## 2 Materials and Methods
### Experimental Implementation
#### 2.3.2 Practical Implementation of the Scanning
For the rotation stage, the endpoints \(\alpha_{rot}\)! were defined by \(\Delta\alpha\) and the spatial density taper. The rotation velocity and acceleration were set to their maxima: 90 deg\(\cdot\)s\({}^{-1}\) and 500 deg\(\cdot\)s\({}^{-2}\), respectively. Most rotation moves had a triangular velocity profile. Their duration was then limited by the maximum rotation acceleration. The translation velocity was set constant for each one-way translation at \(\alpha_{rot}\) and equal to:  
\[v(\alpha_{\text{rot}})=\frac{\text{PRF}}{N_{\text{st}}}\frac{\Delta l}{\cos( \alpha_{\text{rot}})}, \tag{3}\]  
where \(PRF\) corresponds to the trigger generator of the synchronization part and \(N_{\text{st}}\) is the number of electronic steering angles. \(N_{\text{st}}\) = 1 in this acquisition mode as only straight transmits were performed, and \(\Delta l\) was equal to \(H\) = 1 mm. The translation acceleration and the \(PRF\) were determined empirically with the following criteria. We wanted that the rotation duration and the translation time between two successive endpoints at different \(\alpha_{rot}\)! (such as B and C in Figure 2) were similar. The rotation duration was already reduced to its minimum; therefore, we had to adapt the translation parameters. We decided to adjust the translation acceleration. We calculated the maximum translation acceleration so that the translation part was covered only when at least 80% of the corresponding rotation distance was traveled. With this acceleration, we determined the maximum translation velocity so that, for a translation travel equal to L = 30 mm, 50% of the translation distance was traveled at a constant velocity (i.e., not in the acceleration or deceleration phase). The \(PRF\) was then deduced from Equation (3) by taking the maximum possible angle \(\alpha_{rot}\) = 45\({}^{\circ}\). With these criteria, we found the following set of parameters: a \(PRF\) of \(N_{\text{st}}\)\(\times\) 50 Hz and, for the translation stage, an acceleration of 235 mm\(\cdot\)s\({}^{-2}\) and a maximum velocity of 60 mm\(\cdot\)s\({}^{-1}\) (maximum velocity from the manufacturer specifications: 90 mm\(\cdot\)s\({}^{-1}\)). With these parameters for L = 30 mm and \(\Delta\alpha_{2}\), 64% of the desired tomographic positions were acquired with an inter-position translation distance greater than 90% of \(\Delta l/\cos(\alpha_{rot})\), the targeted translation sampling period. The motion parameters (endpoints, direction, and velocity) of both stages were coded in a macro, stored in the controller memory. Motion parameters were automatically modified each time an endpoint was reached. In particular, the controller started the rotation motion when the translation coordinate of the corresponding endpoint was exceeded. This mode was implemented for the three angular sampling periods (Table 1). The second acquisition mode was a 3-D, rotate-translate tomographic scan with steered transmit events. The parameters for the stages were the same as for the first acquisition mode. However, we used \(N_{\text{st}}\) = 5 steering angles and the PRF was thus increased to 250 Hz (Table 1). We can note that the translation velocities stayed the same but the targeted inter-position translation distance was \(\Delta l/(\cos(\alpha_{rot})\times N_{\text{st}})\). Consequently, the number of tomographic positions was around five times higher for the same \(\Delta\alpha\). In this second acquisition mode, coherent compounding was performed both in the elevation direction of the array with the mechanical scanning and, additionally, in the lateral direction with electronic beam steering. We studied the effect of the additional compounding on the contrast and resolution of the 3-D image. This mode was implemented only for the median angular sampling period \(\Delta\alpha_{2}\). The third acquisition mode was a translate-only scan with straight transmit events.