## 5 Experiment of Imaging Detection
### Analysis of the Results of the Test for Imaging Detection
\begin{table}
\begin{tabular}{c c} \hline
**Transducer Frame Rate (No.)** & **Image Background Gray Level (\(f\))** \\ \hline
1 & 21.25 \\
2 & 13.71 \\
3 & 12.59 \\
4 & 11.28 \\
5 & 9.13 \\
6 & 7.43 \\
7 & 6.69 \\
8 & 6.12 \\
9 & 6.49 \\
10 & 6.03 \\
11 & 6.89 \\
12 & 7.13 \\
13 & 6.80 \\
14 & 6.62 \\ \hline \end{tabular}
\end{table} 
Table 3: Background gray level testing data of multi-frame images with left-rank arc sparse array. The data in Table 3 show that the image background gray of the left-ranked curved sparse array shows the change rule of first decreasing and then leveling off with the increase in the receiving aperture. For the multi-frame imaging of the left-rank arc sparse array, the gray information of the defects in the multi-frame images of the detected left-rank arc sparse array is shown in Table 4. The variation in image gray values for the same scatterer at the natural focus is relatively small and tends to be stable. As depicted in Figure 7, the image gray values of holes \(A\), \(B\), \(C\), and \(D\), located on both sides of the natural focus of the arc sparse array, remain almost unchanged across multiple frames. However, the image gray value of hole \(E\) on the natural focus demonstrates a significant change range. This is primarily due to the occurrence of the \"edge effect\" at hole \(E\), leading to a substantial fluctuation in the signal-to-noise ratio of the image. Specifically, with the eighth frame sequence as the reference, its signal-to-noise ratio is the lowest and follows a general trend of initially decreasing and then increasing. Furthermore, the 14 th frame image corresponds to the full-frame left-rank image, representing full-frame full-rank imaging. Interestingly, the gray level of this image remains approximately equal to the gray levels observed in other frame sequence images. In other words, if we focus solely on the gray level of the scatterer image, single-frame left-rank imaging can be employed as a substitute for full-frame imaging, as it requires less time to obtain the desired imaging results. The data in Table 4 show that the gray values of the images of holes \(A\), \(B\), \(C\), and \(D\) located on either side of the natural focus of the curved sparse array are almost constant over multiple frames, and the gray value of the image of hole E located at the natural focus varies greatly. The signal-to-noise ratio of the left-rank arc sparse array multi-frame imaging is employed to characterize the relationship between the gray level of the defect and the background gray level. The signal-to-noise-ratio is calculated as the logarithmic ratio between the gray level of the defect area and the gray level of the image background. As previously mentioned, the arc sparse array exhibits a \"natural focusing\" effect at the natural focus. The signal-to-noise ratio simulation data of the multi-frame images of the left-rank arc sparse array are as detailed in Table 5. Consequently, the gray level of the image background follows a decreasing trend, enhancing the signal-to-noise ratio of the defect by varying degrees, as depicted in Figure 8. With an increase in the rank of the receiving aperture, the signal-to-noise ratios of holes \(A\), \(B\), \(C\), \(D\), and \(E\) all demonstrate varying degrees of improvement. Holes \(A\), \(B\), \(C\), and \(D\) exhibit a pattern of initially decreasing and then increasing signal-to-noise ratio, ultimately stabilizing.