Abstract

We present a numerical tool to compare directly the contrast-to-noise-ratio (CNR) of the attenuation- and differential phase-contrast signals available from grating-based X-ray imaging for single radiographs. The attenuation projection is differentiated to bring it into a modality comparable to the differential phase projection using a Gaussian derivative filter. A Relative Contrast Gain (RCG) is then defined as the ratio of the CNR of image values in a region of interest (ROI) in the differential phase projection to the CNR of image values in the same ROI in the differential attenuation projection. We apply the method on experimental data of human breast tissue acquired using a grating interferometer to compare the two contrast modes for two regions of interest differing in the type of tissue. Our results indicate that the proposed method can be used as a local estimate of the spatial distribution of the ratio δ/β, i.e., real and imaginary part of the complex refractive index, across a sample.

© 2012 OSA

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  1. U. Bonse and M. Hart, “An x-ray interferometer with long separated interfering beam paths,” Appl. Phys. Lett.6, 155–156 (1965).
    [CrossRef]
  2. R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today53, 23–26 (2000).
    [CrossRef]
  3. A. Momose, “Phase-sensitive imaging and phase tomography using x-ray interferometers,” Opt. Express11, 2303–2314 (2003).
    [CrossRef] [PubMed]
  4. A. Momose, T. Takeda, A. Yoneyama, I. Koyama, and Y. Itai, “Phase-contrast x-ray imaging using an x-ray interferometer for biological imaging,” Anal. Sci.17(Suppl.), i527–i530 (2001).
  5. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
    [CrossRef]
  6. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources,” Nat. Phys.2, 258–261 (2006).
    [CrossRef]
  7. F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 105–108 (2007).
    [CrossRef]
  8. 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, 6296–6304 (2005).
    [CrossRef] [PubMed]
  9. F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography.” Phys. Med. Biol.52, 6923–6930 (2007).
    [CrossRef] [PubMed]
  10. G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
    [CrossRef] [PubMed]
  11. T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
    [CrossRef]
  12. J. Herzen, T. Donath, F. Pfeiffer, O. Bunk, C. Padeste, F. Beckmann, A. Schreyer, and C. David, “Quantitative phase-contrast tomography of a liquid phantom using a conventional x-ray tube source,” Opt. Express17, 10010–10018 (2009).
    [CrossRef] [PubMed]
  13. G.-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys.38, 584–588 (2011).
    [CrossRef] [PubMed]
  14. J. Zambelli, N. Bevins, Z. Qi, and G.-H. Chen, “Radiation dose efficiency comparison between differential phase contrast CT and conventional absorption CT,” Med. Phys.37, 2473–2479 (2010).
    [CrossRef] [PubMed]
  15. K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A648, 202–207 (2010).
    [CrossRef]
  16. M. Bech, “X-ray imaging with a grating interferometer,” Ph.D. thesis, University of Copenhagen (2009).
  17. T. Thuering, P. Modregger, B. R. Pinzer, Z. Wang, and M. Stampanoni, “Non-linear regularized phase retrieval for unidirectional X-ray differential phase contrast radiography,” Opt. Express19, 25545–25558 (2011).
    [CrossRef]
  18. J. Hsieh, Computed Tomography - Principles, Design, Artifacts, and Recent Advances, 2nd ed. (Wiley, Hoboken, NJ, 2009).
  19. A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 2nd ed. (Prentice-Hall, Upper Saddle River, NJ, 1999).
  20. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed., Vol. 3 of Texts in Computer Science (Pearson Prentice Hall, Upper Saddle River, NJ, 2008).

2011 (2)

G.-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys.38, 584–588 (2011).
[CrossRef] [PubMed]

T. Thuering, P. Modregger, B. R. Pinzer, Z. Wang, and M. Stampanoni, “Non-linear regularized phase retrieval for unidirectional X-ray differential phase contrast radiography,” Opt. Express19, 25545–25558 (2011).
[CrossRef]

2010 (4)

G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
[CrossRef] [PubMed]

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

J. Zambelli, N. Bevins, Z. Qi, and G.-H. Chen, “Radiation dose efficiency comparison between differential phase contrast CT and conventional absorption CT,” Med. Phys.37, 2473–2479 (2010).
[CrossRef] [PubMed]

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A648, 202–207 (2010).
[CrossRef]

2009 (1)

2007 (2)

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 105–108 (2007).
[CrossRef]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography.” Phys. Med. Biol.52, 6923–6930 (2007).
[CrossRef] [PubMed]

2006 (1)

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

2005 (1)

2003 (2)

A. Momose, “Phase-sensitive imaging and phase tomography using x-ray interferometers,” Opt. Express11, 2303–2314 (2003).
[CrossRef] [PubMed]

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

2001 (1)

A. Momose, T. Takeda, A. Yoneyama, I. Koyama, and Y. Itai, “Phase-contrast x-ray imaging using an x-ray interferometer for biological imaging,” Anal. Sci.17(Suppl.), i527–i530 (2001).

2000 (1)

R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today53, 23–26 (2000).
[CrossRef]

1965 (1)

U. Bonse and M. Hart, “An x-ray interferometer with long separated interfering beam paths,” Appl. Phys. Lett.6, 155–156 (1965).
[CrossRef]

Baruchel, J.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

Bech, M.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography.” Phys. Med. Biol.52, 6923–6930 (2007).
[CrossRef] [PubMed]

M. Bech, “X-ray imaging with a grating interferometer,” Ph.D. thesis, University of Copenhagen (2009).

Beckmann, F.

G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
[CrossRef] [PubMed]

J. Herzen, T. Donath, F. Pfeiffer, O. Bunk, C. Padeste, F. Beckmann, A. Schreyer, and C. David, “Quantitative phase-contrast tomography of a liquid phantom using a conventional x-ray tube source,” Opt. Express17, 10010–10018 (2009).
[CrossRef] [PubMed]

Bernard, P.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

Bevins, N.

G.-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys.38, 584–588 (2011).
[CrossRef] [PubMed]

J. Zambelli, N. Bevins, Z. Qi, and G.-H. Chen, “Radiation dose efficiency comparison between differential phase contrast CT and conventional absorption CT,” Med. Phys.37, 2473–2479 (2010).
[CrossRef] [PubMed]

Bonse, U.

U. Bonse and M. Hart, “An x-ray interferometer with long separated interfering beam paths,” Appl. Phys. Lett.6, 155–156 (1965).
[CrossRef]

Bravin, A.

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography.” Phys. Med. Biol.52, 6923–6930 (2007).
[CrossRef] [PubMed]

Bunk, O.

J. Herzen, T. Donath, F. Pfeiffer, O. Bunk, C. Padeste, F. Beckmann, A. Schreyer, and C. David, “Quantitative phase-contrast tomography of a liquid phantom using a conventional x-ray tube source,” Opt. Express17, 10010–10018 (2009).
[CrossRef] [PubMed]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography.” Phys. Med. Biol.52, 6923–6930 (2007).
[CrossRef] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 105–108 (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, 258–261 (2006).
[CrossRef]

Chen, G.-H.

G.-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys.38, 584–588 (2011).
[CrossRef] [PubMed]

J. Zambelli, N. Bevins, Z. Qi, and G.-H. Chen, “Radiation dose efficiency comparison between differential phase contrast CT and conventional absorption CT,” Med. Phys.37, 2473–2479 (2010).
[CrossRef] [PubMed]

Cloetens, P.

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography.” Phys. Med. Biol.52, 6923–6930 (2007).
[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, 6296–6304 (2005).
[CrossRef] [PubMed]

David, C.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
[CrossRef] [PubMed]

J. Herzen, T. Donath, F. Pfeiffer, O. Bunk, C. Padeste, F. Beckmann, A. Schreyer, and C. David, “Quantitative phase-contrast tomography of a liquid phantom using a conventional x-ray tube source,” Opt. Express17, 10010–10018 (2009).
[CrossRef] [PubMed]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography.” Phys. Med. Biol.52, 6923–6930 (2007).
[CrossRef] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 105–108 (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, 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. Express13, 6296–6304 (2005).
[CrossRef] [PubMed]

Deyhle, H.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

Diaz, A.

Donath, T.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

J. Herzen, T. Donath, F. Pfeiffer, O. Bunk, C. Padeste, F. Beckmann, A. Schreyer, and C. David, “Quantitative phase-contrast tomography of a liquid phantom using a conventional x-ray tube source,” Opt. Express17, 10010–10018 (2009).
[CrossRef] [PubMed]

Engel, K. J.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A648, 202–207 (2010).
[CrossRef]

Fitzgerald, R.

R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today53, 23–26 (2000).
[CrossRef]

Geller, D.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A648, 202–207 (2010).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed., Vol. 3 of Texts in Computer Science (Pearson Prentice Hall, Upper Saddle River, NJ, 2008).

Hamaishi, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

Hart, M.

U. Bonse and M. Hart, “An x-ray interferometer with long separated interfering beam paths,” Appl. Phys. Lett.6, 155–156 (1965).
[CrossRef]

Herzen, J.

Hsieh, J.

J. Hsieh, Computed Tomography - Principles, Design, Artifacts, and Recent Advances, 2nd ed. (Wiley, Hoboken, NJ, 2009).

Itai, Y.

A. Momose, T. Takeda, A. Yoneyama, I. Koyama, and Y. Itai, “Phase-contrast x-ray imaging using an x-ray interferometer for biological imaging,” Anal. Sci.17(Suppl.), i527–i530 (2001).

Kawamoto, S.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

Kenntner, J.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

Köhler, T.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A648, 202–207 (2010).
[CrossRef]

Kottler, C.

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 105–108 (2007).
[CrossRef]

Koyama, I.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

A. Momose, T. Takeda, A. Yoneyama, I. Koyama, and Y. Itai, “Phase-contrast x-ray imaging using an x-ray interferometer for biological imaging,” Anal. Sci.17(Suppl.), i527–i530 (2001).

Lang, S.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

Le Duc, G.

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography.” Phys. Med. Biol.52, 6923–6930 (2007).
[CrossRef] [PubMed]

Li, K.

G.-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys.38, 584–588 (2011).
[CrossRef] [PubMed]

Martens, G.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A648, 202–207 (2010).
[CrossRef]

Modregger, P.

Mohr, J.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

Momose, A.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

A. Momose, “Phase-sensitive imaging and phase tomography using x-ray interferometers,” Opt. Express11, 2303–2314 (2003).
[CrossRef] [PubMed]

A. Momose, T. Takeda, A. Yoneyama, I. Koyama, and Y. Itai, “Phase-contrast x-ray imaging using an x-ray interferometer for biological imaging,” Anal. Sci.17(Suppl.), i527–i530 (2001).

Müller, B.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
[CrossRef] [PubMed]

Oppenheim, A. V.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 2nd ed. (Prentice-Hall, Upper Saddle River, NJ, 1999).

Padeste, C.

Pfeiffer, F.

G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
[CrossRef] [PubMed]

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

J. Herzen, T. Donath, F. Pfeiffer, O. Bunk, C. Padeste, F. Beckmann, A. Schreyer, and C. David, “Quantitative phase-contrast tomography of a liquid phantom using a conventional x-ray tube source,” Opt. Express17, 10010–10018 (2009).
[CrossRef] [PubMed]

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography.” Phys. Med. Biol.52, 6923–6930 (2007).
[CrossRef] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard x-ray phase tomography with low-brilliance sources,” Phys. Rev. Lett.98, 105–108 (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, 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. Express13, 6296–6304 (2005).
[CrossRef] [PubMed]

Pinzer, B. R.

Qi, Z.

G.-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys.38, 584–588 (2011).
[CrossRef] [PubMed]

J. Zambelli, N. Bevins, Z. Qi, and G.-H. Chen, “Radiation dose efficiency comparison between differential phase contrast CT and conventional absorption CT,” Med. Phys.37, 2473–2479 (2010).
[CrossRef] [PubMed]

Reznikova, E.

G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
[CrossRef] [PubMed]

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

Rössl, E.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A648, 202–207 (2010).
[CrossRef]

Rutishauser, S.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
[CrossRef] [PubMed]

Schafer, R. W.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 2nd ed. (Prentice-Hall, Upper Saddle River, NJ, 1999).

Schreyer, A.

Schulz, G.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
[CrossRef] [PubMed]

Schusser, S.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A648, 202–207 (2010).
[CrossRef]

Stampanoni, M.

Suzuki, Y.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

Takai, K.

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

Takeda, T.

A. Momose, T. Takeda, A. Yoneyama, I. Koyama, and Y. Itai, “Phase-contrast x-ray imaging using an x-ray interferometer for biological imaging,” Anal. Sci.17(Suppl.), i527–i530 (2001).

Tapfer, A.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

Thuering, T.

Valade, J.-P.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

Vogtmeier, G.

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A648, 202–207 (2010).
[CrossRef]

Wang, Z.

Weitkamp, T.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
[CrossRef] [PubMed]

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

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express13, 6296–6304 (2005).
[CrossRef] [PubMed]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed., Vol. 3 of Texts in Computer Science (Pearson Prentice Hall, Upper Saddle River, NJ, 2008).

Yoneyama, A.

A. Momose, T. Takeda, A. Yoneyama, I. Koyama, and Y. Itai, “Phase-contrast x-ray imaging using an x-ray interferometer for biological imaging,” Anal. Sci.17(Suppl.), i527–i530 (2001).

Zambelli, J.

G.-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys.38, 584–588 (2011).
[CrossRef] [PubMed]

J. Zambelli, N. Bevins, Z. Qi, and G.-H. Chen, “Radiation dose efficiency comparison between differential phase contrast CT and conventional absorption CT,” Med. Phys.37, 2473–2479 (2010).
[CrossRef] [PubMed]

Zanette, I.

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
[CrossRef] [PubMed]

Ziegler, E.

Anal. Sci. (1)

A. Momose, T. Takeda, A. Yoneyama, I. Koyama, and Y. Itai, “Phase-contrast x-ray imaging using an x-ray interferometer for biological imaging,” Anal. Sci.17(Suppl.), i527–i530 (2001).

Appl. Phys. Lett. (1)

U. Bonse and M. Hart, “An x-ray interferometer with long separated interfering beam paths,” Appl. Phys. Lett.6, 155–156 (1965).
[CrossRef]

J. R. Soc. Interface (1)

G. Schulz, T. Weitkamp, I. Zanette, F. Pfeiffer, F. Beckmann, C. David, S. Rutishauser, E. Reznikova, and B. Müller, “High-resolution tomographic imaging of a human cerebellum: comparison of absorption and grating-based phase contrast.” J. R. Soc. Interface7(53), 1665–1676 (2010).
[CrossRef] [PubMed]

Jpn. J. Appl. Phys. (1)

A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of x-ray Talbot interferometry,” Jpn. J. Appl. Phys.42, L866–L868 (2003).
[CrossRef]

Med. Phys. (2)

G.-H. Chen, J. Zambelli, K. Li, N. Bevins, and Z. Qi, “Scaling law for noise variance and spatial resolution in differential phase contrast computed tomography,” Med. Phys.38, 584–588 (2011).
[CrossRef] [PubMed]

J. Zambelli, N. Bevins, Z. Qi, and G.-H. Chen, “Radiation dose efficiency comparison between differential phase contrast CT and conventional absorption CT,” Med. Phys.37, 2473–2479 (2010).
[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, 258–261 (2006).
[CrossRef]

Nucl. Instrum. Meth. A (1)

K. J. Engel, D. Geller, T. Köhler, G. Martens, S. Schusser, G. Vogtmeier, and E. Rössl, “Contrast-to-noise in x-ray differential phase contrast imaging,” Nucl. Instrum. Meth. A648, 202–207 (2010).
[CrossRef]

Opt. Express (4)

Phys. Med. Biol. (1)

F. Pfeiffer, O. Bunk, C. David, M. Bech, G. Le Duc, A. Bravin, and P. Cloetens, “High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography.” Phys. Med. Biol.52, 6923–6930 (2007).
[CrossRef] [PubMed]

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, 105–108 (2007).
[CrossRef]

Phys. Today (1)

R. Fitzgerald, “Phase-sensitive x-ray imaging,” Phys. Today53, 23–26 (2000).
[CrossRef]

Proc. SPIE (1)

T. Weitkamp, I. Zanette, C. David, J. Baruchel, M. Bech, P. Bernard, H. Deyhle, T. Donath, J. Kenntner, S. Lang, J. Mohr, B. Müller, F. Pfeiffer, E. Reznikova, S. Rutishauser, G. Schulz, A. Tapfer, and J.-P. Valade, “Recent developments in x-ray Talbot interferometry at ESRF-ID19,” Proc. SPIE7804, 780406 (2010).
[CrossRef]

Other (4)

J. Hsieh, Computed Tomography - Principles, Design, Artifacts, and Recent Advances, 2nd ed. (Wiley, Hoboken, NJ, 2009).

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 2nd ed. (Prentice-Hall, Upper Saddle River, NJ, 1999).

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed., Vol. 3 of Texts in Computer Science (Pearson Prentice Hall, Upper Saddle River, NJ, 2008).

M. Bech, “X-ray imaging with a grating interferometer,” Ph.D. thesis, University of Copenhagen (2009).

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