## 5 Conclusions  
This study aimed to measure the thermal conductivity of transparent materials by using the rear-side photothermal deflection method, selecting quartz as a transparent isotropic material and sapphire glass as a transparent anisotropic material. The existing methods were incapable of measuring the thermal conductivity of the transparent material with a low absorption rate or were limited in using the conventional photothermal effect with a large error. However, this study significantly improved the limitations, and the results were obtained as follows:  
1. By applying the phase delay derived through the numerical analysis of quartz and the phase delay measured through the optical alignment to the thermal conductivity determination algorithm, the absolute error and the relative error of the thermal conductivity were derived to be 0.2 W/m-K and 5%, respectively.
2. For sapphire glass, which is an orthogonal anisotropic material, valid thermal conductivity for crystal orientations of \(0^{\circ},\ 30^{\circ},\ 60^{\circ},\ 90^{\circ}\), and \(90^{\circ}\) was derived and confirmed from the theoretical value. The sapphire glass used for the measurement is a plane having \(k_{11}\), \(k_{22}\), and \(k_{33}\), respectively known to be 36.1 W/m-K, 27.1 W/m-K, and 36.1 W/m-K.
3. As a result of determining the thermal conductivity by applying the phase delay derived through the experiment with respect to each crystal orientation of sapphire glass and the phase delay measured through the numerical analysis of the thermal conductivity determination algorithm.  
Figure 11: Results of thermal conductivity determination for sapphire glass.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Crystal Orientation** (\({}^{\circ}\)) & **Thermal Conductivity** & **Thermal Conductivity** & **Absolute Error** & **Relative Error** \\  & **Reference Value** & **Experimental Value** & **(W/m-K)** & **(\%)** \\  & **(W/m-K)** & **(W/m-K)** & **(W/m-K)** & **(\%)** \\ \hline
0 & 27.10 & 26.87 & 0.23 & 0.8 \\
30 & 29.40 & 29.33 & 0.07 & 0.2 \\
60 & 33.85 & 34.06 & 0.21 & 0.6 \\
90 & 36.10 & 36.65 & 0.55 & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Result thermal conductivity determination according to the crystal orientation of sapphire glass.  
conductivity determination algorithm, the maximum absolute error and relative error were derived to be 0.55 W/m-K and 1.5%, respectively.
4. The limitation of anisotropic materials is that they must be measured in a situation where the main crystal orientation can be known. This limitation may be overcome in the future by experimentally developing a mechanism that can determine this information.  
Conceptualization, G.K. and J.Y.; methodology, G.K.; software, S.K.; validation, G.K., D.K., and S.K.; formal analysis, H.K.; investigation, D.K.; resources, S.K.; data curation, S.K.; Writing--Original draft preparation, G.K.; Writing--Review and editing, H.K.; visualization, D.K.; supervision, H.K.; project administration, J.Y.; funding acquisition, J.Y. and H.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT), grant number NRF-2018R1A2B2001082. This research was also supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, grant number NRF-2015R1D1A1A01060704.  
Not applicable.  
The authors declare no conflict of interest.