# Requirements and Hardware Limitations of High-Frame-Rate 3-D Ultrasound Imaging Systems
## 3 Experiments  
Five HFR experimental tests were performed by using, in each case, both star and ring topologies. In all experiments, a 2-D spiral array probe [41] capable of scanning either a single plane, a bi-plane, or a full volume, was used. Such a probe was obtained by selecting 256 elements from the 1024-element Vermon matrix probe [42]. In addition, 3.7 MHz 4-cycle sinusoidal bursts were used as TX signals. The ULA-OP 256 was programmed to transmit sequences of diverging waves originating from one (DW1), three (DW3), or five (DW5) virtual sources. The position (x, y, z) of each virtual source was defined as follows:  
\[\left\{ \begin{array}{l}z=\frac{-\rho}{\sqrt{1+\text{tg}\left(\theta_{\text{ xz}}\right)^{2}+\text{tg}\left(\theta_{\text{yz}}\right)^{2}}}\\ \text{x}=\text{z}\text{tg}\left(\theta_{\text{xz}}\right)\\ \text{y}=\text{z}\text{tg}\left(\theta_{\text{yz}}\right)\end{array} \right. \tag{6}\]  
where \(\rho\) is the virtual source distance from the center of the array, \(\theta_{\text{xz}}\) and \(\theta_{\text{yz}}\) are the projection of the steering angle over the xz and yz planes, respectively. The FPGA beamformers [40] were configured to reconstruct all the lines of one frame during each RX interval. Therefore, for DW1 sequences the FR was equal to PRF. For DW3 and DW5, in which three and five frames were coherently compounded, the corresponding FR values were calculated by dividing the PRF by three or five, respectively. Table 2 summarizes the main settings used in the experiments. A depth range of 25 mm (from 5 to 30 mm) was covered in all cases. In experiments I-III such range was obtained through 1280 RF samples (N\({}_{\text{depths}}\)) at F\({}_{\text{S}}\) = 39.06 MHz, while in the remaining experiments N\({}_{\text{depths}}\) was 896 and F\({}_{\text{S}}\) was 26.04 MHz. In all experiments, N\({}_{\text{G}}\) was set to 512. N\({}_{\text{L}}\) represents the number of lines contributing to the final image or volume. In Experiment I, 128 active elements (i.e., N\({}_{\text{FE}}\) = 4) contributed to the formation of. 2-D images composed of 96 lines each. These settings allowed us to evaluate the performance achievable when a small number of elements/channels are involved in 2-D HFR imaging. Experiment II aimed to demonstrate the performance obtainable with a higher number of elements (N\({}_{\text{CH}}\) = 256). Since 2-D images over the xz-plane were obtained in both Experiment I and Experiment II, the positions of the virtual sources were steered only over the xz-plane (\(\theta_{\text{yz}}\) = 0\({}^{\circ}\) and \(\theta_{\text{xz}}\) = \(-\)5, \(-\)2.5, 0, 2.5, 5\({}^{\circ}\)), as shown in the left panel of Figure 3, \(\rho\) was here 6.28 mm, to ensure a diverging wave opening angle of 60\({}^{\circ}\). In Experiment III, the 2-D probe was used to perform bi-plane imaging, i.e., the simultaneous creation of two images, each of 96 lines, over planes at rotational angles of 0\({}^{\circ}\) and 90\({}^{\circ}\), respectively. Bi-plane imaging was also performed in Experiment IV, but the computational load was reduced by decreasing the sampling frequency (from 39.06 to 26.04 MHz) and the number (N\({}_{\text{depths}}\)) of RF samples (from 1280 to 896). This test permitted us to evaluate whether relaxing the requirements on the memories through a reduction of the number of samples could improve the overall system performance. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Experiment I** & **Experiment II** & **Experiment III** & **Experiment IV** & **Experiment V** \\ \hline \multirow{3}{*}{Mode} & DW1 & DW1 & DW1 & DW1 & DW1 \\  & DW3 & DW3 & DW5 & DW5 & DW5 \\ \hline F\({}_{\text{s}}\) [MHz] & & 39.06 & & & 26.04 \\ \hline N\({}_{\text{CH}}\) & 128 & & & 256 & \\ \hline N\({}_{\text{depths}}\) & & 1280 & & & 896 \\ \hline N\({}_{\text{L}}\) & & 96 & & \(96\times 2\) & & \(32\times 30\) \\ \hline \end{tabular}
\end{table} 
Table 2: Table of the experiments performed on star and ring topologies.