## 3 Results
### Experimental Validation of the 4-D US Platform Developped  
An example of two different 3-D volumes obtained experimentally with 1024-channels US platform is illustrated in Figure 4). Data were obtained on a standard phantom (Gammex Sono410 SCG, schema illustrated Figure 2b) with a cyst and a \"grappe\" and the orthogonal \((x,z)\) (a) and \((y,z)\) (b) planes are shown. The planes are taken in the center of the transducer's array, at \(x=0\) mm or \(y=0\) mm, respectively. 9 PW were used for the acquisition illustrated in the first row, while 9 DW were used for the acquisition shown in the lower row. Figure 3: Numerical simulations results from Field II on equidistant scatters (2 nd row) and based on an MR image of the heart (3 rd row) corresponding to different configurations of the US array (1 st row) in \((y,z)\) plane. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Axial Resolution (mm)** & **Full Array** & \begin{tabular}{c} **1 Line ON/1** \\ **Line OFF** \\ \end{tabular} & \begin{tabular}{c} **4 Lines ON/4** \\ **Lines OFF** \\ \end{tabular} & \
\begin{tabular}{c} **2 Lines ON/2** \\ **Lines OFF** \\ \end{tabular} &
\begin{tabular}{c} **1 Line ON/3** \\ **Lines OFF** \\ \end{tabular} \\ \hline \((y,z)\) plane & \(\begin{array}{c}40\,\mathrm{dB}\\ -6\,\mathrm{dB}\end{array}\) & 1.2 & 2 & 4.6 & 2.6 & 2.2 \\  & \(\begin{array}{c}-6\,\mathrm{dB}\end{array}\) & 0.7 & 0.8 & 0.9 & 0.6 & 0.6 \\ \hline \((x,z)\) plane & \(\begin{array}{c}40\,\mathrm{dB}\\ -6\,\mathrm{dB}\end{array}\) & 1.2 & 1.2 & 1.2 & 1.2 & 1.2 \\  & \(\begin{array}{c}-6\,\mathrm{dB}\end{array}\) & 0.6 & 0.6 & 0.5 & 0.6 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Axial resolution (the mean value) measured in \((x,z)\) and \((y,z)\) planes for the equidistant scatters when using different configurations of the matrix array. Different configurations of the US matrix array, by using 256, 512 or 1024 elements, were also investigated using the 4-D US platform described above. Figure 5 illustrates an example of volumetric acquisition on a standard phantom with several wires positioned at different depths. Nine DW were transmitted in each of the \(x\) and \(y\) directions for this example. The (\(x\), \(z\)) and (\(y\), \(z\)) planes are shown here, the planes being taken at the center of the active array. As we expected, after visual inspection, the experimental results obtained here clearly indicate the full active array of the US probe as the best configuration. At a rapid inspection, the (\(x\), \(z\)) plane indicates similar results, but at a closer view, some differences are identified. The wire positioned in the near field (depth = 10 mm) is very accurate with this configuration, while the configurations with 512 active elements still illustrate good accuracy. The 256-elements configuration (the last column) presents the worst case, as expected, taking into account the low number of active elements. The same observations are done if we inspect the wire situated in the far-field (depth = 50 mm), where the best accuracy is visible in the full active array configuration. At the same time, the (\(y\), \(z\)) plane illustrates the degradation of the image quality with lower numbers of active elements. The step in the \(y\) direction is modified according to the configuration used, this leading to apparition of important artefacts for some cases, in the near and far-field. Not all the lengths of the wires are visible in this plane, due to small misalignment between the US probe and the wires. Figure 4: Experimental data obtained for the Gammex phantom with 1024 active elements in (\(x\), \(z\)) (**a**,**c**) and (\(y\), \(z\)) (**b**,**d**) planes on a cyst (**a**,**b**) by using 9 PW and “grappe” wires (**c**,**d**) by using 9 DW. A dynamic of 50 dB has been used in all images. Further quantitative results of FWHM are measured and displayed in Table 4, for the \((x,\,z)\) plane, in axial and lateral direction.