## 2 Numerical Model
### Exemplary Results
Figure 8: The raw results of the numerical modeling for the case of modulated excitation presented for the chosen time step (t = 100 s): (**a**) the case without the defect, (**b**) the case with the defect located away from the sample’s center, and (**c**) the defect located in the center of the sample. Figure 10: The results of the numerical modeling for the case of modulated excitation presented for the chosen time steps (50 s, 100 s, and 150 s): (**a**) the case without the defect, (**b**) the defect located in the center of the sample, and (**c**) the case with the defect located away from the sample’s center. The thermograms in (**a,b**) were reconstructed using mirror reflection. Figure 9: The results of the numerical modeling for the case of continuous excitation presented for the chosen time steps (50 s, 100 s, and 150 s): (**a**) the case without the defect, (**b**) the defect located in the center of the sample, and (**c**) the case with the defect located away from the sample’s center. The thermograms in (**a,b**) were reconstructed using mirror reflection. The data presented below displays the time-temperature characteristics for all cases for both continuous and modulated excitation (Figure 12). Evidently, in the case of continuous excitation, there was a marked escalation in the overall temperature, particularly in relation to the centrally positioned defect. The disparity between the peak of the mean temperature for the region exhibiting the defect (as represented by the blue solid line in Figure 12a) and that of the region devoid of the defect (as depicted by the red dotted line in Figure 12a) was equal to 1.78 \({}^{\circ}\)C. In the context of comparison, it can be observed that for modulated excitation, the aforementioned difference amounted to 0.31 \({}^{\circ}\)C. It is noteworthy that these variations can be detected through the utilization of highly sensitive thermal imaging cameras. The sample with a defect located outside its central region presented a more intriguing scenario. In regard to both excitations, there existed a disparity of approximately 0.28 \({}^{\circ}\)C between the peak of the mean temperature for the region with a defect (indicated by the yellow dashed line in both Figure 12a,b) and the region without a defect (indicated by the red dotted line in both Figure 12a,b). In the scenario where the excitation was modulated, the observed distinction bore a striking resemblance to the situation involving a central defect. This implies that this approach may be more efficacious in instances where numerous defects are distributed throughout the sample in diverse locations. Significantly, in the context of modulated excitation, the temperature differential between the regions with and without the defect became evident within approximately 15 s of heating. In contrast, under continuous excitation, this temperature differential manifested after approximately 35 s. This likely implies enhanced operational speed of the modulated excitation-based approach. Figure 11: Chosen ROIs for all the simulated cases: (**a**) without the defect, (**b**) defect located centrally, and (**c**) defect away from the sample’s center. Figure 12: Average temperature dynamics computed from the chosen ROI: (**a**) for continuous excitation and (**b**) for modulated excitation. In the legend, “def center” denotes the sample with the defect located in the center, “no defect” indicates the sample without the defect, and “defect no center” is the sample with the defect located outside the center.