## 3 Results and Discussion  
### Spatial Coherence Trends in MLT Images of a Homogeneous Phantom  
Figure 2 shows the trend of backscattered signals SC (averaged over a small region around the focal depth, as said before), measured on the simulated uniform phantom images. The trend is plotted for SLT and 4/6/8/12 MLT in the three scenarios described in Section 2.4. Figure 3 represents the total spatial coherence values obtained by computing a summation over lags of the values plotted in Figure 2, for each MLT configuration (i.e., for each curve). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{1}{c}{**Scenario 1**} & \multicolumn{2}{c}{**Scenario 2**} & \multicolumn{2}{c}{**Scenario 3**} \\ \hline \(N_{TX}\) & \(\theta_{TX}\) & \(N_{TX}\) & \(\theta_{TX}\) & \(N_{TX}\) & \(\theta_{TX}\) \\ \hline
1 & \(\theta_{1}\) = 90\({}^{\circ}\) & 1 & \(\theta_{12}\) & - & - \\
4 & \(\theta_{4}\) = \(\theta_{1}\)/4 & 4 & \(\theta_{12}\) & 4  
Figure 2 shows that SC has a triangular trend in SLT, which decreases from 1 at lag 0 to about \(-0.1\) at lag 63. This trend is consistent with the one predicted by the VCZ theorem, which states that (at the focal depth) the SC of backscattered signals is the Fourier transform of the field intensity. By looking at Figure 2a, we can also see that, when the number of TX beams increases (decreasing at the same time the angle among them), SC decreases more rapidly in the short-lag region, immediately after the peak at lag 0, and varies following a sort of damped oscillation for each different MLT case. On the whole, as shown by Figure 3a, total coherence decreases non-linearly as the number of MLT beams increases. In order to understand which factor determines such trends and an overall decrease of SC, we can look at Figure 2b,c and Figure 3b,c. Figure 2b refers to the case in which only the number of  
Figure 3: Total average spatial coherence, measured in a 5 \(\times\) 5 mm\({}^{2}\) area around (\(x\), \(z\)) = (0, 70) mm in the different scenarios of Table 1: (**a**) both the number of TX beams and the angle among them varies (as in SLT or 4/6/8/12-MLT); (**b**) only the number of TX beams varies (\(N_{TX}\) = 1/4/6/8/12), while the angular distance among them is fixed to the one of 12-MLT; (**c**) the number of TX beams is set to four, while the angular distance among them is the one of 4/6/8/12-MLT (in this last case, the legend refers to the number of TX beams which would determine the angular distance). Figure 2: Normalized spatial covariance trend vs. lags, measured on the simulated uniform phantom data, and averaged over a 5 \(\times\) 5 mm\({}^{2}\) area around (\(x\), \(z\)) = (0, 70) mm in the different scenarios of Table 1: (**a**) both the number of TX beams and the angle among them varies (as in SLT or 4/6/8/12-MLT); (**b**) only the number of TX beams varies (\(N_{TX}\) = 1/4/6/8/12), while the angular distance among them is fixed to the one of 12-MLT; (**c**) the number of TX beams is set to four, while the angular distance among them is the one of 4/6/8/12-MLT (in this last case, the legend refers to the number of TX beams which would determine the angular distance). simultaneous TX beams varies, but the angle among them is fixed; in this way, it is possible to analyze the dependence of the SC trend on \(N_{TX}\) only. The plots clearly show that this time the SC oscillatory trend becomes similar for all MLT configurations (except for SLT), but the lobes have different peak amplitudes and widths, which still makes the total SC decrease when increasing the number of TX beams (Figure 3b). On the other hand, when the number of MLT beams \(N_{TX}\) is fixed, while the angle among them varies, we see in Figure 2c that the SC trend shows a different pitch between secondary lobes. Instead, total SC becomes similar in all cases (Figure 3c).