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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 2, Iss. 5 — May. 17, 2007

X-ray phase-contrast imaging: transmission functions separable in Cartesian coordinates

Guohua Cao, Theron J. Hamilton, Christoph Rose-Petruck, and Gerald J. Diebold  »View Author Affiliations


JOSA A, Vol. 24, Issue 4, pp. 1201-1208 (2007)
http://dx.doi.org/10.1364/JOSAA.24.001201


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Abstract

In-line, x-ray phase-contrast imaging is responsive to both phase changes and absorption as the x radiation traverses a body. Expressions are derived for phase-contrast imaging of objects having transmission functions separable in Cartesian coordinates. Starting from the Fresnel–Kirchhoff integral formula for image formation, an expression is found for the phase-contrast image produced by an x-ray source with nonvanishing dimensions. This expression is evaluated in limiting cases where the source-to-object distance is large, where the source acts as a point source, and where the weak phase approximation is valid. The integral expression for the image is evaluated for objects with simple geometrical shapes, showing the influence of the source dimensions on the visibility of phase-contrast features. The expressions derived here are evaluated for cases where the magnification is substantially greater than one as would be employed in biological imaging. Experiments are reported using the in-line phase-contrast imaging method with a microfocus x-ray source and a CCD camera.

© 2007 Optical Society of America

OCIS Codes
(110.7440) Imaging systems : X-ray imaging
(340.0340) X-ray optics : X-ray optics

ToC Category:
X-ray Optics

History
Original Manuscript: September 1, 2006
Revised Manuscript: October 19, 2006
Manuscript Accepted: October 27, 2006
Published: March 14, 2007

Virtual Issues
Vol. 2, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Guohua Cao, Theron J. Hamilton, Christoph Rose-Petruck, and Gerald J. Diebold, "X-ray phase-contrast imaging: transmission functions separable in Cartesian coordinates," J. Opt. Soc. Am. A 24, 1201-1208 (2007)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=josaa-24-4-1201


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References

  1. P. Cloetens, R. Barrett, J. Baruchel, J.-P. Guigay, and M. Schlenker, "Phase objects in synchrotron radiation hard x-ray imaging," J. Phys. D 29, 133-146 (1996). [CrossRef]
  2. S. W. Wilkins, T. Gureyev, D. Gao, A. Pogany, and A. W. Stevenson, "Phase-contrast imaging using polychromatic hard x-rays," Nature 384, 335-338 (1996). [CrossRef]
  3. F. Arfelli, M. Assante, V. Bonvicini, A. Bravin, G. Cantatore, E. Castelli, L. D. Palma, M. DiMichiel, R. Longo, A. Olivo, S. Pani, D. Pontoni, P. Poropat, M. Prest, A. Rashevsky, G. Tromba, A. Vacchi, E. Vallazza, and F. Zanconati, "Low-dose phase contrast x-ray medical imaging," Phys. Med. Biol. 43, 2845-2852 (1998). [CrossRef] [PubMed]
  4. P. Cloetens, W. Ludwig, J. Baruchel, D. V. Dyck, J. V. Landuyt, J. P. Guigay, and M. Schlenker, "Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays," Appl. Phys. Lett. 75, 2912-2914 (1999). [CrossRef]
  5. S. Zabler, P. Cloetens, J. P. Guigay, and J. Baruchel, "Optimization of phase contrast imaging using hard x-rays," Rev. Sci. Instrum. 76, 073705 (2005). [CrossRef]
  6. M. Born and E. Wolf, Principles of Optics (Pergamon, 1980).
  7. A. Pogany, D. Gao, and S. Wilkins, "Contrast and resolution in imaging with a microfocus x-ray source," Rev. Sci. Instrum. 68, 2774-2782 (1997). [CrossRef]
  8. J. M. Cowley, Diffraction Physics (North-Holland, 1984). The use of the Fresnel and the small-angle approximations require that parameters of the form (x?X)2/R be small compared with unity; hence, in experiments, the coordinates of the object and the image should be restricted to small distances from the axis of propagation of the x radiation.
  9. M. V. Klein, Optics (Wiley, 1970).
  10. The electric field is taken as proportional to 1/r. The intensity is expressed in units where the dielectric constant and permittivity are taken as unity so that the intensity becomes proportional to 1/r2.
  11. We use the convention used in Ref. where the field is attenuated proportional to exp[??(z)]. The intensity therefore is attenuated as exp[?2?(z)]. The parameter ?0 is taken as an intensity absorption coefficient.
  12. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 4th ed. (Academic, 1965).
  13. The spectrum of the x-ray tube, which uses only a Be window, can be found in Ref. , p. 99.
  14. J. Bushberg, J. Seibert, and E. Leidholdt, Jr., The Essential Physics of Medical Imaging (Williams and Wilkins, 1994).
  15. B. D. Arhatari, A. P. Mancuso, A. G. Peele, and D. A. Nugent, "Phase contrast radiography: image modeling and optimization," Rev. Sci. Instrum. 75, 5271-5276 (2004). [CrossRef]
  16. For objects where the weak phase approximation is not applicable, Fourier transformation (with respect to ?) of functions of the form exp[iphiv(?+?Df/2)], where D is a length parameter and f is spatial frequency, is required to determine the intensity in the frequency domain; that is, for each value of f in the frequency domain, a Fourier transformation with respect to ? must first be carried out. See Appendix A2 in Ref. .

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