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

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

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]

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]

2009

2007

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]

2006

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

2003

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]

2001

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

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

1965

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.

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.

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

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.

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.

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.

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

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

Phys. Med. Biol.

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.

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

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

Proc. SPIE

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

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

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).

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Figures (3)

Fig. 1
Fig. 1

overview of the experimental data used in the analysis. Panel (a) shows a photograph of the breast sample. The RCG method is applied on the two distinct sample regions marked (A) and (B) in the photograph. Panel (b) shows the transmission T for the same region as in the photograph. This projection is the attenuation signal and proportional to ln (I/I0). In panel (c) the differential phase projection is shown. It is proportional to α and shows the signal according to eq. (3). Both projections are obtained from the same set of raw projections from a grating interferometer experiment. Finally, panel (d) shows the derivative of the attenuation signal, i.e. the projection proportional to xT. It represents the signal according to eq. (4). The projections in panels (b–d) have pixel dimensions of 1300x373.

Fig. 2
Fig. 2

power spectra of the experimental data shown in fig. 1, calculated by computing the absolute squared Fourier transform in x-direction for each image row and averaging in y-direction. (a) power spectrum of the DPC projection, (b) power spectra of the differential attenuation projection calculated with different filter functions as indicated in the figure, (c) corresponding filter functions (solid green: Dirichlet windowed, short-dashed red: Hamming windowed, long-dashed blue: Gaussian windowed with σ = 1/2π pixel−1).

Fig. 3
Fig. 3

In the main part of each subfigure the values of xT and xΦ for each position (x, y) in the projection are presented in the form of a scatterplot for regions (A) (left) and (B) (right), respectively. The horizontal axis corresponds to the differential phase-contrast projection, the vertical axis to the differential attenuation projection. Histograms showing the distribution of values for both signals for the sample and reference (i.e. blank scan) regions are plotted on top of the respective axes of the signals. Green color denotes the sample region and blue the corresponding reference regions. The definition of the RCG in eq. (6) can equivalently be stated in terms of the geometry of the ellipses formed by the pixel values of the sample region and the widths of the reference region histograms. The width of the ellipse corresponds to ΔxΦ and the height corresponds to ΔxT. This means that the RCG is inversely proportional to the slope of the ellipses major axis.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

n = 1 δ + i β .
T ( x , y ) = ln ( I ( x , y ) I 0 ( x , y ) ) ,
x Φ ( x , y ) = 2 π λ α ( x , y ) ,
x T = x ln ( I I 0 ) .
CNR = max ( A ) min ( A ) σ 0 ,
RCG = CNR Φ CNR T = Δ ( x Φ ) / σ x Φ Δ ( x T ) / σ x T ,

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