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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. 18, Iss. 3 — Mar. 1, 2001
  • pp: 600–609

Quadratic distorted approximation for the inverse scattering of dielectric cylinders

Giovanni Leone, Adriana Brancaccio, and Rocco Pierri  »View Author Affiliations


JOSA A, Vol. 18, Issue 3, pp. 600-609 (2001)
http://dx.doi.org/10.1364/JOSAA.18.000600


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Abstract

The nonlinear (quadratic) distorted approximation of the inverse scattering of dielectric cylinders is investigated, with the aim of pointing out the influence of the background medium. We refer to a canonical geometry consisting of a radially symmetric dielectric cylinder illuminated at a single frequency. We discuss how the spatial variations of those unknown dielectric profile functions that can be reconstructed by a stable inversion procedure are related to the permittivity of the background cylinder. First, results for the linear distorted approximation, obtained by means of the singular-value decomposition, are recalled and compared with the Born approximation. It turns out that the distorted model provides a smoother behavior of the singular values, and thus the inversion is more sensitive to the presence of uncertainties in the data. Furthermore, a stable inversion procedure can reconstruct only a very limited class of unknowns in correspondence with fast spatial variations related to the background permittivity and the excitation frequency. On the other hand, the quadratic model improves the approximation in the distorted case. This can be traced not only to the higher allowable level of permittivity but mainly to the fact that the model makes it possible to reconstruct different spatial features as the solution space changes. Numerical results show that the quadratic inversion performs better than the linear one for the same amount of uncertainty in the data.

© 2001 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(290.0290) Scattering : Scattering

History
Original Manuscript: May 18, 2000
Revised Manuscript: September 5, 2000
Manuscript Accepted: September 5, 2000
Published: March 1, 2001

Citation
Giovanni Leone, Adriana Brancaccio, and Rocco Pierri, "Quadratic distorted approximation for the inverse scattering of dielectric cylinders," J. Opt. Soc. Am. A 18, 600-609 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-3-600


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