# Depth Retrieval Procedures in Pulsed Thermography: Remarks in Time and Frequency Domain Analyses
## 3 Results and Discussion
### Comparison of Temporal and Frequency Domain Analysis for the Acquisition of Depth Information  
In the previous subsections, results from the quantitative analysis of the CFRP sample were presented, based on the use of the two depth prediction methods. Figure 12 shows a comparison of the measured depths from each individual method in terms of prediction errors. These 3D plots intend to summarise the above discussed quantitative results in a single imaging result, enabling relative comparisons. For this purpose, the scale of the error axis was fixed to be the same in all the three plots, enabling the qualitative evaluation of the produced errors according to the height of each respective bar. The above can be performed as the plots include all the detected defects and the location of each error bar corresponds to the location of the specific insertion with respect to the defect description figure included on the top right side of the figure.  
As can be seen from the previously mentioned plots, generally, temporal analysis for depth determination produced larger prediction errors with respect to the correspondent method on the frequency domain. For instance, while peak slope time method provided large divergences on depth prediction of Series B and C defects, this was importantly reduced on the results acquired from the two respective procedures on the frequency domain. Additionally, for some defects mainly in the deeper series which were estimated with a considerable error in the frequency domain, these were not able to be detected and quantified in the temporal domain. Contrarily, the comparison of quantification results acquired by the phase data showed that the selection of the entire surface as sound area either produced similar results with those provided from the random sound area or in some instances this method provided results closer to the actual depth.  
As regards the error production and its correlation with the depth, it can be seen that larger errors were produced mainly on Series B and C when working with temperature data, while, in phase data manipulation, a considerable error was produced for defects located at depths of 0.2 mm and 0.4 mm, respectively. Contrarily, more efficient results were produced for Series A, D and E in time domain analysis and for the deeper Series C, D and E in the respective frequency domain analysis. As stated above, the increased errors produced for Series B and C on the temporal analysis can be attributed to the 3D conduction problem, which is not presented on the shallower defects series due to the early time detection and on the deepest ones due to weak signal that they produced. One other hand, the deviations from the actual depth observed from frequency analysis can be attributed to the increased noise levels on the phase contrast plots when the defect is visible in a large frequency range.  
Figure 12: 3D representation of insertions estimated depth in terms of error production for all the detected defects in the trapezoid specimen through: (**a**) peak slope time; (**b**) blind frequency (random sound area); and (**c**) blind frequency (overall surface).