# Depth Retrieval Procedures in Pulsed Thermography: Remarks in Time and Frequency Domain Analyses
## 3 Results and Discussion
### Depth Retrieval with Blind Frequency  
The second depth estimation procedure was performed by means of quantitative pulsed phase thermography, investigating the accuracy produced on depth information retrieval from the analysis of the phase data, the phase contrast calculations and the determination of the blind frequency \(f_{b}\). As presented above, when working with temperature data, the selection of the sound area may have an impact on the thermal contrast calculations and this impact can be additionally enhanced in the case of uneven heating. As a result, in the previous case study different sound areas were selected for the retrieval of depth information, minimising the risk of plotting inappropriate temperature-time  
Figure 8: 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 1 mm (Series E). evolution curves. However, from the qualitative interpretation of phase images, it was observed that the frequency domain analysis greatly increased the background uniformity (as presented in Figure 3b). Based on the aforesaid, the first depth estimation method in the frequency domain was performed by measuring the correspondent phase contrasts between the defective areas and a region acting as the sound area pre-selected from the background (top left corner of the CFRP surface). Additionally, this procedure was repeated by calculating the average phase intensity from all the pixels on the surface (as the overall surface occupied by the defects was much smaller than the field of view). In such a manner, the use of the overall surface as a sound area was also assessed, aiming primary to evaluate the possibility of overcoming the need for a sound area/point selection in similar inspections. For the purposes of this study, similar to the temporal analysis, the phase contrasts profiles were plotted as a function of frequency for all the detected inserts, aiming to define the characteristic frequency point when the phase contrast diverged zero. Additionally, a comparison of sound area selection impact is performed through the two above mentioned procedures. Similar to the presentation of results in the time domain, before continue with the actual depth characterisation procedure, the phase contrast profiles obtained from the study of the CFRP sample are discussed, investigating the influence of depth and size on the produced contrast and the blind frequency determination. Figure 9 illustrates the phase contrasts produced from the shallowest insertions (Series A), either selecting a random sound area from the background (left column plot) or by using the entire surface as a sound area (right column plot). Similar to the thermal contrast slope function, phase contrasts were plotted only at the region of interest (frequencies region where the defect was visible), removing the information from the frequency spectrum in which only noise variations were appeared. As can be seen from the 1D phase contrast profiles, similar to the thermal data, in general, larger defects produced a greater phase contrast. A deviation can be seen between the phase contrast intensities measured for defects No. 3 and No. 4 (located at the centre of the panel) and that of defect No. 5 (located at the lower edge of the panel). Nevertheless, for depth calculations the parameter of interest is the blind frequency, which as can be seen from the correspondent plots, it is approximately the same regardless the size of the insertion inspected. The comparison of the two procedures used for the determination of the blind frequency, is revealing that an enhanced similarity was produced regarding the phase contrast evolutions either working with the random sound area or the overall surface, thus its selection has a low impact on the measurement of the blind frequency on Series A defects.