# Terahertz Inspection of Buildings and Architectural Art
## 4 Monitoring of the Conservation Process of a Mural
The separation between echoes as function of time after the sample preparation is shown in Figure 7d. From an exponential fit as function of time T of the form  
\[\Delta t(T)=T_{\infty}+T_{i}e^{-T/\tau}, \tag{1}\]  
where the parameters \(T_{\infty}\), \(T_{i}\) and they were obtained for each data set finding that the parameter \(\Delta t\) decays with a time constant of \(\tau=111\pm 26\,\)days, which implies that the sublimation half-life of the cyclododecane under those conditions is \(t_{1/2}=76\pm 18\,\)days. The disappearance of the cyclododecane layer was confirmed by cutting the samples after the experiment and taking micrographs, such as the one shown in Figure 7e, where a free-space gap can be seen between the two plaster layers. In situ measurements could not be performed as frequently for practical reasons; however, a set of initial measurements within a few days of the cyclododecane and plaster coating procedure were taken and another set was obtained one year after. The waveforms and deconvolved impulse response functions show a similar pattern to the one from the mockups and the duration of t. Measurements were made in two different positions that we identify as A and B, as shown in Figure 6. The separation for the two peaks that correspond to the interfaces around the cyclododecane/air gap changed, in A, from \(3.4\pm 0.3\,\)ps to \(2.8\pm 0.1\,\)ps, and in B, from \(4.0\pm 0.2\,\)ps to \(2.7\pm 0.1\,\)ps demonstrating that the cyclododecane content in the layer disappeared, at least partially, leaving an air-gap behind between the original artwork and the protective coating applied. This is consistent with the estimation that we can perform from the mockup  
Figure 7: Measurements on a mockup sample. (**a**) Electric field time-domain signal as function of the delay, the vertical dashed lines show the positions where echoes were found by using the deconvolved data. (**b**) Impulse function obtained from sparse deconvolution of the time-domain signal, the vertical dashed lines are provided in order to identify the main features that correspond to the air-mortar reflection, mortar-gap and gap-mortar interfaces. (**c**) is a closeup of the data in (**b**) in the 45 to 70 ps window, in which the parameter \(\delta\)t that corresponds to the delay between the two interfaces around the gap is indicated. (**d**) The evolution of the temporal separation \(\delta\)t between the peaks. The evolution is caused by the sublimation of the cyclododecane layer. (**e**) The micrograph of cross-section of one of the mock-ups showing that the cyclododecane layer disappeared after 300 days. measurements, which is that between 93% and 99% of the cyclododecane would have sublimated over a year. In conclusion, we were able to monitor the changes of the cyclododecane-plaster material system used for the conservation intervention in-situ at the Konstantinbasilika in Trier, Germany. We could confirm that the cyclododecane layer used as a spacer between the original artwork and the protective plaster coating almost completely disappeared over the course of one year. Furthermore, this is the first report of non-destructive monitoring of the evolution of the cyclododecane layer on mockups, which allowed us to determine that the sublimation half-life of cyclododecane under these conditions is between 58 and 94 days. These numbers are, of course, dependent on the temperature and atmospheric pressure, but they give a good estimate of the times that are involved in the sublimation process. This is, to the best of our knowledge, the first report of an in-situ conservation intervention monitored in a non-destructive way using terahertz time-domain spectroscopy.