Abstract

X-ray differential phase contrast computed tomography (DPC CT) with a Talbot-Lau interferometer setup allows visualizing the three-dimensional distribution of the refractive index by measuring the shifts of an interference pattern due to phase variations of the X-ray beam. Unfortunately, severe reconstruction artifacts appear in the presence of differential phase wrapping and clipping. In this paper, we propose to use the attenuation contrast, which is obtained from the same measurement, for correcting the DPC signal. Using the example of a DPC CT measurement with pronounced phase artifacts, we will discuss the efficiency of our phase artifact correction method.

© 2011 OSA

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  2. B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
    [CrossRef]
  3. C. T. Chantler, “Theoretical form factor, attenuation and scattering tabulation for Z=1-92 from E=1-10 eV to E=0.4-1.0 MeV,” J. Phys. Chem. Ref. Data 24(1), 71–643 (1995).
    [CrossRef]
  4. A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express 11(19), 2303–2314 (2003).
    [CrossRef] [PubMed]
  5. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13(16), 6296–6304 (2005).
    [CrossRef] [PubMed]
  6. A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
    [CrossRef]
  7. 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(4), 258–261 (2006).
    [CrossRef]
  8. F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
    [CrossRef] [PubMed]
  9. C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (2007).
    [CrossRef]
  10. J. F. Clauser and M. W. Reinsch, “New theoretical and experimental results in Fresnel optics with applications to matter-wave and X-ray interferometry,” Appl. Phys. B 54(5), 380–395 (1992).
    [CrossRef]
  11. F. Pfeiffer, M. Bech, O. Bunk, P. Kraft, E. F. Eikenberry, Ch. Brönnimann, C. Grünzweig, and C. David, “Hard-X-ray dark-field imaging using a grating interferometer,” Nat. Mater. 7(2), 134–137 (2008).
    [CrossRef] [PubMed]
  12. I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
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    [CrossRef] [PubMed]
  15. L. A. Feldkamp, L. C. Davis, and J. W. Kress, “Practical cone-beam algorithm,” J. Opt. Soc. Am. 1(6), 612–619 (1984).
    [CrossRef]

2010 (2)

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
[CrossRef]

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(7), 073709 (2010).
[CrossRef] [PubMed]

2008 (1)

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

2007 (2)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (2007).
[CrossRef]

2006 (2)

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[CrossRef]

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(4), 258–261 (2006).
[CrossRef]

2005 (1)

2003 (1)

1995 (1)

C. T. Chantler, “Theoretical form factor, attenuation and scattering tabulation for Z=1-92 from E=1-10 eV to E=0.4-1.0 MeV,” J. Phys. Chem. Ref. Data 24(1), 71–643 (1995).
[CrossRef]

1993 (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

1992 (1)

J. F. Clauser and M. W. Reinsch, “New theoretical and experimental results in Fresnel optics with applications to matter-wave and X-ray interferometry,” Appl. Phys. B 54(5), 380–395 (1992).
[CrossRef]

1984 (1)

L. A. Feldkamp, L. C. Davis, and J. W. Kress, “Practical cone-beam algorithm,” J. Opt. Soc. Am. 1(6), 612–619 (1984).
[CrossRef]

Bech, M.

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

Brönnimann, Ch.

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

Bruder, J.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (2007).
[CrossRef]

Bunk, O.

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

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (2007).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 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(4), 258–261 (2006).
[CrossRef]

Chantler, C. T.

C. T. Chantler, “Theoretical form factor, attenuation and scattering tabulation for Z=1-92 from E=1-10 eV to E=0.4-1.0 MeV,” J. Phys. Chem. Ref. Data 24(1), 71–643 (1995).
[CrossRef]

Clauser, J. F.

J. F. Clauser and M. W. Reinsch, “New theoretical and experimental results in Fresnel optics with applications to matter-wave and X-ray interferometry,” Appl. Phys. B 54(5), 380–395 (1992).
[CrossRef]

Cloetens, P.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (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 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

David, C.

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

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (2007).
[CrossRef]

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(4), 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(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

Davis, L. C.

L. A. Feldkamp, L. C. Davis, and J. W. Kress, “Practical cone-beam algorithm,” J. Opt. Soc. Am. 1(6), 612–619 (1984).
[CrossRef]

Diaz, A.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (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 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Eikenberry, E. F.

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

Feldkamp, L. A.

L. A. Feldkamp, L. C. Davis, and J. W. Kress, “Practical cone-beam algorithm,” J. Opt. Soc. Am. 1(6), 612–619 (1984).
[CrossRef]

Groso, A.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (2007).
[CrossRef]

Grünzweig, C.

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

Gullikson, E. M.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

Hack, E.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
[CrossRef]

Hattori, T.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[CrossRef]

Henke, B. L.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

Jerjen, I.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
[CrossRef]

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(7), 073709 (2010).
[CrossRef] [PubMed]

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
[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(7), 073709 (2010).
[CrossRef] [PubMed]

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
[CrossRef]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

Kraft, P.

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

Kress, J. W.

L. A. Feldkamp, L. C. Davis, and J. W. Kress, “Practical cone-beam algorithm,” J. Opt. Soc. Am. 1(6), 612–619 (1984).
[CrossRef]

Luethi, T.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
[CrossRef]

Momose, A.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[CrossRef]

A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express 11(19), 2303–2314 (2003).
[CrossRef] [PubMed]

Pfeiffer, F.

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

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (2007).
[CrossRef]

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(4), 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(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Rastogi, P. K.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
[CrossRef]

Reinsch, M. W.

J. F. Clauser and M. W. Reinsch, “New theoretical and experimental results in Fresnel optics with applications to matter-wave and X-ray interferometry,” Appl. Phys. B 54(5), 380–395 (1992).
[CrossRef]

Revol, V.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
[CrossRef]

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(7), 073709 (2010).
[CrossRef] [PubMed]

Rohbeck, T.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (2007).
[CrossRef]

Sennhauser, U.

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
[CrossRef]

Stampanoni, M.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (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 13(16), 6296–6304 (2005).
[CrossRef] [PubMed]

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(7), 073709 (2010).
[CrossRef] [PubMed]

Suzuki, Y.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 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,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[CrossRef]

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(7), 073709 (2010).
[CrossRef] [PubMed]

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
[CrossRef]

Weitkamp, T.

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (2007).
[CrossRef]

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(4), 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(16), 6296–6304 (2005).
[CrossRef] [PubMed]

Yashiro, W.

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[CrossRef]

Ziegler, E.

AIP Conf. Proc. (1)

I. Jerjen, V. Revol, C. Kottler, T. Luethi, U. Sennhauser, R. Kaufmann, C. Urban, P. K. Rastogi, and E. Hack, “Phase contrast cone beam tomography with an X-ray grating interferometer,” AIP Conf. Proc. 1236, 227–231 (2010).
[CrossRef]

Appl. Phys. B (1)

J. F. Clauser and M. W. Reinsch, “New theoretical and experimental results in Fresnel optics with applications to matter-wave and X-ray interferometry,” Appl. Phys. B 54(5), 380–395 (1992).
[CrossRef]

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92,” At. Data Nucl. Data Tables 54(2), 181–342 (1993).
[CrossRef]

J. Opt. Soc. Am. (1)

L. A. Feldkamp, L. C. Davis, and J. W. Kress, “Practical cone-beam algorithm,” J. Opt. Soc. Am. 1(6), 612–619 (1984).
[CrossRef]

J. Phys. Chem. Ref. Data (1)

C. T. Chantler, “Theoretical form factor, attenuation and scattering tabulation for Z=1-92 from E=1-10 eV to E=0.4-1.0 MeV,” J. Phys. Chem. Ref. Data 24(1), 71–643 (1995).
[CrossRef]

Jpn. J. Appl. Phys. (1)

A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Jpn. J. Appl. Phys. 45(6A), 5254–5262 (2006).
[CrossRef]

Nat. Mater. (1)

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

Nat. Phys. (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(4), 258–261 (2006).
[CrossRef]

Opt. Express (2)

Phys. Rev. Lett. (1)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett. 98(10), 108105 (2007).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

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(7), 073709 (2010).
[CrossRef] [PubMed]

Spectrochim. Acta, B At. Spectrosc. (1)

C. David, T. Weitkamp, F. Pfeiffer, A. Diaz, J. Bruder, T. Rohbeck, A. Groso, O. Bunk, M. Stampanoni, and P. Cloetens, “Hard X-ray phase imaging and tomography using a grating interferometer,” Spectrochim. Acta, B At. Spectrosc. 62(6-7), 626–630 (2007).
[CrossRef]

Other (2)

A. C. Kak and M. Slaney, Principles of Computerized Tomography (IEEE, 1987).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley-Interscience, 1998).

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Figures (5)

Fig. 1
Fig. 1

Scheme of the measurement setup (a) (all distances are given in mm) and image of the test sample (b). The test cube is made of 6 pyramids of different plastic materials (PE, PA6, PA66, PMMA, POM and PTFE).

Fig. 2
Fig. 2

Illustration of the differential phase clipping and wrapping correction: The top row shows the DPC image with incorrect differential phase values (a), the AC image used for the correction (b), and the corrected DPC image (c). The bottom row shows the corresponding regions in the uncorrected DPC sinogram (d), the attenuation sinogram (e), and the corrected DPC sinogram (f).

Fig. 3
Fig. 3

Cuts through the reconstructed 3D distribution of the refractive index obtained without (a), (b), (c) and with differential phase wrapping and clipping correction (d), (e), (f). (a) and (d) show the interface between two parts of the test object. The dark grey regions denote the glue. The partial filling of the gap in the uncorrected image (a) is an artifact. (b) and (e) show a cross section of the test object cutting through the PTFE pyramid (white square in the center). The “shadows” originating from the PTFE square are artifacts. (c) and (f) show a cross section cutting through the POM pyramid (square in the center). The stripes originating from the gaps are artifacts.

Fig. 4
Fig. 4

One of the surfaces (PE) of the cube reconstructed from the uncorrected (a) and corrected (b) DPC projections, and the AC projections (c). (d) and (e) are zoomed in regions of the absorption (c) and phase (b) images, respectively.

Fig. 5
Fig. 5

Comparison between DPC (a) and AC (b) images in a region where the attenuation contrast is worse than the phase contrast. The images show the glue between two neighboring pyramids. The AC image is noisier and the voids in the glue are not as visible as in the DPC image. Also the visibility of the numbers is impaired by the noise of the AC image, whereas some numbers can be deciphered in the DPC image.

Tables (1)

Tables Icon

Table 1 Density, Decrement of the Real Part of the Complex Refraction Index δ, φlin, and Linear Attenuation Coefficient μ of the Materials of the Test Object at 20.1 keV

Equations (8)

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n = 1 δ i β = 1 r 0 2 π λ 2 q n q f q ( 0 , E ) ,
ln I 0 ( y , z ) I ( y , z ) = ( μ ( l ) d l ) ( y , z ) ,
α = λ 2 π Φ ( y , z ) y = y ( δ ( l ) d l ) ( y , z ) ,
ϕ = 2 π α d p 2 = 2 π d p 2 y ( δ ( l ) d l ) ( y , z ) ,
ϕ = 2 π d p 2 y δ L ( y , z ) 2 π d p 2 Δ Δ y δ L ( y , z ) ,
Δ Δ y δ L ( y , z ) = δ Δ y Δ L ( y , z ) ,
ϕ 2 π d p 2 δ Δ Δ y L ( y , z ) = ϕ l i n Δ L ( y , z ) ,
ϕ l i n = 2 π d p 2 δ Δ y ,

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