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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
Radio Science ( IF 1.6 ) Pub Date : 2021-01-25 , DOI: 10.1029/2020rs007115
E. A. Sheina 1 , Y. V. Shestopalov 2 , A. P. Smirnov 1
Affiliation  

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.

中文翻译:

用于确定矩形波导和自由空间中的层介电常数的多频实验的优势

考虑了使用散射矩阵的显式表达式从实验数据重建完美导电的矩形波导或自由空间中的平面平行层的实际介电常数的反问题。通常,此问题是不适当的,并且由于实验数据的不准确而可能无法解决,对于完美的无噪声实验,由于散射系数曲线具有自相交点,因此该解决方案可能不是唯一的。结果表明,在矢量网络分析仪中采用传统的多频测量方法是合理的。本文严格证明了以下事实:如果频率分辨率足够小,则可以消除解决方案的非唯一性;
更新日期:2021-03-25
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