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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Stephen A. Burns
  • Vol. 22, Iss. 12 — Dec. 1, 2005
  • pp: 2651–2661

Image reconstruction in spherical-wave intensity diffraction tomography

Mark A. Anastasio, Daxin Shi, Yin Huang, and Greg Gbur  »View Author Affiliations

JOSA A, Vol. 22, Issue 12, pp. 2651-2661 (2005)

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A reconstruction theory for intensity diffraction tomography (I-DT) has been proposed that permits reconstruction of a weakly scattering object without explicit knowledge of phase information. We investigate the I-DT reconstruction problem assuming an incident (paraxial) spherical wave and scanning geometries that employ fixed source-to-object distances. Novel reconstruction methods are derived by identifying and exploiting tomographic symmetries and the rotational invariance of the problem. An underlying theme is that symmetries in tomographic imaging systems can facilitate solutions for phase-retrieval problems. A preliminary numerical investigation of the developed reconstruction methods is presented.

© 2005 Optical Society of America

OCIS Codes
(110.6960) Imaging systems : Tomography
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(290.3200) Scattering : Inverse scattering

ToC Category:
Imaging Systems

Original Manuscript: December 15, 2004
Revised Manuscript: April 22, 2005
Manuscript Accepted: May 6, 2005
Published: December 1, 2005

Mark A. Anastasio, Greg Gbur, Daxin Shi, and Yin Huang, "Image reconstruction in spherical-wave intensity diffraction tomography," J. Opt. Soc. Am. A 22, 2651-2661 (2005)

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  1. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969). [CrossRef]
  2. E. Wolf, “Principles and development of diffraction tomography,” in Trends in Optics, A. Consortini, ed. (Academic, 1996). [CrossRef]
  3. A. J. Devaney, “Diffraction tomography,” in Inverse Methods in Electromagnetic Imaging, Part 2, W. M. Boerner, ed., NATO ASI Series (Reidel, 1983), pp. 1107–1135.
  4. A. J. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Remote Sens. 22, 3–13 (1984). [CrossRef]
  5. T. Wedberg, J. Stamnes, “Quantitative imaging by optical diffraction tomography,” Opt. Rev. 2, 28–31 (1995). [CrossRef]
  6. G. Gbur, E. Wolf, “Diffraction tomography without phase information,” Opt. Lett. 27, 1890–1892 (2002). [CrossRef]
  7. G. Gbur, E. Wolf, “Hybrid diffraction tomography without phase information,” J. Opt. Soc. Am. A 19, 2194–2202 (2002). [CrossRef]
  8. V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. (Oxford) 205, 165–176 (2001). [CrossRef]
  9. T. C. Wedberg, J. J. Stamnes, “Recent results in optical diffraction microtomography,” Meas. Sci. Technol. 7, 414–418 (1996). [CrossRef]
  10. A. S. T. Beetz, C. Jacobsen, “Soft x-ray diffraction tomography: simulations and first experimental results,” J. Phys. IV 104, 31–34 (2003).
  11. K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, Z. Barnea, “Quantitative phase imaging using hard x-rays,” Phys. Rev. Lett. 77, 2961–2964 (1996). [CrossRef] [PubMed]
  12. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]
  13. G. Gbur, M. A. Anastasio, Y. Huang, D. Shi, “Spherical-wave intensity diffraction tomography,” J. Opt. Soc. Am. A 22, 230–238 (2005). [CrossRef]
  14. A. J. Devaney, “Generalized projection-slice theorem for fan-beam diffraction tomography,” Ultrason. Imaging 7, 264–275 (1985). [CrossRef] [PubMed]
  15. M. Born, E. Wolf, Principles of Optics (Cambridge U. Press, 1999). [CrossRef]
  16. M. A. Anastasio, X. Pan, “An improved reconstruction algorithm for 3D diffraction tomography using spherical-wave sources,” IEEE Trans. Biomed. Eng. 50, 517–521 (2003). [CrossRef] [PubMed]
  17. Z. Lu, “Multidimensional structure diffraction tomography for varying object orientation through generalised scattered waves,” Inverse Probl. 1, 339–356 (1985). [CrossRef]
  18. M. Bertero, P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, 1998). [CrossRef]
  19. M. Slaney, A. C. Kak, L. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. 32, 860–874 (1984). [CrossRef]
  20. B. Chen, J. Stamnes, “Validity of diffraction tomography based on the first-Born and first-Rytov approximations,” Appl. Opt. 37, 2996–3006 (1998). [CrossRef]
  21. M. A. Anastasio, X. Pan, “Full- and minimal-scan reconstruction algorithms for fan-beam diffraction tomography,” Appl. Opt. 40, 3334–3345 (2001). [CrossRef]
  22. S. Mayo, T. Davis, T. Gureyev, P. Miller, D. Paganin, A. Pogany, A. Stevenson, S. Wilkins, “X-ray phase-contrast microscopy and microtomography,” Opt. Express 11, 2289–2302 (2003). [CrossRef] [PubMed]
  23. A. Barty, K. A. Nugent, A. Roberts, D. Paganin, “Quantitative phase tomography,” Opt. Commun. 175, 329–336 (2000). [CrossRef]
  24. T. Gureyev, T. Davis, A. Pogany, S. Mayo, S. Wilkins, “Optical phase retrieval by use of first Born- and Rytov-type approximations,” Appl. Opt. 43, 2418–2430 (2004). [CrossRef] [PubMed]

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