# THz-TDS Techniques of Thickness Measurements in Thin Shim Stock Films and Composite Materials
## 4 Results and Discussion
### Relation between Nominal Thickness and Thickness Measured from T-ray Techniques  
The Shim stock films and GFRP plates with non-conductivity were not dependent on the direction of the T-ray, so the measurement was possible. In addition, the T-ray reflection mode which could enable the measurement in one direction was adopted. Figure 9  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample No.**} & **Delay Time (\(\Delta t\), ps)** & **Resonance** & **T-ray Measure** & **Reference** & **Others** \\  & **(\(\Delta t\), ps)** & **Frequency (\(\Delta f\))** & **ment (mm)** & **Thickness (mm)** & **Others** \\ \hline
1 & 24.480 & 0.041 & 2.000 & 2.020 & Shim Stock Co., Ltd. \\
2 & 50.000 & 0.020 & 3.180 & 3.080 & \\
3 & 75.130 & 0.013 & 5.600 & 5.740 & \\
4 & 83.30 & 0.012 & 5.920 & 5.920 & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Measurements of the GFRP composites with various thicknesses using the THz techniques.  
Figure 8: A TOF and FFT image of the GFRP composites under the reflection mode (2.02 mm in thickness).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample No.**} & **Delay Time (\(\Delta t\), ps)** & **Resonance** & **T-ray Measure** & **Reference** & **Others** \\  & **(\(\Delta t\), ps)** & **Frequency (\(\Delta f\))** & **ment (mm)** & **Thickness (mm)** & **Others** \\ \hline
1 & 1.322 & 0.750 & 0.137 & 0.127 & Shim stock Co., Ltd. \\
2 & 2.551 & 0.392 & 0.250 & 0.254 & \\
3 & 3.846 & 0.260 & 0.396 & 0.381 & \\
4 & 5.881 & 0.170 & 0.539 & 0.508 & \\
5 & 8.600 & 0.115 & 0.789 & 0.762 & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Measurements of the Shim stock films with various thicknesses using the THz techniques.  
exhibits the comparison between the nominal thickness in the thin Shim stock films and the thickness measured using the T-ray. As shown in Figure 9, the thicknesses of the thin Shim stock films were 0.127 mm, 0.254 mm, 0.381 mm, 0.508 mm, and 0.762 mm. The thickness of the thin Shim stock films was shown in a straight, solid line. This line shows the proportional relation with the standard thickness. Here, -- represents the nominal thickness; \(\square\) represents the measured data in the case of the measurement, assuming that the T-ray was vertical to the specimen; and \(\triangle\) represents the measured data in the case of the inclined T-ray. Here, to effectively obtain the Refractive index (\(n\)), a suitable sample is the case with a thickness of several ones of mm. In case of the films, we did not prepare such a thicker sample. In this testing, this value is the average value of all the samples.  
Thus, the difference of data could be considered to be due to the average value of the refractive index to some degree. Even though there was a difference of \(\pm\)2%, the results tended to be in agreement in the linear aspect.  
Figure 10 shows the comparison between the nominal thickness of the GFRP composites and the thickness measured using the T-ray. The thicknesses of the GFRP composites were 2.02 mm, 3.08 mm, 5.74 mm, and 5.92 mm. In Figure 9, -- represents the nominal thickness; \(\square\) represents the case of the measurement, assuming that the T-ray was vertical to the specimen; and \(\triangle\) represents the case of the inclined T-ray. Unlike the thickness at the microgram scale, the case of the inclined T-ray matched with the standard thickness at the millimeter scale. This can be attributed to the thickness of the specimen, the relatively small effect from the error, the strong received signal in electric field according to the fiber orientation of the GFRP composites, and the high penetration ratio of T-ray, enabling us to optimize a reception strong signal. Therefore, we found that it had potential reproducibility.  
Figure 9: The relation between the nominal thickness and the thickness measured from the T-ray techniques in the Shim stock films.