## 2 Materials and Methods  
To create a block phantom, gelatin (10% by weight; VMR International, Leuven, Belgium) was dissolved in demineralized water and heated to 90 \({}^{\circ}\)C and cooled to 35 \({}^{\circ}\)C while continuously stirring using a magnetic stirrer. During the cooling process, silica particles (2% by weight; silica gel 60, 0.015-0.040 mm; Merck KGaA, Darmstadt, Germany) were added, which act as scatterers. Next, the mixed solution was poured in an open container (200 \(\times\) 100 \(\times\) 100 mm) leaving a 20 mm space under the top surface. Finally, the phantom was placed in a fridge to consolidate for 24 h.  
The phantom, including the container, was positioned on top of a seesaw to enable rotation of the phantom. One of the four different linear array transducers utilized in this study (Table 1) was positioned above the phantom top surface such that the transducer footprint was unable to touch the phantom after rotation at the maximum angle of 10 degrees. Water was poured on the top surface of the phantom to fill the remaining 20 mm space and to ensure acoustic coupling between the transducer and phantom. The transducer was connected to a Verasonics V1 system (MS250 to Verasonics Vantage)  
Figure 3: Overview of beam-forming in the fk-space: acquired element data is transformed to the fk-space using 2-D Fourier transform, and Lu’s-fk or Stolt’s-fk migration is applied to convert the data into the k-space. If required, this spectrum can be multiplied by a template (green overlay) to filter the data. Finally, the reconstructed data can be obtained by the 2-D inverse Fourier transform. to enable 0\({}^{\circ}\) plane-wave transmissions and element data collection using the center 128 elements of the transducer (MS250: all 256 elements). Element data were recorded prior to and after rotation (\(\sim\)2\({}^{\circ}\)) of the phantom. The experimental setup is also visualized in Figure 4.  
Element data were beam-formed using three different strategies: (1) Lu's-fk [11; 12], Stolt's-fk [13], and DaS [10]; (2) with and without angular weighting (Lu's-fk; Stolts-fk) [14] or apodization by Hamm function (DaS); and (3) a beam-forming ultrasound grid (USGrid) with 8 samples per wave length and 1, 2, 3 and 4 lines per pitch. These strategies were implemented in Matlab (2016a; Mathworks Inc., Natick, MA, USA). Zero-padding was applied in the k-space to achieve higher line-densities for the fk-based strategies. Beam-forming settings were empirically determined: plane-wave element data were acquired in a multi-purpose phantom and beam-forming settings were tuned resulting in optimal contrast and resolution after beam-forming (see Appendix A for more details). For all transducers, the F-number (DaS) and angle weighting range (Lu's-fk; Stolts-fk) were set to 0.875 and \(\pm\)20\({}^{\circ}\), respectively. Next, displacements were estimated by two step coarse-to-fine normalized cross correlation of pre- and post-rotation beam-formed ultrasound envelope and RF data in the first and second step respectively [18; 19]. The cross-correlation peak was interpolated (2-D spline) after the final iteration to estimate sub-sample displacements. After each iteration, displacements were median filtered to remove outliers. Template and search windows, and other settings can be found in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline
**Transducer** & **Bandwidth** & \(\mathbf{f_{c}}\) & **Pitch** & **Manufacturer** \\ \hline L7-4 & 4–7 MHz & 5.0 MHz & 298 \(\upmu\)m & ATL 1  \\
12L4 VF & 4–12 MHz & 8.2 MHz & 266 \(\upmu\)m & Siemens 2  \\ L12-5 & 5–12 MHz & 9.0 MHz & 198 \(\upmu\)m & ATL 1  \\ MS250 & 13–24 MHz & 21 MHz & 88 \(\upmu\)m & VisualSonics 3  \\ \end{tabular}
\end{table} 
Table 1: Transducers used in this study with their bandwidth, central frequency (f\({}_{\mathrm{c}}\)), and pitch.