## 3 Results  
### Influence of the Translation Range on the Imaged Volume  
The cross section of the volume probed at all orientations \(\alpha_{\rm rot}\) of the array and perpendicular to the rotation axis is presented in Figure 1c. This cross-sectional area was expected to have a diamond shape and its area should depend on the translation range L. We name DSCA this diamond-shaped, cross-sectional area. The cross section of the volume probed by none of the tomographic positions is named the blind area (Figure 1c). The regions outside of the DSCA (and the blind area) were probed with fewer orientations of the array. Therefore, we expected a degraded resolution and a lower amplitude for this part of the image.  
To experimentally study the influence of L on the cross section of the imaged volume perpendicular to the rotation axis, we performed several tomographic acquisitions of Ph1 for three different translation ranges. The angular sampling was kept constant and equal to \(\Delta\alpha_{2}\). Ph1 contained 200-\(\upmu\)m-diameter microspheres that were sparsely distributed over the cross section of its 26.5-mm-diameter cylindrical form (Figure 4a). We chose L values equal to 30 mm, 20 mm, and 10 mm, corresponding to 508, 396, and 280 tomographic positions and scanning durations of 10.2, 7.9, and 5.6 s, respectively. The ratio of the scanning duration relative to L became lower as L increased, while the sampling parameters and, in particular, the translation velocities computed from Equation (3) were identical for all scans. This is due to fact that the acceleration and deceleration phases of the translation motions had the same duration for all three scans, but these phases, during which the translation velocity was lower, were proportionally shorter as L increased. The plane of microspheres was placed around y = 0 mm. Each microsphere could be identified individually, allowing a qualitative evaluation of the effective imaged area and a comparison of the image quality inside and outside the DSCA. We reconstructed images of dimensions \(\Delta\)x \(\times\)\(\Delta\)y \(\times\)\(\Delta\)z = 30 \(\times\) 2 \(\times\) 30 mm\({}^{3}\). Figure 4b-d presents the maximum amplitude projection (MAP) of the 3-D US image along the y-axis.  
Figure 4b presents the US image for the largest translation range L = 30 mm. As illustrated by the circular markers, which are landmarks, the spatial distributions of the microspheres in the US image and in the optical pictures match (Figure 4a). This result demonstrates the ability of our system to perform US images in the xz-plane and to localize small scatterers.  
For L = 30 mm, almost all microspheres were included in the DSCA. However, when the translation range was reduced, some microspheres entered the blind area on the side of the DSCA (along the x-direction), as illustrated by the microsphere marked with the yellow arrow in Figure 4, which is no longer visible for L = 10 mm. Red arrows in Figure 4d illustrate that microspheres were indeed reconstructed with better resolution and amplitude when they were in the vicinity or inside the DSCA, compared to when they were located in the vicinity of the blind area. The islets (Figure 4e-g) further show the image amplitude degradation with a zoom on one microsphere.  
With the developed scanner, the operator can adjust the translation range to fit the region of interest within the DSCA. Thus, the scan duration can be reduced when the object to image is smaller and the translation range can be more strongly limited.