## 4 Results and Discussion  
### Thinning Defect Detection  
In this study, only phase images, which are less sensitive to non-uniform heating effects and surface emissivity, were considered for thinning rate evaluation. In the LIT experiment, an excitation frequency of two complete cycles was applied. To determine phase data using the four-point method, the raw data from thermography was computed for all pixels and converted to a phase image. The phase image results processed by the four-point method for each of the modulation frequencies are shown in Figure 7. As can be seen in the phase image in Figure 7, the detectability of thinning defects with different thinning rates varies depending on the modulation frequency. Defect A1 (thinning rate: 10%) is not detected in the phase images of any applied modulation frequencies. In addition, defects A2 (thinning rate: 20%) and A3 (thinning rate: 30%) defects were detected in the phase images of all of the modulation frequencies, but their shapes were not clear. On the other hand, defects with a thinning rate of 40% to 90% were detected in all of the modulation frequency phase images, and the shape of the defect was also maintained. In particular, the A7 (thinning rate: 70%) defect, A8 (thinning rate: 80%) defect, and A9 (thinning rate: 90%) defect had good detection ability at all modulation frequencies, showed excellent phase contrast, and the defect shape was like a square. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Frequency** & **Frame/ Cycle** & **Frame Interval** & \multicolumn{4}{c}{**Frame Considered**} \\ \cline{4-7}
0.1 & 500 & 125 & 125 & 250 & 375 & 500 \\
0.05 & 1000 & 250 & 250 & 500 & 750 & 1000 \\
0.04 & 1250 & 312.5 & 312 & 625 & 937 & 1250 \\
0.03 & 1666 & 416.5 & 416 & 833 & 1249 & 1666 \\
0.02 & 2500 & 625 & 625 & 1250 & 1875 & 2500 \\
0.01 & 5000 & 1250 & 1250 & 2500 & 3750 & 5000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Details of LIT raw data to determine phase by 4-point method. Figure 7: Results of phase images by the four-point method: (**a**) 0.01 Hz, (**b**) 0.02 Hz, (**c**) 0.03 Hz, (**d**) 0.04 Hz, (**e**) 0.05 Hz, and (**f**) 0.1 Hz. Figure 8 shows the absolute phase contrast value of the C3 (thinning rate: 90%) defect between the defective area and the sound area. For defect areas in phase contrast calculations, the average value of 10 \(\times\) 10 pixels was considered at each defect center. For the sound area, the average value of 10 \(\times\) 10 pixels in the area adjacent to the defect was considered. As shown in Figure 8, the phase contrast improves as the modulation frequency decreases. The maximum phase contrast is 2.2006 radian at 0.01 Hz, and the minimum phase contrast is 0.86 radian at 0.1 Hz. Figure 9 shows the trend of phase change according to thinning defect depth and modulation frequency. As can be seen in Figure 9, for all thinning defects, the phase angle tended to increase as the depth increased. In addition, it was found that as the modulation frequency increases from 0.01 Hz to 0.1 Hz, the phase change decreases and the phase difference between the sound area and the thinning area decreases. Figure 8: Absolute phase contrast trend with thinning rate: 90%. Figure 9: Plot of defect depth and phase difference as a function of modulation frequency. To evaluate the performance of the proposed technique, the signal-to-noise ratio (SNR) values of phase data were calculated. The SNR value was calculated from the pixel value in the same area used when calculating the phase contrast. The SNR can be expressed by Equation (8). \[\text{SNR}=20\text{log}_{10}\bigg{(}\frac{|\text{DROI}_{\text{mean}}-\text{ SROI}_{\text{mean}}|}{\sigma}\bigg{)} \tag{8}\]  
where SROI is the average value of the sound area, DROI is the average value of the thinning area, and \(\sigma\) is the standard deviation of the thinning area. Table 3 shows the SNR values for defects with a thinning rate of 40% or more according to each modulation frequency.