## 4 Results and Analysis  
### Imaging Results  
A set of experiments was carried out to verify the validity of vector coherence factor weighting. Images are shown on a logarithmic scale with a dynamic range of 100 dB. Figures 7 and 8 show the images of grooves with a depth of 0.1 mm, and the buried depths of 70 mm and 90 mm, respectively. Figure 7 (left) shows original images obtained with phased array ultrasonic S\(-\)scan imaging without further processing, including (a), (d), (g), (j), and (m), whose focus depths are 30 mm, 40 mm, 50 mm, 60 mm, and 70 mm, respectively. As shown in the red rectangle in Figure 7a, the sidewall secondary echo caused by waveform conversion is seen in the middle of the sector\(-\)scan image, while the reflected echo of the sidewall on the bolt shank is vaguely observed. The defect echo of crack appears on the sidewall of the bolt shank, located at the depth of 70 mm and can be intuitively distinguished from the structural interference wave in the DAS images. Figure 7 (middle) shows the images of VCF weighting factors, including (b), (e), (h), (k), and (n) with focus depths of 30 mm, 40 mm, 50 mm, 60 mm, and 70 mm, respectively. All of the defect echoes, reflected echoes of the sidewall on the bolt shank, and artifacts caused by waveform conversion are seen in the middle of the VCF image. Figure 7 (right) shows S\(-\)scan images weighted by the VCF, including (c), (f), (i), (l), and (o) with focus depths of 30 mm, 40 mm, 50 mm, 60 mm, and 70 mm, respectively. Dynamic range and signal\(-\)to\(-\)noise rate improve with regard to original S\(-\)scan images. Moreover, both amplitudes of background noise and artifacts caused by waveform conversion are reduced in the DAS_VCF image. Moreover, in both cases with VCF weights or without, the display of defects in the DAS_VCF image is clearer with the focus depth increasing. However, due to the attenuation of acoustic energy, the echo of defects at 90 mm depth is less than 70 mm. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** \\ \hline Nut diameter (mm) & 30 \\ Nut height (mm) & 14 \\ Bolt shank diameter (mm) & 18 \\ Bolt shank length (mm) & 90 \\ Bolt length (mm) & 120 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main parameters of bolts. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Buried Depth 1** & **Groove Depth** & **Groove Width** & **Groove Length** \\ \hline \multirow{2}{*}{Value (mm)} & 70.00 & 0.10 & 0.10 & 10.00 \\ \cline{2-5}  & 90.00 & 0.10 & 0.10 & 10.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main parameters of two artificial grooves. Mostly, the size of the crystal grain for the heterogeneous medium is smaller than the wavelength. In contrast, the continuous interface of steel-air is equivalent to a large scatter. Therefore, the received signals of the pulse\(-\)echo are mainly from the sidewall of the bolt shank, and little from the bolt inside, thus the VCF in the sidewall echo higher than inside. While in the case that there is a groove on the surface of the bolt shank, the consistency of phase for defect is highest, i.e., the value of VCF factor of the groove is highest and close to 1 and that of the medium scattering signal is close to 0, as shown in Figure 7b. Figure 7: Imaging results of groove with depth 0.1 mm and buried depth 70 mm. (**a**) DAS, (**b**) VCF, and (**c**) DAS_VCF with focus depth 30 mm; (**d**) DAS, (**e**) VCF, and (**f**) DAS_VCF with focus depth 40 mm; (**g**) DAS, (**h**) VCF, and (**i**) DAS_VCF with focus depth 50 mm; (**j**) DAS, (**k**) VCF, and (**l**) DAS_VCF with focus depth 60 mm; (**m**) DAS, (**n**) VCF, and (**o**) DAS_VCF with focus depth 70 mm. Furthermore, in addition to the noise introduced by the inhomogeneous medium, there is very strong electrical noise in the image, as shown in the orange rectangle of Figure 8m.