Abstract

In this analysis some limitations of the linear Born approximation in the diffraction tomography problem from far-zone data are pointed out. The analysis is performed by means of singular-value decomposition of the scattering operator in the scalar two-dimensional case of a circular dielectric cylinder illuminated by a TM-polarized plane wave. It is shown that the validity of the Born approximation entails the important condition that the scattering object not present too-fast spatial variations of the permittivity profile. For the rotationally symmetric cylinder, evidence is presented that the imaginary part of the normalized scattered far field has no information content for real permittivity objects. Moreover, for angularly varying cylinders the information content of the scattered far field for a single view is approximately the same as in the multiview case. Examples of singular-value and singular-function behavior and of profile reconstruction are depicted for the considered geometries.

© 1998 Optical Society of America

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  1. D. Colton, R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1992).
  2. A. J. Devaney, “Diffraction tomographic reconstruction from intensity data,” IEEE Trans. Image Process. 1, 221–228 (1992).
    [CrossRef] [PubMed]
  3. M. H. Maleki, A. J. Devaney, A. Shatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
    [CrossRef]
  4. M. H. Maleki, A. J. Devaney, “Noniterative reconstruction of complex-valued objects from two intensity measurements,” Opt. Eng. 33, 3243–3253 (1994).
    [CrossRef]
  5. T. C. Wedberg, W. C. Wedberg, “Tomographic reconstruction of the cross sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsccopy 177, 53–67 (1995).
    [CrossRef]
  6. T. C. Wedberg, J. J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995).
    [CrossRef]
  7. W. Tabbara, B. Duchene, C. Pichot, D. Lesselier, L. Chommeloux, N. Joachimovicz, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
    [CrossRef]
  8. L. Monch, “A Newton method for solving the inverse scattering problem for a sound-hard obstacle,” Inverse Probl. 12, 309–323 (1996).
    [CrossRef]
  9. C. Lu, J. Lin, W. Chew, G. Otto, “Image reconstruction with acoustic measurement using distorted Born iteration method,” Ultrason. Imaging 18, 140–156 (1996).
    [CrossRef] [PubMed]
  10. I. Akduman, “An inverse scattering problem related to buried cylindrical bodies illuminated by gaussian beams,” Inverse Probl. 10, 213–226 (1994).
    [CrossRef]
  11. S. Gutman, M. Klibanov, “Iterative method for multi-dimensional inverse scattering problems at fixed frequencies,” Inverse Probl. 10, 573–599 (1994).
    [CrossRef]
  12. N. Joachimowitz, C. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 39, 1742–1752 (1991).
    [CrossRef]
  13. M. Moghaddam, W. C. Chew, “Study of some practical issues in inversion with the Born iterative method using time-domain data,” IEEE Trans. Antennas Propag. 41, 177–184 (1993).
    [CrossRef]
  14. N. G. Gencer, M. Kuzouglu, Y. Z. Ider, “Electrical impedance tomography using induced currents,” IEEE Trans. Med. Imaging 13, 338–350 (1994).
    [CrossRef] [PubMed]
  15. C. Torres-Verdin, T. M. Habashy, “A two-step linear inversion of two-dimensional electrical conductivity,” IEEE Trans. Antennas Propag. 43, 405–415 (1995).
    [CrossRef]
  16. A. Brancaccio, V. Pascazio, R. Pierri, “A quadratic model for inverse profiling: the one dimensional case,” J. Electromagn. Waves Appl. 9, 673–696 (1995).
    [CrossRef]
  17. R. Pierri, G. Leone, “Inverse scattering of dielectric cylinders by second order Born approximation,” IEEE Trans. Geosci. Remote Sens. (to be published).
  18. R. Pierri, A. Brancaccio, “Imaging of a rotationally symmetric cylinder by a quadratic approach,” J. Opt. Soc. Am. A 14, 2777–2785 (1997).
    [CrossRef]
  19. T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
    [CrossRef]
  20. M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
    [CrossRef]
  21. J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. AP-13, 334–341 (1965).
    [CrossRef]
  22. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
  23. R. P. Porter, A. J. Devaney, “Generalized holography and computational solutions to inverse source problems,” J. Opt. Soc. Am. 72, 1707–1713 (1982).
    [CrossRef]
  24. D. Slepian, “On bandwidth,” Proc. IEEE 64, 292–300 (1976).
    [CrossRef]
  25. H. Harada, D. J. N. Wall, T. Takenaka, M. Tanaka, “Conjugate gradient method applied to inverse scattering problem,” IEEE Trans. Antennas Propag. 43, 784–792 (1995).
    [CrossRef]
  26. M. Azimi, K. C. Kak, “Distortion in diffraction tomography caused by multiple scattering,” IEEE Trans. Med. Imaging MI-2, 176–195 (1983).
    [CrossRef]
  27. R. Pierri, A. Tamburino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997).
    [CrossRef]
  28. R. Pierri, F. Soldovieri, “On the information content of the radiated fields in near zone over bounded domains,” Inverse Probl. 14, 321–337 (1998).
    [CrossRef]

1998 (1)

R. Pierri, F. Soldovieri, “On the information content of the radiated fields in near zone over bounded domains,” Inverse Probl. 14, 321–337 (1998).
[CrossRef]

1997 (3)

R. Pierri, A. Tamburino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997).
[CrossRef]

R. Pierri, A. Brancaccio, “Imaging of a rotationally symmetric cylinder by a quadratic approach,” J. Opt. Soc. Am. A 14, 2777–2785 (1997).
[CrossRef]

T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
[CrossRef]

1996 (2)

L. Monch, “A Newton method for solving the inverse scattering problem for a sound-hard obstacle,” Inverse Probl. 12, 309–323 (1996).
[CrossRef]

C. Lu, J. Lin, W. Chew, G. Otto, “Image reconstruction with acoustic measurement using distorted Born iteration method,” Ultrason. Imaging 18, 140–156 (1996).
[CrossRef] [PubMed]

1995 (5)

T. C. Wedberg, W. C. Wedberg, “Tomographic reconstruction of the cross sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsccopy 177, 53–67 (1995).
[CrossRef]

T. C. Wedberg, J. J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995).
[CrossRef]

C. Torres-Verdin, T. M. Habashy, “A two-step linear inversion of two-dimensional electrical conductivity,” IEEE Trans. Antennas Propag. 43, 405–415 (1995).
[CrossRef]

A. Brancaccio, V. Pascazio, R. Pierri, “A quadratic model for inverse profiling: the one dimensional case,” J. Electromagn. Waves Appl. 9, 673–696 (1995).
[CrossRef]

H. Harada, D. J. N. Wall, T. Takenaka, M. Tanaka, “Conjugate gradient method applied to inverse scattering problem,” IEEE Trans. Antennas Propag. 43, 784–792 (1995).
[CrossRef]

1994 (4)

N. G. Gencer, M. Kuzouglu, Y. Z. Ider, “Electrical impedance tomography using induced currents,” IEEE Trans. Med. Imaging 13, 338–350 (1994).
[CrossRef] [PubMed]

M. H. Maleki, A. J. Devaney, “Noniterative reconstruction of complex-valued objects from two intensity measurements,” Opt. Eng. 33, 3243–3253 (1994).
[CrossRef]

I. Akduman, “An inverse scattering problem related to buried cylindrical bodies illuminated by gaussian beams,” Inverse Probl. 10, 213–226 (1994).
[CrossRef]

S. Gutman, M. Klibanov, “Iterative method for multi-dimensional inverse scattering problems at fixed frequencies,” Inverse Probl. 10, 573–599 (1994).
[CrossRef]

1993 (1)

M. Moghaddam, W. C. Chew, “Study of some practical issues in inversion with the Born iterative method using time-domain data,” IEEE Trans. Antennas Propag. 41, 177–184 (1993).
[CrossRef]

1992 (2)

A. J. Devaney, “Diffraction tomographic reconstruction from intensity data,” IEEE Trans. Image Process. 1, 221–228 (1992).
[CrossRef] [PubMed]

M. H. Maleki, A. J. Devaney, A. Shatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
[CrossRef]

1991 (1)

N. Joachimowitz, C. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 39, 1742–1752 (1991).
[CrossRef]

1988 (1)

W. Tabbara, B. Duchene, C. Pichot, D. Lesselier, L. Chommeloux, N. Joachimovicz, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

1984 (1)

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

1983 (1)

M. Azimi, K. C. Kak, “Distortion in diffraction tomography caused by multiple scattering,” IEEE Trans. Med. Imaging MI-2, 176–195 (1983).
[CrossRef]

1982 (1)

1976 (1)

D. Slepian, “On bandwidth,” Proc. IEEE 64, 292–300 (1976).
[CrossRef]

1965 (1)

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. AP-13, 334–341 (1965).
[CrossRef]

Abramowitz, M.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Akduman, I.

I. Akduman, “An inverse scattering problem related to buried cylindrical bodies illuminated by gaussian beams,” Inverse Probl. 10, 213–226 (1994).
[CrossRef]

Azimi, M.

M. Azimi, K. C. Kak, “Distortion in diffraction tomography caused by multiple scattering,” IEEE Trans. Med. Imaging MI-2, 176–195 (1983).
[CrossRef]

Brancaccio, A.

R. Pierri, A. Brancaccio, “Imaging of a rotationally symmetric cylinder by a quadratic approach,” J. Opt. Soc. Am. A 14, 2777–2785 (1997).
[CrossRef]

A. Brancaccio, V. Pascazio, R. Pierri, “A quadratic model for inverse profiling: the one dimensional case,” J. Electromagn. Waves Appl. 9, 673–696 (1995).
[CrossRef]

Chew, W.

C. Lu, J. Lin, W. Chew, G. Otto, “Image reconstruction with acoustic measurement using distorted Born iteration method,” Ultrason. Imaging 18, 140–156 (1996).
[CrossRef] [PubMed]

Chew, W. C.

M. Moghaddam, W. C. Chew, “Study of some practical issues in inversion with the Born iterative method using time-domain data,” IEEE Trans. Antennas Propag. 41, 177–184 (1993).
[CrossRef]

Chommeloux, L.

W. Tabbara, B. Duchene, C. Pichot, D. Lesselier, L. Chommeloux, N. Joachimovicz, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Colton, D.

D. Colton, R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1992).

Devaney, A. J.

M. H. Maleki, A. J. Devaney, “Noniterative reconstruction of complex-valued objects from two intensity measurements,” Opt. Eng. 33, 3243–3253 (1994).
[CrossRef]

A. J. Devaney, “Diffraction tomographic reconstruction from intensity data,” IEEE Trans. Image Process. 1, 221–228 (1992).
[CrossRef] [PubMed]

M. H. Maleki, A. J. Devaney, A. Shatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
[CrossRef]

R. P. Porter, A. J. Devaney, “Generalized holography and computational solutions to inverse source problems,” J. Opt. Soc. Am. 72, 1707–1713 (1982).
[CrossRef]

Duchene, B.

W. Tabbara, B. Duchene, C. Pichot, D. Lesselier, L. Chommeloux, N. Joachimovicz, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Gencer, N. G.

N. G. Gencer, M. Kuzouglu, Y. Z. Ider, “Electrical impedance tomography using induced currents,” IEEE Trans. Med. Imaging 13, 338–350 (1994).
[CrossRef] [PubMed]

Gutman, S.

S. Gutman, M. Klibanov, “Iterative method for multi-dimensional inverse scattering problems at fixed frequencies,” Inverse Probl. 10, 573–599 (1994).
[CrossRef]

Habashy, T. M.

C. Torres-Verdin, T. M. Habashy, “A two-step linear inversion of two-dimensional electrical conductivity,” IEEE Trans. Antennas Propag. 43, 405–415 (1995).
[CrossRef]

Harada, H.

H. Harada, D. J. N. Wall, T. Takenaka, M. Tanaka, “Conjugate gradient method applied to inverse scattering problem,” IEEE Trans. Antennas Propag. 43, 784–792 (1995).
[CrossRef]

Hugonin, J. P.

N. Joachimowitz, C. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 39, 1742–1752 (1991).
[CrossRef]

Ider, Y. Z.

N. G. Gencer, M. Kuzouglu, Y. Z. Ider, “Electrical impedance tomography using induced currents,” IEEE Trans. Med. Imaging 13, 338–350 (1994).
[CrossRef] [PubMed]

Isernia, T.

T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
[CrossRef]

Joachimovicz, N.

W. Tabbara, B. Duchene, C. Pichot, D. Lesselier, L. Chommeloux, N. Joachimovicz, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Joachimowitz, N.

N. Joachimowitz, C. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 39, 1742–1752 (1991).
[CrossRef]

Kak, A. C.

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

Kak, K. C.

M. Azimi, K. C. Kak, “Distortion in diffraction tomography caused by multiple scattering,” IEEE Trans. Med. Imaging MI-2, 176–195 (1983).
[CrossRef]

Klibanov, M.

S. Gutman, M. Klibanov, “Iterative method for multi-dimensional inverse scattering problems at fixed frequencies,” Inverse Probl. 10, 573–599 (1994).
[CrossRef]

Kress, R.

D. Colton, R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1992).

Kuzouglu, M.

N. G. Gencer, M. Kuzouglu, Y. Z. Ider, “Electrical impedance tomography using induced currents,” IEEE Trans. Med. Imaging 13, 338–350 (1994).
[CrossRef] [PubMed]

Larsen, L. E.

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

Leone, G.

R. Pierri, G. Leone, “Inverse scattering of dielectric cylinders by second order Born approximation,” IEEE Trans. Geosci. Remote Sens. (to be published).

Lesselier, D.

W. Tabbara, B. Duchene, C. Pichot, D. Lesselier, L. Chommeloux, N. Joachimovicz, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Lin, J.

C. Lu, J. Lin, W. Chew, G. Otto, “Image reconstruction with acoustic measurement using distorted Born iteration method,” Ultrason. Imaging 18, 140–156 (1996).
[CrossRef] [PubMed]

Lu, C.

C. Lu, J. Lin, W. Chew, G. Otto, “Image reconstruction with acoustic measurement using distorted Born iteration method,” Ultrason. Imaging 18, 140–156 (1996).
[CrossRef] [PubMed]

Maleki, M. H.

M. H. Maleki, A. J. Devaney, “Noniterative reconstruction of complex-valued objects from two intensity measurements,” Opt. Eng. 33, 3243–3253 (1994).
[CrossRef]

M. H. Maleki, A. J. Devaney, A. Shatzberg, “Tomographic reconstruction from optical scattered intensities,” J. Opt. Soc. Am. A 9, 1356–1363 (1992).
[CrossRef]

Moghaddam, M.

M. Moghaddam, W. C. Chew, “Study of some practical issues in inversion with the Born iterative method using time-domain data,” IEEE Trans. Antennas Propag. 41, 177–184 (1993).
[CrossRef]

Monch, L.

L. Monch, “A Newton method for solving the inverse scattering problem for a sound-hard obstacle,” Inverse Probl. 12, 309–323 (1996).
[CrossRef]

Otto, G.

C. Lu, J. Lin, W. Chew, G. Otto, “Image reconstruction with acoustic measurement using distorted Born iteration method,” Ultrason. Imaging 18, 140–156 (1996).
[CrossRef] [PubMed]

Pascazio, V.

T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
[CrossRef]

A. Brancaccio, V. Pascazio, R. Pierri, “A quadratic model for inverse profiling: the one dimensional case,” J. Electromagn. Waves Appl. 9, 673–696 (1995).
[CrossRef]

Pichot, C.

N. Joachimowitz, C. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 39, 1742–1752 (1991).
[CrossRef]

W. Tabbara, B. Duchene, C. Pichot, D. Lesselier, L. Chommeloux, N. Joachimovicz, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Pierri, R.

R. Pierri, F. Soldovieri, “On the information content of the radiated fields in near zone over bounded domains,” Inverse Probl. 14, 321–337 (1998).
[CrossRef]

R. Pierri, A. Brancaccio, “Imaging of a rotationally symmetric cylinder by a quadratic approach,” J. Opt. Soc. Am. A 14, 2777–2785 (1997).
[CrossRef]

R. Pierri, A. Tamburino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997).
[CrossRef]

T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
[CrossRef]

A. Brancaccio, V. Pascazio, R. Pierri, “A quadratic model for inverse profiling: the one dimensional case,” J. Electromagn. Waves Appl. 9, 673–696 (1995).
[CrossRef]

R. Pierri, G. Leone, “Inverse scattering of dielectric cylinders by second order Born approximation,” IEEE Trans. Geosci. Remote Sens. (to be published).

Porter, R. P.

Richmond, J. H.

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. AP-13, 334–341 (1965).
[CrossRef]

Shatzberg, A.

Slaney, M.

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

Slepian, D.

D. Slepian, “On bandwidth,” Proc. IEEE 64, 292–300 (1976).
[CrossRef]

Soldovieri, F.

R. Pierri, F. Soldovieri, “On the information content of the radiated fields in near zone over bounded domains,” Inverse Probl. 14, 321–337 (1998).
[CrossRef]

Stamnes, J. J.

Stegun, I.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

Tabbara, W.

W. Tabbara, B. Duchene, C. Pichot, D. Lesselier, L. Chommeloux, N. Joachimovicz, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

Takenaka, T.

H. Harada, D. J. N. Wall, T. Takenaka, M. Tanaka, “Conjugate gradient method applied to inverse scattering problem,” IEEE Trans. Antennas Propag. 43, 784–792 (1995).
[CrossRef]

Tamburino, A.

R. Pierri, A. Tamburino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997).
[CrossRef]

Tanaka, M.

H. Harada, D. J. N. Wall, T. Takenaka, M. Tanaka, “Conjugate gradient method applied to inverse scattering problem,” IEEE Trans. Antennas Propag. 43, 784–792 (1995).
[CrossRef]

Torres-Verdin, C.

C. Torres-Verdin, T. M. Habashy, “A two-step linear inversion of two-dimensional electrical conductivity,” IEEE Trans. Antennas Propag. 43, 405–415 (1995).
[CrossRef]

Wall, D. J. N.

H. Harada, D. J. N. Wall, T. Takenaka, M. Tanaka, “Conjugate gradient method applied to inverse scattering problem,” IEEE Trans. Antennas Propag. 43, 784–792 (1995).
[CrossRef]

Wedberg, T. C.

T. C. Wedberg, W. C. Wedberg, “Tomographic reconstruction of the cross sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsccopy 177, 53–67 (1995).
[CrossRef]

T. C. Wedberg, J. J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995).
[CrossRef]

Wedberg, W. C.

T. C. Wedberg, W. C. Wedberg, “Tomographic reconstruction of the cross sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsccopy 177, 53–67 (1995).
[CrossRef]

IEEE Trans. Antennas Propag. (5)

N. Joachimowitz, C. Pichot, J. P. Hugonin, “Inverse scattering: an iterative numerical method for electromagnetic imaging,” IEEE Trans. Antennas Propag. 39, 1742–1752 (1991).
[CrossRef]

M. Moghaddam, W. C. Chew, “Study of some practical issues in inversion with the Born iterative method using time-domain data,” IEEE Trans. Antennas Propag. 41, 177–184 (1993).
[CrossRef]

C. Torres-Verdin, T. M. Habashy, “A two-step linear inversion of two-dimensional electrical conductivity,” IEEE Trans. Antennas Propag. 43, 405–415 (1995).
[CrossRef]

J. H. Richmond, “Scattering by a dielectric cylinder of arbitrary cross section shape,” IEEE Trans. Antennas Propag. AP-13, 334–341 (1965).
[CrossRef]

H. Harada, D. J. N. Wall, T. Takenaka, M. Tanaka, “Conjugate gradient method applied to inverse scattering problem,” IEEE Trans. Antennas Propag. 43, 784–792 (1995).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

T. Isernia, V. Pascazio, R. Pierri, “A nonlinear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
[CrossRef]

IEEE Trans. Image Process. (1)

A. J. Devaney, “Diffraction tomographic reconstruction from intensity data,” IEEE Trans. Image Process. 1, 221–228 (1992).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging (2)

N. G. Gencer, M. Kuzouglu, Y. Z. Ider, “Electrical impedance tomography using induced currents,” IEEE Trans. Med. Imaging 13, 338–350 (1994).
[CrossRef] [PubMed]

M. Azimi, K. C. Kak, “Distortion in diffraction tomography caused by multiple scattering,” IEEE Trans. Med. Imaging MI-2, 176–195 (1983).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

M. Slaney, A. C. Kak, L. E. Larsen, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
[CrossRef]

Inverse Probl. (6)

W. Tabbara, B. Duchene, C. Pichot, D. Lesselier, L. Chommeloux, N. Joachimovicz, “Diffraction tomography: contribution to the analysis of some applications in microwaves and ultrasonics,” Inverse Probl. 4, 305–331 (1988).
[CrossRef]

L. Monch, “A Newton method for solving the inverse scattering problem for a sound-hard obstacle,” Inverse Probl. 12, 309–323 (1996).
[CrossRef]

I. Akduman, “An inverse scattering problem related to buried cylindrical bodies illuminated by gaussian beams,” Inverse Probl. 10, 213–226 (1994).
[CrossRef]

S. Gutman, M. Klibanov, “Iterative method for multi-dimensional inverse scattering problems at fixed frequencies,” Inverse Probl. 10, 573–599 (1994).
[CrossRef]

R. Pierri, A. Tamburino, “On the local minima problem in conductivity imaging via a quadratic approach,” Inverse Probl. 13, 1547–1568 (1997).
[CrossRef]

R. Pierri, F. Soldovieri, “On the information content of the radiated fields in near zone over bounded domains,” Inverse Probl. 14, 321–337 (1998).
[CrossRef]

J. Electromagn. Waves Appl. (1)

A. Brancaccio, V. Pascazio, R. Pierri, “A quadratic model for inverse profiling: the one dimensional case,” J. Electromagn. Waves Appl. 9, 673–696 (1995).
[CrossRef]

J. Microsccopy (1)

T. C. Wedberg, W. C. Wedberg, “Tomographic reconstruction of the cross sectional refractive index distribution in semi-transparent, birefringent fibres,” J. Microsccopy 177, 53–67 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Opt. Eng. (1)

M. H. Maleki, A. J. Devaney, “Noniterative reconstruction of complex-valued objects from two intensity measurements,” Opt. Eng. 33, 3243–3253 (1994).
[CrossRef]

Proc. IEEE (1)

D. Slepian, “On bandwidth,” Proc. IEEE 64, 292–300 (1976).
[CrossRef]

Ultrason. Imaging (1)

C. Lu, J. Lin, W. Chew, G. Otto, “Image reconstruction with acoustic measurement using distorted Born iteration method,” Ultrason. Imaging 18, 140–156 (1996).
[CrossRef] [PubMed]

Other (3)

D. Colton, R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1992).

R. Pierri, G. Leone, “Inverse scattering of dielectric cylinders by second order Born approximation,” IEEE Trans. Geosci. Remote Sens. (to be published).

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

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