## 3 Results
### Detectability Enhancement with Coarse Measurement Grid
Interpolation method (**a**) “nearest”; (**b**) “linear”; (**c**) “cubic”; (**d**) “spline” and (**e**) “makima”. Sensitivity of the Measurement Grid Point Distance in Respect to the Identification of the Flaw with a Refined Grid  
Starting from the previously determined interpolation method \"spline\" for the best reproduction, we will now examine how coarse the measuring grid may be in order to obtain a well-interpretable detectability. It is assumed here that a certain number of real measured points must be present in the measuring surface which are in the sound field within the sphere of influence of the flaw. Therefore, it is indispensable to know the influence area of the flaw in the measured plane. To determine it, the following points are assumed:  
* The opening angle of the sound field of the main lobe does not change. * The flaw located behind the sound field shows its influence only in the sound field considering the opening angle of the main lobe. The area of the sound field within the area of influence of the flaw is given in Figure 15. The area of the used circular flaws can be calculated from the truncated cone using the assumptions made. For this purpose, the opening angle of the transmitter is determined according to [PERSON] [28], and the area is calculated:  
\[A=\pi r_{2}^{2}=\pi(\tan(\gamma)h+r_{\rm Flaw})^{2}=\pi(\tan(\arcsin(1.22\frac {\lambda}{D_{\rm Trans}}))h+r_{\rm Flaw})^{2}, \tag{7}\]  
where \(\gamma\) is the opening angle, \(r_{2}\) is the radius of the flaw influenced sound area in the measuring plane, \(h\) the distance between the particleboard and the measuring plane, \(r_{\rm Flaw}\) the radius of the circular flaw, and \(D_{\rm Trans}\) the diameter of the transmitter. Figure 14: Time for the evaluation of the different refinement methods related to the “default” evaluation time. Figure 13: Accuracy of the reproduction related to the best reproduction of the individual interpolation methods. With knowledge of the area of influence of the flaw, it is now possible to check how coarse the measuring grid can be in order to identify a corresponding flaw. It is clear that, above a certain size, not only does the grid point distance of the measuring grid play a role, but also the position of the measuring grid points in relation to the position of the flaw. With this method, we ensure that the desired flaw size can also be identified with the desired coarse measuring grid. Therefore, we have shifted the measuring grid in relation to the position of the flaw in 2 mm steps by up to 40 mm in x- and y-direction. In the process, we have continuously coarsened the measuring grid and checked at which measurement grid point distance the flaw can still be identified at each position of the measuring grid. Due to the coarsened grid and the interpolation, the position of the flaw in the result image can lightly shift. Shown in Figure 16 are the results of the coarsest identified measuring grid of the different flaws with different measuring grid positions. Each line shows that the flaw can be roughly identified. At one grid position better than at another, it is always possible to identify the flaw. It has been shown that, for the 4 mm flaw (Figure 16, first row), an 8 mm grid is sufficient to identify it; for the 5 mm flaw (Figure 16, second row), a 10 mm grid is sufficient; for the 10 mm flaw (Figure 16, third row), a 14 mm grid; and for the 20 mm flaw (Figure 16, fourth row), an 18 mm grid is sufficient. As expected, there is increased noise with a coarser grid because, if there is only one measuring point which is strongly afflicted with noise, this affects the results more and more the less real measuring points are present for the interpolation. Figure 15: Schematic representation of the sound fields and the measuring grid. Figure 11:0 Results of the coarsest identified measuring grid of the different flaws with different measuring grid position.