# 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
On the other hand, the 3D heat conduction around the defects seems to affect the peak values of either the thermal contrast or of its slope. In particular, in Figure 4, it can be seen that larger inserts generally presented higher peak contrast and peak contrast slope values with respect to these produced by the smaller ones. For instance, the peak thermal contrast and peak contrast slope for defect A5 (15 mm) were 2.25 and 52.95, respectively, while the correspondent values for defect A1 (3 mm) were 0.63 and 8.19, indicating that as smaller is the dimension of the defect, the heat diffusion can take place around this region more easily, producing as well a reduced contrast. Nevertheless, some differentiations detected regarding this phenomenon (i.e., peak contrast values of defects A5 and A4) can be possibly attributed to the selection of different sound areas for each individual peak determination along with the non-uniformity of heat deposition on the inspected surface. Figure 4: Temporal evolution of: (**a**) the thermal contrast curves; and (**b**) the correspondent slope of the thermal contrasts for the detected insertions on the trapezoid surface located to the depth of 0.2 mm (Series A). Contrary to the results produced from the shallowest defects, as the depth of the Teflon insertions was increased, the consistency detected regarding the time points of the peak contrast appearance was altered. More specifically, by studying the produced thermal contrasts and their evolution to time for all the insertions to the depth of 0.4 mm (Figure 5a), it can be generally seen that the smaller defects produced an earlier time point of maximum thermal contrast appearance and vice versa. For instance, the temporal region where the peak thermal contrasts occurred for the five defects of this series was ranging from 0.3312 s (for defect B1) to 0.4331 s (for defects B4 and B5), indicating that smaller lateral sizes produced an easier path for heat to be laterally diffused and consequently a reduced contrast on an earlier time interval. Thus, the above results verify that the peak contrast time is appropriate for relative comparisons but not reliable for quantitative information retrieval on deeper probing, as the 3D conduction effect has an impact on the acquired information. Some deviations from the above general observation were detected in this case (i.e., time points of defect B3 and defect B4), which can be also a result of the procedure used to produce these temperature difference functions (selection of different sound areas). On the other hand, the study of contrast slope evolution to time (Figure 5b), revealed that the characteristic time points of this peak occurrence remained more constant and less affected from the negative effects of lateral heat conduction around the detected features. For instance, the time range when the peak slopes occurred was between 0.2547 s and 0.3057 s and even though the peak slope times did not have exactly the same value, the shorter time range (approximately half) observed in this case, indicates the reliability of this quantity for depth prediction. However, similar to the temperature difference evolution study, the 3D conduction is strongly influencing only the peak slope values, but this parameter is not of prime interest when the objective is the quantitative depth analysis. The thermal behaviour assessment regarding the detected defects on the Series C, D and E provided similar results, as shown in Figures 6-8. As can be seen from the respective plots, the observations discussed above were further confirmed from the study of the thermal profiles acquired for the deeper defects. In particular, as the probing became deeper, a high divergence on the characteristic peak contrast time range was observed for defects of the same depth but with different lateral dimensions.