## 4 Results and Discussion  
In this part, the results on the sample described in Section 2 are measured under the following parameters: (i) flash duration of 1 ms, (ii) camera frequency acquisition of 200 Hz, and (iii) 4000 images corresponding to a final time of 20 s and a pixel area of 300 \(\times\) 300 \(\upmu\)m\({}^{2}\) for the spatial resolution. The obtained results are plotted in Figure 6:  
From these measurements, 5 regions of interest (ROIs) appeared. For each ROI, the corresponding temperature evolution of one pixel can be extracted: 4 of them in the center of the thermal resistance square hole and the fifth in the center of the image. All these temperatures plot are normalized (baseline subtraction and reference division \(T_{n}^{*}(t)\) = \(\dfrac{T^{*}(t\geq t_{ref})}{T^{*}(t_{ref})}\) with \(T_{n}^{*}(t)=T_{n}^{*}(t\geq t_{0})-T_{0}^{*}(t_{0})\), where \(t_{0}(s)\) is the time of the flash and \(t_{ref}(s)\) any time during the -1/2 slope) and superposed onto the \"healthy\" analytical model (calculated for the bilayer of Figure 2) assuming perfect contact between all the layers. This normalization also avoid the non-uniformity of the global temperature coming from the non-homogeneity of the flash lamp. The results represented in Figure 7 show a -1/2 slope for a short time and the influence of the thermal resistance as well as the different depth effects as a function of time. In the Figure 7, it can be clearly observed that for the deepest ROI the temperature evolution quit the -1/2 slope further. For higher thermal resistance, the behavior is closer to adiabatic case with variable inflexion tendencies. Moreover, it is very interesting to note that the ROI extracted in the center of the image seems to be affected by a small thermal resistance (no exact superposition with the supposed healthy model can be achieved). Figure 5: Results of the autoregressive inverse method based on the simulated analytical temperature response from Figure 4: (**a**) estimated amplitude \(A\) as a function of time, the solid lines corresponds to the different \(Rth\) of the Figure 4 and (**b**), calibration curve obtained from the extraction of the maximum amplitude \(A\) as a function of the thermal resistance and amplitude at any time step of 19.7 s.  
From this, we can estimate in Figure 8 the corresponding parameters. First, in Figure 8a, the obtained amplitude is plotted. Here, one can see that the estimated values are in good agreement with the ones estimated using the analytical solution represented in Figure 5a. Then, from the calibrated curves calculated and represented in Figure 5b, the absolute and quantitative fields of the amplitude value can be represented, as shown in Figure 8b. Here, the time required to calculate the parameters with the inverse process (4) is approximately 7 s with a 2.3 GHz quad-core i5 MacBook Pro with 16 GB of RAM. This computational time includes the inversion of a 51,012 \(\times\) 4000 matrix representative of the number of pixels in space (218 \(\times\) 234) and the number of time steps of the thermograms. In this validation case, the geometry and thermal properties of the studied sample are well known (see Figure 2). Then, from the results in Figure 8, the agreement with the value is good, and the respective theoretical and estimated values are reported in Table 1.  
From the data Table 1 one can see that the error is always lower than 5%, with the maximum uncertainty for ROI number 3 corresponding to a hole of 500 \(\upmu\)m. One can also note that a threshold has been performed before the identification in order to treat only the pertinent points belonging to the patches. Indeed, a certain number of points in the ROIs borders are not pertinent because of the strong gradient present here due to the 3D effect of the diffusion not taken into account in the identification process (see Figure 8). For example, for ROI3, 1500 points over 1900 have been used for the identification.