## 3 Results
### Experiments  
#### 3.2.1 Experiment A  
Three experiments were also conducted to validate the performance of the proposed method. The setup of experiment A is shown in Figure 6. Most of the parameters were the same as those in the simulation, except for the specimen. The specimen used in the experiment was an aluminum block, with a sound velocity of 6450 m/s. The reflectors were four SDHs aligned in an angular direction with a diameter of 1 mm. The horizontal distance of these SDHs was 3 mm, as was the vertical distance. The ultrasonic transducer used in the experiment was a linear array produced by Olympus Corporation Company in Japan. The detailed parameters of the array were the same as those used in the simulation, and are listed in Table 1. The FMC data acquisition was implemented with the EXPLORER 64/128 FMC equipment produced by The Phased Array Company (TPAC, West Chester, OH, USA), and the transmission and reception parameters were as shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{2}{c}{**SDH 2**} & \multicolumn{2}{c}{**SDH 4**} & \multicolumn{2}{c}{**SDH 6**} & \multicolumn{2}{c}{**SDH 8**} & \multicolumn{2}{c}{**SDH 10**} & \multicolumn{2}{c}{**Average**} & \multicolumn{2}{c}{**Time**} \\ \cline{2-13}  & **API** & **FWHM** & **API** & **FWHM** & **API** & **FWHM** & **API** & **FWHM** & **API** & **FWHM** & **API** & **FWHM** & **Cost** \\ \hline Time- & & & & & & & & & & & & & & \\ domain & 0.7068 & 0.9937 & 0.7013 & 1.0313 & 0.7233 & 1.05 & 0.7365 & 1.0125 & 0.7648 & 1.0125 & 0.7264 & 1.02 & 258.12 s \\ TFM & & & & & & & & & & & & & \\ Proposed & 0.7666 & 1.0813 & 0.6853 & 1.0125 & 0.6670 & 0.9 & 0.6756 & 0.9188 & 0.7431 & 0.9562 & 0.7070 & 0.9738 & 4.31 s \\ method & +8.5\% & +8.8\% & \(-2.3\%\) & \(-1.8\%\) & \(-7.8\%\) & \(-14.3\%\) & \(-8.2\%\) & \(-9.3\%\) & \(-2.8\%\) & \(-5.6\%\) & \(-2.3\%\) & \(-4.5\%\) & \(-98.3\%\) \\ \hline \hline \end{tabular} Note: the unit of FWHM is millimeters (mm).  
\end{table} 
Table 2: Representative APIs and time costs with different imaging methods in simulation. Figure 6: The geometry of oblique incidence situation for experiment. The experimental data were also processed by both the TFM and the proposed method. The raw dataset size was 4096 \(\times\) 64 \(\times\) 64 and the reconstructed image sizes were 300 \(\times\) 300. Figure 7a,b shows the results reconstructed by the TFM and the proposed method, respectively. Figure 7c-f shows the local enlarged images of the four SDHs in the result of the TFM from left to right, respectively. Figure 7g-j shows the same enlarged images in the result of the proposed method. The results show that both TFM and the proposed method can compensate for the wave-field rotation very well. However, as in the simulation, the experimental result of the TFM has a problem with distortion. The proposed method can reconstruct the reflectors more accurately. The normalized amplitudes of the experimental results are given in Figure 8. From this figure we can see that the background noise level of the TFM result is higher than that of the proposed method. The SNRs of the reconstruction results of the TFM and the proposed method were 5.85 and 9.19, respectively. In order to compare the experimental results of these two methods in detail, we calculated the APIs and FWHMs of four SDHs in the reconstructed results of the two methods, as listed in Table 4. Furthermore, the time consumptions required for the two methods to reconstruct the experimental result are also listed in Table 4. It can be seen that the TFM costs about 255.89 s to reconstruct the image with an average API of 0.7302 and an FWHM of 1.0315 mm. In contrast, the proposed method only takes 4.25 s to reconstruct the same sized image with an average API of 0.6691 and an FWHM of 0.9726 mm. This shows that the proposed method can enhance the \(-6\) dB lateral resolution by about 5.7% over the TFM and improve the computational efficiency by about 60 times.