## 5 Experiment of Imaging Detection
### Analysis of the Results of the Test for Imaging Detection
Overall, the gray value change pattern of the scatterers remains consistent with the change patterns observed in other frame sequences. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Image Gray Level (\(f\))**} \\ \hline
**Transducer Frame** & & & & \\
**Rate (No.)** & **Hole \(A\)** & **Hole \(B\)** & **Hole \(C\)** & **Hole \(D\)** & **Hole \(E\)** \\ \hline
1 & 53.75 & 85.00 & 97.50 & 81.25 & 162.5 \\
2 & 27.50 & 80.00 & 92.50 & 63.75 & 125.0 \\
3 & 35.24 & 85.00 & 91.22 & 80.85 & 124.4 \\
4 & 30.60 & 79.90 & 59.90 & 45.90 & 110.5 \\
5 & 25.99 & 55.22 & 84.46 & 50.35 & 63.34 \\
6 & 27.55 & 54.39 & 67.11 & 39.56 & 98.19 \\
7 & 31.26 & 55.63 & 59.38 & 50.63 & 78.13 \\
8 & 24.59 & 59.01 & 69.55 & 36.53 & 59.01 \\
9 & 28.33 & 52.73 & 83.43 & 30.69 & 81.85 \\
10 & 26.60 & 44.59 & 65.71 & 39.89 & 111.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Multi-frame image gray testing data of left-rank arc sparse array. Figure 8: Signal-to-noise ratio of multi-frame images of left-rank arc sparse array. Table 2 indicates the grayscale trend of the multi-frame images of the left-rank arc sparse array. The data of Hole \(B\), Hole \(C\), and Hole \(E\) all show an increasing pattern, but with little change in gray level. Their test data are plotted as an image, as shown in Figure 5.  
In the multi-frame imaging of the left-rank arc sparse array, the variation in image gray values corresponds to changes in the background gray value. The image background gray level of the left-rank arc sparse array is tested and its test data are shown in Table 3. The background gray value is determined by the gray value in the region surrounding the defect. Notably, the gray values of defect holes \(A\), \(B\), \(C\), \(D\), and \(E\) consistently exhibit a decreasing trend. Examining individual frame sequence images, as portrayed in Figure 6, the background gray values of the first, second, third, fourth, and fifth frames in the left-rank receiving aperture are relatively higher. However, they also display a declining pattern. This can be attributed to the \"edge effect\" of the array elements, which causes the background gray values to be larger compared to other receiving array elements within the array. The background gray values of the other frame sequences in the left-rank array comparatively are smaller and exhibit a consistent and close pattern. The background gray values of the array elements located in the middle and right of the left-rank receiving aperture show a gradual change, maintaining a relatively consistent horizontal line. In contrast, when the frame sequence of the left-rank receiving aperture in the arc sparse array is at the 10 th frame, the background gray value of the image is the lowest. Subsequently, the background gray values of the eleventh, twelfth, thirteenth, and fourteenth frames experience a slight increase, but this increase is not significant and remains largely consistent with the gray values of the eighth, ninth, and tenth frames. As the background gray value of the image approaches about 64% of the full rank in the left rank, the image gray value gradually decreases. A smaller background gray value in the image results in relatively higher contrast, thereby enhancing the imaging process and yielding improved imaging results, as exemplified in Figure 6. \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{6}{c}{**Image Gray Level (\(f\))**} \\ \hline
**Transducer Frame** & **Hole \(A\)** & **Hole \(B\)** & **Hole \(C\)** & **Hole \(D\)** & **Hole \(E\)** \\ \hline
11 & 23.33 & 41.67 & 57.50 & 45.00 & 113.3 \\
12 & 41.44 & 58.44 & 85.00 & 62.69 & 100.9 \\
13 & 70.83 & 85.00 & 99.17 & 75.56 & 132.2 \\
14 & 32.08 & 65.57 & 87.43 & 78.69 & 109.3 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._