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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 7 — Mar. 29, 2010
  • pp: 6423–6436

2D and 3D X-ray phase retrieval of multi-material objects using a single defocus distance

M.A. Beltran, D.M. Paganin, K. Uesugi, and M.J. Kitchen  »View Author Affiliations

Optics Express, Vol. 18, Issue 7, pp. 6423-6436 (2010)

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A method of tomographic phase retrieval is developed for multi-material objects whose components each have a distinct complex refractive index. The phase-retrieval algorithm, based on the Transport-of-Intensity equation, utilizes propagation-based X-ray phase contrast images acquired at a single defocus distance for each tomographic projection. The method requires a priori knowledge of the complex refractive index for each material present in the sample, together with the total projected thickness of the object at each orientation. The requirement of only a single defocus distance per projection simplifies the experimental setup and imposes no additional dose compared to conventional tomography. The algorithm was implemented using phase contrast data acquired at the SPring-8 Synchrotron facility in Japan. The three-dimensional (3D) complex refractive index distribution of a multi-material test object was quantitatively reconstructed using a single X-ray phase-contrast image per projection. The technique is robust in the presence of noise, compared to conventional absorption based tomography.

© 2010 OSA

OCIS Codes
(100.5070) Image processing : Phase retrieval
(100.6950) Image processing : Tomographic image processing
(340.7440) X-ray optics : X-ray imaging
(090.1995) Holography : Digital holography

ToC Category:
Image Processing

Original Manuscript: November 30, 2009
Revised Manuscript: January 14, 2010
Manuscript Accepted: February 5, 2010
Published: March 15, 2010

Virtual Issues
Vol. 5, Iss. 7 Virtual Journal for Biomedical Optics

M.A. Beltran, D.M. Paganin, K. Uesugi, and M.J. Kitchen, "2D and 3D X-ray phase retrieval of
multi-material objects using a
single defocus distance," Opt. Express 18, 6423-6436 (2010)

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  1. A. C. Kak, and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).
  2. S. Bayat, G. Le Duc, L. Porra, G. Berruyer, C. Nemoz, S. Monfraix, S. Fiedler, W. Thomlinson, P. Suortti, C. G. Standertskjöld-Nordenstam, and A. R. A. Sovijärvi, “Quantitative functional lung imaging with synchrotron radiation using inhaled xenon as contrast agent,” Phys. Med. Biol. 46(12), 3287–3299 (2001). [CrossRef]
  3. S. Monfraix, S. Bayat, L. Porra, G. Berruyer, C. Nemoz, W. Thomlinson, P. Suortti, and A. R. A. Sovijärvi, “Quantitative measurement of regional lung gas volume by synchrotron radiation computed tomography,” Phys. Med. Biol. 50(1), 1–11 (2005). [CrossRef] [PubMed]
  4. B. Driehuys and L. W. Hedlund, “Imaging techniques for small animal models of pulmonary disease: MR microscopy,” Toxicol. Pathol. 35(1), 49–58 (2007). [CrossRef] [PubMed]
  5. D. P. Schuster, A. Kovacs, J. Garbow, and D. Piwnica-Worms, “Recent advances in imaging the lungs of intact small animals,” Am. J. Respir. Cell Mol. Biol. 30(2), 129–138 (2004). [CrossRef] [PubMed]
  6. U. Bonse and M. Hart, “An x-ray interferometer,” Appl. Phys. Lett. 6(8), 155–156 (1965). [CrossRef]
  7. E. Förster, K. Goetz, and P. Zaumseil, “Double crystal diffractometry for the characterization of targets for laser fusion experiments,” Krist. Tech. 15(8), 937–945 (1980). [CrossRef]
  8. F. Pfeiffer, T. Weitkamp, O. Bunk, and O. David, “Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources,” Nature 2, 258–261 (2006).
  9. 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(12), 5486–5492 (1995). [CrossRef]
  10. S. W. Wilkins, T. E. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, “Phase-contrast imaging using polychromatic hard X-rays,” Nature 384(6607), 335–338 (1996). [CrossRef]
  11. 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(1), 133–146 (1996). [CrossRef]
  12. M. R. Teague, “Deterministic phase retrieval: a Green's function solution,” J. Opt. Soc. Am. 73(11), 1434–1441 (1983). [CrossRef]
  13. T. E. Gureyev and K. A. Nugent, “Phase retrieval with the transport-of-intensity equation. II. Orthogonal series solution for nonuniform illumination,” J. Opt. Soc. Am. A 13(8), 1670–1682 (1996). [CrossRef]
  14. T. E. Gureyev and K. A. Nugent, “Rapid quantitative phase imaging using the transport of intensity equation,” Opt. Commun. 133(1-6), 339–346 (1997). [CrossRef]
  15. D. Paganin and K. A. Nugent, “Noninterferometric phase imaging with partially coherent light,” Phys. Rev. Lett. 80(12), 2586–2589 (1998). [CrossRef]
  16. O. M. Bucci, L. Crocco, M. D'Urso, and T. Isernia, “Inverse scattering from phaseless measurements of the total field open lines,” J. Opt. Soc. Am. A 23(10), 2566–2577 (2006). [CrossRef]
  17. L. Crocco, M. D’Urso, and T. Isernia, “Faithful non-linear imaging from only-amplitude measurements of incident and total fields,” Opt. Express 15(7), 3804–3815 (2007). [CrossRef] [PubMed]
  18. J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32(12), 1617–1619 (2007). [CrossRef] [PubMed]
  19. M. D'Urso, K. Belkerbir, L. Crocco, T. Isernia, and A. Litman, “Phaseless imaging with experimantal data: facts and challenges,” J. Opt. Soc. Am. A 25(1), 271–281 (2008). [CrossRef]
  20. A. Pogany, D. Gao, and S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68(7), 2774–2782 (1997). [CrossRef]
  21. P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M. Schlenker, “Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation X-rays,” Appl. Phys. Lett. 75(19), 2912–2914 (1999). [CrossRef]
  22. D. Paganin, S. C. Mayo, T. E. Gureyev, P. R. Miller, and S. W. Wilkins, “Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object,” J. Microsc. 206(1), 33–40 (2002). [CrossRef] [PubMed]
  23. S. C. Mayo, T. J. Davis, T. E. Gureyev, P. R. Miller, D. Paganin, A. Pogany, A. W. Stevenson, and S. W. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11(19), 2289–2302 (2003). [CrossRef] [PubMed]
  24. T. E. Gureyev, D. M. Paganin, G. R. Myers, Y. I. Nesterets, and S. W. Wilkins, “Phase-and-amplitude computer tomography,” Appl. Phys. Lett. 89(3), 034102 (2006). [CrossRef]
  25. G. R. Myers, T. E. Gureyev, D. M. Paganin, and S. C. Mayo, “The binary dissector: phase contrast tomography of two- and three-material objects from few projections,” Opt. Express 16(14), 10736–10749 (2008). [CrossRef] [PubMed]
  26. A. V. Bronnikov, “Reconstruction formulas in phase-contrast tomography,” Opt. Commun. 171(4-6), 239–244 (1999). [CrossRef]
  27. A. V. Bronnikov, “Theory of quantitative phase-contrast computed tomography,” J. Opt. Soc. Am. A 19(3), 472–480 (2002). [CrossRef]
  28. J. Als-Nielsen, and D. McMorrow, Elements of Modern X-ray Physics (John Wiley & Sons, New York, 2001).
  29. D. M. Paganin, Coherent X-Ray Optics (Oxford University Press, New York, 2006).
  30. X. Wu, H. Liu, and A. Yan, “X-ray phase-attenuation duality and phase retrieval,” Opt. Lett. 30(4), 379–381 (2005). [CrossRef] [PubMed]
  31. M. J. Kitchen, R. A. Lewis, M. J. Morgan, M. J. Wallace, M. L. Siew, K. K. W. Siu, A. Habib, A. Fouras, N. Yagi, K. Uesugi, and S. B. Hooper, “Dynamic measures of regional lung air volume using phase contrast x-ray imaging,” Phys. Med. Biol. 53(21), 6065–6077 (2008). [CrossRef] [PubMed]
  32. S. Goto, K. Takeshita, Y. Suzuki, H. Ohashi, Y. Asano, H. Kimura, T. Matsushita, N. Yagi, M. Isshiki, H. Yamazaki, Y. Yoneda, K. Umetani, and T. Ishikawa, “Construction and commissioning of a 215m-long beamline at SPring-8,” Nucl. Instrum. Meth. A. 467-468, 682–685 (2001). [CrossRef]
  33. A. Abrami, F. Arfelli, R. C. Barroso, A. Bergamaschi, F. Bille, P. Bregant, F. Brizzi, K. Casarin, E. Castelli, V. Chenda, L. Dalla Palma, D. Dreossi, C. Fava, R. Longo, L. Mancini, R.-H. Menk, F. Montanari, A. Olivo, S. Pani, A. Pillon, E. Quai, S. R. Kaiser, L. Rigon, T. Rokvic, M. Tonutti, G. Tromba, A. Vascotto, C. Venanzi, F. Zanconati, A. Zanetti, and F. Zanini, “Medical applications of synchrotron radiation at the SYRMEP beamline of ELETTRA,” Nucl. Instrum. Meth. A 548(1-2), 221–227 (2005). [CrossRef]
  34. P. Cloetens, W. Ludwig, J. Baruchel, J.-P. Guigay, P. Pernot-Rejmánková, M. Salomé-Pateyron, M. Schlenker, J.-Y. Buffière, E. Malre, and G. Peix, “Hard X-ray phase imaging using simple propagation of a coherent synchrotron radiation beam,” J. Phys. D Appl. Phys. 32(10A), 145–151 (1999). [CrossRef]
  35. C. T. Chantler, C. Q. Tran, Z. Barnea, D. Paterson, D. J. Cookson, and D. X. Balaic, “Measurement of the x-ray mass attenuation coefficient of copper using 8.85-20 keV synchrotron radiation,” Phys. Rev. A 64(6), 062506 (2001). [CrossRef]

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