## 3 Results and Discussion
Figure 4: (**a**) Scanning electron micrographs (SEM) of double-void defects with various diameters and gap widths (diameter-gap width-diameter: 612-554-604 \(\upmu\)m; 502-442-496 \(\upmu\)m; 395-319-382 \(\upmu\)m; and 281-194-266 \(\upmu\)m, denoted S1, S2, S3, and S4, respectively). The depths of the defects are 1.2 mm. For the sake of clarity, the unit lengths in the upper and lower figures are different. (**b**) Two-dimensional amplitude image of transmitted CW–THz waves with 1 THz frequency. (**c**) Cross-sectional profile along the \(x\)-axis at the center of the amplitude dips that originate from the four double-void defects. For S1, the center-to-center distance between the two Gaussian peaks is 1.32 \(\upmu\)m, which corresponds to the actual value of 1.16 \(\upmu\)m obtained from the SEM image. The widths of peaks calculated by the double Gaussian fitting are 1.12 and 0.85 \(\upmu\)m. Although the measured values are somewhat larger than the actual sizes, the two adjacent defects are sufficiently distinguishable, not only using the raw image of the transmitted THz amplitude but also by data analysis based on the double Gaussian fitting method. In contrast, for S2, it is difficult to distinguish the double defects from the raw profiles shown in Figure 5b,d. The cross-sectional profile along the \(x\)-axis at the center of the amplitude peaks in Figure 5b was also analyzed using the double Gaussian fitting method. The center-to-center distance and the widths of the peaks extracted by the fitting signals are 1.02, 1.09, and 0.70 \(\upmu\)m, respectively. Despite the theoretical difficulty in distinguishing the two defects in S2 because of similar values of the widths of the peaks and the center-to-center distance, the discriminability between two adjacent defects can be increased by employing data analysis and suitable image processing methods. The blind spot problem in the coherent system, finding the difference in thickness of materials by the phase change, occurs when the difference in optical path length from the surroundings matches the wavelength used in the system. The coherent CW-THz system cannot distinguish bulk XLPE without any defect from defects occurring at a phase change of 2\(\uppi\). In that case, the transmitted THz waves can be undetectable. Therefore, to ensure the reliability of the measurements, it is necessary to verify that all defects of varying depths are measurable. We fabricated defects with 1.0 mm diameter and various depths, D, from 1.0 to 1.7 mm with a step size of 100 \(\upmu\)m, and measured the samples at a frequency of 1 THz. Based on the void defects with a refractive index of 1.0 and the XLPE material with a refractive index of approximately 1.5, the optical path difference corresponding to a phase shift of 2\(\uppi\) at a frequency of 1 THz will be 600 \(\upmu\)m. There is no way to prevent void defects with depths equal to multiples of 600 \(\upmu\)m from being blind spots. Otherwise, the results shown in Figure 6 show that each defect is  
Figure 5: (**a,b**) Three-dimensional plots near the double-void defects of S1 and S2, respectively. (**c,d**) Cross-sectional profiles along the \(x\)-axis at the center of the amplitude dips for S1 and S2 (black solid curves) and the double Gaussian fittings (red dot-dashed curves). The amplitude curves are well fitted by the double Gaussian components that are plotted with filled area two-dimensional plots (the areas that appear in purple). clearly identified, and only the amplitudes of the dips change slightly depending on D. In addition, the results do not include negative values, which are inevitably predicted to occur near the phase difference of \(\pi\) in the coherent CW-THz imaging system. The fundamental mechanism of this phenomenon can be assumed to be related to the fact that the width of the beam waist of the CW-THz waves at the focal point is larger than the diameter of the defects.