## 4 Results and Discussion
In these two cases both the target dimension and composition are the same, as well as the target depth, which is almost 1.5 cm in both configurations. However, by comparing the resulting images, a bigger target can be seen in Figure 12 than in Figure 10. This result agrees with the theoretical expectation, because the signal attenuation in _Phantom3_ is higher than the one in _Phantom2_; therefore, the effective array dimension in the case with highest dielectric losses is smaller, proving a worse resolution. Concerning the diameter (8 mm) used for the water-gelatin inclusion, it should also be pointed out that this choice was determined by the fabrication procedure. Indeed, while offering great benefits such as low cost, safety, and ease of handling, out phantoms can only be modeled at high temperatures (before the solidification process takes place), and when the target mixture is injected in the background material [35] its high temperature causes a minimal melting of the background surrounding the inclusion. For this reason, in this work it was not possible to use cylinders with smaller diameters, although one of our next goals is to further modify the phantom fabrication procedure to overcome this limitation. Targets with a smaller diameter (2 mm) were in any case used for simulation analyses of the Point Spread Function presented in Section 2.3. The distance between the radiator line and the phantom never exceeded a few cm; therefore, the phantom is in the near-field region of the antennas. Because of this proximity, the propagating electromagnetic wave is a spherical wave. This choice was based on the following considerations: on the one hand, in the final application the breast is expected to be in the vicinity of the antenna array (thus reasonably in the near-field region); on the other hand, moving the phantom farther from the antennas would have required a larger sample (along the lateral direction) due to the Half Power BeamWidth, becoming no longer compatible with the size of the standard phantom molds available in our laboratory. Finally, let us clarify the aspects related to the resolution of microwave and mm-wave systems for imaging of highly adipose tissues. Let us suppose, for example, a simple case, i.e., a linear array of 14 cm size (please note that this is a fixed value that cannot be rescaled with frequency, it is imposed by the geometrical considerations about breasts) with a target placed 4 cm away from the center of the array surrounded by fat tissue, with very low dielectric permittivity values, which are constant for all the frequencies of interest (\(\epsilon^{\prime}=3\), \(\epsilon^{\prime\prime}=0.3\)). This last assumption can be approximately correct only when low water content tissues, such as fatty ones, are considered. Let us also suppose that between the fat tissue and the antenna array there is neither a matching layer nor an air layer, so 4 cm are entirely within fat. Under these hypotheses, we can make a comparison between the expected theoretical resolutions achievable by common microwave systems and our own. If we consider, for example, two possible central working frequencies for a microwave imaging system of 5 GHz and 10 GHz, with bandwidths of 3 GHz and 6 GHz, respectively, the achievable range/lateral resolutions (computed by means of the formulas proposed in [31; 33]) are 2.88 cm/9.89 mm and 1.44 cm/4.94 mm, respectively. In our system, the central working frequency is 29 GHz with a 22 GHz band, so the expected theoretical range and lateral resolutions are 3.9 mm and 1.7 mm, respectively. Therefore, an improvement in terms of theoretical resolutions obtained when using higher frequencies in particularly fatty tissues is evident, which could allow an earlier diagnosis. On the other hand, the main limitation of mm-waves in the biomedical field is the reduced penetration depth of the signal into tissues, due to the high values of attenuation during propagation.