## 3 Results  
### Free-Space Calibration  
The two horn antennas (AH Systems 248 SAS-571 Double Ridge Horn Antenna 700 MHz-18 GHz) are connected to a N9918A FieldFox handheld VNA 26.5 GHz [X] through high stable coaxial cables (Figure 4). Measurements are performed at 10 GHz, with an RF output power set to 0 dBm and intermediate frequency bandwidth IFBW set to 100 Hz. No coaxial calibration is considered. The antenna aperture is set at a distance L = 24.4 mm from the metallic base for the reasons discussed in Section 2. The reference calibration plane is set to 24.05 mm (take into account the thickness of the material under investigation, i.e., 0.35 mm). Prior to the measurements, free-space calibration considers 11 distance separations \(\Delta r\) between the antenna aperture and a metallic plate (electrical standard with \(S_{11}=-1\)) and  
Figure 4: (**a**) A front and (**b**) an isometric view of the R2R pilot line with the free space antenna system integrated. Figure 3: (**a**) CAD representation of the free-space quality module. (**b**) CAD representation of the dedicated module in position Control Point #2 of the R2R pilot line. the nominal position (L = 24 mm) are considered in this study (three for calibration and others for validation). The distance is changed by positioning calibrated metallic plates with thickness 1.5 mm on the metallic base. Each measurement is repeated two times to check the measurement reproducibility. To that end, the metallic plates are removed and repositioned between two consecutive measurements. The measurement raw data are given in the Figure 5.  
The plot shows that the \(S_{11}\) signal, i.e., measurement of interest, is mixed with complex error terms. The calibration procedure consists in the determination of the complex error terms \(\Gamma_{1}\), \(\Gamma_{2}\) and \(T_{1}T_{2}\) by applying the modified SOL algorithm described in Section 2. As mentioned, the calibration standards considered lossless (\(|S_{11}|=1\)) are summarized in Table 2.  
From the calibration procedure, the complex error terms are determined (Table 3). From the calibration data, the modelling of the complex reflection coefficient is established according to the model (3). The comparison between measurement and modelling is given in Figure 6a. From these data associated to the analytical inversion of the model (3), the calibrated complex reflection \(S_{11}\) of the reference devices (metallic plates with different stand-off) in the measurement reference plane can be retrieved. The results are depicted in Figure 6b. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Standard** & \(\Delta\tau\) **(mm)** & \(|S_{11}^{E}|\) **[Lin]** & **Phase (\(S_{11}^{E}\)) **[deg]** & \(|S_{11}|\) **[Lin]** & **Phase (\(S_{11}\)) **[deg]** \\ \hline CAL 1 & \(-\)0.35 & 0.2365 & 63.13 & 1 & \(-\)8 \\ CAL2 & 1.15 & 0.2206 & 34.18 & 1 & 28 \\ CAL3 & 4.15 & 0.4017 & 35.67 & 1 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Free-space electrical standards used for calibration—f = 10 GHz. Figure 5: Measured empty free-space complex reflection coefficient \(S_{11}^{E}\) as a function of the stand-off distance \(\Delta_{r}\) from the reference plane (L\({}_{\tau}\) = 24.04 mm)—f = 10 GHz (+ amplitude\(|S_{11}^{E}|\) and \(\square\) Phase of \(S_{11}^{E}\)). From these data, the amplitude of the amplitude of the complex reflection coefficient is nearly unity in the proximity of the measurement reference plane. Therefore, the validity of the calibration concerns only material with low thickness in the vicinity of the reference plane. After calibration, the phase-shift exhibits a linear behavior as expected. In the same manner, as a lossless model is considered in this study, deviation from the theoretical phase occurs when the measurement is taken far from the reference plane.