# Depth Retrieval Procedures in Pulsed Thermography: Remarks in Time and Frequency Domain Analyses
## 2 Materials and Methods  
To evaluate the potential of pulsed thermography for quantitative depth characterisation, experimental testing was carried out in a trapezoid CFRP laminate, having fabricated defects of known characteristics. The CFRP sample was a laminate 30 cm \(\times\) 30 cm trapezoid structure consisted of ten (10) plies giving a total specimen thickness of 2 mm and a laminae orientation of 0\({}^{\circ}\)/90\({}^{\circ}\) crossply through its volume. As illustrated in the schematic of Figure 1, 25 square Teflon\({}^{\text{TM}}\) insertions of different dimensions ranging from 3 mm to 15 mm were placed between the plies simulating local detached regions. These insertions were divided into five series (A-E in the schematic), placed at different depths ranging from 0.2 mm to 1 mm, while each series consisted of five square insertions of different lateral dimensions (No. 1 to No. 5 in the schematic). As stated above, the sample was inspected by depositing heat energy on its rear surface, the opposite from this presented in Figure 1, allowing a depths' range investigation from 0.2 mm to 1 mm. The convenience of inspecting this component (widely used in several studies) is derived from the fact that its characteristics and the presence of similar defects at different depths enable the conduction of relative comparisons. For data acquisition, a flash thermographic system in reflection mode was used and two high energy flash lamps were triggered at \(t=0\) s to deposit an instantaneous (of a 5 ms pulse duration) heat pulse on the sample's surface. The temporal and spatial surface temperature variations after the application of the energy pulse were monitored through the aid of a high-speed infrared camera, capturing a sequence of thermal images during the cooling down phase. The camera used in this study was a mid-wave (3-5 um) device, containing a focal plane array of 320 \(\times\) 256 infrared detectors. The experimental parameters used to acquire the thermographic sequence along with the characteristics of the inspection equipment are summarised in Table 1.  
The acquired pulsed thermal dataset measured the two dimensional surface temperature distribution \(T(x,y)\) as a function of time \(t\). Because quantification in the frequency domain requires the application of PPT technique to treat the raw data, which is a pixel-wise transformation technique,  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Experimental Equipment** & **Acquisition Parameters** \\ \hline \multicolumn{3}{c}{_Thermal stimulation:_} \\ Photographic Flashes: Balcar FX 60 & Sampling rate, \(t_{s}\) & 157 Hz \\ pulse duration: 5 ms thermal pulse, & Acquisition duration, \(t_{acq}\) & 6.7 s \\ deposited energy: 3.2 KJ/ flash (total energy deposited 6.4 KJ) & Time interval, \(\Delta t=1/f_{s}\) & 6.3 ms \\ \cline{2-3} \cline{1-  
and to increase the data processing speed, it should be noted that before continuing to the data analysis phase, the recorded data were sub-sampled by a factor of 4. As a result, the parameters of the truncated sequence were redefined as \(N=263\) frames, \(f=39.25\) Hz, and time interval \(\Delta t=25\) ms. The adoption of the above sub-sampling procedure had a dual objective, initially to overcome the long computation times and secondly to assess the impact degree of the sampling resolution to the acquisition of quantitative depth results. In such a manner and by capturing the data at the highest sampling rate of the apparatus, an inefficient resolution could be easily re-optimised through the selection of a lower sub-sampling factor and without the need of capturing a new dataset. As stated above, the quantitative depth determination procedures applied in this study, evaluated the performance of two contrast-based methods. The correlation expressions used to determine the depth \(z\) of the inserts were based on the determination of the thermal contrast peak slope time (time domain analysis) and of the blind frequency (frequency domain analysis) using the Equations (1) and (2), respectively.