## 6 Results and Discussion
### Analysis for Frequency and Permittivity (Conductivity Is Fixed)  
In the first example, the conductivity of the matching medium is taken as \(\sigma_{\mathrm{mm}}=0\). The image plot depicted in Figure 2 represents the amplitude variation of the functional \(F(f,e_{r\,\mathrm{mm}})\) as a function of the frequency and relative permittivity of the matching medium.  
Figure 2: Amplitude variation of the functional \(F(f,e_{r\,\mathrm{mm}})\) with \(\sigma_{mm}=0\).  
The frequency is varying in the range from 0.2 to 2 GHz and the relative permittivity from 1 to 50, respectively. The points in the yellow-colored regions of the image plot display the frequency and the relative permittivity pairs that correspond to the highest reflected field coefficient values, while the darker blue-colored regions of the image plot comply with \((f,\epsilon_{r\,\mathrm{mm}})\) pairs and appropriate the lowest reflected field values. As labeled on Figure 2, two pairs with values \((f,\epsilon_{r\,\mathrm{mm}})=(1.7\,\mathrm{GHz},5.9)\) from the yellow-colored region and \((f,\epsilon_{r\,\mathrm{mm}})=(0.5\,\mathrm{GHz},3.45)\) from the darker blue-colored region are arbitrarily chosen and they comply with respective highest and lowest amplitude values of the functional \(F(f,\epsilon_{r\,\mathrm{mm}})\). In order to illustrate the matching medium effect in terms of the penetrated field, two different background spaces regarding the values from Figure 2 are taken into account. Figure 3 shows graphically the amplitude changes of the total transmitted electric field versus observation angle in the innermost layer of the arm structure along a horizontal line through the origin depending on the respective matching medium parameters.  
It is evident from Figure 3 that the presence of the matching medium owning appropriate parameters from Figure 2 has increased the amplitude of the penetrating electric field in the arm structure. To be able to give a more quantitative measure for the correspondence of two curves, as how close one curve is to the other curve, one of the possibilities is the comparison of the areas under these curves. When the definite integrals of the curves shown in Figure 3 are evaluated via the trapezoid method, the ratio of the areas under the curves gives the value 13.96, which indicates that the considerable part of the energy penetrates into the arm structure. Figure 4 shows the amplitude variation of the scattered field by the internal object placed in the innermost layer of the arm model in the presence and absence of the matching medium.  
The scattered electric field \(|E_{s}|\) is calculated outside the arm model on a circle of radius 0.3 m and inside the arm model on a circle of radius 0.025 m. The amplitude changes versus observation angle are plotted in Figure 4 adapting the values of the pair \((f,\epsilon_{r\,\mathrm{mm}})=(0.5\,\mathrm{GHz},3.45)\) in the presence and \((f,\epsilon_{r\,\mathrm{mm}})=(0.5\,\mathrm{GHz},1)\) in the absence of the matching medium, both values from Figure 2. As can be seen from Figure 4, the scattered field changes differ for different background spaces. In this example, when the dielectric  
Figure 3: Comparison of the total transmitted field amplitude variations along the line \(x_{2}=0\) in the innermost layer of the model for the \((f,\epsilon_{r\,\mathrm{mm}})\) pairs.  
permittivity of the matching medium increases, the scattered field amplitude decreases and, hence, the amount of the energy penetrating into the arm structure becomes larger.