## 4 Imaging Data and Results
### Phantom Study  
We applied the beamformers to experimental data acquired with a gelatin-phantom with five nylon targets and an anechoic cyst. The nylon targets and anechoic cyst are designed to evaluate lateral resolution and contrast resolution performance, respectively. Figure 5 shows the different SCF based beamformers results, and all beamformers are applied to the same data.  
The images about the lateral resolution result are shown in Figure 5a-d. The horizontal distances of the center of the point target line are 4, 3, 2, and 1 mm. In the phantom study, images generated by the SCF-based beamformers also show an enhanced effect over DAS. Similar to the simulation results, uSCF still performs best as the boundary between every two points is clearest. For each beamformer, we measured the lateral resolution over all five nylon targets and the average result is in Table 3.  
To show the performance of the SCF-based beamformers in more details, Figure 6 plots the lateral responses to the two rightmost point targets. As expected, the uSCF achieves a higher lateral resolution and lower side lobes, which means better ability to distinguish two close-up points.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Beamformer** & **FWHM (mm)** & **25 mm CR (dB)** & **25 mm gCNR** & **35 mm CR (dB)** & **35 mm gCNR** \\ \hline DAS & 0.1397 \(\pm\) 0.0025 & 9.12 & 0.63 & 11.45 & 0.75 \\ sSCF & 0.1105 \(\pm\) 0.0045 & 13.88 & 0.70 & 15.70 & 0.79 \\ aSCF & 0.1068 \(\pm\) 0.0173 & 15.15 & 0.70 & 17.85 & 0.78 \\ uSCF & 0.0966 \(\pm\) 0.0030 & 20.77 & 0.74 & 22.48 & 0.82 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Contrast performance from simulation.  
Figure 5: Experimental point targets and cyst images of different methods (**a**) (**e**) DAS, (**b**) (**f**) sSCF, (**c**) (**g**) aSCF, (**d**) (**h**) uSCF, All images are shown in a 70 dB dynamic range.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Beamformer** & **FWHM (mm)** & **CR (dB)** & **gCNR** & **CR (dB)** & **gCNR** \\  & **(phantom)** & **(phantom)** & **(phantom)** & **(phantom)** & **(in vivo)** & **(in vivo)** \\ \hline DAS & 0.3192 \(\pm\) 0.0150 & 11.50 & 0.39 & 3.57 & 0.58 \\ sSCF & 0.2304 \(\pm\) 0.0090 & 16.98 & 0.54 & 7.73 & 0.67 \\ aSCF & 0.2484 \(\pm\) 0.0180 & 16.68 & 0.53 & 5.75 & 0.62 \\ uSCF & 0.2028 \(\pm\) 0.0090 & 22.17 & 0.61 & 10.59 & 0.70 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Contrast performance from phantom and _in vivo_.  
Figure 5e-h shows the images of an experimental phantom with a cyst (4 mm in diameter) suspended against the speckle background. Images are shown with the same dynamic range using different methods. These images show noticeable improvement in contrast resolution for the SCF-based beamformers compared with DAS. The cyst is much cleaner with a much sharper edge for uSCF. We also take the white region as ROI and the black as background to analyze the images' CR and gCNR. The results are also shown in Table 3. Compared with other methods, uSCF could offer improvements to CR and gCNR better than the best performance of other beamformers, which means the uSCF image has better ability in distinguishing cyst from background. The uSCF improves CR (92%) and gCNR (56%) over DAS, and it also improves CR (30%) and gCNR (12%) over the best of conventional methods (sSCF).