Abstract

We report on a setup for differential x-ray phase-contrast imaging and tomography, that measures the full 2D phase-gradient information. The setup uses a simple one-dimensional x-ray grating interferometer, in which the grating structures of the interferometer are oriented at a tilt angle with respect to the sample rotation axis. In such a configuration, the differential phase images from opposing tomography projections can be combined to yield both components of the gradient vector. We show how the refractive index distribution as well as its x, y, and z gradient components can be reconstructed directly from the recorded projection data. The method can equally well be applied at conventional x-ray tube sources, to analyzer based x-ray imaging or neutron imaging. It is demonstrated with measurements of an x-ray phantom and a rat brain using synchrotron radiation.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Fitzgerald, “Phase-Sensitive X-Ray Imaging,” Phys. Today 53(7), 23–26 (2000).
    [CrossRef]
  2. A. Momose, “Recent Advances in X-ray Phase Imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
    [CrossRef]
  3. C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
    [CrossRef]
  4. A. Momose, “Phase-sensitive imaging and phase tomography using X-ray interferometers,” Opt. Express 11, 2303–2314 (2003).
    [CrossRef] [PubMed]
  5. T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express 13, 6296–6304 (2005).
    [CrossRef] [PubMed]
  6. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nat. Phys. 2, 258–261 (2006).
    [CrossRef]
  7. 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]
  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. F. Pfeiffer, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, “Neutron Phase Imaging and Tomography,” Phys. Rev. Lett. 96, 215505 (2006).
    [CrossRef] [PubMed]
  10. C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15, 1175–1181 (2007).
    [CrossRef] [PubMed]
  11. I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-Dimensional X-Ray Grating Interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
    [CrossRef]
  12. H. Wen, E. Bennett, R. Kopace, A. Stein, and V. Pai, “Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings,” Opt. Lett. 35, 1932–1934 (2010).
    [CrossRef] [PubMed]
  13. H. Itoh, K. Nagai, G. Sato, K. Yamaguchi, T. Nakamura, T. Kondoh, C. Ouchi, T. Teshima, Y. Setomoto, and T. Den, “Two-dimensional grating-based X-ray phase-contrast imaging using Fourier transform phase retrieval,” Opt. Express 19, 3339–3346 (2011).
    [CrossRef] [PubMed]
  14. 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]
  15. M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
    [CrossRef]
  16. 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]
  17. S. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (2009).
    [CrossRef] [PubMed]
  18. R. Frankot and R. Chellapa, “A Method for Enforcing Integrability in Shape from Shading Algorithms,” IEEE Trans. Pattern Anal. Mach. Intel. 10, 439–451 (1988).
    [CrossRef]
  19. A. Agrawal, R. Raskar, and R. Chellapa, “What is the Range of Surface Reconstructions from a Gradient Field?” 9th European Conference on Computer Vision,  3951, 578–591 (2006).
  20. Z. Fu, A. Robles-Kelly, and F. Lu, “A Linear Programming Approach to Surface Fitting,” 9th Biennial Conference of the Australian Pattern Recognition Society on Digital Image Computing Techniques and Applications, 189–195 (2007).
  21. The out-of-plane component cancels out because the phase integration, which is implicit in the modified reconstruction kernel, is always performed along the same direction in the camera coordinate system. Considering for instance an integral from left to right through the PMMA cylinder at the bottom of Fig. 2(d), the signal at its left edge is ∂tΦ + ∂zΦ where the signal in the tomographic rotation plane is ∂t Φ > 0 and the out-of-plane signal ∂zΦ < 0. Integrating through the same edge of the sample in Fig. 2(e), the out-of-plane signal has changed sign ∂zΦ > 0, while the in-plane signal has again the same sign as before ∂tΦ > 0. Reconstructing a slice using filtered back projection over a full sample rotation of 2π, each projection pair corresponds to a single line in two-dimensional Fourier space. The out of plane component cancels out since it is once added and once subtracted to this line.
  22. P. Zhu, J. Wang, Q. Yuan, W. Huang, H. Shu, B. Gao, T. Hu, and Z. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
    [CrossRef]

2011 (1)

2010 (3)

H. Wen, E. Bennett, R. Kopace, A. Stein, and V. Pai, “Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings,” Opt. Lett. 35, 1932–1934 (2010).
[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]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-Dimensional X-Ray Grating Interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

2009 (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]

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

2007 (3)

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, C. Kottler, O. Bunk, and C. David, “Hard X-Ray Phase Tomography with Low-Brilliance Sources,” Phys. Rev. Lett. 98, 108105 (2007).
[CrossRef] [PubMed]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15, 1175–1181 (2007).
[CrossRef] [PubMed]

2006 (4)

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

F. Pfeiffer, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, “Neutron Phase Imaging and Tomography,” Phys. Rev. Lett. 96, 215505 (2006).
[CrossRef] [PubMed]

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

A. Agrawal, R. Raskar, and R. Chellapa, “What is the Range of Surface Reconstructions from a Gradient Field?” 9th European Conference on Computer Vision,  3951, 578–591 (2006).

2005 (3)

P. Zhu, J. Wang, Q. Yuan, W. Huang, H. Shu, B. Gao, T. Hu, and Z. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

A. Momose, “Recent Advances in X-ray Phase Imaging,” Jpn. J. Appl. Phys. 44, 6355–6367 (2005).
[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]

2003 (1)

2002 (1)

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[CrossRef]

2000 (1)

R. Fitzgerald, “Phase-Sensitive X-Ray Imaging,” Phys. Today 53(7), 23–26 (2000).
[CrossRef]

1988 (1)

R. Frankot and R. Chellapa, “A Method for Enforcing Integrability in Shape from Shading Algorithms,” IEEE Trans. Pattern Anal. Mach. Intel. 10, 439–451 (1988).
[CrossRef]

Abela, R.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

Agrawal, A.

A. Agrawal, R. Raskar, and R. Chellapa, “What is the Range of Surface Reconstructions from a Gradient Field?” 9th European Conference on Computer Vision,  3951, 578–591 (2006).

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]

Bennett, E.

Bertrand, A.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

Betemps, R.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

Böhler, P.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

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, 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]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15, 1175–1181 (2007).
[CrossRef] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard X-Ray Phase Tomography with Low-Brilliance Sources,” Phys. Rev. Lett. 98, 108105 (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]

F. Pfeiffer, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, “Neutron Phase Imaging and Tomography,” Phys. Rev. Lett. 96, 215505 (2006).
[CrossRef] [PubMed]

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

Chellapa, R.

A. Agrawal, R. Raskar, and R. Chellapa, “What is the Range of Surface Reconstructions from a Gradient Field?” 9th European Conference on Computer Vision,  3951, 578–591 (2006).

R. Frankot and R. Chellapa, “A Method for Enforcing Integrability in Shape from Shading Algorithms,” IEEE Trans. Pattern Anal. Mach. Intel. 10, 439–451 (1988).
[CrossRef]

Chen, Q.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

Cloetens, P.

David, C.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-Dimensional X-Ray Grating Interferometer,” Phys. Rev. Lett. 105, 248102 (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]

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]

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

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15, 1175–1181 (2007).
[CrossRef] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard X-Ray Phase Tomography with Low-Brilliance Sources,” Phys. Rev. Lett. 98, 108105 (2007).
[CrossRef] [PubMed]

F. Pfeiffer, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, “Neutron Phase Imaging and Tomography,” Phys. Rev. Lett. 96, 215505 (2006).
[CrossRef] [PubMed]

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

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

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[CrossRef]

Den, T.

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]

Donath, T.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-Dimensional X-Ray Grating Interferometer,” Phys. Rev. Lett. 105, 248102 (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]

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]

Fitzgerald, R.

R. Fitzgerald, “Phase-Sensitive X-Ray Imaging,” Phys. Today 53(7), 23–26 (2000).
[CrossRef]

Frankot, R.

R. Frankot and R. Chellapa, “A Method for Enforcing Integrability in Shape from Shading Algorithms,” IEEE Trans. Pattern Anal. Mach. Intel. 10, 439–451 (1988).
[CrossRef]

Frei, G.

F. Pfeiffer, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, “Neutron Phase Imaging and Tomography,” Phys. Rev. Lett. 96, 215505 (2006).
[CrossRef] [PubMed]

Frommherz, U.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

Fu, Z.

Z. Fu, A. Robles-Kelly, and F. Lu, “A Linear Programming Approach to Surface Fitting,” 9th Biennial Conference of the Australian Pattern Recognition Society on Digital Image Computing Techniques and Applications, 189–195 (2007).

Gao, B.

P. Zhu, J. Wang, Q. Yuan, W. Huang, H. Shu, B. Gao, T. Hu, and Z. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

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]

Groso, A.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[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]

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, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, “Neutron Phase Imaging and Tomography,” Phys. Rev. Lett. 96, 215505 (2006).
[CrossRef] [PubMed]

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]

Henein, S.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

Hintermüller, C.

S. McDonald, F. Marone, C. Hintermüller, G. Mikuljan, C. David, F. Pfeiffer, and M. Stampanoni, “Advanced phase-contrast imaging using a grating interferometer,” J. Synchrotron Radiat. 16, 562–572 (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]

Hu, T.

P. Zhu, J. Wang, Q. Yuan, W. Huang, H. Shu, B. Gao, T. Hu, and Z. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

Huang, W.

P. Zhu, J. Wang, Q. Yuan, W. Huang, H. Shu, B. Gao, T. Hu, and Z. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

Isenegger, A.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

Itoh, H.

Kondoh, T.

Kopace, R.

Kottler, C.

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]

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15, 1175–1181 (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]

Lange, M.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

Lehmann, E.

F. Pfeiffer, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, “Neutron Phase Imaging and Tomography,” Phys. Rev. Lett. 96, 215505 (2006).
[CrossRef] [PubMed]

Lu, F.

Z. Fu, A. Robles-Kelly, and F. Lu, “A Linear Programming Approach to Surface Fitting,” 9th Biennial Conference of the Australian Pattern Recognition Society on Digital Image Computing Techniques and Applications, 189–195 (2007).

Marone, F.

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

McDonald, S.

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

Meister, D.

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

Mikuljan, G.

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

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

Momose, A.

Nagai, K.

Nakamura, T.

Nöhammer, B.

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[CrossRef]

Ouchi, C.

Pai, V.

Pfeiffer, F.

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]

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

C. Kottler, C. David, F. Pfeiffer, and O. Bunk, “A two-directional approach for grating based differential phase contrast imaging using hard x-rays,” Opt. Express 15, 1175–1181 (2007).
[CrossRef] [PubMed]

F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard X-Ray Phase Tomography with Low-Brilliance Sources,” Phys. Rev. Lett. 98, 108105 (2007).
[CrossRef] [PubMed]

F. Pfeiffer, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, “Neutron Phase Imaging and Tomography,” Phys. Rev. Lett. 96, 215505 (2006).
[CrossRef] [PubMed]

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

T. Weitkamp, A. Diaz, C. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, and E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. 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]

Raskar, R.

A. Agrawal, R. Raskar, and R. Chellapa, “What is the Range of Surface Reconstructions from a Gradient Field?” 9th European Conference on Computer Vision,  3951, 578–591 (2006).

Robles-Kelly, A.

Z. Fu, A. Robles-Kelly, and F. Lu, “A Linear Programming Approach to Surface Fitting,” 9th Biennial Conference of the Australian Pattern Recognition Society on Digital Image Computing Techniques and Applications, 189–195 (2007).

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]

Rutishauser, S.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-Dimensional X-Ray Grating Interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

Sato, G.

Setomoto, Y.

Shu, H.

P. Zhu, J. Wang, Q. Yuan, W. Huang, H. Shu, B. Gao, T. Hu, and Z. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

Solak, H.

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[CrossRef]

Stampanoni, M.

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

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (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]

Stein, A.

Teshima, T.

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]

Wang, J.

P. Zhu, J. Wang, Q. Yuan, W. Huang, H. Shu, B. Gao, T. Hu, and Z. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

Weitkamp, T.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-Dimensional X-Ray Grating Interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

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

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

Wen, H.

Wu, Z.

P. Zhu, J. Wang, Q. Yuan, W. Huang, H. Shu, B. Gao, T. Hu, and Z. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

Yamaguchi, K.

Yuan, Q.

P. Zhu, J. Wang, Q. Yuan, W. Huang, H. Shu, B. Gao, T. Hu, and Z. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

Zanette, I.

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-Dimensional X-Ray Grating Interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

Zhu, P.

P. Zhu, J. Wang, Q. Yuan, W. Huang, H. Shu, B. Gao, T. Hu, and Z. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

Ziegler, E.

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. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[CrossRef]

9th European Conference on Computer Vision (1)

A. Agrawal, R. Raskar, and R. Chellapa, “What is the Range of Surface Reconstructions from a Gradient Field?” 9th European Conference on Computer Vision,  3951, 578–591 (2006).

Appl. Phys. Lett. (2)

C. David, B. Nöhammer, H. Solak, and E. Ziegler, “Differential x-ray phase contrast imaging using a shearing interferometer,” Appl. Phys. Lett. 81, 3287–3289 (2002).
[CrossRef]

P. Zhu, J. Wang, Q. Yuan, W. Huang, H. Shu, B. Gao, T. Hu, and Z. Wu, “Computed tomography algorithm based on diffraction-enhanced imaging setup,” Appl. Phys. Lett. 87, 264101 (2005).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intel. (1)

R. Frankot and R. Chellapa, “A Method for Enforcing Integrability in Shape from Shading Algorithms,” IEEE Trans. Pattern Anal. Mach. Intel. 10, 439–451 (1988).
[CrossRef]

Invest. Radiol. (1)

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. Synchrotron Radiat. (1)

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

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]

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]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. Lett. (3)

F. Pfeiffer, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, “Neutron Phase Imaging and Tomography,” Phys. Rev. Lett. 96, 215505 (2006).
[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]

I. Zanette, T. Weitkamp, T. Donath, S. Rutishauser, and C. David, “Two-Dimensional X-Ray Grating Interferometer,” Phys. Rev. Lett. 105, 248102 (2010).
[CrossRef]

Phys. Today (1)

R. Fitzgerald, “Phase-Sensitive X-Ray Imaging,” Phys. Today 53(7), 23–26 (2000).
[CrossRef]

Proc. SPIE (1)

M. Stampanoni, A. Groso, A. Isenegger, G. Mikuljan, Q. Chen, A. Bertrand, S. Henein, R. Betemps, U. Frommherz, P. Böhler, D. Meister, M. Lange, and R. Abela, “Trends in synchrotron-based tomographic imaging: the SLS experience,” Proc. SPIE,  6318, 63180M (2006).
[CrossRef]

Rev. Sci. Instrum. (1)

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]

Other (2)

Z. Fu, A. Robles-Kelly, and F. Lu, “A Linear Programming Approach to Surface Fitting,” 9th Biennial Conference of the Australian Pattern Recognition Society on Digital Image Computing Techniques and Applications, 189–195 (2007).

The out-of-plane component cancels out because the phase integration, which is implicit in the modified reconstruction kernel, is always performed along the same direction in the camera coordinate system. Considering for instance an integral from left to right through the PMMA cylinder at the bottom of Fig. 2(d), the signal at its left edge is ∂tΦ + ∂zΦ where the signal in the tomographic rotation plane is ∂t Φ > 0 and the out-of-plane signal ∂zΦ < 0. Integrating through the same edge of the sample in Fig. 2(e), the out-of-plane signal has changed sign ∂zΦ > 0, while the in-plane signal has again the same sign as before ∂tΦ > 0. Reconstructing a slice using filtered back projection over a full sample rotation of 2π, each projection pair corresponds to a single line in two-dimensional Fourier space. The out of plane component cancels out since it is once added and once subtracted to this line.

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 (4)

Fig. 1
Fig. 1

Scheme of phase-contrast tomography using a one-dimensional grating interferometer. The sample is mounted on a rotation axis θ to enable tomographic scans. Downstream of the sample are the beam splitter phase grating G1, the absorbing analyzer grating G2 and an imaging detector (not shown here). (a) Conventional arrangement with the grating lines parallel to the sample rotation axis and (b) tilted grating interferometer arrangement with the grating structures tilted, here by an angle of ξ = π/4. The normal nξ to the grating structures (gray arrows) points along the direction of the measured gradient component.

Fig. 2
Fig. 2

Projections of the x-ray phantom. (a,b) DPC projection pair g0 and gπ recorded with vertical gratings at tomographic projection angles θ = 0 and π respectively. (c) flipped projection (gπ)′, same data as (b) but flipped at the sample rotation axis. (d,e) DPC projection pair recorded with tilted gratings at ξ = π/4 (45°). (f) projection data from (e) flipped at the sample rotation axis. While (a) and (c) only provide the horizontal component of the phase gradient, the projections recorded with tilted gratings (d) and (f) yield two linearly independent components and thus the full 2D gradient vector. All images are displayed with a linear gray scale with deflection angles in the range of [−2.6,2.6] μrad.

Fig. 3
Fig. 3

Tomographic phase reconstructions of x-ray phantom (top) and rat brain (bottom). The phantom reconstruction shows a slice through the homogeneous PMMA rod. (a) and (d) show the refractive index decrement δ, averaged from two neighboring slices. (b) and (e) show the z gradient calculated from the difference of the two neighboring slices. (c) and (f) show the direct reconstruction of the z gradient, which uses the additional information gained by tilting the gratings. All images are displayed with a linear gray scale with the following ranges: (a) δ = [−0.1, 0.4] · 10−7, (b,c) Δzδ = zδ = [−1.8, 1.8] · 10−3 m−1, (d) δ = [3,4] · 10−7 and (e,f) Δzδ = zδ = [−1.5, 1.5] · 10−3 m−1.

Fig. 4
Fig. 4

Tomographic phase reconstruction of sagittal slices of a rat brain. On the left side are the three components of the reconstructed gradient (a) xδ in horizontal direction, (b) yδ perpendicular to the sagittal plane and (c) zδ in vertical direction. (d) shows the reconstruction of δ using only the gradient components in the tomographic rotation plane, as available in a conventional interferometer setup with vertical gratings. The standard deviation within the white square of constant δ is σδ = 3.9 · 10−9. (e) shows the much cleaner reconstruction of δ obtained by combining the reconstructed gradient components xδ and zδ. Here the standard deviation is σδ = 1.6 · 10−9. All images are displayed with a linear gray scale with the following ranges: (a–c) ∂δ = [−1.5, 1.5] · 10−3 m−1 and (d,e) δ = [3,4] · 10−7.

Equations (2)

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

n ξ = ( cos ξ sin ξ ) = ( cos ξ sin ξ ) = n π ξ .
t Φ = g 0 ( g π ) 2 cos ξ and z Φ = g 0 + ( g π ) 2 sin ξ .

Metrics