## 2 Materials and Methods  
### Coherent Dual-Array Imaging  
A CoMTUS imaging system, created using two identical linear arrays (LA332, Esaote, Firenze, Italy), was investigated using both simulations and experiments. Each array had 144 active elements, a pitch of 245 um, a central frequency of 3 MHz, and 80% bandwidth. The arrays were constrained to share an overlapping FOV in the same elevational plane. A transmission imaging sequence was implemented in which both arrays take turns to transmit a PW while simultaneously receiving the backscattered echoes. Note that, compared to a single probe system using the same imaging sequence, the frame rate would be halved. The notation \(T_{i}R_{j}\) was used to denote radiofrequency (RF) data received by array \(j\) when array \(i\) transmits.  
The beamforming process for this coherent dual-array system is described in detail in [11]. Briefly, delay and sum beamforming was applied to each received RF dataset in the same coordinate system [20]. Here, delays accounted for the complete pathway between the transmit array and the receive elements. Then, a CoMTUS image is generated by coherently summing all beamformed data for all transmissions and all receivers. Finally, the delayed and compounded signals are envelope detected and log-compressed.  
As shown in Figure 1, the relative position of the two arrays was defined by the angle between the axes of the arrays, \(\theta\), and the gap between the arrays, which consequently define the imaging depth defined at the center of the common FOV of both arrays. The scan sequence was defined by the maximum steering angle, \(\alpha_{max}\), and the number of transmitted PWs. The specific steering angle of PWs was determined in linear steps between \(-\alpha_{max}\) and \(\alpha_{max}\). The transducers were excited using a Gaussian-windowed 3-cycle sinusoidal burst at 3 MHz. CoMTUS images were beamformed in the coordinate system of the resulting effective aperture (Figure 1). This is the coordinate system defined at the center of the extended aperture created by the two arrays, where the best spatial resolution is aligned with the \(x\)-axis (3). To reduce artifacts, different apodizations were investigated on transmit: rectangular window (no apodization) and 50%-Tukey window. A rectangular window was used on receive. This specific window (Tukey) was chosen because it is flat for the majority of the window length, which allows the propagation of a plane wavefront for a long depth of field with very limited diffraction [24]. Moreover, Tukey apodization was previously shown effective to better reduce the cross-talk artifacts in multi-line transmit beamforming when compared to other window functions [22; 23].  
Figure 1: Schematic representation of the relative spatial location of the two linear arrays (blue and red rectangles) and the simulated point target (gray dot). The investigated geometrical parameters are shown: angle, \(\theta\), and gap between the arrays, imaging depth, and possible steering angle, \(\alpha\). The gray dashed horizontal line represents the distance used to calculate the cross-talk depth. Axes [x, z] show the image coordinate system defined by the CoMTUS aperture where all acquired data are beamformed.