## 3 Results and Discussion
### Nondestructive Evaluation of Porosity
Additionally, the enhanced heterogeneity of the TBCs due to increased porosity led to THz signal scattering and attenuation, thereby reducing the overall energy and resulting in a decrease in APSD. By extracting features from the frequency-domain data, the frequency-response characteristics and energy distribution of the TBCs could be quantitatively analyzed. The parameter variations associated with porosity provided insights into the internal structure and physical properties, thereby offering crucial information for performance assessment and optimization of the thermal barrier coatings. Subsequently, the occurrence of phase jumps was attributed to the periodic and discontinuous nature of the signal. To mitigate these jumps, a phase unwrapping method was applied to the phase spectrum, as shown in Figure 14a, resulting in a reconstructed phase curve that was continuous and smooth. Additionally, feature parameters were derived from the number of extremal points in the first-order and second-order derivatives. As shown in Figure 14b, a slight decrease in the number of extremal points was observed with increasing porosity. More precisely, despite the limited significance of the number of extremal points in the first-order and second-order derivatives in reflecting the variation pattern of the phase curve with increasing porosity, the feature parameters still provided information regarding the rate of change in the phase curve. As porosity increased, the phase curve tended to exhibit a greater number of local extremal points. Although these extremal points might be affected by the complexity of the phase curve, they still captured the overall trend and characteristics of the phase curve. Therefore, the investigation of porosity evaluation using terahertz analysis remained necessary as it served as a strong foundation for terahertz signal analysis. By combining these feature parameters with others, more comprehensive and integrated information was obtained to collectively characterize the changes in porosity within the TBCs. Such a comprehensive analysis contributed to a more accurate assessment of the performance and characteristics of TBCs. Reflectance spectrum contained essential information regarding the material's electromagnetic response and exhibited a certain level of sensitivity towards porosity. The  
Figure 14: Feature extraction of phase spectrum: (**a**) removal of the phase jump; (**b**) extreme points of the first and second derivatives. extracted feature parameters, including average reflectance, reflectance standard deviation, maximum reflectance, minimum reflectance, and reflectance peak, were employed to quantitatively characterize the variations in porosity. Furthermore, these parameters were visually represented to showcase their correlation with porosity, as shown in Figure 15a-e.  
More precisely, increasing porosity resulted in greater attenuation of the terahertz signal within the coating, leading to a decrease in overall reflectance. The reflectance standard deviation measured the degree of variation between individual reflectance values and the average reflectance in the reflectance spectrum. As porosity increased, the internal structure and composition of the coating became more complex and heterogeneous, causing greater fluctuations and differences in the terahertz signal reflectance, thus increasing the reflectance standard deviation. The maximum reflectance exhibited a decreasing trend, while the minimum reflectance showed an increasing trend. With increasing porosity, the dielectric interface of the coating increased, and the synergistic effect of multiple interfaces affected the terahertz reflection properties. This increased the reflection and scattering, causing a decrease in the maximum reflectance. Simultaneously, in the porous regions, the penetration capability of the terahertz signal was enhanced, resulting in an increase in the minimum.