# Depth Retrieval Procedures in Pulsed Thermography: Remarks in Time and Frequency Domain Analyses
## 3 Results and Discussion
### Depth Retrieval with Thermal-Contrast Peak Slope Time  
After the application of the pulse thermal energy and the recording of the surface temperature response, the delaminated regions' detection was produced due to the lower thermal conductivity that these features have with respect to the host material. The variation in the thermal properties affected the penetration rate of the heat flux into the composite bulk and therefore the surface temperature distribution, resulting to the appearance of local \"hot spots\". The time points of these hot spots appearance were varied according to the inserts' location (depth) and size. Thus, when raw temperature data are handled, the depth at which these inserts are located to, can be determined by subtracting the cooling curve over a reference area from the cooling curve over the damaged one. The resulting temperature difference curve can produce the correlation of the detected feature's depth with two characteristic points, this of peak temperature difference and this of the peak slope of this difference, which are further associated with the correspondent times when these phenomena occur (peak contrast time and peak slope time). Before the actual depth information retrieval through the correlation of these specific time points with the depth of the detected features, the temporal functions of the thermal contrast and of the slope of this contrast were studied, verifying that the selection of peak slope time for depth calculations is a more appropriate method, when working with raw temperature data. The experimental results  
Figure 3: (**a**) Raw thermal image of the inspected surface at \(t=1.25\) s after the application of the heating pulse; and (**b**) phase image of the inspected surface at \(f=0.16\) Hz. in terms of thermal contrast curves and of the correspondent slope curves as a function of time are illustrated in Figures 4-8. More specifically, each figure indicates the thermal contrast evolutions and their respective contrast slope curves for all the detected defects in each individual series. To achieve a clearer presentation and a higher resolution-clarity for these peaks determination, the time-dependent 1D contrast slope profiles were plotted only at the time region where the peaks occurred. Additionally, as the flash energy deposition was not uniform over the sample surface, the negative values of slopes measured at the very early time intervals were adjusted to zero, until the time point in which the slope of the thermal contrast was departing the zero value [32]. In other words, the initial temperature rise at each defect was scaled to be the same as that of the respective reference area. The previously mentioned thermal response representations provided the required information for quantitative analysis, determining the peak thermal contrast and the peak slope of this contrast along with the correspondent peak times. As regards the shallowest defect series on the trapezoid sample (Figure 4), the time of peak thermal contrast occurrence was measured to be the same for all the detected defects, regardless the size of each square insertion. Usually, for features having larger lateral dimensions, it takes more time for the trapped heat above them to be diffused out through the sides of the \"_trap_\", and this can be seen on the plot from the different time points in which each temperature difference curve is approaching zero. However, the evolution of these temperature difference curves is indicating that when the defect depth is approaching zero, the peak thermal contrast time approaches zero as well (\(t\) = 0.1019 s) and thus the temporal characteristics of this phenomenon remain unaffected from the 3D conduction problem. Similar results were also produced by the study of the temporal function of the thermal contrast slopes, as these peaks occurred as well at exactly the same time for all five insertions of Series A. However, the peak slope appeared much earlier (\(t\) = 0.02447 s) with respect to peak thermal contrast.