OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Glenn D. Boreman
  • Vol. 44, Iss. 28 — Oct. 1, 2005
  • pp: 5847–5854

Phase-space formulation for phase-contrast x-ray imaging

Xizeng Wu and Hong Liu  »View Author Affiliations


Applied Optics, Vol. 44, Issue 28, pp. 5847-5854 (2005)
http://dx.doi.org/10.1364/AO.44.005847


View Full Text Article

Enhanced HTML    Acrobat PDF (329 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Phase-space formulation based on the Wigner distribution has been presented for analyzing phase-contrast image formation. Based on the statistical nature and affine canonical covariance of Wigner distributions in the phase space, we show that the partial coherence effects of incident x-ray wave field on image intensity are simply accounted for by a multiplication factor, which is the reduced complex degree of coherence of the incident x-ray wave field. We show especially that with the undulator sources one cannot obtain the phase-contrast intensity by summing over the contributions from all electron positions, since the van Cittert–Zernike theorem fails in general for undulators. We derive a comprehensive formula that quantifies the effects of partial spatial coherence, polychromatic spectrum, body attenuation, imaging-detector resolution, and radiation dose on phase-contrast visibility in clinical imaging. The results of our computer modeling and simulations show how the formula can provide design guidelines and optimal parameters for clinical x-ray phase-contrast imaging systems.

© 2005 Optical Society of America

OCIS Codes
(030.0030) Coherence and statistical optics : Coherence and statistical optics
(030.1640) Coherence and statistical optics : Coherence
(030.1670) Coherence and statistical optics : Coherent optical effects
(340.7440) X-ray optics : X-ray imaging

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: January 21, 2005
Revised Manuscript: May 6, 2005
Manuscript Accepted: May 7, 2005
Published: October 1, 2005

Citation
Xizeng Wu and Hong Liu, "Phase-space formulation for phase-contrast x-ray imaging," Appl. Opt. 44, 5847-5854 (2005)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-44-28-5847


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, I. Schelokov, “On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation,” Rev. Sci. Instrum. 66, 5486–5492 (1995). [CrossRef]
  2. F. Arfelli, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. Dalla Palma, M. Di Michiel, M. Fabrizioli, R. Longo, R. H. Menk, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, M. Ratti, L. Rigon, G. Tromba, A. Vacchi, E. Vallazza, F. Zanconati, “Mammography with synchrotron radiation: phase-detection techniques,” Radiology 215, 286–293 (2000). [CrossRef]
  3. X. Wu, A. Dean, H. Liu, “X-ray diagnostic techniques,” in Biomedical Photonics Handbook, T. VoDinh, ed. (CRC, Tampa, Fla., 2003), Chap. 26, pp. 26-1–26-34.
  4. S. Wilkins, T. Gureyev, D. Gao, A. Pogany, A. Stevenson, “Phase contrast imaging using polychromatic hard x-ray,” Nature 384, 335–338 (1996). [CrossRef]
  5. A. Pogany, D. Gao, S. W. Wilkins, “Contrast and resolution in imaging with a microfocus x-ray source,” Rev. Sci. Instrum. 68, 2774–2782 (1997). [CrossRef]
  6. C. J. Kotre, I. P. Birch, “Phase contrast enhancement of x-ray mammography: a design study,” Phys. Med. Biol. 44, 2853–2866 (1999). [CrossRef] [PubMed]
  7. E. Donnelly, R. Price, “Effect of kVp on edge-enhancement index in phase-contrast radiography,” Med. Phys. 29, 999–1002 (2002). [CrossRef] [PubMed]
  8. X. Wu, H. Liu, “A general formalism for x-ray phase contrast imaging,” J. X-Ray Sci. Technol. 11, 33–42 (2003).
  9. X. Wu, H. Liu, “Clinical implementation of phase contrast x-ray imaging: theoretical foundation and design considerations,” Med. Phys. 30, 2169–2179 (2003). [CrossRef] [PubMed]
  10. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  11. X. Wu, H. Liu, “A new theory of phase-contrast x-ray imaging based on Wigner distributions,” Med. Phys. 31, 2378–2384 (2004). [CrossRef] [PubMed]
  12. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995). [CrossRef]
  13. A. Wax, S. Bali, G. A. Alphonse, J. E. Thomas, “Characterizing the coherence of broadband sources using optical phase space contours,” J. Biomed. Opt. 4, 482–489 (1999). [CrossRef] [PubMed]
  14. A. Wax, J. E. Thomas, “Measurement of smoothed Wigner phase-space distributions for small-angle scattering in a turbid medium,” J. Opt. Soc. Am. A 15, 1896–1908 (1998). [CrossRef]
  15. K. F. Lee, F. Reil, S. Bali, A. Wax, J. E. Thomas, “Heterodyne measurement of Wigner distributions for classical optical fields,” Opt. Lett. 24, 1370–1372 (1999). [CrossRef]
  16. R. G. Littlejohn, “The semiclassical evolution of wave packets,” Phys. Rep. 138, 193–291 (1986). [CrossRef]
  17. H. Wiedemann, Synchrotron Radiation (Springer-Verlag, Berlin, 2003). [CrossRef]
  18. R. Coisson, “Spatial coherence of synchrotron radiation,” Appl. Opt. 34, 904–908 (1995). [CrossRef] [PubMed]
  19. J. Guigay, “Fourier transform analysis of Fresnel diffraction and in-line holograms,” Optik (Stuttgart) 49, 121–125 (1977).
  20. M. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]
  21. T. Gureyev, A. Pogany, D. Paganin, S. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004). [CrossRef]
  22. X. Wu, H. Liu, “An experimental method of determining relative phase-contrast factor for x-ray imaging systems,” Med. Phys. 31, 997–1002 (2004). [CrossRef]
  23. F. Ouandji, E. Potter, W. R. Chen, Y. Li, D. Tang, H. Liu, “Characterization of a CCD-based digital x-ray imaging system for small animal studies: properties of spatial resolution,” Appl. Opt. 41, 2420–2427 (2002). [CrossRef] [PubMed]
  24. X. Wu, G. Barnes, D. Tucker, “Spectral dependence of glandular tissue dose in screen-film mammography,” Radiology 179, 143–148 (1991). [PubMed]
  25. X. Wu, E. Gingold, G. Barnes, D. Tucker, “Normalized average glandular dose in molybdenum target–rhodium filter and rhodium target–rhodium filter mammography,” Radiology 193, 83–89 (1994). [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
 

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited