# Terahertz Frequency-Scaled Differential Imaging for Sub-6 GHz Vehicular Antenna Signature Analysis
## 4 Discussion  
The measured fields are focused on different image planes along the \(z\)-axis (\(z\) = 0.4787 m) where the capability of the system for focusing on different longitudinal distances (along the \(z\)-axis) and different frequency ranges and bandwidths, over different transversal planes (\(XY\) planes), may be observed. The experimental results show that using a wide bandwidth (110 GHz) is not required in order to obtain a good performance. The performance was of sufficient quality using 10 GHz bandwidth around 300 GHz. The resolutions would be:  
\[\Delta z\sim\
icefrac{{1}}{{\Delta B}} \tag{9}\]  
\[\Delta x,\Delta y\sim\
icefrac{{\lambda y}}{{2}}(\sin\theta_{0}) \tag{10}\]  
\[\tan\theta_{0}\sim\
icefrac{{X_{0}}}{{Z_{0}}}\;or\;\
icefrac{{Y_{0}}}{{Z_{0}}} \tag{11}\]  
where \(\Delta B\) is the frequency bandwidth of the measurement, \(\lambda_{0}\) is the central frequency wavelength, \(\theta_{0}\) is the target angle visualization seen from the measurement distance, and \(Z_{0}\) and \(X_{0}\), are the scanning distances along the \(x\)-axis and \(y\)-axis, respectively.  
Differential imaging is obtained by means of calculating the difference of the experimental data (total image obtained from focused field amplitude) measured using the car, including with a monopole antenna short-circuited (ON state) and without the antenna (OFF state or open-circuited antenna). As stated in Section 2, the short-circuited antenna represents the antenna placed on the top of the car, which is in contact with the car's metal surface.  
The objective is to obtain the currents created by the antenna over the surface of the vehicle without getting dazzled (\"flash-out\") by the higher intensity of the currents on the antenna itself. A differential image may be produced due to the difference in module between the focused field amplitude images with the antenna (see Figures 6 and 7) and without the antenna (see Figures 4 and 5), resulting in the current distribution of the antenna that is shown in Figures 8 and 9.  
Figure 7: The focused field amplitude of a metallic car with an antenna. Frequency range: 295 GHz–305 GHz (BW = 10 GHz). (**a**) \(XY\) plane representation; (**b**) 3D representation of the focused field.  
Figure 8: Differential focused field amplitude between the metallic car with and without an antenna. Frequency range: 220 GHz to 330 GHz (BW = 110 GHz).  
Figure 9: Differential focused field amplitude between the metallic car with and without an antenna. Frequency range: 295 GHz to 305 GHz (BW = 10 GHz).  
In Figure 8, it can be identified that the strong central spot corresponding to the antenna has disappeared and, instead, the nearby currents to the antenna are visualized. The maximum can be clearly identified.  
Figure 9 depicts the current distribution calculated as a differential focused field amplitude using a frequency range from 295 GHz to 305 GHz (BW = 10 GHz) to assess influence of bandwidth in differential imaging.  
The differential focused field amplitude is higher with a bandwidth of 10 GHz around 300 GHz compared with a BW of 110 GHz from 220 GHz to 330 GHz. This effect is due to the gain variation of the horns across the frequency range. The imaging system performs an averaging through all the bandwidths, and the horn antenna gain variation generates this change in the amplitude, with higher amplitude when the BW is lower. However, the image resolution is better when the BW is greater [3]. If the application requires high resolution, then the BW parameter should be maximized.