## 3 Results
### The FWHM Resolution  
The resolution of isolated microspheres and their amplitude in the DSCA were evaluated for L = 30 mm, according to the method detailed in Section 2.5.1. Ph1 was comprised of about 100 microspheres (Figure 4a). The final data set excluded any pairs of microspheres positioned within 900 \(\upmu\)m of each other and contained 52 microspheres distributed across the DSCA (Figure 5a). Ph1 was also imaged using the translate-only scanning mode (L = 30 mm). For this mode, the resolution along the x-axis was degraded. The fits with the Gaussian blobs were performed in volumes of \(\delta\)\(\lambda\)\({}_{\mathrm{c}}\)\(\times\) 4 \(\lambda\)\({}_{\mathrm{c}}\)\(\times\) 1.5 \(\lambda\)\({}_{\mathrm{c}}\) around each microsphere. Due to the small distance along x between neighboring microspheres, only 16 of them could be isolated in such volumes and included in the data set. The microspheres had a finite diameter of about 200 \(\upmu\)m in diameter. Therefore, they could not exactly be considered as point-like, and the measured FWHM values were expected to be slightly larger than the actual resolution of the system. However, this diameter of microspheres ensured an efficient scattering of the ultrasound waves and a sufficient contrast to the supporting medium (agar gel). Table 2 compares the median \(\pm\) IQR values of the FWHM along the three directions of the coordinate system for the rotate-translate scan at \(\Delta\)\(\alpha\)\({}_{\mathrm{z}}\) and the translate-only scan. We noted that FWHMy and FWHMz are barely influenced by the rotation scan. Indeed, the resolution along the y-axis was mainly limited by the finite length of the active aperture of the linear array, and the resolution along the z-axis was mostly influenced by the duration of the pulsed echo. Figure 5c shows that FWHMy had a small deviation for z \(<\) 30 mm due to the fixed lateral f-number used in the reconstruction method (Appendix A). For z \(>\) 30 mm, the effective lateral f-number could no longer be maintained fixed by adjusting the apodized reception aperture of the array as the full length of the array was used. Therefore, the effective lateral f-number increased and the resolution degraded with the increasing depth z. The FWHMy values reported in Table 2 were computed for the full range of depths. Figure 5c illustrates that the estimated median value of FWHMy is robust to the outliers for z \(>\) 30 mm. The reported IQR values, which measure the statistical dispersion were, however, larger than they would have been if the microspheres at z \(>\) 30 mm had been discarded. Figure 5d shows the homogeneity of  
Figure 4: US images of phantom Ph1 performed with different translation ranges \(L\). **(a)** Optical picture showing the spatial distribution of microspheres. **(b–d)** Maximum amplitude projection (MAP) images along the y-axis for \(L\) = 30, 20, and 10 mm, respectively. The dotted diamond indicates the area probed with all the different orientations of the array, named diamond-shaped, cross-sectional area (DSCA) (Figure 1c). The MAP images are in linear gray scale. The same gray scale was used for **(b–d)**. For a better readability, the gray scale was fixed. White pixels correspond to the maxima of the MAP image for L = 30 mm. Black pixels correspond to an amplitude equal to zero. The islets **(e–g)** show a zoom of the microsphere, indicated with the yellow arrow for L = 30, 20, and 10 mm, respectively. The pixels displayed in white correspond to the maximum for L = 30 mm. The red arrows show microspheres located outside of the DSCA in **(d)**. The yellow arrow points to a microsphere inside the blind area in **(d)**. Full-size images corresponding to **(c,d)** are displayed in Figure S1. FWHMz with z. Unlike FWHMy and FWHMz, FWHMx was found to be 3.1 times smaller with the rotate-translate scan. The resolution along the x-axis was linked to the angular aperture along the elevation direction of the array.