## 4 Results  
Figure 9a shows that there is a clear maximum point in the coefficient of determination, both in measurements of the phase delay according to the relative position of quartz and the measurements through numerical analysis. The same thermal conductivity used for the numerical analysis was set as the thermal conductivity of the measurement target material. The resulting measurements of the designated thermal conductivity along with the experimental delay results are shown in Figure 9b. The phase delay measurement used the mean of the 300 result values measured for 30 s with an interval of 0.1 s in each relative position, with a 95% confidence level. The phase delay of the point of each graph was used the three repeated measurements to the average value, and the standard deviation us represented through an error bar. As mentioned previously, the rear-side mirage deflection method, applying a light absorption thin film, physically prevented mutual interference between the pump and the probe beam, as compared to the collinear deflection method [31], which is one of the existing measurement methods for transparent materials. Thus, the relative position at 0 mm can be accurately measured for the phase delay signal. That is typically applied to quartz and sapphire glass as shown in the figures. Upon comparing the experimental results with the reference value of the thermal conductivity of the target materials shown in Table 5, the absolute error was confirmed to be 0.069 W/m-K, as shown in Table 7. \begin{table}
\begin{tabular}{c c} \hline \hline
**Condition** & **Value** \\ \hline Intensity of pump beam (W) & 1 \\ Radius of pump beam (\(\upmu\)m) & 75 \\ Distance to probe beam from rear side surface (\(\upmu\)m) & 150 \\ Relative position (mm) & 0 to 0.6 (interval 0.1) \\ Modulated frequency (Hz) & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Optical Conditions used in the experiment. Figure 8: Schematic diagram of optical align of rear-side photothermal deflection method. Figure 10 shows that there is a clear maximum point of the coefficient of determination through comparison of the measured phase delay results at a relative position according to the crystal orientation of sapphire glass and the phase delay calculated through numerical analysis with the material properties shown in Table 5. The thermal conductivity to the maximum coefficient of determination input into the numerical analysis was designated as the thermal conductivity of the measurement target material. The phase delay measurement was conducted at crystal orientations between 0\({}^{\circ}\) and 90\({}^{\circ}\) with an interval of 30\({}^{\circ}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Thermal Conductivity**} & \multicolumn{1}{c}{**Thermal Conductivity**} & \multicolumn{1}{c}{**Absolute Error**} & \multicolumn{1}{c}{**Relative Error**} \\ \multicolumn{1}{c}{**Reference Value**} & \multicolumn{1}{c}{**Experimental Value**} & \multicolumn{1}{c}{**(W/m-K)**} & \multicolumn{1}{c}{**(W/m-K)**} & \multicolumn{1}{c}{**(\%)**} \\ \multicolumn{1}{c}{**(W/m-K)**} & \multicolumn{1}{c}{**(W/m-K)**} & \multicolumn{1}{c}{**(W/m-K)**} & \multicolumn{1}{c}{**(W/m-K)**} & \multicolumn{1}{c}{**(\%)**} \\ \hline Quartz & 1.4 & 1.331 & 0.069 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Result of thermal conductivity determination for quartz. Figure 10: _Cont._  
Figure 9: (a) Thermal conductivity showing a maximum coefficient of determination for quartz; (b) phase delay experiment analysis results according to the relative position. Figure 10: (**a–d**) Thermal conductivity curves of sapphire glass, showing a maximum coefficient of determination; (**e–h**) phase delay experiment and analysis results according to the relative position. Upon comparing the experimental results with the reference values of the thermal conductivity of sapphire glass shown in Table 5, the maximum absolute error was confirmed to be 0.25 W/m-K.