## 4 Results and Discussion  
The mm-wave imaging prototype was first tested in air (Figure 8) and then on different kinds of phantoms with increasing values for dielectric losses (Figures 9-12), both including perfect scattering targets and more realistic ones, as previously summarized in Section 2. Six cases will be presented in the following part of this paper. The first two tests are in air, both on a perfect scatterer (i.e., a metallic sphere, with 4 mm diameter, placed 7 cm (\(d_{interface}\) = 7 cm) far from the center of the array and 3 cm laterally (\(\,\mid\,x_{disp}\,\mid\,\) = 3 cm), (Test 1), and on a non-perfect scatterer, corresponding to a cylinder of deionized water and gelatin, with 8 mm diameter, placed 7 cm far from the center of the array in air and 0.5 cm laterally (\(d_{interface}\) = 7 cm, \(\mid\,x_{disp}\,\mid\,\) = 0.5 cm) (_Test 2_). Subsequently, a different test involving the wave propagation in an almost lossless medium at 30 GHz is done on _Plantom1_. In this case (_Test 3_), the phantom top surface is 3 cm from the antenna array axis (\(d_{interface}\) = 3 cm), and includes a cylinder made of deionized water and gelatin (diameter of 8 mm) at a depth of 1.2 cm (\(d_{target}\) = 1.2 cm). The lateral position of this target is about 1 cm (\(\,\mid\,x_{disp}\,\mid\,\) = 1 cm) with respect to the center of the array. Two further tests on tissue mimicking phantoms are then performed, this time using materials with non-zero dielectric losses, i.e., _Phantom2_. In both cases, the phantom included again a cylinder made by deionized water and gelatin or agar (diameter of 8 mm). First (_Test 4_), the _Phantom2_ is placed 5 cm (\(d_{interface}\) = 5 cm) from the antenna array, and the target inside it is at a 1.5 cm depth from the top surface (\(d_{target}\) = 1.5 cm). In the second case (_Test 5_),  
Figure 11: Reconstructed mm-wave image for _Test 5_. Figure 12: Reconstructed mm-wave image for _Test 6_. Figure 10: Reconstructed mm-wave image for _Test 4_. _Phantom2_ is 2.5 cm from the synthetic antenna array (\(d_{interface}\) = 2.5 cm) and the inclusion is placed at 3 cm depth (\(d_{target}\) = 3 cm). The last test (_Test 6_) reported in this paper is done on a phantom with high dielectric losses (_Phantom3_ in Figure 7). In this case, the 8 mm cylindrical inclusion is made of deionized water and agar. It is placed at a depth of 1.5 cm below the surface of the phantom (\(d_{target}\) = 1.5 cm), while laterally it is almost aligned to the center of the array. The phantom is placed 3.5 cm from the antennas (\(d_{interface}\) = 3.5 cm). In Table 3, a summary of the presented tests is shown. In all cases where the target is embedded into a phantom (i.e., not in air), the depth (\(Z\) axis) of the target shown in the following figures is computed considering the real propagation velocity of the signal in the phantom (which is equal to \(v=2\pi f/\beta\), where \(f\) is the frequency and \(\beta\) is the phase constant of the wave, computed by considering the dielectric properties of the phantom [34]). Therefore, calling \(d_{air}\) the equivalent distance in air of the target and \(d_{interface}\) the distance between the phantom top surface and the axis of the synthetic antenna array (cf. Figure 2), the real depth of the target within the phantom (called \(d_{target}\)) is determined as:  
\[(d_{air}-d_{interface})/c=\big{(}d_{target}\big{)}/v \tag{7}\]  
The DAS images corresponding to the six case studies explained above are shown in the following pages. In particular, Figure 8a refers to _Test 1_, Figure 8b to _Test 2_, and Figures 9-12 to _Test 3_-_Test 6_. In addition, the multiple reflections presented in the image derived from measurements on _Phantom2_ (Figures 10 and 11) are higher than those derived from measurements on _Phantom3_ (Figure 12), index of a higher air bubble presence within _Phantom2_ due to the fabrication procedure. By comparing Figures 10 and 12 another consideration could be done.