## 3 Calibration Technique  
After a standard SOLT calibration procedure executed in the reference plane of the coaxial port inputs of each horn antenna, an additional homemade calibration steps performed for measurements deembedding at the front face of the sample. This step is based on scattering parameters measurement between the two horn antennas connected to the VNA, obtained from a metallic plate used as reference short circuit and placed at three different phase references (SSS) thanks to a piezoelectric sample holder, solving errors measurements made in a quadrupole configuration as in Figure 3. These error factors are attributed to multiple reflections between transmitting and receiving signals through MUT top face, as well as from non protected EM environment. As in Figure 2, \(a_{0}\) and \(b_{0}\) coefficients correspond to incident and reflected voltage wave amplitudes from transmit and receive antennas, respectively, and \(b_{1}\) and \(a_{1}\) coefficients being incident and reflected voltage wave amplitudes at a reference plane located at the top face of the MUT, respectively, as indicated in the schematic given in Figure 3.  
Figure 2: Schematic description of the experimental set-up.  
This latter helps in the definition of the relationship between effective reflection coefficient of the MUT \(\Gamma_{a}\) and raw reflection coefficient \(\Gamma_{m}\) from \(S_{21}\) coefficient measurement, through error coefficients introduction (\(e_{00}\), \(e_{01}\), \(e_{10}\) and \(e_{11}\)).  
From equivalent circuit in Figure 3, we can write that \(b_{0}\) coefficient is equal to \(e_{00}a_{0}+e_{01}a_{1}\), \(b_{1}\) is equivalent to \(e_{10}a_{0}+e_{11}a_{1}\) and that \(\Gamma_{m,a}\) are defined by \(b_{0,1}/a_{0,1}\), respectively. Then, the corrected and raw reflection coefficients \(\Gamma_{a}\) and \(\Gamma_{m}\), respectively, are expressed as in (3),  
\[\Gamma_{m}=\frac{a\Gamma_{a}+b}{c\Gamma_{a}+1} \tag{3}\]  
where \(a=(e_{10}e_{01}-e_{00}e_{11})\), \(b=e_{00}\) and \(c=-e_{11}\).  
To estimate the corrected reflection coefficient, it is necessary to determine the unknown parameters \(a\), \(b\) and \(c\), as it is reachable by testing three calibration standards at different phase reference planes delivering known \(\Gamma_{a}\).  
The first calibration standard consists of a metallic sample acting as a short circuit, placed at the reference plane. The second and third calibration standards are defined by moving this metallic sample by a distance of \(\lambda_{zm}/8\) and \(\lambda_{zm}/4\), respectively, from the reference plane, leading to their reflection coefficient expression derived from the standard transmission line theory (4):  
\[\Gamma_{a,i}=\frac{(j\tan(\beta_{zm}z)-1)}{(j\tan(\beta_{zm}z)+1)} \tag{4}\]  
With, for i = 2, \(z=\lambda_{zm}/8\) and i = 3, \(z=\lambda_{zm}/4\). The Equation (3) can be rewritten in analytic form as in (5) leading to a better definition of error coefficients \(a\), \(b\) and \(c\).  
\[\Gamma_{a,i}a+b-\Gamma_{a,i}\Gamma_{m,i}c=\Gamma_{m,i}\quad\{i=1,2,3\} \tag{5}\]  
Experimental reflection coefficient magnitude and phase values of \(\Gamma\) of a 2 cm\({}^{2}\) metallic sample, placed at the reference plane, are provided in Figure 4 in frequency, attesting calibration technique accuracy.  
Figure 3: Quadrupole representation of microwave set-up errors.