## 3 Results  
Figure 6 provides an overview of the estimated axial and lateral displacement and strain fields for all probes using Lu's-fk beam-forming and a line density of two lines per pitch. As expected from Equations (2) to (6), the axial displacement fields (Figure 6a-d) were constant in the axial direction and so the gradient of the axial displacements in axial directions (\(s_{zz}\)) were approximately 0% (see Figure 6f-i). For the 12L4 VF transducer the results revealed some artifacts in the left top corner (Figure 6b,g). These artifacts were visible for all beam-forming strategies and line densities. The MS250 transducer showed more outliers at lower depths (30-52.5 mm) which were probably caused by attenuation of the ultrasound signal at relatively large depths for this frequency. The lateral displacement (Figure 6k-n) and strain fields (Figure 6p-s) resulted in similar observation as the axial results: constant displacement values in lateral direction and so approximately 0% gradient of lateral displacements in that direction (\(s_{xx}\)). Similar artefacts were also visible for the 12L4 VF and MS250 transducers since the axial and lateral displacements were estimated using two-dimensional cross-correlations, which implies these estimations were coupled. Compared to the axial displacement and strain fields (Figure 6a-j), the lateral fields (Figure 6k-t) were noisier for all  
Figure 5: Summary of the processing flow described in the Material and Methods section. This work flow was repeated for every transducer (Table 1). Rectangles represent processing steps (acquisitions or calculations) and parallelograms represent (intermediate) results. transducers, beam-forming strategies and line densities. In the case of two lines per pitch and Lu's-fk beam-forming as shown in Figure 6, \(s_{zz}\) varied between \(\pm\)0.5%, whereas \(s_{xx}\) varied between \(\pm\)1%. Figure 6: Overview of displacement and strain fields after rotation using Lu’s-fk and two lines per pitch as a beam-forming strategy and for line density, respectively: (**a**–**c**) axial displacements; (**f**–**n**) axial strains (\(s_{zz}\)); (**k**–**n**) lateral displacements; (**p**–**s**) lateral strains (\(s_{xx}\)); (**e**,**o**) color bar in millimeters related to the figures in the same row; (**j**,**t**) color bar in percentages related to the figures in the same row. The axis of the displacement and gradient fields represents the position below the transducer in millimeters. In Figure 7, the performances of the axial displacement estimates are summarized for all transducers, beam-forming strategies (including angular weighting and apodization) and line densities. As can be noticed for L7-4 (Figure 7a), the RMSE seemed to be almost constant for all beam-forming strategies and line-densities except DaS with one line per pitch, in which the RMSE increased. For the 12L4 VF (Figure 7b), three lines per pitch provided the lowest RMSE using Lu's-fk, Stolf's-fk or DaS, with apodization or angular weighting. Furthermore, apodization or angular weighting seemed to decrease the RMSE for this transducer. However, the opposite effect of weighting and apodization can be seen for both the L12-5 and MS250 (Figure 7c,d) in which the RMSE increased. Multiple lines seemed to slightly increase the RMSE compared to one line per pitch for all strategies in these transducers. DaS or Lu's-fk with one line per pitch resulted in the lowest RMSE in both L12-5 and MS250. The RMSE by the lateral displacements estimates (Figure 8) decreased for each method and transducer using over 1 line per pitch. The RMSE increased when applying angular weighting or apodization for all transducers except 12L4 VF, for which the RMSE decreased.