Abstract

Potential applications of grating-based X-ray phase-contrast imaging are investigated in various fields due to its compatibility with laboratory X-ray sources. So far the method was mainly restricted to X-ray energies below 40 keV, which is too low to examine dense or thick objects, but a routine operation at higher energies is on the brink of realisation. In this study, imaging results obtained at 82 keV are presented. These comprise a test object consisting of well-defined materials for a quantitative analysis and a tooth to translate the findings to a biomedical sample. Measured linear attenuation coefficients μ and electron densities ρe are in good agreement with theoretical values. Improved contrast-to-noise ratios were found in phase contrast compared to attenuation contrast. The combination of both contrast modalities further enables to simultaneously assess information on density and composition of materials with effective atomic numbers Z̃ > 8. In our biomedical example, we demonstrate the possibility to detect differences in mass density and calcium concentration within teeth.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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, 6296–6304 (2005).
    [CrossRef] [PubMed]
  2. A. Momose, “Recent advances in X-ray phase imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
    [CrossRef]
  3. 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, 258–261 (2006).
    [CrossRef]
  4. 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]
  5. 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]
  6. M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an X-ray tube source,” Phys. Med. Biol. 54, 2747–2753 (2009).
    [CrossRef] [PubMed]
  7. A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17, 12540–12545 (2009).
    [CrossRef] [PubMed]
  8. T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical X-ray phase-contrast CT: Demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Radiol. 45, 445–452 (2010).
    [PubMed]
  9. 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. Interface 7, 1665–1676 (2010).
    [CrossRef] [PubMed]
  10. J. Herzen, T. Donath, F. Beckmann, M. Ogurreck, C. David, J. Mohr, F. Pfeiffer, and A. Schreyer, “X-ray grating interferometer for materials-science imaging at a low-coherent wiggler source,” Rev. Sci. Instrum. 82, 113711 (2011).
    [CrossRef] [PubMed]
  11. T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
    [CrossRef] [PubMed]
  12. T. Thuering, P. Modregger, T. Grund, J. Kenntner, C. David, and M. Stampanoni, “High resolution, large field of view X-ray differential phase contrast imaging on a compact setup,” Appl. Phys. Lett. 99, 41111 (2011).
    [CrossRef]
  13. D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast X-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56, 5697–5720 (2011).
    [CrossRef] [PubMed]
  14. M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
    [CrossRef] [PubMed]
  15. A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
    [CrossRef]
  16. A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
    [CrossRef] [PubMed]
  17. T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
    [CrossRef] [PubMed]
  18. C. Kottler, V. Revol, R. Kaufmann, and C. Urban, “Dual energy phase contrast X-ray imaging with Talbot-Lau interferometer,” J. Appl. Phys. 108, 114906 (2010).
    [CrossRef]
  19. P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, T. Weber, and G. Anton, “Grating-based high energy X-ray interferometry with the Medipix-detector in simulation and measurement,” J. Instrum. 5, P10008 (2010).
    [CrossRef]
  20. J. Kenntner, V. Altapova, T. Grund, F. J. Pantenburg, J. Meiser, T. Baumbach, and J. Mohr, “Fabrication and characterization of analyzer gratings with high aspect ratios for phase contrast imaging using a Talbot interferometer,” AIP Conf. Proc. 1437, 89–93 (2012).
    [CrossRef]
  21. 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. Express 17, 10010–10018 (2009).
    [CrossRef] [PubMed]
  22. Z. Qi, J. Zambelli, N. Bevins, and G.-H. Chen, “Quantitative imaging of electron density and effective atomic number using phase contrast CT,” Phys. Med. Biol. 55, 2669–2677 (2010).
    [CrossRef] [PubMed]
  23. 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. SPIE 7804, 780406 (2010).
    [CrossRef]
  24. I. Zanette, T. Weitkamp, S. Lang, M. Langer, J. Mohr, C. David, and J. Baruchel, “Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation,” Phys. Status Solidi A 208, 2526–2532 (2011).
    [CrossRef]
  25. E. C. McCullough, “Photon attenuation in computed tomography,” Med. Phys. 2, 307–320 (1975).
    [CrossRef] [PubMed]
  26. M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, “XCOM: Photon Cross Section Database,” (2010).
  27. C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, “X-Ray Form Factor, Attenuation and Scattering Tables,” (2005).
  28. M. d. P. Gutiérrez-Salazar and J. Reyes-Gasga, “Microhardness and chemical composition of human tooth,” Mater. Res. 6, 367–373 (2003).
    [CrossRef]
  29. S. M. Weidmann, J. A. Weatherell, and S. M. Hamm, “Variations of enamel density in sections of human teeth,” Arch. Oral Biol. 12, 85–97 (1967).
    [CrossRef] [PubMed]
  30. V. Coklica, F. Brudevold, and B. H. Amdur, “The distribution and composition of density fractions from human crown dentine,” Arch. Oral Biol. 14, 451–460 (1969).
    [CrossRef] [PubMed]
  31. A. Lange, M. P. Hentschel, A. Kupsch, and B. R. Müller, “Numerical correction of X-ray detector backlighting,” Int. J. Mater. Res. 103, 174–178 (2012).
    [CrossRef]
  32. X. Wu, H. Lu, and A. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett. 30, 379–381 (2005).
    [CrossRef] [PubMed]

2013 (1)

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

2012 (3)

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

J. Kenntner, V. Altapova, T. Grund, F. J. Pantenburg, J. Meiser, T. Baumbach, and J. Mohr, “Fabrication and characterization of analyzer gratings with high aspect ratios for phase contrast imaging using a Talbot interferometer,” AIP Conf. Proc. 1437, 89–93 (2012).
[CrossRef]

A. Lange, M. P. Hentschel, A. Kupsch, and B. R. Müller, “Numerical correction of X-ray detector backlighting,” Int. J. Mater. Res. 103, 174–178 (2012).
[CrossRef]

2011 (6)

I. Zanette, T. Weitkamp, S. Lang, M. Langer, J. Mohr, C. David, and J. Baruchel, “Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation,” Phys. Status Solidi A 208, 2526–2532 (2011).
[CrossRef]

J. Herzen, T. Donath, F. Beckmann, M. Ogurreck, C. David, J. Mohr, F. Pfeiffer, and A. Schreyer, “X-ray grating interferometer for materials-science imaging at a low-coherent wiggler source,” Rev. Sci. Instrum. 82, 113711 (2011).
[CrossRef] [PubMed]

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

T. Thuering, P. Modregger, T. Grund, J. Kenntner, C. David, and M. Stampanoni, “High resolution, large field of view X-ray differential phase contrast imaging on a compact setup,” Appl. Phys. Lett. 99, 41111 (2011).
[CrossRef]

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast X-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56, 5697–5720 (2011).
[CrossRef] [PubMed]

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

2010 (6)

T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical X-ray phase-contrast CT: Demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Radiol. 45, 445–452 (2010).
[PubMed]

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. Interface 7, 1665–1676 (2010).
[CrossRef] [PubMed]

Z. Qi, J. Zambelli, N. Bevins, and G.-H. Chen, “Quantitative imaging of electron density and effective atomic number using phase contrast CT,” Phys. Med. Biol. 55, 2669–2677 (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. SPIE 7804, 780406 (2010).
[CrossRef]

C. Kottler, V. Revol, R. Kaufmann, and C. Urban, “Dual energy phase contrast X-ray imaging with Talbot-Lau interferometer,” J. Appl. Phys. 108, 114906 (2010).
[CrossRef]

P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, T. Weber, and G. Anton, “Grating-based high energy X-ray interferometry with the Medipix-detector in simulation and measurement,” J. Instrum. 5, P10008 (2010).
[CrossRef]

2009 (4)

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an X-ray tube source,” Phys. Med. Biol. 54, 2747–2753 (2009).
[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. Express 17, 10010–10018 (2009).
[CrossRef] [PubMed]

A. Momose, W. Yashiro, H. Maikusa, and Y. Takeda, “High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation,” Opt. Express 17, 12540–12545 (2009).
[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, 108105 (2007).
[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]

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, 258–261 (2006).
[CrossRef]

2005 (3)

2003 (1)

M. d. P. Gutiérrez-Salazar and J. Reyes-Gasga, “Microhardness and chemical composition of human tooth,” Mater. Res. 6, 367–373 (2003).
[CrossRef]

1975 (1)

E. C. McCullough, “Photon attenuation in computed tomography,” Med. Phys. 2, 307–320 (1975).
[CrossRef] [PubMed]

1969 (1)

V. Coklica, F. Brudevold, and B. H. Amdur, “The distribution and composition of density fractions from human crown dentine,” Arch. Oral Biol. 14, 451–460 (1969).
[CrossRef] [PubMed]

1967 (1)

S. M. Weidmann, J. A. Weatherell, and S. M. Hamm, “Variations of enamel density in sections of human teeth,” Arch. Oral Biol. 12, 85–97 (1967).
[CrossRef] [PubMed]

Altapova, V.

J. Kenntner, V. Altapova, T. Grund, F. J. Pantenburg, J. Meiser, T. Baumbach, and J. Mohr, “Fabrication and characterization of analyzer gratings with high aspect ratios for phase contrast imaging using a Talbot interferometer,” AIP Conf. Proc. 1437, 89–93 (2012).
[CrossRef]

Amdur, B. H.

V. Coklica, F. Brudevold, and B. H. Amdur, “The distribution and composition of density fractions from human crown dentine,” Arch. Oral Biol. 14, 451–460 (1969).
[CrossRef] [PubMed]

Anton, G.

P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, T. Weber, and G. Anton, “Grating-based high energy X-ray interferometry with the Medipix-detector in simulation and measurement,” J. Instrum. 5, P10008 (2010).
[CrossRef]

Auweter, S. D.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

Bamberg, F.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

Bartl, P.

P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, T. Weber, and G. Anton, “Grating-based high energy X-ray interferometry with the Medipix-detector in simulation and measurement,” J. Instrum. 5, P10008 (2010).
[CrossRef]

Baruchel, J.

I. Zanette, T. Weitkamp, S. Lang, M. Langer, J. Mohr, C. David, and J. Baruchel, “Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation,” Phys. Status Solidi A 208, 2526–2532 (2011).
[CrossRef]

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. SPIE 7804, 780406 (2010).
[CrossRef]

Baumbach, T.

J. Kenntner, V. Altapova, T. Grund, F. J. Pantenburg, J. Meiser, T. Baumbach, and J. Mohr, “Fabrication and characterization of analyzer gratings with high aspect ratios for phase contrast imaging using a Talbot interferometer,” AIP Conf. Proc. 1437, 89–93 (2012).
[CrossRef]

Bayer, F.

P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, T. Weber, and G. Anton, “Grating-based high energy X-ray interferometry with the Medipix-detector in simulation and measurement,” J. Instrum. 5, P10008 (2010).
[CrossRef]

Bech, M.

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[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. SPIE 7804, 780406 (2010).
[CrossRef]

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an X-ray tube source,” Phys. Med. Biol. 54, 2747–2753 (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]

Beck, T. J.

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast X-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56, 5697–5720 (2011).
[CrossRef] [PubMed]

Beckmann, F.

J. Herzen, T. Donath, F. Beckmann, M. Ogurreck, C. David, J. Mohr, F. Pfeiffer, and A. Schreyer, “X-ray grating interferometer for materials-science imaging at a low-coherent wiggler source,” Rev. Sci. Instrum. 82, 113711 (2011).
[CrossRef] [PubMed]

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. Interface 7, 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. Express 17, 10010–10018 (2009).
[CrossRef] [PubMed]

Bednarzik, M.

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

Berger, M. J.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, “XCOM: Photon Cross Section Database,” (2010).

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. SPIE 7804, 780406 (2010).
[CrossRef]

Bevins, N.

Z. Qi, J. Zambelli, N. Bevins, and G.-H. Chen, “Quantitative imaging of electron density and effective atomic number using phase contrast CT,” Phys. Med. Biol. 55, 2669–2677 (2010).
[CrossRef] [PubMed]

Bingham, C. O.

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast X-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56, 5697–5720 (2011).
[CrossRef] [PubMed]

Boettiger, A.

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

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]

Brudevold, F.

V. Coklica, F. Brudevold, and B. H. Amdur, “The distribution and composition of density fractions from human crown dentine,” Arch. Oral Biol. 14, 451–460 (1969).
[CrossRef] [PubMed]

Bruyndonckx, P.

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

Bunk, O.

T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical X-ray phase-contrast CT: Demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Radiol. 45, 445–452 (2010).
[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. Express 17, 10010–10018 (2009).
[CrossRef] [PubMed]

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an X-ray tube source,” Phys. Med. Biol. 54, 2747–2753 (2009).
[CrossRef] [PubMed]

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

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

Carrino, J. A.

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast X-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56, 5697–5720 (2011).
[CrossRef] [PubMed]

Chang, J.

C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, “X-Ray Form Factor, Attenuation and Scattering Tables,” (2005).

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, “XCOM: Photon Cross Section Database,” (2010).

Chantler, C. T.

C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, “X-Ray Form Factor, Attenuation and Scattering Tables,” (2005).

Chen, G.-H.

Z. Qi, J. Zambelli, N. Bevins, and G.-H. Chen, “Quantitative imaging of electron density and effective atomic number using phase contrast CT,” Phys. Med. Biol. 55, 2669–2677 (2010).
[CrossRef] [PubMed]

Christensen, L. B.

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[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. Express 13, 6296–6304 (2005).
[CrossRef] [PubMed]

Coklica, V.

V. Coklica, F. Brudevold, and B. H. Amdur, “The distribution and composition of density fractions from human crown dentine,” Arch. Oral Biol. 14, 451–460 (1969).
[CrossRef] [PubMed]

Coursey, J. S.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, “XCOM: Photon Cross Section Database,” (2010).

David, C.

T. Thuering, P. Modregger, T. Grund, J. Kenntner, C. David, and M. Stampanoni, “High resolution, large field of view X-ray differential phase contrast imaging on a compact setup,” Appl. Phys. Lett. 99, 41111 (2011).
[CrossRef]

I. Zanette, T. Weitkamp, S. Lang, M. Langer, J. Mohr, C. David, and J. Baruchel, “Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation,” Phys. Status Solidi A 208, 2526–2532 (2011).
[CrossRef]

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

J. Herzen, T. Donath, F. Beckmann, M. Ogurreck, C. David, J. Mohr, F. Pfeiffer, and A. Schreyer, “X-ray grating interferometer for materials-science imaging at a low-coherent wiggler source,” Rev. Sci. Instrum. 82, 113711 (2011).
[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. SPIE 7804, 780406 (2010).
[CrossRef]

T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical X-ray phase-contrast CT: Demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Radiol. 45, 445–452 (2010).
[PubMed]

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. Interface 7, 1665–1676 (2010).
[CrossRef] [PubMed]

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an X-ray tube source,” Phys. Med. Biol. 54, 2747–2753 (2009).
[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. Express 17, 10010–10018 (2009).
[CrossRef] [PubMed]

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

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. 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, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 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. Express 13, 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. SPIE 7804, 780406 (2010).
[CrossRef]

Diaz, A.

Donath, T.

J. Herzen, T. Donath, F. Beckmann, M. Ogurreck, C. David, J. Mohr, F. Pfeiffer, and A. Schreyer, “X-ray grating interferometer for materials-science imaging at a low-coherent wiggler source,” Rev. Sci. Instrum. 82, 113711 (2011).
[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. SPIE 7804, 780406 (2010).
[CrossRef]

T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical X-ray phase-contrast CT: Demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Radiol. 45, 445–452 (2010).
[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. Express 17, 10010–10018 (2009).
[CrossRef] [PubMed]

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

Dragoset, R. A.

C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, “X-Ray Form Factor, Attenuation and Scattering Tables,” (2005).

Durst, J.

P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, T. Weber, and G. Anton, “Grating-based high energy X-ray interferometry with the Medipix-detector in simulation and measurement,” J. Instrum. 5, P10008 (2010).
[CrossRef]

Feidenhans’l, R.

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an X-ray tube source,” Phys. Med. Biol. 54, 2747–2753 (2009).
[CrossRef] [PubMed]

Groot, W.

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

Grund, T.

J. Kenntner, V. Altapova, T. Grund, F. J. Pantenburg, J. Meiser, T. Baumbach, and J. Mohr, “Fabrication and characterization of analyzer gratings with high aspect ratios for phase contrast imaging using a Talbot interferometer,” AIP Conf. Proc. 1437, 89–93 (2012).
[CrossRef]

T. Thuering, P. Modregger, T. Grund, J. Kenntner, C. David, and M. Stampanoni, “High resolution, large field of view X-ray differential phase contrast imaging on a compact setup,” Appl. Phys. Lett. 99, 41111 (2011).
[CrossRef]

Grünzweig, C.

T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical X-ray phase-contrast CT: Demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Radiol. 45, 445–452 (2010).
[PubMed]

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

Gutiérrez-Salazar, M. d. P.

M. d. P. Gutiérrez-Salazar and J. Reyes-Gasga, “Microhardness and chemical composition of human tooth,” Mater. Res. 6, 367–373 (2003).
[CrossRef]

Haas, W.

P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, T. Weber, and G. Anton, “Grating-based high energy X-ray interferometry with the Medipix-detector in simulation and measurement,” J. Instrum. 5, P10008 (2010).
[CrossRef]

Hahn, D.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

Hamm, S. M.

S. M. Weidmann, J. A. Weatherell, and S. M. Hamm, “Variations of enamel density in sections of human teeth,” Arch. Oral Biol. 12, 85–97 (1967).
[CrossRef] [PubMed]

Hauser, N.

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

Hellerhoff, K.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

Hempel, E.

T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical X-ray phase-contrast CT: Demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Radiol. 45, 445–452 (2010).
[PubMed]

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

Hentschel, M. P.

A. Lange, M. P. Hentschel, A. Kupsch, and B. R. Müller, “Numerical correction of X-ray detector backlighting,” Int. J. Mater. Res. 103, 174–178 (2012).
[CrossRef]

Herzen, J.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

J. Herzen, T. Donath, F. Beckmann, M. Ogurreck, C. David, J. Mohr, F. Pfeiffer, and A. Schreyer, “X-ray grating interferometer for materials-science imaging at a low-coherent wiggler source,” Rev. Sci. Instrum. 82, 113711 (2011).
[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. Express 17, 10010–10018 (2009).
[CrossRef] [PubMed]

Hoheisel, M.

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

Hohl, M. K.

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

Hubbell, J. H.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, “XCOM: Photon Cross Section Database,” (2010).

Jensen, T. H.

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an X-ray tube source,” Phys. Med. Biol. 54, 2747–2753 (2009).
[CrossRef] [PubMed]

Kaufmann, R.

C. Kottler, V. Revol, R. Kaufmann, and C. Urban, “Dual energy phase contrast X-ray imaging with Talbot-Lau interferometer,” J. Appl. Phys. 108, 114906 (2010).
[CrossRef]

Kenntner, J.

J. Kenntner, V. Altapova, T. Grund, F. J. Pantenburg, J. Meiser, T. Baumbach, and J. Mohr, “Fabrication and characterization of analyzer gratings with high aspect ratios for phase contrast imaging using a Talbot interferometer,” AIP Conf. Proc. 1437, 89–93 (2012).
[CrossRef]

T. Thuering, P. Modregger, T. Grund, J. Kenntner, C. David, and M. Stampanoni, “High resolution, large field of view X-ray differential phase contrast imaging on a compact setup,” Appl. Phys. Lett. 99, 41111 (2011).
[CrossRef]

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. SPIE 7804, 780406 (2010).
[CrossRef]

Kishore, A. R.

C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, “X-Ray Form Factor, Attenuation and Scattering Tables,” (2005).

Kotochigova, S. A.

C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, “X-Ray Form Factor, Attenuation and Scattering Tables,” (2005).

Kottler, C.

C. Kottler, V. Revol, R. Kaufmann, and C. Urban, “Dual energy phase contrast X-ray imaging with Talbot-Lau interferometer,” J. Appl. Phys. 108, 114906 (2010).
[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]

Kubik-Huch, R. A.

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

Kupsch, A.

A. Lange, M. P. Hentschel, A. Kupsch, and B. R. Müller, “Numerical correction of X-ray detector backlighting,” Int. J. Mater. Res. 103, 174–178 (2012).
[CrossRef]

Lang, S.

I. Zanette, T. Weitkamp, S. Lang, M. Langer, J. Mohr, C. David, and J. Baruchel, “Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation,” Phys. Status Solidi A 208, 2526–2532 (2011).
[CrossRef]

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. SPIE 7804, 780406 (2010).
[CrossRef]

Lange, A.

A. Lange, M. P. Hentschel, A. Kupsch, and B. R. Müller, “Numerical correction of X-ray detector backlighting,” Int. J. Mater. Res. 103, 174–178 (2012).
[CrossRef]

Langer, M.

I. Zanette, T. Weitkamp, S. Lang, M. Langer, J. Mohr, C. David, and J. Baruchel, “Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation,” Phys. Status Solidi A 208, 2526–2532 (2011).
[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]

Liebhardt, S.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

Liu, X.

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

Lu, H.

Maikusa, H.

Mayr, D.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

McCullough, E. C.

E. C. McCullough, “Photon attenuation in computed tomography,” Med. Phys. 2, 307–320 (1975).
[CrossRef] [PubMed]

Meiser, J.

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

J. Kenntner, V. Altapova, T. Grund, F. J. Pantenburg, J. Meiser, T. Baumbach, and J. Mohr, “Fabrication and characterization of analyzer gratings with high aspect ratios for phase contrast imaging using a Talbot interferometer,” AIP Conf. Proc. 1437, 89–93 (2012).
[CrossRef]

Michel, T.

P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, T. Weber, and G. Anton, “Grating-based high energy X-ray interferometry with the Medipix-detector in simulation and measurement,” J. Instrum. 5, P10008 (2010).
[CrossRef]

Modregger, P.

T. Thuering, P. Modregger, T. Grund, J. Kenntner, C. David, and M. Stampanoni, “High resolution, large field of view X-ray differential phase contrast imaging on a compact setup,” Appl. Phys. Lett. 99, 41111 (2011).
[CrossRef]

Mohr, J.

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

J. Kenntner, V. Altapova, T. Grund, F. J. Pantenburg, J. Meiser, T. Baumbach, and J. Mohr, “Fabrication and characterization of analyzer gratings with high aspect ratios for phase contrast imaging using a Talbot interferometer,” AIP Conf. Proc. 1437, 89–93 (2012).
[CrossRef]

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

I. Zanette, T. Weitkamp, S. Lang, M. Langer, J. Mohr, C. David, and J. Baruchel, “Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation,” Phys. Status Solidi A 208, 2526–2532 (2011).
[CrossRef]

J. Herzen, T. Donath, F. Beckmann, M. Ogurreck, C. David, J. Mohr, F. Pfeiffer, and A. Schreyer, “X-ray grating interferometer for materials-science imaging at a low-coherent wiggler source,” Rev. Sci. Instrum. 82, 113711 (2011).
[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. SPIE 7804, 780406 (2010).
[CrossRef]

Momose, A.

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. SPIE 7804, 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. Interface 7, 1665–1676 (2010).
[CrossRef] [PubMed]

Müller, B. R.

A. Lange, M. P. Hentschel, A. Kupsch, and B. R. Müller, “Numerical correction of X-ray detector backlighting,” Int. J. Mater. Res. 103, 174–178 (2012).
[CrossRef]

Ogurreck, M.

J. Herzen, T. Donath, F. Beckmann, M. Ogurreck, C. David, J. Mohr, F. Pfeiffer, and A. Schreyer, “X-ray grating interferometer for materials-science imaging at a low-coherent wiggler source,” Rev. Sci. Instrum. 82, 113711 (2011).
[CrossRef] [PubMed]

Olsen, E. V.

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

Olsen, K.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, “XCOM: Photon Cross Section Database,” (2010).

C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, “X-Ray Form Factor, Attenuation and Scattering Tables,” (2005).

Padeste, C.

Pantenburg, F. J.

J. Kenntner, V. Altapova, T. Grund, F. J. Pantenburg, J. Meiser, T. Baumbach, and J. Mohr, “Fabrication and characterization of analyzer gratings with high aspect ratios for phase contrast imaging using a Talbot interferometer,” AIP Conf. Proc. 1437, 89–93 (2012).
[CrossRef]

Pauwels, B.

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

Pfeiffer, F.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

J. Herzen, T. Donath, F. Beckmann, M. Ogurreck, C. David, J. Mohr, F. Pfeiffer, and A. Schreyer, “X-ray grating interferometer for materials-science imaging at a low-coherent wiggler source,” Rev. Sci. Instrum. 82, 113711 (2011).
[CrossRef] [PubMed]

T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical X-ray phase-contrast CT: Demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Radiol. 45, 445–452 (2010).
[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. SPIE 7804, 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. Interface 7, 1665–1676 (2010).
[CrossRef] [PubMed]

M. Bech, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an X-ray tube source,” Phys. Med. Biol. 54, 2747–2753 (2009).
[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. Express 17, 10010–10018 (2009).
[CrossRef] [PubMed]

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

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. 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, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 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. Express 13, 6296–6304 (2005).
[CrossRef] [PubMed]

Popescu, S.

T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical X-ray phase-contrast CT: Demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Radiol. 45, 445–452 (2010).
[PubMed]

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

Qi, Z.

Z. Qi, J. Zambelli, N. Bevins, and G.-H. Chen, “Quantitative imaging of electron density and effective atomic number using phase contrast CT,” Phys. Med. Biol. 55, 2669–2677 (2010).
[CrossRef] [PubMed]

Reiser, M. F.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

Revol, V.

C. Kottler, V. Revol, R. Kaufmann, and C. Urban, “Dual energy phase contrast X-ray imaging with Talbot-Lau interferometer,” J. Appl. Phys. 108, 114906 (2010).
[CrossRef]

Reyes-Gasga, J.

M. d. P. Gutiérrez-Salazar and J. Reyes-Gasga, “Microhardness and chemical composition of human tooth,” Mater. Res. 6, 367–373 (2003).
[CrossRef]

Reznikova, E.

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

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. Interface 7, 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. SPIE 7804, 780406 (2010).
[CrossRef]

Ritter, A.

P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, T. Weber, and G. Anton, “Grating-based high energy X-ray interferometry with the Medipix-detector in simulation and measurement,” J. Instrum. 5, P10008 (2010).
[CrossRef]

Roessl, E.

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

Rutishauser, S.

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

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. Interface 7, 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. SPIE 7804, 780406 (2010).
[CrossRef]

Sasov, A.

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

Schreyer, A.

J. Herzen, T. Donath, F. Beckmann, M. Ogurreck, C. David, J. Mohr, F. Pfeiffer, and A. Schreyer, “X-ray grating interferometer for materials-science imaging at a low-coherent wiggler source,” Rev. Sci. Instrum. 82, 113711 (2011).
[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. Express 17, 10010–10018 (2009).
[CrossRef] [PubMed]

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. SPIE 7804, 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. Interface 7, 1665–1676 (2010).
[CrossRef] [PubMed]

Schulz, J.

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

Seltzer, S. M.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, “XCOM: Photon Cross Section Database,” (2010).

Singer, G.

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

Stampanoni, M.

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

T. Thuering, P. Modregger, T. Grund, J. Kenntner, C. David, and M. Stampanoni, “High resolution, large field of view X-ray differential phase contrast imaging on a compact setup,” Appl. Phys. Lett. 99, 41111 (2011).
[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, 6296–6304 (2005).
[CrossRef] [PubMed]

Stutman, D.

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast X-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56, 5697–5720 (2011).
[CrossRef] [PubMed]

Sukumar, R.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, “XCOM: Photon Cross Section Database,” (2010).

Sztrókay, A.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

Takeda, Y.

Tapfer, A.

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[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. SPIE 7804, 780406 (2010).
[CrossRef]

Thuering, T.

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

T. Thuering, P. Modregger, T. Grund, J. Kenntner, C. David, and M. Stampanoni, “High resolution, large field of view X-ray differential phase contrast imaging on a compact setup,” Appl. Phys. Lett. 99, 41111 (2011).
[CrossRef]

Trippel, M.

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

Urban, C.

C. Kottler, V. Revol, R. Kaufmann, and C. Urban, “Dual energy phase contrast X-ray imaging with Talbot-Lau interferometer,” J. Appl. Phys. 108, 114906 (2010).
[CrossRef]

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. SPIE 7804, 780406 (2010).
[CrossRef]

Velroyen, A.

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

Vock, P.

T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical X-ray phase-contrast CT: Demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Radiol. 45, 445–452 (2010).
[PubMed]

Walter, M.

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

Wang, Z.

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

Weatherell, J. A.

S. M. Weidmann, J. A. Weatherell, and S. M. Hamm, “Variations of enamel density in sections of human teeth,” Arch. Oral Biol. 12, 85–97 (1967).
[CrossRef] [PubMed]

Weber, T.

P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, T. Weber, and G. Anton, “Grating-based high energy X-ray interferometry with the Medipix-detector in simulation and measurement,” J. Instrum. 5, P10008 (2010).
[CrossRef]

Weidmann, S. M.

S. M. Weidmann, J. A. Weatherell, and S. M. Hamm, “Variations of enamel density in sections of human teeth,” Arch. Oral Biol. 12, 85–97 (1967).
[CrossRef] [PubMed]

Weitkamp, T.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

I. Zanette, T. Weitkamp, S. Lang, M. Langer, J. Mohr, C. David, and J. Baruchel, “Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation,” Phys. Status Solidi A 208, 2526–2532 (2011).
[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. Interface 7, 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. SPIE 7804, 780406 (2010).
[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, 258–261 (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, 6296–6304 (2005).
[CrossRef] [PubMed]

Willner, M.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

Wu, X.

Yan, A.

Yashiro, W.

Zambelli, J.

Z. Qi, J. Zambelli, N. Bevins, and G.-H. Chen, “Quantitative imaging of electron density and effective atomic number using phase contrast CT,” Phys. Med. Biol. 55, 2669–2677 (2010).
[CrossRef] [PubMed]

Zanette, I.

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

I. Zanette, T. Weitkamp, S. Lang, M. Langer, J. Mohr, C. David, and J. Baruchel, “Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation,” Phys. Status Solidi A 208, 2526–2532 (2011).
[CrossRef]

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

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. Interface 7, 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. SPIE 7804, 780406 (2010).
[CrossRef]

Ziegler, E.

Zucker, D. S.

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, “XCOM: Photon Cross Section Database,” (2010).

C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, “X-Ray Form Factor, Attenuation and Scattering Tables,” (2005).

AIP Conf. Proc. (1)

J. Kenntner, V. Altapova, T. Grund, F. J. Pantenburg, J. Meiser, T. Baumbach, and J. Mohr, “Fabrication and characterization of analyzer gratings with high aspect ratios for phase contrast imaging using a Talbot interferometer,” AIP Conf. Proc. 1437, 89–93 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

T. Thuering, P. Modregger, T. Grund, J. Kenntner, C. David, and M. Stampanoni, “High resolution, large field of view X-ray differential phase contrast imaging on a compact setup,” Appl. Phys. Lett. 99, 41111 (2011).
[CrossRef]

Arch. Oral Biol. (2)

S. M. Weidmann, J. A. Weatherell, and S. M. Hamm, “Variations of enamel density in sections of human teeth,” Arch. Oral Biol. 12, 85–97 (1967).
[CrossRef] [PubMed]

V. Coklica, F. Brudevold, and B. H. Amdur, “The distribution and composition of density fractions from human crown dentine,” Arch. Oral Biol. 14, 451–460 (1969).
[CrossRef] [PubMed]

Eur. Radiol. (1)

A. Sztrókay, J. Herzen, S. D. Auweter, S. Liebhardt, D. Mayr, M. Willner, D. Hahn, I. Zanette, T. Weitkamp, K. Hellerhoff, F. Pfeiffer, M. F. Reiser, and F. Bamberg, “Assessment of grating-based X-ray phase-contrast CT for differentiation of invasive ductal carcinoma and ductal carcinoma in situ in an experimental ex vivo set-up,” Eur. Radiol. 23, 381–387 (2013).
[CrossRef]

Int. J. Mater. Res. (1)

A. Lange, M. P. Hentschel, A. Kupsch, and B. R. Müller, “Numerical correction of X-ray detector backlighting,” Int. J. Mater. Res. 103, 174–178 (2012).
[CrossRef]

Invest. Radiol. (2)

M. Stampanoni, Z. Wang, T. Thuering, C. David, E. Roessl, M. Trippel, R. A. Kubik-Huch, G. Singer, M. K. Hohl, and N. Hauser, “The first analysis and clinical evaluation of native breast tissue using differential phase-contrast mammography,” Invest. Radiol. 46, 801–806 (2011).
[CrossRef] [PubMed]

T. Donath, F. Pfeiffer, O. Bunk, C. Grünzweig, E. Hempel, S. Popescu, P. Vock, and C. David, “Toward clinical X-ray phase-contrast CT: Demonstration of enhanced soft-tissue contrast in human specimen,” Invest. Radiol. 45, 445–452 (2010).
[PubMed]

J. Appl. Phys. (1)

C. Kottler, V. Revol, R. Kaufmann, and C. Urban, “Dual energy phase contrast X-ray imaging with Talbot-Lau interferometer,” J. Appl. Phys. 108, 114906 (2010).
[CrossRef]

J. Instrum. (1)

P. Bartl, F. Bayer, J. Durst, W. Haas, T. Michel, A. Ritter, T. Weber, and G. Anton, “Grating-based high energy X-ray interferometry with the Medipix-detector in simulation and measurement,” J. Instrum. 5, P10008 (2010).
[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. Interface 7, 1665–1676 (2010).
[CrossRef] [PubMed]

Jpn. J. Appl. Phys. (1)

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

Mater. Res. (1)

M. d. P. Gutiérrez-Salazar and J. Reyes-Gasga, “Microhardness and chemical composition of human tooth,” Mater. Res. 6, 367–373 (2003).
[CrossRef]

Meat Sci. (1)

T. H. Jensen, A. Boettiger, M. Bech, I. Zanette, T. Weitkamp, S. Rutishauser, C. David, E. Reznikova, J. Mohr, L. B. Christensen, E. V. Olsen, R. Feidenhans’l, and F. Pfeiffer, “X-ray phase-contrast tomography of porcine fat and rind,” Meat Sci. 88, 379–383 (2011).
[CrossRef] [PubMed]

Med. Phys. (1)

E. C. McCullough, “Photon attenuation in computed tomography,” Med. Phys. 2, 307–320 (1975).
[CrossRef] [PubMed]

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

Opt. Express (3)

Opt. Lett. (1)

Phys. Med. Biol. (4)

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, T. H. Jensen, R. Feidenhans’l, O. Bunk, C. David, and F. Pfeiffer, “Soft-tissue phase-contrast tomography with an X-ray tube source,” Phys. Med. Biol. 54, 2747–2753 (2009).
[CrossRef] [PubMed]

Z. Qi, J. Zambelli, N. Bevins, and G.-H. Chen, “Quantitative imaging of electron density and effective atomic number using phase contrast CT,” Phys. Med. Biol. 55, 2669–2677 (2010).
[CrossRef] [PubMed]

D. Stutman, T. J. Beck, J. A. Carrino, and C. O. Bingham, “Talbot phase-contrast X-ray imaging for the small joints of the hand,” Phys. Med. Biol. 56, 5697–5720 (2011).
[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, 108105 (2007).
[CrossRef] [PubMed]

Phys. Status Solidi A (1)

I. Zanette, T. Weitkamp, S. Lang, M. Langer, J. Mohr, C. David, and J. Baruchel, “Quantitative phase and absorption tomography with an X-ray grating interferometer and synchrotron radiation,” Phys. Status Solidi A 208, 2526–2532 (2011).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

A. Tapfer, M. Bech, A. Velroyen, J. Meiser, J. Mohr, M. Walter, J. Schulz, B. Pauwels, P. Bruyndonckx, X. Liu, A. Sasov, and F. Pfeiffer, “Experimental results from a preclinical X-ray phase-contrast CT scanner,” Proc. Natl. Acad. Sci. USA 109, 15691–15696 (2012).
[CrossRef] [PubMed]

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. SPIE 7804, 780406 (2010).
[CrossRef]

Rev. Sci. Instrum. (2)

T. Donath, F. Pfeiffer, O. Bunk, W. Groot, M. Bednarzik, C. Grünzweig, E. Hempel, S. Popescu, M. Hoheisel, and C. David, “Phase-contrast imaging and tomography at 60 keV using a conventional X-ray tube source,” Rev. Sci. Instrum. 80, 053701 (2009).
[CrossRef] [PubMed]

J. Herzen, T. Donath, F. Beckmann, M. Ogurreck, C. David, J. Mohr, F. Pfeiffer, and A. Schreyer, “X-ray grating interferometer for materials-science imaging at a low-coherent wiggler source,” Rev. Sci. Instrum. 82, 113711 (2011).
[CrossRef] [PubMed]

Other (2)

M. J. Berger, J. H. Hubbell, S. M. Seltzer, J. Chang, J. S. Coursey, R. Sukumar, D. S. Zucker, and K. Olsen, “XCOM: Photon Cross Section Database,” (2010).

C. T. Chantler, K. Olsen, R. A. Dragoset, J. Chang, A. R. Kishore, S. A. Kotochigova, and D. S. Zucker, “X-Ray Form Factor, Attenuation and Scattering Tables,” (2005).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Principle of a grating-based X-ray interferometer. The phase grating creates a periodic intensity pattern that can be resolved by placing an analyzer grating in front of the detector. A sample in the incident beam causes slight refraction, which results in a local shift of the analyzed pattern.

Fig. 2
Fig. 2

Imaging results. Attenuation contrast (a) and phase contrast (b) of a test object consisting of PMMA (1), glass (2), aluminum (3), PVC (4), PTFE (5) and titanium (6).

Fig. 3
Fig. 3

Measured linear attenuation coefficients μ versus corresponding electron densities ρe. Standard deviations are indicated by error bars and the solid green line represents the linear attenuation coefficient for Compton scattering μincoh.

Fig. 4
Fig. 4

The ratio of Compton scattering to the linear attenuation coefficient μincoh/μ of single elements decreases with atomic number Z as illustrated by the black markers. The combination of attenuation and phase contrast allows to determine the contribution of Compton scattering to the attenuation process within a material (solid green lines) and, thus, to draw conclusions on its effective atomic number .

Fig. 5
Fig. 5

Attenuation-contrast (a) and phase-contrast (b) imaging results of a tooth. Mass densities ρ evaluated at 50 positions in enamel and 20 positions in dentin are presented in (c) and (d), respectively. Effective atomic numbers obtained by exploiting both contrast modalities are displayed in (e).

Tables (2)

Tables Icon

Table 1 Properties and quantitative analysis results of the materials used in the test object. Linear attenuation coefficients μ are obtained from attenuation contrast; refractive index decrements δ and electron densities ρe are extracted from phase contrast. Theoretical values (theo) are based on NIST databases and material compositions.

Tables Icon

Table 2 Contrast-to-noise ratios in phase contrast CNRph and attenuation contrast CNRatt for selected material combinations. A contrast gain by phase-contrast imaging can be noticed in all cases.

Equations (10)

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

δ = r 0 h 2 c 2 2 π E 2 N i f i 1 ,
ρ e ( x , y , z ) = 2 π E 2 r 0 h 2 c 2 δ ( x , y , z ) .
ρ = ρ e / N g .
μ = μ incoh + μ p h + μ coh = ρ e ( σ incoh e ( E ) + σ ph e ( E , Z ˜ ph ) + σ coh e ( E , Z ˜ coh ) )
σ p h e ( E , Z ˜ p h ) = C 1 Z ˜ p h k E l
σ coh e ( E , Z ˜ coh ) = C 1 Z ˜ coh m E n
Z ˜ p h = ( α i Z i k ) 1 / k and Z ˜ c o h = ( α i Z i m ) 1 / m ,
μ incoh μ ρ e σ k n μ ,
μ incoh μ ρ e σ k n ρ e σ tot e = σ k n σ tot ( Z ) / Z .
C N R = | S A S B | σ A 2 + σ B 2 ,

Metrics