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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 24, Iss. 3 — Mar. 1, 2007
  • pp: 626–642

Statistically principled use of in-line measurements in intensity diffraction tomography

Yin Huang and Mark A. Anastasio  »View Author Affiliations


JOSA A, Vol. 24, Issue 3, pp. 626-642 (2007)
http://dx.doi.org/10.1364/JOSAA.24.000626


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Abstract

Intensity diffraction tomography (I-DT) reconstruction theory provides a mathematical mapping between two in-line intensity measurements acquired at a given tomographic view angle and Fourier components of the object function. Poles in this mapping will cause certain Fourier components to contain greatly amplified noise levels when applied to noisy measurement data, which can result in noisy and distorted images in practice. We investigate the statistically principled use of multiple in-line intensity measurements in I-DT. Reconstruction methods are developed that exploit the statistical structure of the in-line measurements to minimize the variance of the estimated Fourier components of the object function.

© 2007 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(110.6960) Imaging systems : Tomography
(290.3200) Scattering : Inverse scattering

ToC Category:
Imaging Systems

History
Original Manuscript: April 27, 2006
Revised Manuscript: August 2, 2006
Manuscript Accepted: August 5, 2006
Published: February 14, 2007

Citation
Yin Huang and Mark A. Anastasio, "Statistically principled use of in-line measurements in intensity diffraction tomography," J. Opt. Soc. Am. A 24, 626-642 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-3-626


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References

  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, "Reconstructive tomography with diffracting wavefields," Inverse Probl. 2, 161-183 (1986). [CrossRef]
  4. P. Guo and A. J. Devaney, "Comparison of reconstruction algorithms for optical diffraction tomography," J. Opt. Soc. Am. A 22, 2338-2347 (2005). [CrossRef]
  5. A. J. Devaney and A. Schatzberg, "Coherent optical tomographic microscope," Proc. SPIE 1767, 62-71 (1992). [CrossRef]
  6. V. Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," J. Microsc. 205, 165-176 (2001). [CrossRef]
  7. T. C. Wedberg and J. J. Stamnes, "Quantitative imaging by optical diffraction tomography," Opt. Rev. 2, 28-31 (1995). [CrossRef]
  8. P. S. Carney and J. C. Schotland, "Inverse scattering for near-field microscopy," Appl. Phys. Lett. 77, 2798-2800 (2000). [CrossRef]
  9. W. Tabbara, B. Duchene, Ch. Pichot, D. Lesselier, L. Chommeloux, and N. Joachimowicz, "Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics," Inverse Probl. 4, 305-331 (1998). [CrossRef]
  10. T. Beetz, C. Jacobsen, and A. Stein, "Soft x-ray diffraction tomography: simulations and first experimerimental results," J. Physiol. Paris IV104, 31-34 (2003).
  11. M. R. Howells, B. Calef, C. J. Jacobsen, J. H. Spence, and W. Yun, "A modern approach to x-ray holography," AIP Conf. Proc. 507, 587-592 (2000). [CrossRef]
  12. S. Semenov, R. Svenson, A. Bulyshev, A. Souvorov, V. Borisov, Y. Sizov, A. Starostin, K. Dezern, G. Tatsis, and V. Baranov, "Microwave tomography: two-dimensional system for biological imaging," IEEE Trans. Biomed. Eng. 43, 869-877 (1996). [CrossRef] [PubMed]
  13. T. C. Wedberg and J. J. Stamnes, "Comparison of phase retrieval methods for optical diffraction tomography," Pure Appl. Opt. 4, 39-54 (1995). [CrossRef]
  14. T. C. Wedberg and J. J. Stamnes, "Recent results in optical diffraction microtomography," Meas. Sci. Technol. 7, 414-418 (1996). [CrossRef]
  15. M. Maleki and A. J. Devaney, "Phase-retrieval and intensity-only reconstruction algorithms for optical diffraction tomography," J. Opt. Soc. Am. A 10, 1086-1092 (1993). [CrossRef]
  16. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982). [CrossRef] [PubMed]
  17. G. Gbur and E. Wolf, "Diffraction tomography without phase information," Opt. Lett. 27, 1890-1892 (2002). [CrossRef]
  18. G. Gbur and E. Wolf, "Hybrid diffraction tomography without phase information," J. Opt. Soc. Am. A 19, 2194-2202 (2002). [CrossRef]
  19. G. Gbur, M. A. Anastasio, Y. Huang, and D. Shi, "Spherical-wave intensity diffraction tomography," J. Opt. Soc. Am. A 22, 230-238 (2005). [CrossRef]
  20. D. Shi, M. A. Anastasio, Y. Huang, and G. Gbur, "Half-scan and single-plane intensity diffraction tomography for phase objects," Phys. Med. Biol. 49, 2733-2752 (2004). [CrossRef] [PubMed]
  21. M. A. Anastasio, D. Shi, Y. Huang, and G. Gbur, "Image reconstruction in spherical wave intensity diffraction tomography," J. Opt. Soc. Am. A 22, 2651-2661 (2005). [CrossRef]
  22. M. A. Anastasio, D. Shi, and G. Gbur, "Multi-spectral intensity diffraction tomography reconstruction theory: I. Quasi-nondispersive objects," J. Opt. Soc. Am. A 23, 1359-1368 (2006). [CrossRef]
  23. A. Barty, K. A. Nugent, A. Roberts, and D. Paganin, "Quantitative phase tomography," Opt. Commun. 175, 329-336 (2000). [CrossRef]
  24. D. Paganin, A. Barty, P. I. Mcmahon, and K. A. Nugent, "Quantitative phase-amplitude microscopy III. The effects of noise," J. Microsc. 214, 51-61 (2003). [CrossRef]
  25. A. J. Devaney, "Diffraction tomographic reconstruction from intensity data," IEEE Trans. Image Process. 1, 221-228 (1992). [CrossRef] [PubMed]
  26. G. Gbur and E. Wolf, "The information content of the scattered intensity in diffraction tomography," Inf. Sci. (N.Y.) 162, 3-20 (2004). [CrossRef]
  27. M. A. Anastasio, Y. Huang, G. Gbur, and P. S. Carney, "Investigation of 3D microscopy using intensity diffraction tomography," Proc. SPIE 6090, 77-84 (2006).
  28. M. A. Anastasio and D. Shi, "On the relationship between intensity diffraction tomography and phase-contrast tomography," Proc. SPIE 5535, 361-368 (2004). [CrossRef]
  29. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  30. M. A. Anastasio and X. Pan, "Computationally efficient and statistically robust image reconstruction in 3D diffraction tomography," J. Opt. Soc. Am. A 17, 391-400 (2000). [CrossRef]
  31. M. A. Anastasio, Y. Huang, D. Shi, and G. Gbur, "Noise properties of intensity diffraction tomography," in Medical Imaging 2004: Physics of Medical Imaging, M.I.Yaffe and M.J.Flynn, eds., Proc. SPIE 5368, 272-280 (2004).
  32. X. Pan, "A unified reconstruction theory for diffraction tomography with considerations of noise control," J. Opt. Soc. Am. A 15, 2312-2326 (1998). [CrossRef]
  33. C. E. Metz and X. Pan, "A unified analysis of exact methods of inverting the 2-D exponential Radon transform, with implications for noise control in SPECT," IEEE Trans. Med. Imaging 14, 643-658 (1995). [CrossRef] [PubMed]
  34. S. Lowenthal and H. Arsenault, "Image formation for coherent diffuse objects: statistical properties," J. Opt. Soc. Am. 60, 1478-1483 (1970). [CrossRef]
  35. B. P. Lathi, Signal Processing and Linear Systems (Oxford U. Press, 1998).
  36. M. Slaney, A. C. Kak, and L. Larsen, "Limitations of imaging with first-order diffraction tomography," IEEE Trans. Microwave Theory Tech. 32, 860-874 (1984). [CrossRef]
  37. B. Chen and J. J. Stamnes, "Validity of diffraction tomography based on the first-Born and first-Rytov approximations," Appl. Opt. 37, 2996-3006 (1998). [CrossRef]

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