## 3 Results  
### Simulation Results  
The imaging depth, common FOV area, and the theoretical maximum depth affected by the cross-talk artifacts generated by the direct transmissions were calculated for the different configurations defined in Section 2.2. Figure 2 shows the relationships between the investigated parameters. The targeted imaging depth increases at larger angles and separation between the arrays; the area of the common FOV does not depend on the gap between the arrays and increases with the angle between them, while the maximum depth affected by cross-talks is mostly dictated by the gap between the arrays. For the considered ranges of parameters, the imaging depth ranges from 19 mm to 267 mm, the area of the common FOV from 1232 mm\({}^{2}\) to 4742 mm\({}^{2}\), and the theoretical depth affected by the cross-talk artifacts ranges from 26 mm to 52 mm. The effects of \(\alpha_{max}\) on the PSF are shown in Figure 3, where the lateral FWHM, PSMR and SMER are displayed as a function of the imaging depth, angle between arrays, and \(\alpha_{max}\), keeping the number of transmissions per array equal to 3, \((-\alpha_{max},0^{\circ},\alpha_{max})\), and the gap between the arrays equal to zero. These results show that, for a continuous aperture (gap = 0), PSMR and SMER decrease at larger steering angles, while the FWHM does not depend strongly on \(\alpha_{max}\) and, as expected, deteriorates with increasing imaging depth. While for each imaging depth PSMR and SMER have a clear minimum (\(<\)\(-\)25 dB and \(<\)2 dB, respectively, dark blue regions in Figure 3b,c) that corresponds to a certain \(\alpha_{max}\), steering the transmitted PW does not produce any significant effect on the main lobe width (Figure 3). These results suggest that for the best trade-off, \(\alpha_{max}\) can be determined by minimizing both PSMR and SMER at the desired imaging depth. The locus of these values is indicated by the white line in Figure 3.  
The effect of the number of transmitted PWs on the image metrics is depicted in Figure 4, where \(\alpha_{max}\) was set according to the imaging depth (white line in Figure 3). The extreme simulated cases with the minimum (3 PWs) and maximum (11 PWs) number of transmitted PWs per array are shown. For the other cases with 5, 6, 7 and 9 PWs the metrics follow the same trends with values in between. Since \(\theta\) and thus depth is the main determinant of FWHM and the gap between the arrays plays the main role for PSMR and SMER, averaged results over the gap and over the angle between transducers are shown for FWHM, and PSMR and SMER, respectively (Figure 4 bottom row). FWHM and PSMR do not depend on the number of transmitted PWs, and SMER improves (lower values) with increasing transmissions, reaching a plateau after about 5 PWs. Figure 2: **(a)** Imaging depth dependency on angle (\(\theta\)) and gap between arrays. **(b)** Area of the overlapped FOV as function of the angle between arrays. **(c)** Theoretical cross-talk depth dependency on angle and gap between arrays. Figure 5 shows the different metrics as a function of the angle and the separation between the arrays, where \(\alpha_{\text{max}}\) was set according to the imaging depth (chosen using Figure 3) and the number of transmitted PWs per array to 7 (chosen to ensure stable (plateau) performance using Figure 4). Note that 7 PWs is the next number of transmissions investigated after the minimum one obtained from Figure 4 and was chosen as a conservative solution. In agreement with previous results, PSMR and SMER mainly depend on the gap between the arrays, worsening at larger gaps, while FWHM depends on the angle  
Figure 4: FWHM, PSMR and SMER as function of the angle and the separation between the arrays compounding 3 PWs ((**a-c**), first row) and \(11\) PWs ((**d–f**), middle row) per array with \(\alpha_{\text{max}}\) determined according to the imaging depth (Figure 3) and with Tukey apodization on transmit. (**g**) Averaged FWHM over the gap between transducers.