# Implementation of Constrained Swept Synthetic Aperture Using a Mechanical Fixture
## 2 Materials and Methods
### Phantom
#### 3.2.2 Linear Fixture  
With an established baseline case showing that channel correlation and speckle tracking produce motion profiles that create SSA images equivalent to the ground truth for an ideal motion case, the application of the channel correlation approach to a freehand sweep was studied using the linear slide fixture. Figure 10 shows four sweeps over approximately the same phantom region with varying temporal profiles and extents due to the manual motion. For image formation, these profiles were resampled using fixed spatial sampling to avoid artifacts from varying sweep speeds, such as would be caused by the stationary region at the end of the yellow curve. Comparable performance was observed across three cases with FWHM of 1.09 (54 mm sweep), 1.07 (49 mm sweep) and 1.14 (48 mm sweep), while the shortest sweep (37 mm) had a slightly larger FWHM of 1.30 mm.  
Finally, an additional challenge to the estimation was added by inserting an ex vivo tissue layer under between the transducer and phantom. Figure 11 shows the results of the control case and imaging through the three different tissue layers (pork, beef and chicken). The FWHM improved from 1.47 to 0.59 mm, 1.76 to 0.83 mm, 1.73 to 0.67 mm and 1.94 to 1.39 mm, respectively. The control case had the point target at a smaller depth due to the lack of tissue layer and was expected to, therefore, have lower FWHM and additionally had the longest sweep (72 vs. 41, 51 and 52 mm, respectively).  
Qualitatively, the tissue layers were found to add only small amounts of acoustic clutter compared to the control case with the point target in the chicken breast case showing some broadening possibly due to aberration. The gCNR in the reference case was reduced from 0.82 to 0.70, 0.74 and 0.75, respectively, by the tissue layers. These improved to 0.94, 0.93, 0.91 and 0.88, respectively, using SSA imaging.  
The large difference in FWHM after SSA imaging can be explained by the difficulty of performing the sweep procedure on the chicken breast layer. The tissue was slick, soft and of varying thickness, making it very difficult to hold the fixture still on the surface while sweeping the transducer. The case presented is the best of six acquisitions with the others showing severely degraded images (worse than the reference) due to fixture motion. This difficulty was not observed in the other tissue cases or control case, which all consistently produced high quality SSA results. However, the lesion results showed strong improvement in all cases, even in the chicken breast case despite the limited point target improvement. The gain in both SNR and overall resolution at depth due to SSA imaging greatly improved lesion detectability and image quality.  
Figure 10: Results of four manual sweeps using linear slide fixture. (**Left**) Sample SSA image from one manual sweep using channel correlation estimate (50 dB dynamic range). (**Right top**) Motion estimates showing variation in sweep extent and temporal profile of manual sweeps. (**Right bottom**) Lateral PSF for manual sweeps showing consistent results with slight variations due to phantom position and sweep extent. Reference PSF from Figure 8 shown in black.