# THz-TDS Techniques of Thickness Measurements in Thin Shim Stock Films and Composite Materials
## 4 Results and Discussion
### Electric Field Evaluation of Carbon Fiber  
Unlike non-conductive materials, the T-ray has limited penetrating power against conductive materials [17]. At first, the test was carried out by applying the T-ray GFRP composites composed of non-conductive materials and the CFRP composites composed of conductive materials partially. The CFRP composites are composed of carbon fiber with conductive and non-conductive resin. When the CFRP-laminated composite plate is observed with a microscope, it is composed of various fibers and resins that could affect conductivity significantly, so the quantitative characteristic evaluation of carbon fiber composite material of T-ray is necessary. According to the previous reference, the radial conductivity of carbon fiber is approximately three times larger in the case of the electrical conductivity on the carbon fiber axis. The CFRP composites are composed of unidirectional composites, and the conductivity of the CFRP laminated plate composed of various lamination layers is affected. A transverse (vertical to the fiber axis) conductive generator depends on the fiber contact that occurs between adjacent fibers. Studies regarding the electrical conductivity of carbon fiber composite material are scarce. In some references, researchers have reported that the value of longitudinal conductivity (\(\sigma\)l) ranges between 1 \(\times\) 10\({}^{4}\) s/m and 6 \(\times\) 10\({}^{4}\) s/m, and the value of transverse conductivity (\(\sigma\)t) ranges between approximately 2 s/m and 600 s/m, which is much wider [18]. The transverse conductivity value of the laminated plate using the unidirectional Prepreg sheet varies significantly according to the production process and the quality of the laminated plate. The plane conductivity on the flowing current, while forming the \(\theta\) angle with the fiber axis in the unidirectional CFRP composites, is given as follows [19]:  
\[\sigma=\sigma clos^{2}cos\theta+\sigma\text{ts}in^{2}\theta \tag{7}\] \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Materials**} & \multirow{2}{*}{**Refractive Index (\(n\))***} & **Refractive Index (\(n\))** \\ \cline{2-3}  & & **Reflection Mode** \\ \hline PMMA & 1.60 \(\pm\) 0.08 & 1.59 \(\pm\) 0.07 \\ Shim Stock films & - & 1.52 \(\pm\) 0.03 \\ Fused quartz & 1.95 \(\pm\) 0.05 & 1.94 \(\pm\) 0.09 \\ GFRP & - & 2.17 \(\pm\) 0.05 \\ \hline \hline \end{tabular}  
* Data in References [6,11].  
\end{table} 
Table 1: Averaged THz refractive indices of the individually studied materials. Since it is significantly higher than the longitudinal conductivity of the fiber (\(\rm{\sigma}1>>\rm{\sigma}t\)), the T-ray which penetrates the unidirectional CFRP composites significantly varies according to the angle between the electric field vector and the axis of the carbon fiber. When the electric field of the T-ray is parallel to the axial direction of carbon fiber, the conductivity becomes the largest and the penetrating power becomes the smallest. On the contrary, when the electric field vector is perpendicular to the axis of fiber, the conductivity becomes the smallest and the penetrating power becomes the largest. The surface depth of the unidirectional oriented CFRP composites on the T-ray using the value of 10 s/m is 0.2 mm in 1 THz and 0.5 mm in 0.1 THz when the direction of electric field is vertical to the fiber axis. The effect of the penetrating power on the angle in the 24-ply unidirectional CFRP composite-laminated plate was experimentally evaluated using the CW terahertz device. Figure 6 exhibits the amplitude profile of the penetrating power of both the GFRP and CFRP composites by the function of angle under the frequency of 0.1 THz. The amplitude profile of power was obtained, with values ranging from 0\({}^{\circ}\) to 90\({}^{\circ}\) for both the GFRP composites and CFRP composites. Notably, in the case of the GFRP composites, there was no change in the amplitude profile.