OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 25 — Dec. 5, 2011
  • pp: 24890–24896

A tilted grating interferometer for full vector field differential x-ray phase contrast tomography

Simon Rutishauser, Tilman Donath, Christian David, Franz Pfeiffer, Federica Marone, Peter Modregger, and Marco Stampanoni  »View Author Affiliations


Optics Express, Vol. 19, Issue 25, pp. 24890-24896 (2011)
http://dx.doi.org/10.1364/OE.19.024890


View Full Text Article

Enhanced HTML    Acrobat PDF (2754 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

OCIS Codes
(110.7440) Imaging systems : X-ray imaging
(340.7450) X-ray optics : X-ray interferometry
(110.3175) Imaging systems : Interferometric imaging
(110.6955) Imaging systems : Tomographic imaging

ToC Category:
X-ray Optics

History
Original Manuscript: September 19, 2011
Revised Manuscript: October 28, 2011
Manuscript Accepted: November 2, 2011
Published: November 22, 2011

Virtual Issues
Vol. 7, Iss. 2 Virtual Journal for Biomedical Optics

Citation
Simon Rutishauser, Tilman Donath, Christian David, Franz Pfeiffer, Federica Marone, Peter Modregger, and Marco Stampanoni, "A tilted grating interferometer for full vector field differential x-ray phase contrast tomography," Opt. Express 19, 24890-24896 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-24890


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Fitzgerald, “Phase-Sensitive X-Ray Imaging,” Phys. Today53(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. Express11, 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. Express13, 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. Express15, 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. Express19, 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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited