## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline
**A \(\emptyset\) 5 mm** & **B** & **C** & **D** & **E** \\ \hline \(h\) = 2.7 mm & \(h\) = 3.9 mm & \(h\) = 3.5 mm & \(h\) = 3.2 mm & \(h\) = 2.6 mm \\ \(h\) = 3.2 mm & \(\emptyset\) 3 mm & \(\emptyset\) 3 mm & \(\emptyset\) 3 mm & \(\emptyset\) 3 mm \\ \(h\) = 3.4 mm & \(\emptyset\) 8 mm & \(\emptyset\) 8 mm & \(\emptyset\) 8 mm \\ \(h\) = 3.7 mm & \(\emptyset\) 15 mm & \(\emptyset\) 15 mm & \(\emptyset\) 15 mm & \(\emptyset\) 15 mm \\ \hline \end{tabular}
\end{table} 
Table 1: Dimensions of defects simulated in 4.2 mm thick acrylic glass sample. analyzed. The centers of areas B, C, D and E coincided with the centers of the cylindrical defects with the largest diameter (\(\emptyset\) = 15 mm). As shown, there were no defects in the sound area (Sa). Figure 3 shows the curves obtained by computing the mathematical expectation of pixel intensity in the said areas. To better assess the variation in intensity upon test sample irradiation, the number of frames is shown in logarithmic scale. Figure 3 clearly indicates a sudden increase in intensity when the light pulse was emitted. Immediately thereafter, the curves did not change their value due to thermal image saturation [17]. The declining values of these curves were a result of test sample cooling and marked the beginning of the thermal image sequence that could be used to detect the defects. The end of this sequence was determined by the thermal image whose change in intensity was negligible. In the specific case, the 24 th frame was selected as the first (\(k_{0}\)) of 64 frames used in data processing applying the PPT algorithm. It is apparent that the cooling process began in the same way in all the areas. However, after a brief transition process, first curve B began to separate, followed by C, D and E, in that order. The curve denoted by Sa illustrates the cooling process of the sound area. The observed changes correlated with the nature of the simulated defects. Given that their diameters were the same, it was reasonable to expect that the shallowest defect (curve B) would be the first to start cooling. As a result, the cooling process in this case was the quickest (curve B declined the most rapidly). After a sufficiently long time from the beginning of cooling, all curves converged to the same value. This was not visible, of course, as there were not enough recorded frames. Figure 4 shows the change in the mathematical expectation of pixel intensity in areas B, C, D and E, relative to Sa. The occurrence of extremes as the curves changed was in correlation with defect depth, in terms of both value and order of occurrence. First, the most pronounced maximum was noted on curve a, which corresponds to the shallowest defect (\(\emptyset\) = 15 mm along vertical B). The last maximum occurred at the very end of curve d and had the lowest value, as it was related to the deepest defect (\(\emptyset\) = 15 mm along vertical E). Figure 3: Change in mathematical expectation of pixel intensity within the areas denoted by B, C, D, E and Sa in Figure 2.  
Figure 2: Thermal image of acrylic glass test sample: 450 th frame after a light pulse. Figures 5 and 6 show the results of data processing based on the FFT algorithm. The left half of these figures depicts the phase contrast obtained by processing the data extracted from the main sequence according to Procedure A. The shapes of the detected defects clearly indicate that there was a resolution problem. The results of data processing following Procedure B are shown in the right half of the figures, where the correlation of the shapes between detected and simulated defects is apparent. This is consistent with the fact that the total number of spectral components \(X(n)\) in Equation (1) is determined by the number of samples \(N\). A greater number yields more spectral components; this is manifested by better resolution in the figures generated applying the PPT algorithm.