## 2 Materials and Methods
### Experimental Setup
The Stepped Frequency Continuous Wave (SFCW) radar approach was used for data collection, and only transmission measurements were done (therefore, for each couple of antennas, only the S21 coefficient was measured). In the SFCW approach, each antenna-target-antenna combination is considered as a linear transfer function, with its behavior defined by means of its measured scattering matrix. The complete information on the target is derived by the amplitude and the phase of such transfer function between two antennas, and this information is used as input in the image reconstruction process, after the calibration procedure. The synthetic array of 24 elements in 28 positions was achieved by linearly shifting the two antennas along a predetermined line with a phase center shift among adjacent radiators of 5 mm (i.e., half wavelength in air at 30 GHz), except for the physically adjacent antennas, for which the flange limited the spacing at 25 mm. The final width of the synthetic aperture was equal to 135 mm. A MATLAB (The MathWorks, Natick, MA, USA) routine was used to coordinate both the signal acquisition and the antenna movement. The acquisition of each row of the scattering matrix was achieved as follows. Assume that at the beginning of the acquisition the transmitting antenna (#1) is in x_#1 = 0 mm, while the receiving antenna (#2) is in x_#2 = 25 mm. After the acquisition of the transmission parameter corresponding to this position, keeping the position of #1 fixed, #2 is shifted by 5 mm; therefore, we have x_#1 = 0 mm and x_#2 = 30 mm. This procedure is repeated until #2 reaches x_#2 = 135 mm. At this point, #1 (and consequently also #2) is shifted by 5 mm. So, for the acquisition of the whole second row of the scattering matrix we have x_#1 = 5 mm. Antenna #2, instead, is moved in linear steps of 5 mm from the initial position x_#2 = 30 mm to x_#2 = 135 mm. This procedure is repeated until antenna #1 reaches x_#1 = 110 mm. Each time, only the transmission parameters (S21) were measured, and owing to the symmetry of the scattering matrix (reciprocal property of a passive network), it was not necessary to acquire each symmetrical transmission parameter, halving the acquisition time. The antenna positions at each step are shown in Figure 3. Due to the physical dimension of the antenna support (flanges and other fixtures), the final synthetic array is not fully sampled, which turns out into several zeros in the complete scattering matrix. The relative transmit/receive apodization matrix is drawn in Figure 4; in this matrix, we indicated with 1 the cells that correspond to an active combination of transmit/receive antenna position, while 0 indicates that the transmit/receive event has not occurred (as an example, the element in Figure 4 cell (1,1) corresponds to x_#1 = 0 mm and x_#2 = 25 mm). The time  
Figure 2: Sketch of the measurement scenario with the phantom, where \(d_{target}\) is the depth of the inclusion within the phantom, \(d_{interface}\) is the distance of the phantom from the array, and \(x_{disp}\) is the lateral displacement of the target with respect to the center of the array. required by the antennas to cover the full active aperture and record all the data was about one hour per scan.