## 3 Results and Discussion
### Simulated Images with MLT and Short-Lag F-DMAS  
In this section, images generated with the short-lag F-DMAS formulation are analyzed, and the trend of each performance parameter is reported along with the maximum lag, in the MLT configurations considered. First analyses have been performed on the simulated PSF at the focal depth, by measuring the lateral resolution at \(-6\) dB; the results are plotted in Figure 4.  
Figure 4: Lateral resolution (at \(-6\) dB) trends, measured on the PSF images with varying maximum-lag, 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). The plots in Figure 4a show that no significant difference among lateral resolution curves can generally be observed when the number of TX beams and their angular distance vary, from SLT to 4/6/8/12-MLT, both for DAS and F-DMAS images. In any case, a better resolution is always achieved by F-DMAS, with an increasing trend from \(\sim\)1.4 mm at lag 1 to \(\sim\)2.4 mm at lag 63 on average, as compared to \(\sim\)3 mm on average for DAS. When the angular distance between multiple TX beams is fixed (Figure 4b), the trend of F-DMAS image resolution remains almost the same, as observed in Figure 4a. The curves are actually slightly different in the 4/6/8/12-MLT cases, but no significant variation is observed: the trend is always increasing and better values are achieved by F-DMAS than DAS for all maximum-lag values. Similar results are obtained in Figure 4c, when a fixed number (i.e., four) of TX beams is used while varying \(\theta_{TX}\). Therefore, both DAS with Tukey RX apodization and F-DMAS are generally able to keep the lateral resolution unaltered when MLT with an increasing number of TX beams is applied to improve the frame-rate; this is probably because RX cross-talk in MLT mainly affects the lateral sides of the PSFs and not their main lobe width at \(-\)6 dB. However, F-DMAS both reduces RX cross-talk better than DAS and achieves up to a 1.5 mm better lateral resolution. If we consider the short-lag F-DMAS formulation, lateral resolution varies with the maximum lag employed; in particular, it worsens as the maximum lag increases. As an example, Figure 5 (which refers to the 4-MLT configuration of scenario 1, cf. Table 1), clearly shows that the standard F-DMAS always achieves better RX cross-talk reduction than DAS, as well as lower side-lobe levels and a higher lateral resolution, which also makes TX cross-talk (that is suppressed in both cases by Tukey TX apodization) be confined to a narrower region [19]. When the maximum lag is reduced to 40 (Figure 5d) or 10 (Figure 5c), the PSF main-lobes become increasingly narrow as compared to the standard F-DMAS case (Figure 5b), but unfortunately, side-lobes and RX cross-talk artifacts become more visible at the same time (which, on the other hand, affects contrast performance, as will be shown hereinafter), becoming even worse than those of DAS when the maximum lag is limited to 10. Figure 5: 4-MLT PSF images obtained in scenario 1 by applying (**a**) DAS with Tukey apodization in TX/RX, or F-DMAS with (**b**) maximum lag = 63 (standard version), (**c**) maximum lag = 10, (**d**) maximum lag = 40, and Tukey apodization in TX only. Figures are displayed over an 80 dB dynamic range, in order to better highlight the possible presence of small cross-talk artifacts.