, “Hard x-ray quantitative non-interferometric phase-contrast microscopy,” J. Phys. D 32, 563–567 (1999).
[Crossref]

Wilkins, S.W.

Wu, X.Y.

F.A. Dilmanian, Z. Zhong, B. Ren, X.Y. Wu, L.D. Chapman, I. Orion, and W.C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45, 933–946 (2000).
[Crossref] [PubMed]

Zhong, Z.

F.A. Dilmanian, Z. Zhong, B. Ren, X.Y. Wu, L.D. Chapman, I. Orion, and W.C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45, 933–946 (2000).
[Crossref] [PubMed]

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 12, 6296–6304 (2005).
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Figures (3)

Fig. 1.
Fig. 1. X-ray grating interferometer for differential phase-contrast imaging. A phase object in the beam path causes a slight deflection of x-rays changing the locally transmitted intensity through the arrangement formed by the gratings G1 and G2. The sample is placed on a tomographic rotation stage.

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Fig. 2.
Fig. 2. Tomographic reconstructions from the same slice of the phantom showing (a) the attenuation coefficient Δµ(x, y) and (b) the refractive index decrement Δδ(x, y). The color-bar (from black to white) ranges from -2.0 ·10−2 to 3.0 ·10−2 mm−1 in (a) and from -7.5·10−8 to 11.3·10−8 in (b). The fluids in the 13 polyethylene tubes of the phantom have been labeled with their identifiers according to the fluid description in Table 1. A centered, circular averaging region, as shown for one tube in (b), was defined for each tube to obtain the experimental values given in Table 2.

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Fig. 3.
Fig. 3. Scatter plot of measured and calculated attenuation coefficients Δµ, Δµc and refractive index decrements Δδ, Δδc . The plot shows the data given in Table 2.

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Tables (2)

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Table 1. Density and elemental composion of the fluids. These values were used in the calculation of Δµc and Δδc listed in Table 2.

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Table 2 Measured and calculated attenuation coefficients Δµ and refractive index decrements Δδ for all fluids in the phantom (relative to water). The standard deviations σµ and σδ within each averaging region are given. The calculated Δµc and Δδc values were determined for effective photon energies of Eµ =30.1 keV and Eδ =28.3 keV, respectively, as discussed in the text. The data is plotted in Fig. 3.

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Equations (7)

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TΘ(x′)=exp[−∫0d4πλβ(x′,y′)dy′]=exp [−∫0dμ(x′,y′)dy′] ,
(μρ)subst=∑i=1I(μρ)iWi,
αΘ(x′)=λ2π∂ΦΘ(x′)∂x′=∫0d∂δ(x′,y′)∂x′dy′,
δsubst=reλ22π∑i=1INifi1,
μ(x,y)=−∫0πℱ-1{ℱ[lnTΘ(ω)]∙ℱ[k(ω)]}dΘ,
δ(x,y)=∫0πℱ−1{ℱ[αΘ(ω)]∙ℱ[h(ω)]}dΘ,
CNR=∣Sa−Sb∣σS,

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