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Advantages of a multi-frequency experiment for determining the dielectric constant of a layer in a rectangular waveguide and free space
Lomonosov Moscow State University, Russia.
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.ORCID iD: 0000-0002-2691-2820
Lomonosov Moscow State University, Russia.
2021 (English)In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 56, no 3, article id e2020RS007115Article in journal (Refereed) Published
Abstract [en]

An inverse problem of reconstructing real permittivity of a plane‐parallel layer in a perfectly conducting rectangular waveguide or in free space from experimental data using an explicit expression for the scattering matrix is considered. In general, this problem is improperly posed and may be unsolvable due to inaccuracy of the experimental data, and for a perfect noiseless experiment the solution may be not unique because the scattering coefficients curve has self‐intersection points. It is shown that the traditional multi‐frequency method of measurements applied in vector network analyzers can be justified. The following facts are rigorously proved in the paper: nonuniqueness of the solution can be removed if the frequency resolution is sufficiently small; and an algorithm for processing measurement results using least squares provides an approximate solution to the problem that converges to the exact one when the quality of the experiment improves, the convergence rate depends on the number of frequencies used in the experiment.

Place, publisher, year, edition, pages
American Geophysical Union (AGU), 2021. Vol. 56, no 3, article id e2020RS007115
Keywords [en]
Inverse problem, permittivity, plane‐parallel layer, waveguide, multi‐frequency method, experimental data, numerical solution
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-35439DOI: 10.1029/2020RS007115ISI: 000636267100001Scopus ID: 2-s2.0-85103314611OAI: oai:DiVA.org:hig-35439DiVA, id: diva2:1537582
Available from: 2021-03-16 Created: 2021-03-16 Last updated: 2021-04-29Bibliographically approved

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Shestopalov, Yury

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Citation style
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