## 4 Results
### Experimental Results  
Coherent PW imaging with a conventional aperture (using a single probe) provides the reference for image quality with and without the paraffin wax layer.  
To reconstruct these images, the reference SOS in water of 1496 m/s was used, and seven PWs were compounded. Figure 13 shows a comparison of the phantom images acquired with one probe and CoMTUS in the control case and through the paraffin wax sample. The CoMTUS images were reconstructed using the adaptively optimised beamforming parameters, which include the average SOS and compounding six PWs. All images are shown in the same dynamic range of \(-60\) dB. In both cases, one probe and CoMTUS images, little variation is observed between the control and the paraffin images, which is consistent with the simulation results. The values of the optimum beamforming parameters used to reconstruct the CoMTUS images are \(\{c=1488.5\) m/s, \(\theta_{2}=30.04^{\circ},\mathbf{r}_{2}=[46.60,12.33]\) mm\(\}\) for the control case and \(\{c=1482.6\) m/s, \(\theta_{2}=30.00^{\circ},\mathbf{r}_{2}=[46.70,12.37]\) mm\(\}\) for the paraffin. There are slight changes in all the values and a drop in the average SOS, which agrees with the lower SOS of the paraffin wax. Figure 14 summarizes the computed image metrics for both the control and the paraffin cases. Little variation was observed in all the imaging metrics. Although minimum image degradation by aberrating layers was observed in CoMTUS, the overall image quality (particularly resolution) improved compared with the conventional single aperture, and the observed image degradation follows the same trend.  
Figure 12: Computed quality metrics: (**a**) lateral resolution (LR), (**b**) contrast and (**c**) contrast-to-noise-ratio (CNR), as a function of the clutter thickness (fat layer). Three different methods are compared: one probe (solid line), 2 probes (dot line) and CoMTUS (dashed line).  
The first point target located at an 85 mm depth was described using its lateral PSF (Figure 15), with and without the paraffin wax layer. No significant effects due to aberration are observed in the PSF in any of the cases. The PSF shape is similar with and without the paraffin wax layer and agrees with the one observed in simulations. In general, the CoMTUS method leads to a PSF with a significantly narrower main lobe, but also with side lobes of bigger amplitude than the one probe conventional imaging system.  
Figure 14: Computed quality metrics experimentally measured. (**a**) Lateral resolution (LR) measured at an 85 mm depth; (**b**) changes in LR measured in the four point targets when imaging through the paraffin and relative to the control case; (**c**) contrast; and (**d**) contrast-to-noise-ratio (CNR). Two different methods are compared: one probe and CoMTUS.  
Figure 13: Experimental images of the control and the paraffin cases. Two different methods are compared: (**a**) one probe; and (**b**) CoMTUS.  
Figure 16 shows the coherent summation of the delayed echoes from the point-like target before and after optimization. The effects of the paraffin layer are clearly seen. When the beamforming parameters, including the averaged SOS, are optimized by the CoMTUS method, all echoes align better, minimizing the aberrating paraffin effects.  
Figure 16: Experimental delayed RF data acquired from the phantom with the paraffin wax sample. CoMTUS flat backscattered echo from a point-like target, obtained by coherently adding the four delayed backscattered echoes from the same point-like target (\(T_{1}R_{1}\), \(T_{1}R_{2}\), \(T_{2}R_{1}\), \(T_{2}R_{2}\)) using different beamforming parameters: (**a**) initial guess values; (**b**) optimum values.  
Figure 15: Experimental point target images. Column (**a**) corresponds to the control and column (**b**) to the paraffin. The first row corresponds to the one probe system and the middle row to CoMTUS. The bottom row shows the corresponding lateral point spread functions for the two cases displayed: one probe system (dashed line) and CoMTUS (solid line).