## 5 Analysis of Experimental Results  
### Signal-to-Noise Ratio (SNR) Criterion and Absolute Contrast Method  
The SNR has been used to distinguish the detectability or undetectability of delaminations. The positive or negative values indicate that the delamination is detected or undetected, respectively [11; 20; 21; 22; 27; 36]. The SNR represents the contrast between the surface temperature above a defective area and its surroundings (in dB) [20]. Therefore, the degree of SNR shows the visibility level of delamination in concrete structures. The higher the SNR, the more clearly the delamination can be observed. The SNR can be determined by using Equation (7) [20; 36]:  
\[SNR(dB)=\frac{S}{N}=20\log_{10}\biggl{(}\frac{abs(S_{-}area-N_{-}area)}{ \sigma_{noise}}\biggr{)}, \tag{7}\]  
\[\sigma_{noise}=\sqrt{\frac{1}{n-1}\frac{n}{\sum_{i=1}^{n}(x_{i}-\overline{x}) }^{2}}, \tag{8}\]  
where, \(S_{-}area\) and \(N_{-}area\) are the average surface temperature of the signal and noise areas, respectively. The signal and the noise areas are the regions above a defect and its neighborhood correspondingly. \(\sigma_{noise}\) is the standard deviation of the surface temperature of the noise area. For using long pulse thermography, the problem of nonuniform heating is unavoidable. In addition, the effects of environmental conditions on the surface temperature of the specimen during both heating and cooling duration always exist. Therefore, the noise area is chosen to ensure that the effects of nonuniform heating and environment are minimal. For these reasons, the noise area is proposed as the perimeter around the imitating deterioration, whereas the signal area is the region above the delamination. In previous studies, the perimeter of noise has been demonstrated more effectively than cases of one point or group of three points [3; 37; 38; 12]. In this study, all artificial delaminations have the same sizes of 10 cm \(\times\) 10 cm \(\times\) 1 cm, so both signal and noise areas are selected with the same dimensions for each defect to have consistent parameters. Signal area and noise area are expressed using the red square and the blue square, respectively, as shown in Figure 5.  
The heat flux conducting in the concrete specimen is interrupted by defects, because the thermal conductivity of the defect (the air) is much less than that of the concrete. Consequently, the heat flux is slowed down and concentrated above delaminations during heating [39]. After the heat source (halogen lamps) is switched off, at the region surrounding delamination, the heat flux continues transferring without the obstruction from the heated face to the opposite face of the specimen, while it cannot transmit significantly through the delamination, and the concentrated thermal energy on the surface of the defect reflects to the surface at the same side of the heat source. Therefore, the surface temperature above a delamination is higher than its neighborhood solid area. Figure 6 illustrates the heat transfer mechanism using halogen lamps. Figure 5: Selection of \(S_{-}area\) and \(N_{-}area\) for signal-to-noise ratio (SNR) calculation. In this method, absolute contrast and observation time are the two main parameters that are used for defining the visibility of the delamination, and predicting the delamination's depth. The absolute contrast (\(\Delta T(t)\)) is defined as the difference between the average temperature above a defect and its surroundings, while the observation time (\(T_{\text{max}}\)) is the duration from when the time of the heat source was turned off to the peak of the absolute contrast curve [16]. \[\Delta T(t)=T_{d}(t)-T_{Sa}(t), \tag{9}\]  
where, \(T_{d}(t)\) and \(T_{Sa}(t)\) are the mean values of surface temperature within a defect area and reference area, respectively. Therefore, absolute contrast is a function of time, \(t\). In this study, \(T_{d}(t)\) is the average surface temperature of signal area, whereas \(T_{Sa}(t)\) is the average temperature on the perimeter of the noise area.