# Terahertz Frequency-Scaled Differential Imaging for Sub-6 GHz Vehicular Antenna Signature Analysis
## 2 The Imaging Process
### Formulation of the Total Image Reconstruction Process
Then, it may be considered: (i) that interactions of a high order, such as reflections among external illuminating geometry and vehicle antenna or vehicular platform, may be neglected since they are much smaller than the rest; and (ii) that the scattered fields produced by the unchanged parts, like the vehicular platform and the structure of the antenna, are approximately the same for both states of the vehicle antenna: \(\overrightarrow{E}_{ant-on}^{ext-illun}\ \cong\overrightarrow{E}_{ant-off}^{ext-illun}\oriented in the direction of the \(Tx/Rx\) antennas is because, even when the excitation of the monopole mode may be reduced, its mutual coupling with the \(Tx/Rx\) antennas is also reduced and so the multiple reflections between them may certainly be neglected and, at the same time, the surface currents on top of the vehicle due to the antenna should be visible--especially when the \(Tx/Rx\) antennas move out of the perpendicular direction. The object is placed on a radiofrequency-absorbing material located 0.5 m from the \(Tx/Rx\) antennas. The separation between the \(Tx\) antenna with a frequency converter and the \(Rx\) antenna with a frequency converter is 0.1 m, installed in a fixed position in order to avoid any perturbation in the measurement associated with coaxial cables and converter movements. The object under measurement is placed on a positioning table that is capable of moving in two axes (\(x\)-axis and \(y\)-axis) with steps of 1 mm [16]. Figure 2 displays the frequency converter with the horn antenna mounted and the positioning table with the metallic car. The S21 parameter measurements were carried out by sweeping the frequency band from 220 GHz to 330 GHz. The two-frequency converter equipment was manufactured by Rohde & Schwarz (Munich, Germany)(r), with the model being the ZVA-Z325 Frequency Converter, J-Band WR-03 [17]. Table 1 includes the VNA configuration parameters. The \(Tx\) and \(Rx\) antennas were horns produced by Flann Microwave LTD (Cornwall, United Kingdom) [18]. The selected horn model was the 32240-25, with a bandwidth (BW) from \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Start frequency & 220 GHz \\ End frequency & 330 GHz \\ Sampling points & 8192 \\ Intermediate frequency (IF) bandwidth & 1 kHz \\ Emitting power & 0 dBm \\ \hline \end{tabular}
\end{table} 
Table 1: Vector network analyzer (VNA) configuration parameters. Figure 2: Measurement setup. 217 GHz to 330 GHz. The \(E\) and \(H\) plane gain was 23.70 dBi at 217 GHz and 26.99 dBi at 330 GHz. The E and H plane beamwidth was 11.9\({}^{\circ}\) at 217 GHz and 7.8\({}^{\circ}\) at 330 GHz. The selected object is a metallic car with a 1:43 scale and 10 cm length. This is a good model for a real car, in terms of both shape and materials. The scale of the car corresponds with the frequency range between 2.5 and 3.8 GHz. A short 15 mm metal wire was placed on top of the car to act as an antenna, as shown in Figure 3. The measurement was performed with (ON state) and without the antenna (OFF state) mounted in the metallic car with the aim of estimating the induced current on the car after using the imaging system to illuminate.