## 2 Materials and Methods
### Phantoms  
According to the recipes proposed in [25; 26] by our research group, different kinds of tissue-mimicking phantoms with increasing values of dielectric losses have been produced and used for the test of the mm-wave imaging system. In particular, three phantoms based \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Simulated** & **Theoretical** & **Simulated** & **Theoretical** \\  & _Range-Resolution_ & _Range-Resolution_ & _Lateral-Resolution_ & _Lateral-Resolution_ \\ \hline _Case 1_ & 14.6 mm & 14.3 mm & 4.4 mm & 2.7 mm \\ _Case 2_ & 10 mm & 8 mm & 3.4 mm & 2.7 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Spatial Resolution Measured on the Simulated Point Spread Functions (PSFs) and Theoretical Values @ 33.25 GHz. Figure 5: Simulated Point Spread Function for (**a**) _Case 1_ and (**b**) _Case 2_. respectively on solidified oil (_Phantom1_), solidified Polysorbate 80 [26] (_Phantom2_), and oil-in-gelatin mixtures [25] (_Phantom3_) were used. The numbering of phantoms corresponds to the increasing values of dielectric properties, as well as to the logical and temporal progression of the performed tests. In Figure 6, a photo of the produced oil-in-gelatin phantom is shown. Details about the preparation of phantoms are omitted from this paper for brevity (being outside the scope of this work); however, interested researchers can find a detailed description of the recipes and procedures in [25; 26]. In [25], the study of the reproducibility of the produced phantoms was presented. On the same day of phantom preparation and imaging tests, the dielectric properties of the produced phantoms were also measured in order to avoid any alteration of results due to unwanted water evaporation. The dielectric properties were measured by means of an open-ended coaxial probe (Keysight 85070E Dielectric Probe Kit) in the frequency range [0.5-50] GHz, following the approach proposed in [25; 26] to ensure both accurate and repeatable measurements, and they were compared to [8]. The targets embedded within the phantoms were made by water and gelatin or water and agar, in order to ensure a very significant dielectric contrast with the background phantom with a very fast and easy-to-produce mixture. The values of the real and imaginary part of the relative dielectric permittivity of the mixture made by water and gelatin at 30 GHz are 23 and 24.6, respectively; while, for the mixture made by water and agar at 30 GHz, they are 26.8 and 31.9, respectively. The comparison between the dielectric properties of _low-density_ tissues (mean value \(\pm\) one standard deviation) [8] and the ones of the produced phantoms in the frequency range [18; 19; 20] GHz is provided both for the real and imaginary parts of \(\epsilon\) in Figure 7. In addition, the values for the dielectric permittivity of the three phantoms at 30 GHz are summarized in Table 2.  
Figure 6: Picture of the produced phantom (_Phantom3_) used for mm-wave imaging, in which the inclusion is visible. Figure 7: Comparison between the dielectric properties of the produced phantoms and the ones of the _Low density ex vivo_ tissues [8] in the frequency range [18; 19; 20] GHz for the (**a**) real and (**b**) imaginary part of the dielectric permittivity. As may be noted, whereas for healthy tissues we did a categorization based on fat content, for tumor tissues we did not make any categorization. This was due to the physiological fact that tumor tissues are all characterized by increased blood supply and, therefore, higher water content. Our goal in this work was to demonstrate the possibility of detecting dielectric lesions up to a few centimeters in phantom with increasing values of attenuation (from zero to about 40 dB/cm). For these reasons, as well as because of the large variability of the tissues' dielectric properties, we produced simple mixtures composed only of water and gelatin to realize the dielectric inclusion, without focusing on the exact reproduction of the average dielectric properties of tumor tissues.