Table of Contents
X-Ray Optics and Instrumentation
Volume 2008 (2008), Article ID 835172, 8 pages
http://dx.doi.org/10.1155/2008/835172
Research Article

Direct Fan-Beam Reconstruction Algorithm via Filtered Backprojection for Differential Phase-Contrast Computed Tomography

Department of Medical Physics, University of Wisconsin-Madison, 600 Highland Avenue, Madison, WI 53792-1590, USA

Received 10 December 2007; Revised 22 April 2008; Accepted 23 May 2008

Academic Editor: Christian David

Copyright © 2008 Zhihua Qi and Guang-Hong Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. U. Bonse and M. Hart, “An X-ray interferometer,” Applied Physics Letters, vol. 6, no. 8, pp. 155–156, 1965. View at Publisher · View at Google Scholar
  2. A. Momose, T. Takeda, Y. Itai, and K. Hirano, “Phase-contrast X-ray computed tomography for observing biological soft tissues,” Nature Medicine, vol. 2, no. 4, pp. 473–475, 1996. View at Publisher · View at Google Scholar
  3. T. J. 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, vol. 373, no. 6515, pp. 595–598, 1996. View at Publisher · View at Google Scholar
  4. D. Chapman, W. Thomlinson, R. E. Johnston et al., “Diffraction enhanced X-ray imaging,” Physics in Medicine and Biology, vol. 42, no. 11, pp. 2015–2025, 1997. View at Publisher · View at Google Scholar
  5. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Steveson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature, vol. 383, no. 6607, pp. 335–338, 1996. View at Publisher · View at Google Scholar
  6. K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Pagnin, and Z. Barnea, “Quantitative phase imaging using hard X-rays,” Physical Review Letters, vol. 77, no. 14, pp. 2961–2964, 1996. View at Publisher · View at Google Scholar
  7. P. Cloetens, W. Ludwig, J. Baruchel et al., “Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Applied Physics Letters, vol. 75, no. 19, pp. 2912–2914, 1999. View at Publisher · View at Google Scholar
  8. C. David, B. Nöhammer, H. H. Solak, and E. Ziegler, “Differential X-ray phase contrast imaging using a shearing interferometer,” Applied Physics Letters, vol. 81, no. 17, pp. 3287–3289, 2002. View at Google Scholar
  9. A. Momose, S. Kawamoto, I. Koyama, Y. Hamaishi, K. Takai, and Y. Suzuki, “Demonstration of X-ray Talbot interferometry,” Japanese Journal of Applied Physics, vol. 42, part 2, no. 7B, pp. L866–L868, 2003. View at Publisher · View at Google Scholar
  10. T. Weitkamp, B. Nöhammer, A. Diaz, C. David, and E. Ziegler, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Applied Physics Letters, vol. 86, no. 5, Article ID 054101, 3 pages, 2005. View at Publisher · View at Google Scholar
  11. A. Momose, W. Yashiro, T. Takeda, Y. Suzuki, and T. Hattori, “Phase tomography by X-ray Talbot interferometry for biological imaging,” Japanese Journal of Applied Physics, vol. 45, part 1, no. 6A, pp. 5254–5262, 2006. View at Publisher · View at Google Scholar
  12. H. F. Talbot, “Fact relating to optical science,” Philosophical Magazine, vol. 9, pp. 401–407, 1836. View at Google Scholar
  13. J. P. Guigay, “On Fresnel diffraction by one-dimensional periodic objects, with application to structure determination of phase objects,” Journal of Modern Optics, vol. 18, no. 9, pp. 677–682, 1971. View at Publisher · View at Google Scholar
  14. V. Arrizón and J. Ojeda-Castañeda, “Irradiance at Fresnel planes of a phase grating,” Journal of the Optical Society of America A, vol. 9, no. 10, pp. 1801–1806, 1992. View at Google Scholar
  15. O. Kafri and I. Glatt, The Physics of Moire Metrology, Wiley-Interscience, New York, NY, USA, 1990.
  16. T. Weitkamp, A. Diaz, C. David et al., “X-ray phase imaging with a grating interferometer,” Optics Express, vol. 13, no. 16, pp. 6296–6304, 2005. View at Publisher · View at Google Scholar
  17. F. Pfeiffer, T. Weitkamp, O. Bunk, and C. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature Physics, vol. 2, no. 4, pp. 258–261, 2006. View at Publisher · View at Google Scholar
  18. F. Pfeiffer, C. Grünzweig, O. Bunk, G. Frei, E. Lehmann, and C. David, “Neutron phase imaging and tomography,” Physical Review Letters, vol. 96, no. 21, Article ID 215505, 2006. View at Publisher · View at Google Scholar
  19. F. Pfeiffer, C. Kottler, O. Bunk, and C. David, “Hard X-ray phase tomography with low-brilliance sources,” Physical Review Letters, vol. 98, no. 10, Article ID 108105, 2007. View at Publisher · View at Google Scholar
  20. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, IEEE Press, New York, NY, USA, 1988.
  21. G. W. Faris and R. L. Byer, “Three-dimensional beam-deflection optical tomography of a supersonic jet,” Applied Optics, vol. 27, no. 24, pp. 5202–5212, 1988. View at Google Scholar
  22. Z.-F. Huang, K.-J. Kang, Z. Li et al., “Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging,” Applied Physics Letters, vol. 89, no. 4, Article ID 041124, 3 pages, 2006. View at Publisher · View at Google Scholar
  23. M. Born and E. Wolf, Principles of Optics, Pergamon Press, New York, NY, USA, 6th edition, 1980.
  24. D. L. Parker, “Optimal short scan convolution reconstruction for fan beam CT,” Medical Physics, vol. 9, no. 2, pp. 254–257, 1982. View at Publisher · View at Google Scholar
  25. G.-H. Chen and Z. Qi, “Image reconstruction for fan-beam differential phase contrast computed tomography,” Physics in Medicine and Biology, vol. 53, no. 4, pp. 1015–1025, 2008. View at Publisher · View at Google Scholar · View at PubMed
  26. Z. Qi and G.-H. Chen, “A local region of interest image reconstruction via filtered backprojection for fan-beam differential phase-contrast computed tomography,” Physics in Medicine and Biology, vol. 52, no. 18, pp. N417–N423, 2007. View at Publisher · View at Google Scholar · View at PubMed
  27. L. A. Feldkamp, L. C. Davis, and J. W. Kress, “Practical cone-beam algorithm,” Journal of the Optical Society of America A, vol. 1, no. 6, pp. 612–619, 1984. View at Google Scholar