## 3 Results
### Influence of the Grid Point Distance  
For the efficiency of non-destructive testing with air-coupled ultrasound (ACU), the measurement point distance in the experiment is also an important parameter. The more measurement points are required, the more time for the data acquisition or more equipment (e.g., more receivers) is needed. Using the measurement with the \(\omega\)20 mm flaw imitate, the influences of the grid point distance is investigated for both the re-radiation method and the spec-radiation method. Here, and for further investigations, the measurement window size is constant at approximately 200 mm \(\times\) 200 mm, and the evaluation window size is approximately 2.5 times larger, due to zero-padding. Only the grid point distance \(\mathrm{d}x\) and \(\mathrm{d}y\) will change. In order to get a good comparison with the re-radiation method, the amplitude distribution on the surface of the particleboard is first calculated and displayed for different grid point distances using the re-radiation method. Figure 13a depicts this for the 2 mm grid. As expected, this is optically identical to the result of the spec-radiation method in Figure 12 from Section 3.1, with a grid point distance of 2 mm. There are artifacts in the corners that can be misinterpreted as another sound source and thus complicate the evaluation with a 8 mm grid point distance (see Figure 13b). However, if the approximate position of the transmitter is known, the flaw is still detectable. With a grid point distance of 12 mm, these errors occur at a higher rate and are closer to the evaluation area (see Figure 14a). However, with knowledge of the approximate range in which the transmitter is located, the flaw can still be identified since a separation from the artifacts is possible. From a grid point distance of 16 mm, the artifacts are so close to the evaluation area that it is no longer possible to ignore them (see Figure 14b). The flaw can at most be identified by exact knowledge of its position, everything else would be an estimation. When calculating the same situations with the spec-radiation method, these artifacts do not occur. Figure 12: Amplitude at the top of the wooden particleboard with a \(\omega\)20 mm piece of paper. Evaluated with the spec-radiation method for the frequency 50 kHz, with \(\mathrm{d}x\) = \(\mathrm{d}y\) = 2 mm and a grid of the size 256 \(\times\) 256 points. Figure 15a depicts the result for a grid point distance of 8 mm calculated by the spec-radiation method. The transmitter and the flaw can be seen clearly. There are no artifacts that could be mistaken for sound sources. Even with a grid point distance of 12 mm, both the transmitter and the flaw are still clearly visible (see Figure 15b). In the area of the flaw, however, it is noticeable that the amplitude drop is not as strong and, therefore, only a yellowish coloring and no blue coloring appears. While the re-radiation method identifies the e20 mm flaw with a grid point distance of 16 mm (see Figure 14b) through guessing or by exact knowledge of the position of the flaw, the spec-radiation method identifies both the transmitter and the flaw unambiguously (see Figure 16a). At a grid point distance of 18 mm, the flaw can no longer be identified (see Figure 16b). The transmitter and its position can still be identified. These results show that the spec-radiation method gives clearer results than the re-radiation method using rough measurement grids. The extent to which the results with large grid point distances can be improved and thus increase the detectability of flaws with the spec-radiation method using the technique from [PERSON] et al. (2018), as with the re-radiation method, is examined in the following Section 3.3. Figure 14: Amplitude at the top of the wooden particleboard with a e20 mm piece of paper. Evaluated with the re-radiation method for the frequency 48–52 kHz, with (**a**) \(\mathrm{d}x=\mathrm{d}y=12\) mm and (**b**) \(\mathrm{d}x=\mathrm{d}y=16\) mm a grid of the size 512 mm \(\times\) 512 mm.