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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

  • Vol. 22, Iss. 7 — Jul. 1, 2005
  • pp: 1251–1262

Investigating the enhancement of three-dimensional diffraction tomography by using multiple illumination planes

Angelos T. Vouldis, Costas N. Kechribaris, Theofanis A. Maniatis, Konstantina S. Nikita, and Nikolaos K. Uzunoglu  »View Author Affiliations


JOSA A, Vol. 22, Issue 7, pp. 1251-1262 (2005)
http://dx.doi.org/10.1364/JOSAA.22.001251


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Abstract

The three dimensional (3-D) extension of the two well-known diffraction tomography algorithms, namely, direct Fourier interpolation (DFI) and filtered backpropagation (FBP), are presented and the problem of the data needed for a full 3-D reconstruction is investigated. These algorithms can be used efficiently to solve the inverse scattering problem for weak scatterers in the frequency domain under the first-order Born and Rytov approximations. Previous attempts of 3-D reconstruction with plane-wave illumination have used data obtained with the incident direction restricted at the x y plane. However, we show that this restriction results in the omission of the contribution of certain spatial frequencies near the ω z axis for the final reconstruction. The effect of this omission is studied by comparing the results of reconstruction with and without data obtained from other incident directions that fill the spatial frequency domain. We conclude that the use of data obtained for incident direction in only the x y plane is sufficient to achieve a satisfactory quality of reconstruction for a class of objects presenting smooth variation along the z axis, while abrupt variations along the z axis cannot be imaged. This result should be taken into account in the process of designing the acquisition geometry of a tomography scanner.

© 2005 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(100.6890) Image processing : Three-dimensional image processing
(100.6950) Image processing : Tomographic image processing
(290.3200) Scattering : Inverse scattering

History
Original Manuscript: September 16, 2004
Revised Manuscript: January 15, 2005
Manuscript Accepted: January 19, 2005
Published: July 1, 2005

Citation
Angelos T. Vouldis, Costas N. Kechribaris, Theofanis A. Maniatis, Konstantina S. Nikita, and Nikolaos K. Uzunoglu, "Investigating the enhancement of three-dimensional diffraction tomography by using multiple illumination planes," J. Opt. Soc. Am. A 22, 1251-1262 (2005)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-22-7-1251


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References

  1. M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging,” Acoust. Imaging 21, 379–390 (1995). [CrossRef]
  2. H. Liu, C. L. Matson, K. Lau, R. R. Mapakshi, “Experimental validation of a backpropagation algorithm for three-dimensional breast tumor localization,” IEEE J. Sel. Top. Quantum Electron. 5, 1049–1057 (1999). [CrossRef]
  3. P. M. Meany, K. D. Paulsen, S. D. Geimer, S. A Haider, M. W. Fanning, “Quantification of 3-D field effects during 2-D microwave imaging,” IEEE Trans. Biomed. Eng. 49, 708–720 (2002). [CrossRef]
  4. S. Y. Semenov, A. E. Bulyshev, A. E. Souvorov, A. G. Nazarov, Y. E. Sizov, R. H. Svenson, V. G. Posukh, A. Pavlovsky, P. N. Repin, G. P. Tatsis, “Three-dimensional microwave tomography: experimental imaging of phantoms and biological objects,” IEEE Trans. Microwave Theory Tech. 48, 1071–1074 (2000). [CrossRef]
  5. H. Z. Takashi, T. Takenaka, T. Tanaka, “Three-dimensional reconstruction of a shallowly buried mine using time-domain data,” Microwave Opt. Technol. Lett. 39, 276–280 (2003). [CrossRef]
  6. C. N. Kechribaris, K. S. Nikita, N. K. Uzunoglu, “Reconstruction of two-dimensional permittivity distribution using an improved Rytov approximation and nonlinear optimization,”J. Electromagn. Waves Appl. 17, 183–207 (2003). [CrossRef]
  7. T. A. Maniatis, K. S. Nikita, N. K. Uzunoglu, “Two-dimensional dielectric profile reconstruction based on spectral-domain moment method and nonlinear optimization,” IEEE Trans. Microwave Theory Tech. 48, 1831–1840 (2000). [CrossRef]
  8. M. Gustafsson, S. He, “An optimization approach to multi-dimensional time-domain acoustic inverse problems,” J. Acoust. Soc. Am. 108, 1548–1556 (2000). [CrossRef] [PubMed]
  9. A. Abubakar, P. M Van den Berg, S. Y. Semenov, “Two and three dimensional algorithms for microwave imaging and inverse scattering,” J. Electromagn. Waves Appl. 17, 209–231 (2003). [CrossRef]
  10. S. Caorsi, A. Massa, M. Pastorino, M. Donelli, “Improved microwave imaging procedure for nondestructive evaluations of two dimensional structures,” IEEE Trans. Antennas Propag. 52, 1386–1397 (2004). [CrossRef]
  11. R. K. Mueller, M. Kaveh, G. Wade, “Reconstructive tomography and applications to ultrasonics,” Proc. IEEE 67, 567–587 (1979). [CrossRef]
  12. R. K. Mueller, M. Kaveh, R. D. Inverson, “A new approach to acoustic tomography using diffraction techniques,” Acoust. Imaging 8, 615–628 (1980). [CrossRef]
  13. M. Kaveh, M. Sumekh, J. Greenleaf, “Signal processing for diffraction tomography,” IEEE Trans. Sonics Ultrason. SU-31, 230–239 (1984). [CrossRef]
  14. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969). [CrossRef]
  15. Z. Q. Lu, “Multidimensional structure diffraction tomography for varying object orientation through generalised scattered waves,” Inverse Probl. 1, 339–356 (1985). [CrossRef]
  16. A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336–350 (1982). [CrossRef] [PubMed]
  17. A. J. Devaney, “Inversion formula for inverse scattering within the Born approximation,” Opt. Lett. 7, 111–112 (1982). [CrossRef] [PubMed]
  18. A. J. Devaney, “Diffraction tomography,” in Inverse Methods in Electromagnetic Imaging: Part II, W. M. Boerner, ed. (Reidel, Dordrecht, The Netherlands, 1985), pp. 1107–1135.
  19. A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).
  20. N. Sponheim, I. Johansen, “Experimental results in ultrasonic tomography using a filtered backpropagation algorithm,” Ultrason. Imaging 13, 56–70 (1991). [CrossRef] [PubMed]
  21. N. Sponheim, L. J. Gelius, I. Johansen, J. J. Stamnes, “Quantitative results in ultrasonic tomography of large objects using line sources and curved detector arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 370–379 (1991). [CrossRef] [PubMed]
  22. A. J. Devaney, G. Beylkin, “Diffraction tomography using arbitrary transmitter and receiver surfaces,” Ultrason. Imaging 6, 181–193 (1984). [CrossRef] [PubMed]
  23. M. A. Anastasio, X. Pan, “An improved reconstruction algorithm for 3-D diffraction tomography using spherical wave sources,” IEEE Trans. Biomed. Eng. 50, 517–521 (2003). [CrossRef] [PubMed]
  24. X. Pan, M. A. Anastasio, “Minimal-scan filtered backpropagation algorithms for diffraction tomography,” J. Opt. Soc. Am. A 16, 2896–2903 (1999). [CrossRef]
  25. M. A. Anastasio, X. Pan, “A new reconstruction approach for reflection mode diffraction tomography,” IEEE Trans. Image Process. 9, 1262–1271 (2000). [CrossRef]
  26. T. J. Cui, W. C. Chew, “Diffraction tomographic algorithm for the detection of three-dimensional objects buried in lossy half-space,” IEEE Trans. Antennas Propag. 50, 42–49 (2002). [CrossRef]
  27. R. D. March, T. K. K. Chan, “Improving microwave imaging by enhancing diffraction tomography,” IEEE Trans. Microwave Theory Tech. 44, 379–388 (1996). [CrossRef]
  28. S. Pourjavid, O. Tretiak, “Ultrasound imaging through time-domain diffraction tomography,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 38, 74–85 (1991). [CrossRef] [PubMed]
  29. T. Melamed, Y. Ehrlich, E. Heyman, “Short-pulse inversion of inhomogeneous media: a time-domain diffraction tomography,” Inverse Probl. 12, 977–993 (1996). [CrossRef]
  30. M. A. Anastasio, X. Pan, “Computationally efficient and statistically robust image reconstruction in three-dimensional diffraction tomography,” J. Opt. Soc. Am. A 17, 391–400 (2000). [CrossRef]
  31. O. R. Halse, J. J. Stamnes, A. J. Devaney, “Three-dimensional diffraction tomography by two-dimensional sectioning,” Opt. Commun. 224, 185–195 (2003). [CrossRef]
  32. D. T. Borup, O. P. Gandhi, “Fast-Fourier-transform method for calculation of SAR distributions in finely discretized inhomogeneous models of biological bodies,” IEEE Trans. Microwave Theory Tech. 32, 355–360 (1984). [CrossRef]
  33. A. Dutt, V. Rokhlin, “Fast Fourier transforms for nonequispaced data,” SIAM J. Sci. Comput. (USA) 14, 1368–1393 (1993). [CrossRef]
  34. S. Y. Semenov, R. H. Svenson, A. E. Boulyshev, A. E. Souvorov, V. Y. Borisov, Y. Sizor, A. N. Starostin, K. R. Dezern, G. P. Tatsis, V. Y. Baranov, “Microwave tomography: two-dimensional system for biological imaging,” IEEE Trans. Biomed. Eng. 43, 869–877 (1996). [CrossRef] [PubMed]
  35. A. Franchois, A. Joisel, C. Pichot, J. C. Bolomey, “Quantitative microwave imaging with a 2.45-GHz planar microwave camera,” IEEE Trans. Med. Imaging 17, 550–561 (1998). [CrossRef] [PubMed]

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