# The Feasibility of Shadowed Image Restoration Using the Synthetic Aperture Focusing Technique
## 3 Results
### Experimental Results  
To facilitate the objective of this study, the created model is scanned using B-mode and pitch/catch arrangements. For the pitch/catch mode scan, the spacing interval of two active transducers is fixed at 20 mm. The pink line shown in Figure 1 indicates the scan that runs perpendicular to the orientations of the rod of the skew driver and fishing lines. The scan line extends from 30 mm on the left-hand side of SP\({}_{\text{OBS}}\) to 30 mm on the right-hand side of SP\({}_{\text{FR}}\) (Figure 1b). Hence, the total length of the scan line is 90 mm. The offset interval in between each successive scan is 2 mm. In total, 46 observations are performed in a complete scan. Each observation consists of 2500 points sampled at an interval of 8 _ns_, which equates to a time frame of 20 us. Figure 4a shows the result of the B-mode scan. Though the synthetic profile shown in Figure 3a is computed for the pitch/catch scan, it can still be used to assist in identifying images obtained from the B-mode scan (Figure 4a). Once a comparison is made between Figures 3a and 4a, it can be identified that their echo signals observed at 41.3 us and 77.6 us at SP\({}_{\text{OBS}}\) in Figure 4a came from T\({}_{\text{OBS}}\) and T\({}_{3}\), though the echo strength is weak for T\({}_{3}\). In  
Figure 3: (**a**) A synthetic profile of the created model for a pitch/catch scan in the status of shadowed and shadow–free. Based on the theoretical echo paths, echoes that come from eight targets are individually shown as eight hyperbolic trajectories. The dotted rectangular line indicates an anechoic zone. (**b**) The output of the SAFT restoration from (**a**). The intersections of the dark-blue and pink cross shown in the figure stand for the theoretical imaged and restored positions of T\({}_{\text{OBS}}\). terms of the eclipse, T\({}_{1}\), and T\({}_{2}\), which fall within the umbra area and at the intersection of umbra and anumbra of the echo field caused by T\({}_{\text{OBS}}\), fail to be imaged. At SP\({}_{\text{FR}}\), fishing lines labeled T\({}_{4}\), T\({}_{5}\), T\({}_{6}\), and T\({}_{7}\) are detected at 40.8 \(\upmu\)s, 48.7 \(\upmu\)s, 61.1 \(\upmu\)s, and 78.1 \(\upmu\)s. In addition, a question-marked event is observed at the lower center of Figure 4a, and is identified as a multiple-echo of T\({}_{\text{OBS}}\). Once the original observations (Figure 4a) are SAFT-processed, Figure 4b shows the output. In Figure 4b, the images of T\({}_{\text{OBS}}\), T\({}_{3}\), T\({}_{4}\), T\({}_{5}\), T\({}_{6}\), and T\({}_{7}\) are all well restored at the proper positions. The multiple echo, shown by a red question mark in Figure 4a, which comes from T\({}_{\text{OBS}}\), is gone. Figure 5a shows the result of the pitch/catch scan. In Figure 5a, the echoes from T\({}_{\text{OBS}}\) and T\({}_{3}\) are detected at 40.1 \(\upmu\)s and 79.8 \(\upmu\)s at SP\({}_{\text{OBS}}\), respectively. Out of T\({}_{\text{OBS}}\) and T\({}_{3}\), one more echo is detected at 63.3 \(\upmu\)s. Referring to the synthetic profile (Figure 3a), this new echo is identified as T\({}_{2}\). In addition, echoes coming from T\({}_{4}\), T\({}_{5}\), T\({}_{6}\), and T\({}_{7}\) are individually observed at 43.5 \(\upmu\)s, 53.5 \(\upmu\)s, 63.6 \(\upmu\)s, and 81.1 \(\upmu\)s at SP\({}_{\text{FR}}\). However, limited by the overlap of the beam divergence angle, the trajectories of imaged targets show up as an incomplete hyperbolae in the acquired scan [27,28]. Thereafter, the original observations are SAFT-processed. Once again, the intersections of dark blue dashed lines and pink dashed lines indicate the original and SAFT-processed images of T\({}_{\text{OBS}}\) and T\({}_{4}\), respectively. In Figure 5b, it can be seen the original echo image shown in the raw data, i.e., Figure 5a, is not just restored but also properly repositioned. To acquire more details into the performance of SAFT in shadowed image restoration, the acquired echo signals and SAFT-processed data are Hilbert-transformed to perform echo strength analysis [29].