## 3 Results and Discussion  
### Comparison of PT and LST through CNR Analysis  
CNRmax values for all defects and processing techniques are shown in Table 2. The following figures summarize the results of different defects in the porosity samples selected in order to highlight the pros and cons of the different experimental methods (PT vs. LST), signal processing techniques (raw, TSR, PPT, and PCT), and filtering (unfiltered vs. Gaussian filtering). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \multicolumn{2}{c}{**Porosity Samples**} & \multicolumn{4}{c}{**Unfiltered**} & \multicolumn{4}{c}{**Gaussian Filter, \(\sigma^{2}=1\)**} & \multicolumn{4}{c}{**Gaussian Filter, \(\sigma^{2}=3\)**} \\ \hline  
Figure 6 aims to illustrate the difficulty in assessing the efficiency of defect detection under changing situations. Several images from this figure show apparently similar defect contrasts to the human eye, whether they are processed or not, or filtered or not. Profiles representing spatial variations through a horizontal line at the center of these images (dotted white line seen in the first image) are also included at the bottom of each image. Spatial profiles provide a hint of the noise level of images. For instance, TSR considerably denoises data following a synthetic data reconstruction after fitting. This is particularly evident with the phase calculated from TSR data, the 1 st and the 2 nd time derivatives (last three columns of the first line). \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Porosity Samples**} & \multicolumn{4}{c}{**Unfiltered**} & \multicolumn{4}{c}{**Gaussian Filter, \(\sigma^{2}=1\)**} & \multicolumn{4}{c}{**Gaussian Filter, \(\sigma^{2}=3\)**} \\ \hline  
\end{table} 
Table 2: _Cont._It can also be noted that filtering has some impact on image noise as seen by comparing unfiltered (first line in Figure 6) vs. filtered (second and third lines, for which the degree of Gaussian filtering changes from a variance \(\sigma^{2}=1\) to 3, respectively). Still, it is a difficult task to objectively assess denoising by visual examination of these images or even the respective spatial profiles. The CNR is an interesting parameter that can be used as a criterium to quantitatively compare results. The images presented in Figure 6 correspond to the CNR\({}_{\text{max}}\) values (estimated following the procedure presented in Section 2.3.3) for each technique. It can be observed that the CNR significantly increases with advanced signal processing (TSR, PCT, and PPT) and even further when fitted data, e.g., TSR, is used as input (instead of raw data) to PCT and PPT, as well as 1 st and 2 nd time derivatives. Figure 7 presents LST results for the same defect presented in Figure 6 for PT, i.e., defect 1 in sample S45. At first glance, CNR values are considerably higher for PT. This was to be expected since a high-definition, high thermal resolution, cooled camera is used for PT, whilst a microbolometer uncooled camera is used for LST. A second observation is that improvement in CNR is more erratic for LST. For instance, it actually worsens after processing in all cases with the exception of the 1 st time derivative. This is probably related to the data reconstruction which may add some noise due to the dynamic scanning process. This needs to be further investigated. Finally, as expected, Gaussian filtering improves CNR in all cases. The variance has a significant impact as observed from the two options studied herein (\(\sigma^{2}=1\) and 3). Nevertheless, two important observations should be pointed out. First, variance values were selected arbitrarily, using previous empirical knowledge from similar investigations. There must be an optimal variance that could be selected in order to improve defect contrast as much as possible. The determination of this optimal value would require further study, which is out of the scope of the present work.