## 5 Conclusions  
In this study, a transparent anisotropic collinear deflection method was proposed to measure the thermal properties of transparent anisotropic materials, which could not be measured using the existing photothermal deflection methods. To this end, numerical analysis and experimental study were conducted for a single layer anisotropic material, and the following conclusions could be drawn.  
1. Based on the 3D heat conduction equation to which the anisotropic thermal conductivity with the orthorhombic structure was applied, the temperature distribution of the anisotropic material was derived using a complex transformation method and numerical analysis, and it was verified through a comparison with the analytical solution of the well-known mirage deflection method. Deflection analysis was conducted to measure the thermal conductivity of the transparent anisotropic material by applying the derived temperature distribution.
2. The measurement method proposed in this study was verified by measuring the effective thermal conductivity according to the principal thermal conductivity directions (\(k_{11}\), \(k_{22}\)) and measurement directions using A-plane sapphire glass whose \(k_{11}\), \(k_{22}\), and \(k_{33}\) were known to be 36.4, 27.1, and 36.4 W/(mk) from the various literatures.
3. The phase curve method algorithm was applied to derive the thermal conductivity of the measurement specimen using the phase curve results according to the relative position (distance between the pump beam and the probe beam) derived from the experiment. The RMSE ranged from 2.97 to 5.25\({}^{\circ}\) depending on the measurement direction.
4. It was confirmed that the measured thermal conductivity according to the finally derived direction (\(\theta\)) had absolute errors less than about 4 W/(mk) when compared with the average of literature values.  
In this study, a method for measuring the thermal conductivity of a material with transparent anisotropic properties was proposed. However, it was found that the RMSE derived by applying the phase curve method was relatively high. This appears to be because sufficient heat could not be supplied due to the specificity of the material (high transparency), and thus a low temperature field (\(dT=2\)-\(3\,^{\circ}\)C) was generated. It is thought that this problem can be solved by applying materials with high light absorption to the surface. In future research, a measurement method capable of overcoming this drawback will be proposed.  
Conceptualization, M.K. and K.P.; methodology, K.P.; software, M.K.; validation, M.K., K.P. and G.K.; formal analysis, D.-K.K.; investigation, M.K.; resources, D.-K.K.; data curation, K.P.; writing--original draft preparation, M.K. and K.P.; writing--review and editing, H.K.; visualization, G.K.; supervision, J.Y; project administration, H.K.; funding acquisition, J.Y. and H.K., please turn to the CRediT taxonomy for the term explanation. Authors must be limited to those who have contributed substantially to the work reported.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT), grant number NRF-2018R1A2B2001082. This research was also supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, grant number NRF-2015R1D1A1A01060704.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Measurement angle** (_deg_) & 0 & 30 & 45 & 60 & 90 \\ \hline
**Literature value**\((W/mK)\) & 36.40 & 34.10 & 31.75 & 29.43 & 27.10 \\  & (\(\pm\) 8.5) & (\(\pm\) 7.4) & (\(\pm\) 6.3) & (\(\pm\) 5.2) & (\(\pm\) 4.1) \\ \hline
**Measurement value**\((W/mK)\) & 32.23 & 29.97 & 28.17 & 25.58 & 23.54 \\ \hline
**Root mean square error** (_deg_) & 3.3 & 5.52 & 3.18 & 4.47 & 2.97 \\ \hline
**Absolute error**\((W/mK)\) & 4.17 & 4.13 & 3.58 & 3.85 & 3.56 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Measurement results of A-plane sapphire using collinear deflection method.