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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 8 — Aug. 1, 2001
  • pp: 1832–1843

Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems

Ovidio M. Bucci, Nicola Cardace, Lorenzo Crocco, and Tommaso Isernia  »View Author Affiliations

JOSA A, Vol. 18, Issue 8, pp. 1832-1843 (2001)

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Within the framework of inverse scattering problems, the quantifying of the degree of nonlinearity of the problem at hand provides an interesting possibility for evaluating the validity range of the Born series and for quantifying the difficulty of both forward and inverse problems. With reference to the two-dimensional scalar problem, new tools are proposed that allow the determination of the degree of nonlinearity in scattering problems when the maximum value, dimensions, and spatial-frequency content of the unknown permittivity are changed at the same time. As such, the proposed tools make it possible to identify useful guidelines for the solution of both forward and inverse problems and suggest an effective solution procedure for the latter. Numerical examples are reported to confirm the usefulness of the tools introduced and of the procedure proposed.

© 2001 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(100.6950) Image processing : Tomographic image processing
(290.3200) Scattering : Inverse scattering

Ovidio M. Bucci, Nicola Cardace, Lorenzo Crocco, and Tommaso Isernia, "Degree of nonlinearity and a new solution procedure in scalar two-dimensional inverse scattering problems," J. Opt. Soc. Am. A 18, 1832-1843 (2001)

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  1. J. B. Keller, “Accuracy and validity of the Born and Rytov approximations,” J. Opt. Soc. Am. 59, 1003–1004 (1969).
  2. M. Slaney, A. Kak, and L. E. Larsen, “Limitations of imaging with first-order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
  3. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Theory, (Springer-Verlag, Berlin, 1992).
  4. R. E. Kleinman and P. M. Van den Berg, “An extended modified gradient technique for profile inversion,” Radio Sci. 28, 877–884 (1993).
  5. T. Isernia, V. Pascazio, and R. Pierri, “A non-linear estimation method in tomographic imaging,” IEEE Trans. Geosci. Remote Sens. 35, 910–923 (1997).
  6. R. Pierri and A. Brancaccio, “Imaging of a rotationally symmetric dielectric cylinder by a quadratic approach,” J. Opt. Soc. Am. A 14, 2777–2785 (1997).
  7. W. C. Chew and Y. M. Wang, “Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method,” IEEE Trans. Med. Imaging 9, 218–225 (1990).
  8. T. M. Habashy, R. W. Groom, and B. P. Spies, “Beyond the Born and Rytov approximations: a non-linear approach to electromagnetic scattering,” J. Geophys. Res. 98 (B2), 1759–1776 (1993).
  9. W. C. Chew, Waves and Fields in Inhomogenous Media, (IEEE Computer Society, Los Alamitos, Calif., 1995).
  10. A. Kolmogorov and S. V. Fomine, Eléments de la théorie des fonctions et de l’analyse fonctionelle (MIR Editions, Moscow, 1973).
  11. R. E. Kleinman, G. F. Roach, and P. M. Van den Berg, “Convergent Born series for large refractive indices,” J. Opt. Soc. Am. A 7, 890–897 (1990).
  12. O. M. Bucci and T. Isernia, “Electromagnetic inverse scattering: retrievable information and measurement strategies,” Radio Sci. 32, 2123–2138 (1997).
  13. A. Friedman, Partial Different Equations (Krieger, Malaba, Fla., 1976).
  14. O. M. Bucci, L. Crocco, and T. Isernia, “Improving the reconstruction capabilities in inverse scattering problems by exploiting ‘near proximity’ set-ups,” J. Opt. Soc. Am. A 16, 1788–1798 (1999).
  15. W. C. Chew and J. H. Lin, “A frequency-hopping approach for microwave imaging of large inhomogeneous bodies,” IEEE Microwave Guided Wave Lett. 5, 439–441 (1995).
  16. O. M. Bucci, L. Crocco, T. Isernia, and V. Pascazio, “Inverse scattering problems with multi-frequency data: reconstruction capabilities and solution strategies,” IEEE Trans. Geosci. Remote Sens. 38, 1749–1756 (2000).
  17. M. Bertero, “Linear inverse and ill-posed problems,” in Advances in Electronics and Electronic Physics (Academic, New York, 1989), pp. 1–120.
  18. T. C. Wedberg and J. J. Stamnes, “Experimental examination of the quantitative imaging properties of optical diffraction tomography,” J. Opt. Soc. Am. A 12, 493–500 (1995).
  19. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, A. Jeffrey, ed. (Academic, London, 1997).
  20. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).

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