# Measurement of Contrast and Spatial Resolution for the Photothermal Imaging Method
## 6 Conclusions  
In this study, the image quality changed according to different measuring conditions, which included the depth of a subsurface structure from the surface of the object (first layer thickness, \(L_{f}\)) and the pump-beam radius (\(R_{b}\)). As image quality metrics, the spatial resolution and contrast were derived from the FWHM of the LSF and the MTF.  
1. It was verified that the phase delay profile (edge response function, ERF) of the subsurface structure derived by the photothermal imaging method could be nondimensionalized in relation to the thermal diffusion length. Therefore, various studies on \(L_{f}/L_{d}\) and \(R_{b}/L_{d}\) can be conducted  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(R_{b}/L_{d}\) & \multicolumn{3}{c}{\(L_{f}/L_{d}\)} \\ \cline{3-5}  & \(0.362\) & \(0.725\) & \(1.449\) \\ \hline
**Dimensionless resolution (mm/mm)** & \(0.150\) & \(2.344\) & \(1.743\) & none \\  & & \(7\%\) & \(8\%\) & - \\ \hline
**Dimensionless contrast (mm/mm)** & \(0.150\) & \(0.187\) & \(0.204\) & none \\  & & \(4\%\) & \(1\%\) & - \\ \hline \hline \end{tabular}
\end{table}
Table 6: Image quality in the experimental results according to changes in \(L_{f}/L_{d}\).  
Figure 17: LSF of the experimental results.  
Figure 18: MTF of the experimental results.  
to quantitatively analyze the spatial resolution and contrast of photothermal imaging regardless of the absolute size and thermal properties of the material to be measured.
2. Analyzing the spatial resolution and contrast under different measuring conditions revealed that, as the ratio of \(L_{f}/L_{d}\) increases, the spatial resolution and contrast increase as well. On the other hand, the ratio of \(R_{b}/L_{d}\) has an insignificant effect on the spatial resolution and contrast.
3. The range of thermal waves that vary with \(L_{d}\) has a significant effect on the spatial resolution and contrast of photothermal imaging. \(L_{d}\) can be adjusted by the thermal diffusivity of the material to be measured and the modulation frequency of the pump beam as shown in Equation (3). Therefore, to increase the spatial resolution and contrast, it is advantageous for the photothermal imaging method to select \(L_{d}\), which is relatively short compared to \(L_{f}\).
4. As the \(L_{f}/L_{d}\) increases, however, the influence of the subsurface structure within the range of the thermal wave decreases. This means that the phase delay change may not reflect the subsurface structure. Therefore, the photothermal imaging method in large \(L_{f}/L_{d}\) is not effective for the measurement.
5. In conclusion, the image quality analysis of this paper is expected to provide a validation method for the results of photothermal imaging and effective measurement conditions for the photothermal imaging method.  
These results suggest that the experimentally measurable spatial resolution and contrast can be improved if the signal-to-noise ratio of the photothermal imaging system can be increased. The noise of a photothermal signal can be controlled by the surface roughness of the specimen to be measured and the pump-beam intensity of the photothermal imaging system [2]. Therefore, in future research, image quality can be analyzed according to the magnitude of noise in the photothermal imaging method.  
Conceptualization: M.K.; data curation: M.K.; formal analysis: D.-K.K.; funding acquisition: J.Y. and H.K.; investigation: M.K.; methodology: M.K.; project administration: H.K.; resources: D.-K.K.; software: M.K.; supervision: J.Y.; validation: M.K.; visualization: M.K.; writing--original draft: M.K.; writing--review & editing: H.K. 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.