## 4 Results
### Validation Evaluation of FFT algorithm
#### 4.4.2 Quantitative Evaluation Using SNR  
The SNR was evaluated to quantitatively verify the effectiveness of the FFT algorithm for the three types of heat sources. The SNR was calculated for thinning rates of 30, 50, 60,  
Figure 23: Binarization images of B–type specimen with FFT algorithm applied. (**a**) center; (**b**) left side; (**c**) top left.  
Figure 22: Binarization images of B–type specimen without FFT algorithm applied. (**a**) center; (**b**) left side; (**c**) top left.  
70, 80, and 90% and was compared with the amplitude image without FFT applied. The formula for SNR is as follows [23]:  
\[\text{SNR}=20\text{log}_{10}\Big{(}\frac{|\text{DROI}_{\text{mean}}-\text{ SROI}_{\text{mean}}|}{\sigma}\Big{)} \tag{8}\]  
where \(\text{DROI}_{\text{mean}}\) is the detective area, \(\text{SROI}_{\text{mean}}\) is the sound area, and \(\sigma\) is the standard deviation. Figures 24-26 show graphs evaluating the SNR depending on whether or not the FFT algorithm is applied. The red SNR value in the graph means the SNR value without the FFT algorithm is applied.  
Figure 24a shows the effect of the FFT algorithm at thinning rates of 60 and 90%. At thinning rates of 30, 50, 70, and 90%, the SNR decreased when the FFT algorithm was applied. When looking at the trend of the SNR for all the thinning rates, a pattern in which the value of the Gaussian weight decreases and then increases can be seen. For this reason, as shown in Figure 24b,c, the value of the Gaussian weight is approximately 1.0 to 2.0, which is when the high-frequency component begins to move to the side. Additionally, Figure 24d,e show a trend in which the high-frequency component moves to the side and the SNR value increases. As the high-frequency component moves to the side, it overlaps with the defective area, and the SNR value decreases when calculating the defect area of the region of interest (ROI).  
Figure 24: SNR graph of amplitude image based on FFT algorithm applying center thermal excitation. (**a**) center; (**b**) 1.0; (**c**) 1.5; (**d**) 2.5; (**e**) 3.0; (**b**–**e**) refer to Gaussian weights.  
Figure 25a shows the effect of the FFT algorithm at all the thinning rates except for the 70% thinning rate. The SNR decreases when the FFT algorithm is applied at 70% because, as shown in Figure 25b, the high-frequency component overlaps with the area of the 70% thinning rate and is affected when calculating the SNR. Additionally, as seen in Figure 25c, the shape of the defect could not be confirmed, so the SNR was calculated to be close to 0.  
Figure 26a shows the effect of the FFT algorithm at all the thinning rates except for the 50% thinning rate. As shown in Figure 18c, the amplitude image to which the FFT algorithm is not applied cannot confirm the shape of the defect, making the evaluation of the SNR meaningless. In particular, as shown in Figure 26b,c, when compared to the images with amplitudes at which the FFT algorithm was not applied, excellent effects can be seen at the thinning rates of 30, 60, and 90%, corresponding to column C.  
When quantitatively evaluating the amplitude image and the SNR without the FFT algorithm applied, excellent effects can be confirmed in the form of heat excitation on the sides rather than at the center. However, when evaluating the SNR, the ROI location of the \(\text{SROI}_{\text{mean}}\) is very important, but since the normalization process for the image is impossible, clear validation is difficult. However, when analyzed qualitatively (visually), the effect can be clearly confirmed in the binarization image acquired using the Otsu algorithm. By applying the results of this study as basic data, it is expected to be used when inspecting large-area structures, including CLPs, in the future.