OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 9, Iss. 5 — Apr. 29, 2014

Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach

Sergei Gasilov, Alberto Mittone, Emmanuel Brun, Alberto Bravin, Susanne Grandl, Alessandro Mirone, and Paola Coan  »View Author Affiliations


Optics Express, Vol. 22, Issue 5, pp. 5216-5227 (2014)
http://dx.doi.org/10.1364/OE.22.005216


View Full Text Article

Enhanced HTML    Acrobat PDF (500 KB) Open Access





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The refractive-index gradient vector field approach establishes a connection between a tomographic data set of differential phase contrast images and the distribution of the partial spatial derivatives of the refractive index in an object. The reconstruction of the refractive index in a plane requires the integration of its gradient field. This work shows how this integration can be efficiently performed by converting the problem to the Poisson equation, which can be accurately solved even in the case of noisy and large datasets. The performance of the suggested method is discussed and demonstrated experimentally by computing the refractive index distribution in both a simple plastic phantom and a complex biological sample. The quality of the reconstruction is evaluated through the direct comparison with other commonly used methods. To this end, the refractive index is retrieved from the same data set using also (1) the filtered backprojection algorithm for gradient projections, and (2) the regularized phase-retrieval procedure. Results show that the gradient vector field approach combined with the developed integration technique provides a very accurate depiction of the sample internal structure. Contrary to the two other techniques, the considered method does not require a preliminary phase-retrieval and can be implemented with any advanced computer tomography algorithm. In this work, analyzer-based phase contrast images are used for demonstration. Results, however, are generally valid and can be applied for processing differential phase-contrast tomographic data sets obtained with other phase-contrast imaging techniques.

© 2014 Optical Society of America

OCIS Codes
(110.7440) Imaging systems : X-ray imaging
(120.5710) Instrumentation, measurement, and metrology : Refraction
(110.6955) Imaging systems : Tomographic imaging
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
X-ray Optics

History
Original Manuscript: November 28, 2013
Revised Manuscript: January 9, 2014
Manuscript Accepted: January 11, 2014
Published: February 27, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Sergei Gasilov, Alberto Mittone, Emmanuel Brun, Alberto Bravin, Susanne Grandl, Alessandro Mirone, and Paola Coan, "Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach," Opt. Express 22, 5216-5227 (2014)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-22-5-5216


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Momose, “Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer,” Nucl. Instr. Meth. Phys. Res. A 352, 622–628 (1995). [CrossRef]
  2. V.A. Bushuev, A.A. Sergeev, “Inverse problem in the X-ray phase contrast method,” Technical Phys. Lett. 25, 83–85 (1999). [CrossRef]
  3. A. Maksimenko, M. Ando, S. Hiroshi, T. Yausa, “Computed tomographic reconstruction based on x-ray refraction contrast,” Appl. Phys. Lett. 86, 124105 (2005). [CrossRef]
  4. F. Pfeiffer, C. Kottler, O. Bunk, C. Davis, “Hard X-Ray Phase Tomography with Low-Brilliance Sources,” Phys. Rev. Lett. 98, 108105 (2007). [CrossRef] [PubMed]
  5. A. Bravin, P. Coan, P. Suortti, “X-ray phase-contrast imaging: from pre-clinical applications towards clinics,” Phys. Med. Biol 58, R1–R35 (2013). [CrossRef]
  6. F. A. Dilmanian, Z. Zhong, B. Ren, X. Y. Wu, L. D. Chapman, I. Orion, W. C. Thomlinson, “Computed tomography of x-ray index of refraction using the diffraction enhanced imaging method,” Phys. Med. Biol. 45, 933–946 (2000). [CrossRef] [PubMed]
  7. T. Weitkamp, A. Diaz, Ch. David, F. Pfeiffer, M. Stampanoni, P. Cloetens, E. Ziegler, “X-ray phase imaging with a grating interferometer,” Opt. Express. 13, 6296–6304 (2005). [CrossRef] [PubMed]
  8. P. R. T. Munro, L. Rigon, K. Ignatyev, F. C. M. Lopez, D. Dreissi, R.D. Speller, A. Olivo, “A quantitative, non-interferometric X-ray phase contrast imaging techniques,” Opt. Express 21, 647–661 (2012). [CrossRef]
  9. T. Yuasa, A. Maksimenko, E. Hashimoto, H. Sugiyama, K. Hyodo, T. Akatsuka, M. Ando, “Hard-x-ray region tomographic reconstruction of the refractive-index gradient vector field: imaging principles and comparisons with diffraction-enhanced-imaging-based computed tomography,” Opt. Lett. 31, 1818–1820 (2006). [CrossRef] [PubMed]
  10. M. N. Wernick, Y. Yang, I. Mondal, D. Chapman, M. Hasnah, Ch. Parham, E. Pisano, Z. Zhong, “Computation of mass-density images from x-ray refraction-angle images,” Phys. Med. Biol. 51, 1769–1778 (2006). [CrossRef] [PubMed]
  11. T. Thuering, P. Modregger, B. R. Pinzer, Z. Wang, M. Stampanoni, “Non-linear regularized phase retrieval for unidirectional X-ray differential phase contrast radiography,” Opt. Express 19, 25542–25558 (2011).
  12. G. W. Faris, R. L. Byer, “Three-dimensional beam deflection optical tomography of a supersonic jet,” Appl. Opt. 27, 5202–5212 (1988). [CrossRef] [PubMed]
  13. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging(IEEE Press, 1988, Chap. 5).
  14. F. J. Harris, “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform,” Proc. IEEE, 66, 51–83 (1978). [CrossRef]
  15. A. J. Devaney, “A Computer Simulation study of Diffraction Tomography,” IEEE Trans. Biomed. Eng. 30377–386 (1983). [CrossRef] [PubMed]
  16. A. Beck, M. Teboulle, “A fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems,” SIAM J. Imaging Sciences 2, 183–202 (2009). [CrossRef]
  17. R. P. Fedorenko, “A relaxation method for solving elliptic difference equations,” USSR Comput. Math. Math. Phys. 1, 1092 (1961). [CrossRef]
  18. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical recipes in C, 2 (Cambridge University, 1992, pp. 871–872).
  19. J. M. Hyman, M. Shashkov, ”Natural discretizations for the divergence, gradient, and curl on logically rectangular grids”, Computers Math. Applic. 33, 81–104 (1997). [CrossRef]
  20. O. C. Zienkiewicz, K. Morgan, Finite Elements and Approximation (Dover Pubn. Inc., 2006, Chap. 3).
  21. V. N. Ingal, E. A. Beliaevskaya, “X-ray plane-wave topography observation of the phase contrast from a non-crystalline object,” J. Phys. D 28, 2314–2318 (1995). [CrossRef]
  22. A. Maksimenko, “Nonlinear extension of the X-ray diffraction enhanced imaging,” Appl. Phys. Lett. 90, 154106 (2007). [CrossRef]
  23. Tissue Substitutes in Radiation Dosimetry and Measurement, ICRU Report 44 (1989).
  24. G. R. Hammerstein, D. W. Miller, D. R. White, M. E. Masterson, H. Q. Woodard, J. S. Laughlin, “Absorbed radiation dose in mammography,” Radiology 130, 485–491 (1979). [PubMed]

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