# Thermographic Non-Destructive Evaluation for Natural Fiber-Reinforced Composite Laminates
## 4 Infrared Image Processing  
Principal component thermography (PCT) [33] has been used as an infrared image processing technique to extract the image features and reduce undesirable signals. Different from classical principal component analysis, PCT relies on singular value decomposition (SVD) which extracts spatial and temporal data from a matrix in a compact manner by projecting original data onto empirical orthogonal functions (EOFs). Original data can often be adequately represented with only a few EOFs. Usually, an infrared sequence of 1000 images can be replaced by 10 or less EOF [34]. Another advantage of PCT is its suitability to be combined with other image processing techniques, e.g., in [35; 36; 37]. Fast Fourier transform can be used to extract amplitude and phase information from the raw thermal data. It provides the possibility to obtain quantitative results in a straightforward manner. Usually phase is more useful than amplitude because it can retrieve the deeper information. In addition, phase is less affected than raw and amplitude data by environmental reflections, emissivity variations,  
Figure 6: UT experimental set-up. Figure 7: CW THz configuration in reflection mode: (a) schematic set-up; (b) experimental set-up. non-uniform heating, surface geometry and orientation [27]. This method has been used for LT and it is known as phase transform. When used for PT, it is known as pulsed phase thermography (PPT) [38]. The relationship exists between the depth \(z\) of a defect and the thermal diffusion length \(\mu\). Empirical expressions have been proposed [39]:  
\[z=C_{1}\cdot\mu=C_{1}\cdot\sqrt{\frac{\alpha}{\pi\cdot f_{b}}} \tag{1}\]  
where, \(f_{b}\) is known as the blind frequency - the frequency at which a given defect has enough (phase or amplitude) contrast to be detected, and \(C_{1}\) is an empirical constant. It has been observed that \(C_{1}\approx 1\) for amplitude transform [40], while reported values for phase transform are in the range of 1.5 to 2 [40], with \(C_{1}=1.82\) typically adopted [41]. Therefore, phase transform is more important than amplitude because it can access the deeper information [27]. According to Equation (1), the thermal diffusivity \(\alpha\) is a parameter of particular importance for calculating the depth by PPT. \(\alpha\) can be expressed as follows:  
\[\alpha=\frac{k}{\rho c_{p}} \tag{2}\]  
where \(c_{p}\) (J/kgK) is the specific heat at constant pressure, \(\rho\) (kg/m\({}^{3}\)) is the density, and \(k\) (W/mK) is the thermal conductivity. For composite materials, \(\alpha\) can be calculated by:  
\[\alpha_{composite}=\sum_{1}^{N}(weightfractionmaterial\cdot\alpha_{material})_{N} \tag{3}\]  
where N is the number of constituent materials in the composites. Therefore, the thermal diffusivity \(\alpha\) can be obtained by calculating \(c_{p}\), \(\rho\) and \(k\) in Table 5.  
In this paper, recursive median filter (RMF) and cold image subtraction (CIS) [42] were used as the pre-processing methods. Table 6 shows the applied experimental and image processing methods for different specimens. \begin{table}
\begin{tabular}{l c c c} \hline \hline  & **Basalt Fiber (63\%)** & **Vinyl Ester Resin (37\%)** & **BFRP** \\ \hline k (W/mK) & 0.031 & 0.229 & 0.104 \\ \(\rho\) (kg/m\({}^{3}\)) & 2630 & 1220 & 2108.3 \\ \(C_{p}\) (J/kgK) & 860 & 1000 & 1083.8 \\ \(\alpha\) (m\({}^{2}\)/s) & / & / & \(4.5514\times 10^{-8}\) \\ \hline  & **June (30\%)/Hemp (20\%) Fibers** & **Epoxy Resin I-SX10 (50\%)** & **Jute/Hemp Hybrid Laminate** \\ \hline k (W/mK) & 0.365/0.04 & 0.229 & 0.232 \\ \(\rho\) (kg/m\({}^{3}\)) & 1460/25 & 1100 & 993 \\ \(C_{p}\) (J/kgK) & 1360/1800 & 1000 & 1268 \\ \(\alpha\) (m\({}^{2}\)/s) & / & / & \(1.8425\times 10^{-7}\) \\ \hline  & **Bagasse Fiber (60\%)** & **Polyurethane Resin (40\%)** & **SCB** \\ \hline k (W/mK) & 0.475 & 0.209 & 0.369 \\ \(\rho\) (kg/m\({}^{3}\)) & 520 & 1200 & 792 \\ \(C_{p}\) (J/kgK) & 3601.8 & 1400 & 2720.6 \\ \(\alpha\) (m\({}^{2}\)/s) & / & / & \(1.7125\times 10^{-7}\) \\ \hline \hline \end{tabular}
\end{table}