# On the Use of Focused Incident Near-Field Beams in Microwave Imaging
## NF Beams and Results
### Interrogation of Objects by the NF Plate
#### 3.1.3 Separation Resolution Study  
We now study the effect of using a focused incident NF distribution on the achievable separation resolution for one test case under the same two configurations described above. This case study for Configuration I is shown in Figure 9. As can be seen, there are two dielectric objects (the two dark green dielectric boxes in Figure 9) that have been placed approximately \(0.13\lambda\) apart from each other in front of the NF plate. These two dielectric objects have the same relative permittivity of 1.50 and the same size of \(\lambda/20\times\lambda/10\times\lambda/10\) in the \(x\)-, \(y\)-, and \(z\)-directions with the distance between their closest facet to the NF plate being about \(\lambda/60\).  
To perform this study, we assume that the NF plate moves along the \(y\)-direction to scan the two objects in the following three steps. Initially, its main beam is directly toward the first dielectric object, then the main beam is moved directly toward the gap between the two objects, and finally its main beam will be directly toward the second object. Similar to the previous section, this will constitute our Configuration I; for configuration II, we assume the same procedure but without the NF plate. In each of these three steps, the scattered NF data are collected on the receivers' line residing on the yellow plane. For each of these steps, we have a set of distinct receivers which are mainly within the main beam of the NF plate. (The details of these steps and our simulation details are described in Appendix B.)  
We now discuss the obtained scattered NF data from this simulation study which have been depicted in Figure 10a,b. As can be seen from Figure 10a, the gap between the two dielectric boxes is detectable directly from the scattered NF data when the focused incident NF distribution is utilized. However, this is not the case when the NF plate is removed in Configuration II; this can be seen from Figure 10b. As can be seen in Figure 10a,b, the magnitude of the scattered NF data at the center of the figure, which is associated with the gap between the two dielectric objects, is _minimum_ for Configuration I and _maximum_ for Configuration II. Based on the concept of contrast sources that was explained earlier in Section 2.1, this can be explained as follows. In Configuration I, when the NF plate directly illuminates the gap, it will not induce significant contrast sources in the two dielectric objects. Therefore, the resulting scattered signal will be small. On the other hand, when the gap is illuminated in the absence of the NF plate (i.e., Configuration II), more contrast sources will be induced in the two dielectric objects due to the wider illuminating beam. Due to the symmetry of the objects, the induced contrast sources in the two objects will be in-phase. Therefore, the resulting two contrast sources can be thought as a two-element in-phase antenna array that subsequently generates a radiation peak toward its broadside (\(-\hat{z}\) direction in Figure 10). This, therefore, justifies why the maximum of the scattered NF data in Configuration II occurs at the center of the Figure 10b. (The central receiver corresponds to the broadside direction.)  
\begin{table}
\begin{tabular}{l c c c} \hline \hline
**Cases** & **Calibration Object’s Permittivity** & **Configuration I (Focused)** & **Configuration II (Non-Focused)** \\ \hline Case I & 1.20 & \(1.90-j0.29\) & \(1.74-j0.04\) \\ Case II & 1.20 & \(1.89-j0.32\) & \(1.58-j0.25\) \\ \hline Case I & 1.50 & \(1.65-j0.03\) & \(1.71-j0.01\) \\ Case II & 1.50 & \(1.66-j0.01\) & \(1.57-j0.23\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The reconstructed OI’s permittivity for Cases I and II under the two configurations.