# Measurement of Contrast and Spatial Resolution for the Photothermal Imaging Method
## 4 Results of Numerical Analysis
### Image Quality Change with \(L_{f}/L_{d}\)  
Figure 9 shows the phase delay signals (the ERF on the internal structure) derived by the photothermal imaging method with changed various of \(L_{f}/L_{d}\). As \(L_{f}/L_{d}\) decreased (closer to the surface), the response to the internal structural change became more intense. As \(L_{f}/L_{d}\) increased (i.e., farther from the surface), the response weakened.  
The LSF can be obtained by differentiating the ERF as shown in Figure 10. Thus, the spatial resolution from the LSF can be analyzed. As mentioned previously, the spatial resolution of the imaging system is the FWHM of the LSF. Figure 9 indicates that, as \(L_{f}/L_{d}\) increases (located deeper), the FWHM decreases. In other words, the spatial resolution is improved. The spatial resolutions for five different values of \(L_{f}/L_{d}\) are summarized in Table 4.  
The contrast was verified from the MTF derived by applying the FFT to the LSF. Figure 11 shows the contrast according to the change of \(L_{f}/L_{d}\). As in the case of spatial resolution, the contrast increased together with \(L_{f}/L_{d}\). In the case of the MTF, it is difficult to compare the general tendency on the basis  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{5}{c}{\(L_{f}/L_{d}\)} \\ \cline{2-6}  & **0.181** & **0.362** & **0.725** & **1.087** & **1.449** \\ \hline
**Dimensionless resolution (mm/mm)** & 2.549 & 2.191 & 1.881 & 1.775 & 0.903 \\
**Dimensionless contrast (mm/mm)** & 0.155 & 0.180 & 0.206 & 0.223 & 0.433 \\ \hline \end{tabular}
\end{table}
Table 4: Spatial resolution and contrast depending on the change according to \(L_{f}/L_{d}\) (\(R_{b}\) was fixed to 100 \(\mu\)m, \(R_{b}/L_{d}=0.145\)).  
Figure 10: Performance of line-spread function (LSF) with changes in \(L_{f}/L_{d}\).  
Figure 9: Boundary response functional performance with changes in \(L_{f}/L_{d}\).  
of a single value. Instead, Table 4 presents the dimensionless spatial frequency (the thermal diffusion length multiplied by the spatial frequency) at which the MTF became 0.5 and the contrast decreased by half.  
The changes in the spatial resolution and contrast according to \(L_{f}/L_{d}\) revealed that, as \(L_{f}/L_{d}\) increased, the spatial resolution and contrast increased accordingly. A small \(L_{f}/L_{d}\) means that the subsurface structure (resin structure) within the range of the thermal wave has a large influence, and a large \(L_{f}/L_{d}\) means that this influence is small. Figure 12 depicts the physical phenomena depending on \(L_{f}/L_{d}\). As shown in Figure 12, when a thermal wave of the same size exists in the same position, the subsurface structure can be detected when \(L_{f}/L_{d}\) is small but cannot be detected when \(L_{f}/L_{d}\) is large. For this reason, as \(L_{f}/L_{d}\) increases, the FWHM of the LSF decreases and the resolution increases. However, the photothermal imaging signal should come from the phase delay, which reflects the distribution of the thermal properties within the range of the thermal wave. Therefore, if \(L_{f}/L_{d}\) is large, the influence of the subsurface structure on phase delay becomes small, so the intensity of the ERF decreases.  
Therefore, as \(L_{f}/L_{d}\) reached a certain level, the intensity of the ERF decreased significantly. Hence, it is estimated that experimental detection would be impossible, according to the signal noise analysis by the photothermal imaging method suggested by [PERSON] et al. [2].  
Figure 11: Performance of the MTF according to changes in \(L_{f}/L_{d}\).  
Figure 12: Physical phenomena depending on \(L_{f}/L_{d}\).