Abstract

It is known that the sensitivity of X-ray phase-contrast grating interferometry with regard to electron density variations present in the sample is related to the minimum detectable refraction angle. In this article a numerical framework is developed that allows for a realistic and quantitative determination of the sensitivity. The framework is validated by comparisons with experimental results and then used for the quantification of several influences on the sensitivity, such as spatial coherence or the number of phase step images. In particular, we identify the ideal inter-grating distance with respect to the highest sensitivity for parallel beam geometry. This knowledge will help to optimize existing synchrotron-based grating interferometry setups.

© 2011 OSA

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  1. U Bonse and M Hart, “An X-ray interferometer,” Appl. Phys. Lett. 6, 155–156 (1965).
    [CrossRef]
  2. A Momose, T Takeda, Y Itai, and K Hirano, “Phase-contrast x-ray computed tomography for observing biological soft tissues,” Nat. Med. 2, 473–475 (1996).
    [CrossRef] [PubMed]
  3. A Yoneyama, T Takeda, Y Tsuchiya, J Wu, Thet-Thet-Lwin, A Koizumi, K Hyodo, and Y Itai, “A phase-contrast X-ray imaging system-with a 60 x 30 mm field of view based on a skew-symmetric two-crystal X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 523, 217–222 (2004).
    [CrossRef]
  4. A Snigirev, I Snigireva, V Kohn, S Kuznetsov, and I Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
    [CrossRef]
  5. P Cloetens, R Barrett, J Baruchel, J-P Guigay, and M Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
    [CrossRef]
  6. M Langer, P Cloetens, J-P Guigay, and F Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.,  354556–4566 (2008).
    [CrossRef] [PubMed]
  7. TJ Davis, D Gao, T E Gureyev, A W Stevenson, and S W Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
    [CrossRef]
  8. D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
    [CrossRef] [PubMed]
  9. P C Diemoz, P Coan, C Glaser, and A Bravin, “Absorption, refraction and scattering in analyzer-based imaging: comparison of different algorithms,” Opt. Express 18, 3494–3509 (2010).
    [CrossRef] [PubMed]
  10. M Stampanoni, G Borchert, R Abela, and P Rüegsegger, “Bragg magnifier: A detector for submicrometer x-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
    [CrossRef]
  11. P Modregger, D Lübbert, P Schäfer, and R Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).
  12. C David, B Nöhammer, H H Solak, and E Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 813287–3289 (2002).
    [CrossRef]
  13. 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]
  14. 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]
  15. 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]
  16. 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]
  17. F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
    [CrossRef] [PubMed]
  18. Z-T Wang, K-J Kang, Z-F Huang, and Z-Q Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
    [CrossRef]
  19. M Engelhardt, J Baumann, M Schuster, C Kottler, F Pfeiffer, O Bunk, and C David, “High-resolution differential phase contrast imaging using a magnifying projection geometry with a microfocus x-ray source,” Appl. Phys. Lett. 90, 224101 (2007).
    [CrossRef]
  20. M Engelhardt, C Kottler, O Bunk, C David, C G Schroer, J Baumann, M Schuster, and F Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232, 145–157 (2008).
    [CrossRef] [PubMed]
  21. 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]
  22. T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
    [CrossRef]
  23. C David, J Bruder, T Rohbeck, C Grünzweig, C Kottler, A Diaz, O Bunk, and F Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84, 1172–1177 (2007).
    [CrossRef]
  24. E Reznikova, J Mohr, M Boerner, V Nazmov, and P-J Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures. Microsystem Technologies,” Microsyst. Technol. 14, 1683–1688 (2008).
    [CrossRef]
  25. D Noda, M Tanaka, K Shimada, W Yashiro, A Momose, and T Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–11315 (2008).
    [CrossRef]
  26. H F Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401–407 (1836).
  27. P Cloetens, Contribution to phase contrast imaging, reconstruction and tomography with hard synchrotron radiation: principles, implementation and applications. PhD thesis, Vrije Universiteit Brussel, 1999.
  28. T J Suleski, “Generation of Lohmann images from binary-phase Talbot array illuminators,” Appl. Opt. 36, 4686–4691 (1997).
    [CrossRef] [PubMed]
  29. M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).
  30. S A McDonald, F Marone, C Hintermüller, G Mikuljan, C David, F Pfeiffer, and M Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synch. Rad. 16, 562–572 (2009).
    [CrossRef]
  31. F. James, Statistical methods in experimental physics, 2nd ed. (World Scientific Publishing, Singapore, 2006).
  32. V Revol, C Kottler, R Kaufmann, U Straumann, and C Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010)
    [CrossRef] [PubMed]
  33. A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
    [CrossRef]
  34. T Weitkamp, C David, C Kottler, O Bunk, and F Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318 (2006).
    [CrossRef]
  35. R Raupach and T G Flohr, “Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56, 2219–2244 (2011).
    [CrossRef] [PubMed]
  36. M Bech, X-ray imaging with a grating interferometer, PhD thesis, University of Copenhagen (2009).
  37. 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 (2010).
    [CrossRef]
  38. W Yashiro, Y Takeda, and A Momose, “Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry,” J. Opt. Soc. Am. A 25, 2025–2039 (2008).
    [CrossRef]

2011 (1)

R Raupach and T G Flohr, “Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56, 2219–2244 (2011).
[CrossRef] [PubMed]

2010 (5)

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 (2010).
[CrossRef]

V Revol, C Kottler, R Kaufmann, U Straumann, and C Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010)
[CrossRef] [PubMed]

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

P C Diemoz, P Coan, C Glaser, and A Bravin, “Absorption, refraction and scattering in analyzer-based imaging: comparison of different algorithms,” Opt. Express 18, 3494–3509 (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]

2009 (3)

Z-T Wang, K-J Kang, Z-F Huang, and Z-Q Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[CrossRef]

S A McDonald, F Marone, C Hintermüller, G Mikuljan, C David, F Pfeiffer, and M Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synch. Rad. 16, 562–572 (2009).
[CrossRef]

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

2008 (5)

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

E Reznikova, J Mohr, M Boerner, V Nazmov, and P-J Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures. Microsystem Technologies,” Microsyst. Technol. 14, 1683–1688 (2008).
[CrossRef]

D Noda, M Tanaka, K Shimada, W Yashiro, A Momose, and T Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–11315 (2008).
[CrossRef]

W Yashiro, Y Takeda, and A Momose, “Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry,” J. Opt. Soc. Am. A 25, 2025–2039 (2008).
[CrossRef]

M Langer, P Cloetens, J-P Guigay, and F Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.,  354556–4566 (2008).
[CrossRef] [PubMed]

2007 (4)

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

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (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]

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

2006 (2)

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, C David, C Kottler, O Bunk, and F Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318 (2006).
[CrossRef]

2005 (2)

F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[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]

2004 (1)

A Yoneyama, T Takeda, Y Tsuchiya, J Wu, Thet-Thet-Lwin, A Koizumi, K Hyodo, and Y Itai, “A phase-contrast X-ray imaging system-with a 60 x 30 mm field of view based on a skew-symmetric two-crystal X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 523, 217–222 (2004).
[CrossRef]

2003 (1)

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

2002 (2)

M Stampanoni, G Borchert, R Abela, and P Rüegsegger, “Bragg magnifier: A detector for submicrometer x-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[CrossRef]

C David, B Nöhammer, H H Solak, and E Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 813287–3289 (2002).
[CrossRef]

1997 (2)

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[CrossRef] [PubMed]

T J Suleski, “Generation of Lohmann images from binary-phase Talbot array illuminators,” Appl. Opt. 36, 4686–4691 (1997).
[CrossRef] [PubMed]

1996 (2)

P Cloetens, R Barrett, J Baruchel, J-P Guigay, and M Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[CrossRef]

A Momose, T Takeda, Y Itai, and K Hirano, “Phase-contrast x-ray computed tomography for observing biological soft tissues,” Nat. Med. 2, 473–475 (1996).
[CrossRef] [PubMed]

1995 (2)

A Snigirev, I Snigireva, V Kohn, S Kuznetsov, and I Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

TJ Davis, D Gao, T E Gureyev, A W Stevenson, and S W Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[CrossRef]

1965 (1)

U Bonse and M Hart, “An X-ray interferometer,” Appl. Phys. Lett. 6, 155–156 (1965).
[CrossRef]

1836 (1)

H F Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401–407 (1836).

Abela, R

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).

M Stampanoni, G Borchert, R Abela, and P Rüegsegger, “Bragg magnifier: A detector for submicrometer x-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[CrossRef]

Arfelli, F

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[CrossRef] [PubMed]

Barrett, R

P Cloetens, R Barrett, J Baruchel, J-P Guigay, and M Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[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. SPIE 7804 (2010).
[CrossRef]

P Cloetens, R Barrett, J Baruchel, J-P Guigay, and M Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[CrossRef]

Baumann, J

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

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

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

Baumbach, T

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (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. SPIE 7804 (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, PhD thesis, University of Copenhagen (2009).

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 (2010).
[CrossRef]

Betemps, R

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).

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]

Boerner, M

E Reznikova, J Mohr, M Boerner, V Nazmov, and P-J Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures. Microsystem Technologies,” Microsyst. Technol. 14, 1683–1688 (2008).
[CrossRef]

Bonse, U

U Bonse and M Hart, “An X-ray interferometer,” Appl. Phys. Lett. 6, 155–156 (1965).
[CrossRef]

Borchert, G

M Stampanoni, G Borchert, R Abela, and P Rüegsegger, “Bragg magnifier: A detector for submicrometer x-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[CrossRef]

Bravin, A

P C Diemoz, P Coan, C Glaser, and A Bravin, “Absorption, refraction and scattering in analyzer-based imaging: comparison of different algorithms,” Opt. Express 18, 3494–3509 (2010).
[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]

Bruder, J

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

Bunk, O

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

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

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

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

F Pfeiffer, 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, C David, C Kottler, O Bunk, and F Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318 (2006).
[CrossRef]

F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[CrossRef] [PubMed]

Chabior, M

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

Chapman, D

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[CrossRef] [PubMed]

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]

Chen, Q

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).

Chen, Z-Q

Z-T Wang, K-J Kang, Z-F Huang, and Z-Q Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[CrossRef]

Cloetens, P

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

M Langer, P Cloetens, J-P Guigay, and F Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.,  354556–4566 (2008).
[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]

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]

P Cloetens, R Barrett, J Baruchel, J-P Guigay, and M Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[CrossRef]

P Cloetens, Contribution to phase contrast imaging, reconstruction and tomography with hard synchrotron radiation: principles, implementation and applications. PhD thesis, Vrije Universiteit Brussel, 1999.

Coan, P

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. SPIE 7804 (2010).
[CrossRef]

S A McDonald, F Marone, C Hintermüller, G Mikuljan, C David, F Pfeiffer, and M Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synch. Rad. 16, 562–572 (2009).
[CrossRef]

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

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

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

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

F Pfeiffer, O Bunk, C 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, C David, C Kottler, O Bunk, and F Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318 (2006).
[CrossRef]

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

F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[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]

C David, B Nöhammer, H H Solak, and E Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 813287–3289 (2002).
[CrossRef]

Davis, TJ

TJ Davis, D Gao, T E Gureyev, A W Stevenson, and S W Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[CrossRef]

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 (2010).
[CrossRef]

Diaz, A

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

T Weitkamp, A Diaz, C David, F Pfeiffer, M Stampanoni, P Cloetens, and E Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
[CrossRef] [PubMed]

F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[CrossRef] [PubMed]

Diemoz, P C

Dietsch, R

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

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. SPIE 7804 (2010).
[CrossRef]

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

Engelhardt, M

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

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

Flohr, T G

R Raupach and T G Flohr, “Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56, 2219–2244 (2011).
[CrossRef] [PubMed]

Gao, D

TJ Davis, D Gao, T E Gureyev, A W Stevenson, and S W Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[CrossRef]

Glaser, C

Gmür, N

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[CrossRef] [PubMed]

Grigoriev, D

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

Groso, A

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).

Grünzweig, C

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

Guigay, J-P

M Langer, P Cloetens, J-P Guigay, and F Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.,  354556–4566 (2008).
[CrossRef] [PubMed]

P Cloetens, R Barrett, J Baruchel, J-P Guigay, and M Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[CrossRef]

Gureyev, T E

TJ Davis, D Gao, T E Gureyev, A W Stevenson, and S W Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[CrossRef]

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,” Appl. Phys. Lett. 6, 155–156 (1965).
[CrossRef]

Hattori, T

D Noda, M Tanaka, K Shimada, W Yashiro, A Momose, and T Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–11315 (2008).
[CrossRef]

Helfen, L

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

Hempel, E

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

Henein, S

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).

Hintermüller, C

S A McDonald, F Marone, C Hintermüller, G Mikuljan, C David, F Pfeiffer, and M Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synch. Rad. 16, 562–572 (2009).
[CrossRef]

Hirano, K

A Momose, T Takeda, Y Itai, and K Hirano, “Phase-contrast x-ray computed tomography for observing biological soft tissues,” Nat. Med. 2, 473–475 (1996).
[CrossRef] [PubMed]

Hoheisel, M

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

Holz, T

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

Huang, Z-F

Z-T Wang, K-J Kang, Z-F Huang, and Z-Q Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[CrossRef]

Hyodo, K

A Yoneyama, T Takeda, Y Tsuchiya, J Wu, Thet-Thet-Lwin, A Koizumi, K Hyodo, and Y Itai, “A phase-contrast X-ray imaging system-with a 60 x 30 mm field of view based on a skew-symmetric two-crystal X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 523, 217–222 (2004).
[CrossRef]

Isenegger, A

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).

Itai, Y

A Yoneyama, T Takeda, Y Tsuchiya, J Wu, Thet-Thet-Lwin, A Koizumi, K Hyodo, and Y Itai, “A phase-contrast X-ray imaging system-with a 60 x 30 mm field of view based on a skew-symmetric two-crystal X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 523, 217–222 (2004).
[CrossRef]

A Momose, T Takeda, Y Itai, and K Hirano, “Phase-contrast x-ray computed tomography for observing biological soft tissues,” Nat. Med. 2, 473–475 (1996).
[CrossRef] [PubMed]

Jakobs, P-J

E Reznikova, J Mohr, M Boerner, V Nazmov, and P-J Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures. Microsystem Technologies,” Microsyst. Technol. 14, 1683–1688 (2008).
[CrossRef]

James, F.

F. James, Statistical methods in experimental physics, 2nd ed. (World Scientific Publishing, Singapore, 2006).

Johnston, R E

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[CrossRef] [PubMed]

Kang, K-J

Z-T Wang, K-J Kang, Z-F Huang, and Z-Q Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[CrossRef]

Kaufmann, R

V Revol, C Kottler, R Kaufmann, U Straumann, and C Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010)
[CrossRef] [PubMed]

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. SPIE 7804 (2010).
[CrossRef]

Köhler, R

P Modregger, D Lübbert, P Schäfer, and R Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).

Kohn, V

A Snigirev, I Snigireva, V Kohn, S Kuznetsov, and I Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Koizumi, A

A Yoneyama, T Takeda, Y Tsuchiya, J Wu, Thet-Thet-Lwin, A Koizumi, K Hyodo, and Y Itai, “A phase-contrast X-ray imaging system-with a 60 x 30 mm field of view based on a skew-symmetric two-crystal X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 523, 217–222 (2004).
[CrossRef]

Kottler, C

V Revol, C Kottler, R Kaufmann, U Straumann, and C Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010)
[CrossRef] [PubMed]

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

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

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

T Weitkamp, C David, C Kottler, O Bunk, and F Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318 (2006).
[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]

Krämer, M

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

Kuznetsov, S

A Snigirev, I Snigireva, V Kohn, S Kuznetsov, and I Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

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. SPIE 7804 (2010).
[CrossRef]

Lange, M

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).

Langer, M

M Langer, P Cloetens, J-P Guigay, and F Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.,  354556–4566 (2008).
[CrossRef] [PubMed]

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]

Lübbert, D

P Modregger, D Lübbert, P Schäfer, and R Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).

Marone, F

S A McDonald, F Marone, C Hintermüller, G Mikuljan, C David, F Pfeiffer, and M Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synch. Rad. 16, 562–572 (2009).
[CrossRef]

McDonald, S A

S A McDonald, F Marone, C Hintermüller, G Mikuljan, C David, F Pfeiffer, and M Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synch. Rad. 16, 562–572 (2009).
[CrossRef]

Meduna, M

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

Meister, D

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).

Menk, R H

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[CrossRef] [PubMed]

Mikuljan, G

S A McDonald, F Marone, C Hintermüller, G Mikuljan, C David, F Pfeiffer, and M Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synch. Rad. 16, 562–572 (2009).
[CrossRef]

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).

Modregger, P

P Modregger, D Lübbert, P Schäfer, and R Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).

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. SPIE 7804 (2010).
[CrossRef]

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

E Reznikova, J Mohr, M Boerner, V Nazmov, and P-J Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures. Microsystem Technologies,” Microsyst. Technol. 14, 1683–1688 (2008).
[CrossRef]

Momose, A

W Yashiro, Y Takeda, and A Momose, “Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry,” J. Opt. Soc. Am. A 25, 2025–2039 (2008).
[CrossRef]

D Noda, M Tanaka, K Shimada, W Yashiro, A Momose, and T Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–11315 (2008).
[CrossRef]

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, Y Itai, and K Hirano, “Phase-contrast x-ray computed tomography for observing biological soft tissues,” Nat. Med. 2, 473–475 (1996).
[CrossRef] [PubMed]

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 (2010).
[CrossRef]

Nazmov, V

E Reznikova, J Mohr, M Boerner, V Nazmov, and P-J Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures. Microsystem Technologies,” Microsyst. Technol. 14, 1683–1688 (2008).
[CrossRef]

Noda, D

D Noda, M Tanaka, K Shimada, W Yashiro, A Momose, and T Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–11315 (2008).
[CrossRef]

Nöhammer, B

C David, B Nöhammer, H H Solak, and E Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 813287–3289 (2002).
[CrossRef]

Peyrin, F

M Langer, P Cloetens, J-P Guigay, and F Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.,  354556–4566 (2008).
[CrossRef] [PubMed]

Pfeiffer, F

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 (2010).
[CrossRef]

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

S A McDonald, F Marone, C Hintermüller, G Mikuljan, C David, F Pfeiffer, and M Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synch. Rad. 16, 562–572 (2009).
[CrossRef]

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

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

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

F Pfeiffer, O Bunk, C 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, C David, C Kottler, O Bunk, and F Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318 (2006).
[CrossRef]

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

F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[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]

Pisano, E D

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[CrossRef] [PubMed]

Popescu, S

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

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]

Rack, A

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

Rack, T

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

Raupach, R

R Raupach and T G Flohr, “Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56, 2219–2244 (2011).
[CrossRef] [PubMed]

Revol, V

V Revol, C Kottler, R Kaufmann, U Straumann, and C Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010)
[CrossRef] [PubMed]

Reznikova, E

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 (2010).
[CrossRef]

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

E Reznikova, J Mohr, M Boerner, V Nazmov, and P-J Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures. Microsystem Technologies,” Microsyst. Technol. 14, 1683–1688 (2008).
[CrossRef]

Riotte, M

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

Robinson, IK

F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[CrossRef] [PubMed]

Rohbeck, T

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

Rüegsegger, P

M Stampanoni, G Borchert, R Abela, and P Rüegsegger, “Bragg magnifier: A detector for submicrometer x-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[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. SPIE 7804 (2010).
[CrossRef]

Sayers, D

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[CrossRef] [PubMed]

Schäfer, P

P Modregger, D Lübbert, P Schäfer, and R Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).

Schelokov, I

A Snigirev, I Snigireva, V Kohn, S Kuznetsov, and I Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Schlenker, M

P Cloetens, R Barrett, J Baruchel, J-P Guigay, and M Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[CrossRef]

Schroer, C G

M Engelhardt, C Kottler, O Bunk, C David, C G Schroer, J Baumann, M Schuster, and F Pfeiffer, “The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources,” J. Microsc. 232, 145–157 (2008).
[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 (2010).
[CrossRef]

Schulze-Briese, C

F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[CrossRef] [PubMed]

Schuster, M

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

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

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

Shimada, K

D Noda, M Tanaka, K Shimada, W Yashiro, A Momose, and T Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–11315 (2008).
[CrossRef]

Siewert, F

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

Snigirev, A

A Snigirev, I Snigireva, V Kohn, S Kuznetsov, and I Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Snigireva, I

A Snigirev, I Snigireva, V Kohn, S Kuznetsov, and I Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Solak, H H

C David, B Nöhammer, H H Solak, and E Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 813287–3289 (2002).
[CrossRef]

Stampanoni, M

S A McDonald, F Marone, C Hintermüller, G Mikuljan, C David, F Pfeiffer, and M Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synch. Rad. 16, 562–572 (2009).
[CrossRef]

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).

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]

M Stampanoni, G Borchert, R Abela, and P Rüegsegger, “Bragg magnifier: A detector for submicrometer x-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[CrossRef]

Stevenson, A W

TJ Davis, D Gao, T E Gureyev, A W Stevenson, and S W Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[CrossRef]

Straumann, U

V Revol, C Kottler, R Kaufmann, U Straumann, and C Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010)
[CrossRef] [PubMed]

Suleski, T J

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 Yoneyama, T Takeda, Y Tsuchiya, J Wu, Thet-Thet-Lwin, A Koizumi, K Hyodo, and Y Itai, “A phase-contrast X-ray imaging system-with a 60 x 30 mm field of view based on a skew-symmetric two-crystal X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 523, 217–222 (2004).
[CrossRef]

A Momose, T Takeda, Y Itai, and K Hirano, “Phase-contrast x-ray computed tomography for observing biological soft tissues,” Nat. Med. 2, 473–475 (1996).
[CrossRef] [PubMed]

Takeda, Y

Talbot, H F

H F Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401–407 (1836).

Tanaka, M

D Noda, M Tanaka, K Shimada, W Yashiro, A Momose, and T Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–11315 (2008).
[CrossRef]

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. SPIE 7804 (2010).
[CrossRef]

Thet-Thet-Lwin,

A Yoneyama, T Takeda, Y Tsuchiya, J Wu, Thet-Thet-Lwin, A Koizumi, K Hyodo, and Y Itai, “A phase-contrast X-ray imaging system-with a 60 x 30 mm field of view based on a skew-symmetric two-crystal X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 523, 217–222 (2004).
[CrossRef]

Thomlinson, W

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[CrossRef] [PubMed]

Tsuchiya, Y

A Yoneyama, T Takeda, Y Tsuchiya, J Wu, Thet-Thet-Lwin, A Koizumi, K Hyodo, and Y Itai, “A phase-contrast X-ray imaging system-with a 60 x 30 mm field of view based on a skew-symmetric two-crystal X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 523, 217–222 (2004).
[CrossRef]

Urban, C

V Revol, C Kottler, R Kaufmann, U Straumann, and C Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010)
[CrossRef] [PubMed]

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 (2010).
[CrossRef]

van der Veen, JF

F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[CrossRef] [PubMed]

Vartanyants, I.

F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[CrossRef] [PubMed]

Wang, Z-T

Z-T Wang, K-J Kang, Z-F Huang, and Z-Q Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[CrossRef]

Washburn, D

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[CrossRef] [PubMed]

Weitkamp, T

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[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 (2010).
[CrossRef]

T Weitkamp, C David, C Kottler, O Bunk, and F Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318 (2006).
[CrossRef]

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

F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[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]

Wilkins, S W

TJ Davis, D Gao, T E Gureyev, A W Stevenson, and S W Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[CrossRef]

Wu, J

A Yoneyama, T Takeda, Y Tsuchiya, J Wu, Thet-Thet-Lwin, A Koizumi, K Hyodo, and Y Itai, “A phase-contrast X-ray imaging system-with a 60 x 30 mm field of view based on a skew-symmetric two-crystal X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 523, 217–222 (2004).
[CrossRef]

Yashiro, W

W Yashiro, Y Takeda, and A Momose, “Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry,” J. Opt. Soc. Am. A 25, 2025–2039 (2008).
[CrossRef]

D Noda, M Tanaka, K Shimada, W Yashiro, A Momose, and T Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–11315 (2008).
[CrossRef]

Yoneyama, A

A Yoneyama, T Takeda, Y Tsuchiya, J Wu, Thet-Thet-Lwin, A Koizumi, K Hyodo, and Y Itai, “A phase-contrast X-ray imaging system-with a 60 x 30 mm field of view based on a skew-symmetric two-crystal X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 523, 217–222 (2004).
[CrossRef]

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

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 (2010).
[CrossRef]

Zhong, Z

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[CrossRef] [PubMed]

Ziegler, E

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[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]

C David, B Nöhammer, H H Solak, and E Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 813287–3289 (2002).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

P Modregger, D Lübbert, P Schäfer, and R Köhler, “Two dimensional diffraction enhanced imaging algorithm,” Appl. Phys. Lett. 90, 193501 (2007).

C David, B Nöhammer, H H Solak, and E Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 813287–3289 (2002).
[CrossRef]

U Bonse and M Hart, “An X-ray interferometer,” Appl. Phys. Lett. 6, 155–156 (1965).
[CrossRef]

Z-T Wang, K-J Kang, Z-F Huang, and Z-Q Chen, “Quantitative grating-based x-ray dark-field computed tomography,” Appl. Phys. Lett. 95, 094105 (2009).
[CrossRef]

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

J. Appl. Phys. (2)

T Donath, M Chabior, F Pfeiffer, O Bunk, E Reznikova, J Mohr, E Hempel, S Popescu, M Hoheisel, M Schuster, J Baumann, and C David, “Inverse geometry for grating-based x-ray phase-contrast imaging,” J. Appl. Phys. 106, 054703 (2009).
[CrossRef]

M Stampanoni, G Borchert, R Abela, and P Rüegsegger, “Bragg magnifier: A detector for submicrometer x-ray computer tomography,” J. Appl. Phys. 92, 7630–7635 (2002).
[CrossRef]

J. Microsc. (1)

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

J. Opt. Soc. Am. A (1)

J. Phys. D: Appl. Phys. (1)

P Cloetens, R Barrett, J Baruchel, J-P Guigay, and M Schlenker, “Phase objects in synchrotron radiation hard x-ray imaging,” J. Phys. D: Appl. Phys. 29, 133–146 (1996).
[CrossRef]

J. Synch. Rad. (2)

S A McDonald, F Marone, C Hintermüller, G Mikuljan, C David, F Pfeiffer, and M Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synch. Rad. 16, 562–572 (2009).
[CrossRef]

A Rack, T Weitkamp, M Riotte, D Grigoriev, T Rack, L Helfen, T Baumbach, R Dietsch, T Holz, M Krämer, F Siewert, M Meduna, P Cloetens, and E Ziegler, “Comparative study of multilayers used in monochromators for synchrotron-based coherent hard X-ray imaging,” J. Synch. Rad. 17, 496–510 (2010).
[CrossRef]

Jpn. J. Appl. Phys. (1)

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

Med. Phys. (1)

M Langer, P Cloetens, J-P Guigay, and F Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys.,  354556–4566 (2008).
[CrossRef] [PubMed]

Microelectron. Eng. (1)

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

Microsyst. Technol. (2)

E Reznikova, J Mohr, M Boerner, V Nazmov, and P-J Jakobs, “Soft X-ray lithography of high aspect ratio SU8 submicron structures. Microsystem Technologies,” Microsyst. Technol. 14, 1683–1688 (2008).
[CrossRef]

D Noda, M Tanaka, K Shimada, W Yashiro, A Momose, and T Hattori, “Fabrication of large area diffraction grating using LIGA process,” Microsyst. Technol. 14, 1311–11315 (2008).
[CrossRef]

Nat. Med. (1)

A Momose, T Takeda, Y Itai, and K Hirano, “Phase-contrast x-ray computed tomography for observing biological soft tissues,” Nat. Med. 2, 473–475 (1996).
[CrossRef] [PubMed]

Nat. Phys. (1)

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

Nature (1)

TJ Davis, D Gao, T E Gureyev, A W Stevenson, and S W Wilkins, “Phase-contrast imaging of weakly absorbing materials using hard X-rays,” Nature 373, 595–598 (1995).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

A Yoneyama, T Takeda, Y Tsuchiya, J Wu, Thet-Thet-Lwin, A Koizumi, K Hyodo, and Y Itai, “A phase-contrast X-ray imaging system-with a 60 x 30 mm field of view based on a skew-symmetric two-crystal X-ray interferometer,” Nucl. Instrum. Methods Phys. Res. A 523, 217–222 (2004).
[CrossRef]

Opt. Express (2)

Philos. Mag. (1)

H F Talbot, “Facts relating to optical science. No. IV,” Philos. Mag. 9, 401–407 (1836).

Phys. Med. Biol. (4)

D Chapman, W Thomlinson, R E Johnston, D Washburn, E D Pisano, N Gmür, Z Zhong, R H Menk, F Arfelli, and D Sayers, “Diffraction enhanced x-ray imaging,” Phys. Med. Biol. 42, 2015–2025 (1997).
[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]

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]

R Raupach and T G Flohr, “Analytical evaluation of the signal and noise propagation in x-ray differential phase-contrast computed tomography,” Phys. Med. Biol. 56, 2219–2244 (2011).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

F Pfeiffer, O Bunk, C Schulze-Briese, A Diaz, T Weitkamp, C David, JF van der Veen, I. Vartanyants, and IK Robinson, “Shearing interferometer for quantifying the coherence of hard X-ray beams,” Phys. Rev. Lett. 94, 164801 (2005).
[CrossRef] [PubMed]

Proc. SPIE (2)

T Weitkamp, C David, C Kottler, O Bunk, and F Pfeiffer, “Tomography with grating interferometers at low-brilliance sources,” Proc. SPIE 6318 (2006).
[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 (2010).
[CrossRef]

Rev. Sci. Instrum. (2)

V Revol, C Kottler, R Kaufmann, U Straumann, and C Urban, “Noise analysis of grating-based x-ray differential phase contrast imaging,” Rev. Sci. Instrum. 81, 073709 (2010)
[CrossRef] [PubMed]

A Snigirev, I Snigireva, V Kohn, S Kuznetsov, and I Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995).
[CrossRef]

Synch. Rad. Instrum. (1)

M Stampanoni, A Groso, A Isenegger, G Mikuljan, Q Chen, D Meister, M Lange, R Betemps, S Henein, and R Abela, “TOMCAT: A beamline for TOmographic Microscopy and Coherent rAdiology experimenTs,” Synch. Rad. Instrum. 879, 848–851 (2007).

Other (3)

F. James, Statistical methods in experimental physics, 2nd ed. (World Scientific Publishing, Singapore, 2006).

M Bech, X-ray imaging with a grating interferometer, PhD thesis, University of Copenhagen (2009).

P Cloetens, Contribution to phase contrast imaging, reconstruction and tomography with hard synchrotron radiation: principles, implementation and applications. PhD thesis, Vrije Universiteit Brussel, 1999.

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Figures (10)

Fig. 1
Fig. 1

Sketch of the grating interferometer. A phase grating and an absorption grating are exploited in order to provide phase-sensitivity.

Fig. 3
Fig. 3

Phase stepping curve and a representation of additional Gaussian noise, which is used in the numerical investigations. The calculations were performed with a reduced inter-grating distance of η = 0.3 (Eq. (7)).

Fig. 2
Fig. 2

(a) Ideal, rectangular-shaped interference pattern assumed for all inter-grating distances. (b) The interference pattern after convolution with the projected source distribution.

Fig. 4
Fig. 4

For the determination of parameters and the validation of the noise model. (a) The mean of 1000 flat-field images acquired at the phase step of maximum intensity (ref. Fig. 3). While the horizontal stripes are due to surface roughness of the monochromator, the vertical stripes are caused by inhomogeneities. (b) Pixel-wise factor χ (see Eq. (9)). (c) The signal-to-noise ratio of the flat-field series (see Eq. (10)) over the field of view. Vibrations in the monochromator lead to a movement of the stripes between flat-field images. This increases the variance of gray values in the flat-field series for the affected pixel and, consequently, reduces the SNR. (d) Pixel-wise correlation coefficient between the theoretical prediction (see text) and the experimentally obtained gray value distribution in the flat-field series.

Fig. 5
Fig. 5

Sensitivity of the GI as a function of M −1/2 with M the number of phase steps for three different dynamic ranges, which are related to the noise level by Eq. (9). The lines indicate the results of linear regression.

Fig. 6
Fig. 6

Sensitivity of the GI in terms of the minimal detectable refraction angle as a function of the visibility for three different dynamic ranges, which are related to the noise level by Eq. (9).

Fig. 7
Fig. 7

Impact of the duty cycle of the absorption grating on the sensitivity or three different dynamic ranges, which are related to the noise level by Eq. (9). (a) Visibility (Eq. (11)) as a function of the duty cycle. (b) Minimum detectable refraction angle per time unit.

Fig. 8
Fig. 8

For the experimental determination of the minimum detectable refraction angle. (a) The measured refraction angle of a polystyrene cylinder immersed in water. (b) The corresponding pixel-wise standard deviation of ten repeated scans, which is equal to the experimentally determined minimum detectable refraction angle.

Fig. 9
Fig. 9

(a) Visibility (Eq. 11) in dependency on the reduced inter-grating distance η, which was numerically (see text) and analytically determined (Eq. 12). (b) The corresponding uncertainty of the fringe offset Δφ for three different dynamic ranges, which are related to the noise level by Eq. (9).

Fig. 10
Fig. 10

Minimum detectable refraction angle αmin as a function of the reduced inter-grating distance η. M denotes the number of phase steps.

Equations (14)

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

d m = ( m 1 2 ) g 1 2 4 λ , with m = 1 , 2 ,
A = s ^ ( q 0 ) / f ^ ( q 0 ) ,
ϕ = arg ( s ^ ( q n ) ) arg ( f ^ ( q n ) ) ,
B = | ( s ^ ( q n ) f ^ ( q 0 ) ) / ( s ^ ( q 0 ) f ^ ( q n ) ) | .
ϕ = 2 π d m α g 2 .
ϕ = mod ( 2 π d m α g 2 + π , 2 π ) π .
η = d S z g 2 ,
α min = g 2 2 π d Δ ϕ .
χ = σ n μ n
S N R = μ n σ n ,
ν = 2 | f ^ ( q 1 ) f ^ ( q 0 ) | .
ν ( η ) = 8 π 2 e ( 1.887 η ) 2 .
η o p t = d o p t S z g 2 0.4.
( m 1 2 ) g 2 = η o p t z λ S = η o p t L c o h

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