## 3 Results
### Experimental Validation of the 4-D US Platform Developped
These results confirm the previous observations, indicating the degree of degradation of the image quality when downsampled configurations are used. Another example of the 9 DW acquisition with the same configurations of the US transducer is shown in Figure 6. A \"grappe\" wire was imaged in this standard phantom. The same general observations can be done as in the previous example. Additionally, in the \((x,\,z)\) plane, the separation of 2 different wires positioned very close to each-other (at depth = 28 mm) is very hard to identify, except for the case of the full active array (first column). Moreover, the contour of the wires positioned at the border of the image, not directly in front of the US probe, are very hard to identify for configurations with a lower number of elements. Important secondary lobes and image degradation is visible in the \((y,\,z)\) planes illustrated here. The two parallel lines are clearly distinguished when using 1024 elements, but for 256 elements and even for some cases with 512 elements, it is hard to define them. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Resolution (nm)**} & \multirow{2}{*}{**Full Array**} & **1 Line ON/1 Line OFF** & **2 Lines ON/2 Lines OFF** & **4 Lines ON/4 Lines OFF** & **Middle ON** & **1 Line ON/3 Lines OFF** \\ \hline \multirow{6}{*}{(\(x,\,z\)) plane} & axial 10 mm & 1.8 & 2.5 & 2.4 & 2.8 & 2.9 & 4 \\  & axial 20 mm & 1.7 & 2.5 & 3.1 & 2.2 & 2.3 & 3.3 \\  & axial 30 mm & 1.9 & 2.5 & 2 & 1.7 & 2.5 & 2.5 \\  & **Average** & **1.8** & **2.5** & **2.5** & **2.2** & **2.5** & **3.3** \\ \cline{2-6}  & lateral 10 mm & 0.9 & 1.6 & 1.7 & 0.9 & 1 & 2.3 \\  & lateral 20 mm & 3 & 2.9 & 2.8 & 1.9 & 2.9 & 3.1 \\  & lateral 30 mm & 2 & 2.9 & 3 & 3.1 & 3 & 3.4 \\  & **Average** & **2** & **2.4** & **2.5** & **2** & **2.3** & **2.9** \\ \hline \multirow{6}{*}{**CR (dB)**} & Full Array & 1 line ON/1 line OFF & 2 lines ON/2 lines OFF & 4 lines ON/4 lines OFF & Middle ON & 1 line ON/3 lines OFF \\ \cline{1-1}  & (y,\,z) plane & 7.71 & 2.84 & 2.30 & 4.20 & 3.50 & 2.02 \\ \hline \multirow{2}{*}{**CNR (dB)**} & Full array & 1 line ON/1 line OFF & 2 lines ON/2 lines OFF & 4 lines ON/4 lines OFF & Middle ON & 1 line ON/3 lines OFF \\ \cline{1-1}  & (y,\,z) plane & 2.99 & \(-\)5.36 & \(-\)6.54 & \(-\)2.61 & \(-\)4.25 & \(-\)7.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: FWHM calculated in the \((x,\,z)\) plane over three scatters located at depths 10, 20, 30 mm and the CR and CNR evaluated on the \((y,\,z)\) central slices of the acquired volumes. Figure 5: Experimental data acquired with 9 DW on a standard phantom. The \((x,\,z)\) plane (first row) and the \((y,\,z)\) plane (second row) are shown in the center of the US device. Different configurations of the array were used: full array, 1 line ON-1 line OFF, 2 lines ON-2 lines OFF, 4 lines ON-4 lines OFF, middle ON and 1 line ON-3 lines OFF. A dynamic of 50 dB has been used in all the images. An example of 9 PW acquisition on a cyst phantom and wires placed at different depths is illustrated in Figure 7. In the \((x,z)\) plane, in the near field, we can identify the presented scatters (at depth = 7 mm and 19 mm) for all the cases, but in the far-field, the contour of the cyst is affected by lower number of elements compared with the full-matrix array. The anechoic cyst at 40 mm depth is clearly detectable with all the configurations tested, in both \((x,z)\) and \((y,z)\) planes but its borders are less visible in \((y,z)\) planes (second row) with downsampled configurations, the degradation of the obtained images being clearly visible for cases with 512 or 256 elements. The measured values for CR and CNR obtained for each of these acquisitions in \((x,z)\) central planes are quite close for all the configurations due to the presence of the same number of active elements in the \(x\) direction, while the values obtained in the \((y,z)\) plane are displayed in Table 4, the last 2 rows.