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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 12 — Dec. 1, 1999
  • pp: 2887–2895

Linear and quadratic inverse scattering for angularly varying circular cylinders

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

JOSA A, Vol. 16, Issue 12, pp. 2887-2895 (1999)

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We discuss the problem of determining the class of dielectric profile functions that can be reconstructed from scattered electrical field data depending on the model to be inverted. We focus our attention on a cylindrical object with a circular cross section whose permittivity varies only along the angular coordinate. First we examine the linear Born approximation of the relationship between the permittivity function and the field scattered by the cylinder. We provide an analytical answer to this problem by singular-value decomposition of the relevant operator. We find that only slowly varying profiles can be recovered, both in the single-view and in the multiview case. Next we examine a quadratic approximation of the same relationship, which consists in adding a second-order term to the linear term. The effect of changing the model on the class of unknown functions that can be reconstructed is shown by means of both analytical arguments and numerical simulations. The result is that now the model includes more rapidly varying profiles.

© 1999 Optical Society of America

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

Original Manuscript: February 1, 1999
Revised Manuscript: June 18, 1999
Manuscript Accepted: June 18, 1999
Published: December 1, 1999

Giovanni Leone, Adriana Brancaccio, and Rocco Pierri, "Linear and quadratic inverse scattering for angularly varying circular cylinders," J. Opt. Soc. Am. A 16, 2887-2895 (1999)

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