We consider a radial transverse resonance model for a circular cylindrical waveguide composed into two layers with different frequency dependent complex dielectric constants. An inverse problem with four unknowns - three physical material parameters and one dimensional dielectric layer thickness parameter - is solved by employing TE110 and TE210 modes with different radial field distribution. First the resonance frequencies and quality factors are found fitting a Lorentzian function to the ‘measured’ data, using the method of least squares. Then found resonance frequencies and quality factors are used in a second inverse Newton-Raphson algorithm which solves four transverse resonance equations in order to get four unknown parameters. The use of TE110 and TE210 models offers one-dimensional radial tomographic capability. An open ended coaxial waveguide quarter-wave resonator is added to the sensor topology, and the effect on the convergence of numerical method is investigated.

中文翻译：

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圆柱波导截面中环形双层介质的重建

我们考虑一个圆柱状波导的径向横向共振模型，该模型由具有不同频率相关复数介电常数的两层组成。通过采用具有不同径向场分布的TE110和TE210模式，可以解决具有四个未知数（三个物理材料参数和一维介电层厚度参数）的反问题。首先，使用最小二乘法，找到使洛伦兹函数适合“测量”数据的共振频率和品质因数。然后将发现的共振频率和品质因数用于第二个牛顿-拉夫森逆算法，该算法求解四个横向共振方程，以获得四个未知参数。TE110和TE210模型的使用可提供一维径向层析成像功能。