OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 1 — Jan. 1, 2004
  • pp: 35–45

One-dimensional inverse scattering with a Born model in a three-layered medium

Raffaele Persico and Francesco Soldovieri  »View Author Affiliations

JOSA A, Vol. 21, Issue 1, pp. 35-45 (2004)

View Full Text Article

Acrobat PDF (384 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We deal with the inverse-scattering problem for a dielectric slab embedded in a three-layered medium starting from multifrequency scattered field data under the framework of the Born approximation. This allows us to state the problem as a linear inverse one, and the singular-value decomposition (SVD) of the relevant operator makes it possible to investigate and to solve it. In particular, the SVD tool allows an analysis of the reconstruction capabilities of the algorithm in terms of spatial variability of the unknowns that can be retrieved. The new contribution consists in an analysis of the role of the discontinuity of the dielectric properties between the second and the third medium. This analysis is performed with regard both to the class of retrievable dielectric profiles and to the model error deriving from the Born approximation and shows, finally, that this discontinuity can be troublesome.

© 2004 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems

Raffaele Persico and Francesco Soldovieri, "One-dimensional inverse scattering with a Born model in a three-layered medium," J. Opt. Soc. Am. A 21, 35-45 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. J. Daniels, Surface Penetrating Radar (Institution of Electrical Engineers, London, 1996).
  2. E. Nyfors, “Industrial microwave sensors,” Subsurface Sens. Technol. Appl. 1, 23–43 (2000).
  3. D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory (Springer-Verlag, Berlin, 1992).
  4. A. N. Tichonov and V. Y. Arsenine, Solution of Ill-Posed Problems (Winston, Washington, D.C., 1977).
  5. R. Persico, F. Soldovieri, and R. Pierri, “On the convergence properties of a quadratic approach to the inverse scattering problem,” J. Opt. Soc. Am. A 19, 2424–2428 (2002).
  6. W. C. Chew, Waves and Fields in Inhomogeneous Media (IEEE Press, Piscataway, N.J., 1995).
  7. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics, Bristol, UK, 1998).
  8. J. Xia, A. K. Jordan, and J. A. Kong, “Electromagnetic inverse-scattering theory for inhomogeneous dielectrics: the local reflection model,” J. Opt. Soc. Am. A 11, 1081–1086 (1994).
  9. D. B. Ge, “An iterative technique in one dimensional profile inversion,” Inverse Probl. 3, 399–406 (1987).
  10. T. Uno and S. Adachi, “Inverse scattering method for one dimensional inhomogeneous layered media,” IEEE Trans. Antennas Propag. AP-35, 1456–1466 (1987).
  11. I. Akudman and M. Idemen, “On the use of Gaussian beams in one-dimensional profile inversion connected with lossy dielectric slabs,” Inverse Probl. 11, 315–328 (1995).
  12. C. J. Trantanella, D. G. Dudley, and K. A. Nabulsi, “Beyond the Born approximation in one-dimensional profile reconstruction,” J. Opt. Soc. Am. A 12, 1469–1478 (1995).
  13. A. G. Tijhuis, “Born-type reconstruction of material parameters in an inhomogeneous lossy dielectric slab from reflected-field data,” Wave Motion 11, 151–173 (1989).
  14. G. Leone, R. Persico, and R. Pierri, “Inverse scattering under the distorted Born approximation for cylindrical geometries,” J. Opt. Soc. Am. A 16, 1779–1787 (1999); “Errata,” J. Opt. Soc. Am. A 16, 2310 (1999).
  15. R. Pierri, R. Persico, and R. Bernini, “Information content of the Born field scattered by an embedded slab: multifrequency, multiview, and multifrequency–multiview approach,” J. Opt. Soc. Am. A 16, 2392–2399 (1999).
  16. R. Pierri, G. Leone, R. Persico, and F. Soldovieri, “Electromagnetic inversion for subsurface applications under the distorted Born approximation,” Nuovo Cimento 24, 245–261 (2001).
  17. A. Brancaccio, G. Leone, and R. Pierri, “Information content of Born scattered fields: results in the circular cylindrical case,” J. Opt. Soc. Am. A 15, 1909–1917 (1998).
  18. R. Pierri, A. Brancaccio, G. Leone, and F. Soldovieri, “Electromagnetic prospection via homogeneous and inhomogeneous plane waves: the case of an embedded slab,” AEU Int. J. Electron. Commun. 56, 11–18 (2002).
  19. M. Bertero, “Linear inverse and ill-posed problems,” in Advances in Electronics and Electronic Physics (Academic, New York, 1990), pp. 1–120.
  20. M. Slaney, A. C. Kak, and L. E. Larsen, “Limitations of imaging with first order diffraction tomography,” IEEE Trans. Microwave Theory Tech. MTT-32, 860–874 (1984).
  21. R. W. Deming and A. J. Devaney, “Diffraction tomography for multi-monostatic ground penetrating radar imaging,” Inverse Probl. 13, 29–45 (1997).
  22. O. S. Haddadin and E. S. Ebbini, “Imaging strongly scattering media using a multiple frequency distorted Born iterative method,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 1485–1496 (1998).
  23. A. Brancaccio, V. Pascazio, and R. Pierri, “A quadratic model for inverse profiling: the one-dimensional case,” J. Electromagn. Waves Appl. 9, 673–696 (1995).
  24. O. M. Bucci, L. Crocco, T. Isernia, and V. Pascazio, “Inverse scattering problems with multifrequency data: reconstruction capabilities and solution strategies,” IEEE Trans. Geosci. Remote Sens. 38, 1749–1756 (2000).
  25. A complex contrast function also accounts for possible losses in the investigation domain. This entails that the contrast function also depend on the work frequency. However, in the present analysis we consider this dependence negligible.
  26. D. Slepian and H. O. Pollak, “Prolate spheroidal wave functions, Fourier analysis and uncertainty,” Bell Syst. Tech. J. 40, 43–64 (1961).
  27. S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Dover, New York, 1996).
  28. G. D. de Villiers, B. McNally, and E. R. Pike, “Positive solutions to linear inverse problems,” Inverse Probl. 15, 615–635 (1999).
  29. A. G. Tijhuis, Electromagnetic Inverse Profiling: Theory and Numerical Implementation (VNU Science, Utrecht, The Netherlands, 1987).
  30. L. V. Kantorovic and G. P. Akilov, Functional Analysis (Pergamon, Oxford, UK, 1982).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited