## 3 Results
### The Cyst Resolution (CyR)  
The cystic resolution further characterized the influence of the angular sampling on the image quality by quantifying the effect of the side lobes of the PSF on the image contrast. Figure 7a presents an image of Ph3 for the plane y = 0 with a logarithmic gray scale (\(\Delta\alpha_{2}\) and L = 30 mm). The side lobes of the LSF were visually similar for the four threads that were all included in the DSCA. Figure 8a displays the cyst contrast \(C_{cdB}\) of the image of Thread 2 for the four rotate-translate scans presented in Table 1. The iCyR corresponds to a radius that produces a contrast of \(-\)20 dB. Table 3 presents the iCyR values obtained for each thread. The spatial homogeneity of the iCyR can be noticed for a given angular sampling. One exception was observed for Thread 1 and \(\Delta\alpha_{1}\). In this case, the degraded FWHMx resolution for \(\Delta\alpha_{1}\) and the vicinity of Thread 4 biased the iCyR estimation. For straight transmits, the iCyR decreased with the decreasing value of \(\Delta\alpha\), which means that the spatial extension of the side lobes decreased and the contrast increased. The difference between \(\Delta\alpha_{2}\) and \(\Delta\alpha_{3}\) indicates that the latter angular sampling period should be preferred in case the image contrast is desired for the targeted application. Interestingly, the iCyR was close for the steered transmit at \(\Delta\alpha_{2}\) and for the straight transmit at \(\Delta\alpha_{3}\). The same result was observed  
Figure 6: Boxplots of the FWHM along the three axes of the coordinate system: (**a**) FWHM along the x-axis, FWHMx, (**b**) FWHM along the y-axis, FWHMy, (**c**) FWHM along the z-axis, FWHMz. The median value is shown with the red line. The box indicates the IQR values and the outliers are shown with red crosses. In abscissa, the scanning name corresponds to the type of transmit and the angular period. The angular periods are \(\Delta\alpha_{1}\approx 8^{\circ}\), \(\Delta\alpha_{2}\approx 4^{\circ}\), and \(\Delta\alpha_{3}\approx 2^{\circ}\). for the \(Cc_{dB}\) (Figure 8a). Therefore, globally, the lobes of the LSF for \(\Delta\alpha_{2}\) could be mitigated by generating additional tilted planes waves and thereby reinforcing spatial averaging in the image during the reconstruction process. Figure 8: (**a**) Cyst contrast in dB, \(Cc_{dB}\), computed for line spread function (LSF) of Thread 2 as a function of the radius of disk-shaped void considered for Equation (6). The curves correspond to the different angular sampling periods and transmit modes; (**b**) polar representation of the anisotropic cystic resolution, aCyR, assessed on the LSF of Thread 2 for the different angular sampling periods and transmit modes. Figure 7: (**a**) A xz-image of Ph3 (20 mm \(\times\) 20 mm); (**b**) xz-image of Ph2 (30 mm \(\times\) 30 mm). Both xz-images are at y = 0 and centered on x = 0 and z = 25 mm. They correspond to acquisitions performed in straight transmit at \(\Delta\alpha_{2}\) with L = 30 mm. Numbers identify the threads (**a**) and holes (**b**), respectively. The speckle zone considered to calculate the image contrast is designated with a red circle in (**b**). The images are displayed with \(-\)60-dB dynamic range. Figure 8b compares the anisotropic sectorial cystic resolution aCyR for Thread 2 and the different angular sampling periods. While FWHMz and FWHMx had similar values (Figure 6) indicating an isotropic center peak for the LSF, we noted that the polar plot of the aCyR had the shape of a lemniscate (\(\infty\)-symbol) for every angular sampling period. The aCyR was much smaller around the z-axis than along the x-axis. This anisotropy of the side lobes was linked to the finite synthetic angular aperture (around 90\({}^{\circ}\)) and its orientation. Therefore, the image contrast depended on the orientation of the structure in the xz-plane. Second, the angular sampling mostly influenced the aCyR along the x-axis. A left-right asymmetry of the aCyR can also be noticed.