Advantages of a Multi‐Frequency Experiment for Determining the Dielectric Constant of a Layer in a Rectangular Waveguide and Free Space

• Published in: Radio science 2021-03, Vol.56 (3), p.n/a
• Main Authors: Sheina, E. A., Shestopalov, Y. V., Smirnov, A. P.
• Format: Article
• Language: English
• Subjects: experimental data; Inverse problem; multi‐frequency method; numerical solution; permittivity; plane‐parallel layer; waveguide
• ISSN: 0048-6604; 1944-799X; 1944-799X
• DOI: 10.1029/2020RS007115

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. Key Points The well‐posedness of determining the inclusion parameters by single‐ and multi‐frequency experiments is verified Convergence conditions for the least squares method are established Estimates of the optimal experimental parameters are found