# Implementation of Constrained Swept Synthetic Aperture Using a Mechanical Fixture
## 2 Materials and Methods
### Phantom  
#### 3.2.1 Translation Stage  
The application of the two estimation techniques to SSA imaging in a series of phantom experiments was investigated. Figure 8 shows the initial experiment comparing the estimates to a known motion as applied by a translation stage. Both methods were able to accurately reproduce the applied motion profile over a span of 50 mm with maximum error for the speckle tracking method around 400 \(\upmu\)m and for the channel correlation method under 50 \(\upmu\)m. Interestingly, the estimate for channel correlation is biased, not showing the usual linear trend across the sweep. This may be due to the fixed step size creating the same slightly biased error on each step according to the subsample estimation strategy, meaning it would not be seen in freehand sweeps with varying step sizes.  
Figure 7: Simulation comparison of reference image, SSA images and equivalent transducer matched to the effective length of the SSA acquisition. (**Left**) Images for reference, channel correlation estimated SSA and equivalent transducer, shown with a 50 dB dynamic range and ROIs indicated for the lesion and point. (**Right top**) Lateral PSF for point at 10 cm depth. (**Right bottom**) gCNR for anechoic lesion target located at 6 cm depth.  
Both strategies produced SSA images comparable to the ideal case. This is further explored in Figure 9 by quantifying the FWHM resolution of a point target and gCNR of a lesion target. The resolution was improved from 3.22 mm in the reference case to 1.04, 0.93 and 1.03 mm in the applied motion, speckle tracking and channel correlation cases, respectively. It should be noted that the PSF for the speckle tracked case noticeably improved from even the applied motion case.  
It is possible that the translation stage transducer mount was slightly misaligned from the direction of stage motion and that the speckle tracking technique, directly measuring target motion, compensated for this error. This seems plausible as the channel tracking result shows very small improvements over the applied motion case as well, although not as significantly as with the speckle tracking approach. The lesion detectability measured by gCNR similarly confirms these improvements with the speckle tracked SSA case producing the clearest lesion and lesion boundary but all SSA cases improving on the reference case.  
Figure 8: Phantom experiment with lateral motion applied in the translation stage. (**Left**) SSA images show significant resolution improvements compared to the reference image, produced by a 19.2 mm array (50 dB dynamic range). (**Right**) Estimated motion over 50 mm translation shows strong agreement between speckle and channel tracking estimates compared to the applied motion with the error under 400 \(\upmu\)m.  
Figure 9: (**Top**) Point target images corresponding to the central point target at depth 100 mm from Figure 8. Yellow line indicates the depth for the lateral PSF. (**Bottom**) Lesion target images corresponding to the central large lesion target at depth 60 mm from Figure 8. Yellow circles indicate ROIs inside the dashed circle and outside the solid circle for gCNR calculation. All images show a 50 dB dynamic range. Both metrics show comparable performance for the two motion tracking techniques and similar performance to the applied motion case with slight improvements using speckle tracking.