## 1 Introduction
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Method** & **Limitation** \\ \hline \multirow{4}{*}{Contact} & DC heating [5; 6; 7] & Conductive materials only \\  & Pulse heating [8; 9; 10] & Conductive materials only \\  & Laser calorimetry [11] & Large amount of heat loss \\  & 3\(\omega\) Method [12] & Complexity damage of specimen \\ \hline \multirow{4}{*}{Non-Contact} & Photo Acoustic [11] & Low accuracy \\  & Laser Flash [13; 14] & Damage of specimen and limitation \\  & & of shape/size \\  & Photothermal radiometry [11] & Problem of emissivity factor \\  & Photothermal reflection [11] & Standardization of roughness on \\  & & surface of specimen \\  & Photothermal displacement [11] & Surface treatment of specimen \\  & Photothermal deflection [11] & Increase of S/N \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Limitations of contact and non-contact thermophysical property measurement technologies. Figure 1: Methods of measuring thermal conductivity using photothermal effect: (**a**) displacement method; (**b**) mirage deflection method; (**c**) collinear deflection method. specimen's interior. The displacement and mirage deflection method utilize thermoelastic deformation and change in the refractive index of the air layer, making them suitable for opaque metal materials that can sufficiently absorb the energy of the pump beam. In the case of the displacement and mirage deflection method, the probe and pump beams are irradiated at the same side of the air-layer. Therefore, the part of the reflected pump beam can be detected by the sensor and may cause an error. Conversely, the collinear deflection method determines thermophysical properties by using the change in the refractive index of the air layer and the change in thermoelastic deformation inside the specimen, making it a suitable measurement method for transparent materials [16]. As shown in Figure 1c, the collinear deflection method uses the change in both the refractive indices and thermoelastic deformation by irradiating the probe beam horizontal to the pump beam to measure the thermophysical properties of materials with low absorptivity (high optical transmittance) of the pump beam energy. Furthermore, this method has the limitation of generating a phase delay error because of mutual laser interference where the pump beam and the probe beam intersect. Moreover, in the case of the collinear method, a part of the pump beam can transmit and arrive at the sensor. Although the pump beam is blocked by a bandwidth filter that is equipped in front of the sensor, the pump beam cannot be completely filtered; it causes an error for the phase delay measurement [31]. As stated above, because materials with high optical transmittance generally tend to have low thermal conductivity, it is difficult to secure the necessary change in the refractive index for measurements. To overcome such a limitation, a light absorption thin film comprised of copper and having a thickness of 20 \(\upmu\)m was applied for energy absorption of the pump beam, and the probe beam was irradiated parallel to the rear side of the specimen. Through this mechanism, mutual interference between the two laser beams can be avoided. In this study, the measurement using the rear-side photothermal deflection method was carried out to determine whether thermal conductivity can be measured for a transparent isotropic material (quartz) and anisotropic material (sapphire glass). Since copper has a high optical absorption coefficient, a film with a thickness of 20 \(\upmu\)m can sufficiently absorb the energy of the pump beam. This means that the thermophysical properties can be measured through the light absorption film regardless of the optical characteristics of the target materials. A three-dimensional unsteady heat conduction equation was used to calculate phase delay. This equation was applied to a double-layered structure, which included both the thin light absorption film and the target material.