# Estimating Thermal Material Properties Using Solar Loading Lock-in Thermography
## 4 Results and Discussion
### Field Experiments  
The LWIR camera was set up in a fixed manner with approximately 9.5 m distance to the wall. Thermal images were captured for 96 h. The wall under investigation, positioning of the ROIs and a typical thermogram are depicted in Figures 5-7. Figure 5: Overview of the wall structure under test. The rectangle shows the approximate view of the LWIR camera. Figure 6: ROI location and size. In the lower left are the two reference plates (aluminum plates, each 300 \(\times\) 300 mm size, one 10 mm, the other 20 mm thick). On the right side, a plaster strip is visible from earlier experiments on the wall. Figure 8 shows the time series values for the three evaluated ROIs over the measurement period. This data shows very poor 24 h period amplitude. This is due to the weather being overcast for almost the whole time (see Table 2). The algorithm (Equation (4)) was evaluated on this data set. Even better results are expected on days with strong sun, and no overcasts to disturb the periodic heat input, also advised by [10]. The amplitude image, shown in Figure 9, is calculated and from these amplitudes the effusivity is estimated and depicted in Figure 10.  
Figure 8: Average surface temperature for the ROIs depicted above. Noticeable is the greater temperature difference of the All10 plate vs the Al20 plate, caused by the lower thermal mass. Figure 7: Typical thermogram showing the retaining wall. In the lower left are the two reference plates stacked on top of each other. Note the vignetting effect on the cameras lens has not been fully corrected. However, for the proposed algorithm, this correction is not necessary. Figure 10: Estimated thermal effusivity for each pixel. Note that these results are only valid for regions that are thermally thick. Regions like the reference plates or the steel fence result in meaningless effusivity values. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Day** & **Date** & **Min. Tem.** & **Avg. Tem.** & **Max. Tem.** & **Total Sunshine** & **Avg. Humidity** & **Total Rain** & **Cloud** \\  & & \(\Gamma\)CJ & \(\Gamma\)CJ & \(\Gamma\)CJ & \(\Pi\)BlJ & [\(\%\)RH] & **[mm]** & **Coverage [\(\%\)]** \\ \hline
1 & 9 November 2020 & \(-\)0.3 & 3.2 & 7.0 & 0.5 & 93.2 & 1.1 & 70 \\
2 & 10 November 2020 & \(-\)1.2 & 0.7 & 3.0 & 0.6 & 96.3 & 0.0 & 70 \\
3 & 11 November 2020 & 0.6 & 2.8 & 4.5 & 0.0 & 94.3 & 2.9 & 98 \\
4 & 12 November 2020 & 0.9 & 4.2 & 7.8 & 1.5 & 85.1 & 0.3 & 78 \\
5 & 13 November 2020 & 0.8 & 2.7 & 4.2 & 0.0 & 94.6 & 0.5 & 98 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Weather table for the 96 h experiment. Weather data is collected by [11] for the weather station “Saarbrücken-Ensheim” which is located \(\sim\)11 km from the experiment site. Note the high average cloud coverage and low total sunshine per day. Figure 9: Amplitude image of the fundamental 24 h period. This image depicts the 24 h temperature amplitude average in every pixel over the 96 h measurement period \(|S_{\text{xy}}|\). There are two regions with higher and lower apparent effusivity of particular interest:
* The gaps between bricks (made out of an unknown type of mortar) correctly measure higher values than the bricks themselves
* The plaster strip on the right correctly measures lower effusivity than brick (plaster \(\sim\)900 vs. brick \(\sim\)1100 J/\(\left(\mathrm{K}\cdot\mathrm{m}^{2}\cdot\mathrm{s}^{1/2}\right)\)). Note that the plaster strip is strictly speaking not thermally thick. However, as the sensitivity of the measured effusivity is greatest in the front and less sensitive to the back layers the result correlate well to literature values for these materials. This sensitivity drop along the z-axis stems from the fact that the temperature amplitude of the structure drops exponentially over the depth [8]. Experiencing less amplitude, deep layers cannot influence the surface temperature as much as the front layers. Exact estimations on which layer has how much impact is not fully examined yet.