## 4 Experimental Results
### Two Regular Defects  
The second experiment in which there were two 20 mm diameter circular flat-bottomed holes in the monitored aluminum was conducted, as shown in Figure 8a. One of the holes, whose thickness loss was 50%, was in the center of the plate. The center coordinate of another hole was x = 220 mm, y = 290 mm, whose thickness loss was 30%. The monitored area was divided into 80 \(\times\) 80 grids. The tomographic images reconstructed using the SIRT and our Equation (12) are shown in Figure 8b,c. From Figure 8b, it can be seen that the tomographic reconstruction results using the SIRT confused the defect of the lower thickness loss with the artifacts. By contrast, Figure 8c obtained using the method in this paper clearly shows both the thickness losses on the plate.  
The monitored area was also respectively divided into 20 \(\times\) 20, 40 \(\times\) 40, 60 \(\times\) 60 and 80 \(\times\) 80 grids. The tomographic images reconstructed using the SIRT are shown in Figure 9a-d. From Figure 9a-d, it is clear that using the SIRT, two corrosion areas cannot be easily distinguished. Even if the grid density  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Grid Density**} & \multicolumn{2}{c}{**The Number of Grids**} & \multirow{2}{*}{\
\begin{tabular}{c} **The Number of Grids** \\ **Calculated by the** **SIRT** \\ **Proposed Method** \\ \end{tabular} } & \multicolumn{1}{c}{
\begin{tabular}{c} **The Number of Grids** \\ **Calculated by the** **Calculated by the** **Proposed Method** \\ \end{tabular} } \\ \hline \(20\times 20\) & 4 & 32 & 4 \\ \(40\times 40\) & 12 & 68 & 12 \\ \(60\times 60\) & 32 & 132 & 32 \\ \(80\times 80\) & 52 & 456 & 56 \\ \hline \hline \end{tabular}
\end{table}
Table 1: With different grid density, the number of grids covered by the actual corrosion area were compared to ones calculated respectively by the SIRT and the proposed method.  
Figure 8: Tomographic reconstruction images for a 1.5 mm thick aluminum plate with two 20 mm diameter circular flat-bottomed holes. Their thickness losses were respectively of 50% and 30% within the flaws. (**a**) The actual locations and sizes of the flaws. (**b**) The tomographic reconstruction image using the SIRT. (**c**) The tomographic reconstruction image using our method.  
was increased, the corrosion area of the low thickness loss was confused with the artifacts. By contrast, Figure 10a-d are the tomographic reconstruction images using our method. These tomographic images show that our method could easily identify two corrosion areas, and with an increasing grid density, the detail of corrosion area was gradually clearer. It can also be seen that the number of grids calculated by our methods with different grid density was almost the same as the areas covered by the actual corrosion ones, as shown in Table 2.  
Figure 10: _Cont._  
Figure 9: Tomographic reconstruction images for a 1.5 mm thick aluminum plate with two 20 mm diameter circular flat-bottomed holes with different grid density using SIRT. Their thickness losses were respectively of 50% and 30% within the flaws. (**a**) The number of grids was \(20\times 20\), (**b**) the number of grids was \(40\times 40\), (**c**) the number of grids was \(60\times 60\), and (**d**) the number of grids was \(80\times 80\).