## 3 Results
### Detectability Enhancement with Coarse Measurement Grid  
Without refining the coarse measuring grid point distance of 14 mm, the time data, a section of which is shown in Figure 9b, becomes a non-interpretable image (see Figure 7). However, to save time during the experiment, we take this data and interpolate it to a finer grid. For this, we use different interpolation methods. In order to enable an optical direct comparison of the individual methods with a result that is not refined but finely measured, Figure 11 shows the 6 images of the back propagated sound fields on the surface of the particleboard. Figure 11a shows the result if the measuring grid point distance is 2 mm. For Figure 11b-f, a measuring grid point distance of 14 mm was measured and the time data interpolated to a grid point distance of 2 mm. The round shape of the transmitter can be seen in every image. The 20 mm flaw can also be clearly identified in each image. Figure 11c, interpolated linearly, shows the lowest visible noise. In contrast, Figure 11b shows the highest noise when interpolated with the \"nearest\" method. Compared to other interpolation methods, the amplitude drop in Figure 11c is not as stark. This is shown through the colored areas of yellow through green in the area of the flaw. Moreover, a dark blue color is not present as compared to the other images. Figure 11 clearly shows that this procedure is promising. Since the visual differences are difficult to compare directly, the following error image is calculated in each case:  
\[Error\;Image=20\text{log}_{10}\left(\frac{|Interpolated\;Image-Default\;Image|}{Default\;Image}\right). \tag{6}\]  
Figure 11: Back propagated amplitude at the top of the particleboard. (**a**) The “default” image measured with a 2 mm grid; the rest were measured with a 14 mm grid and refined to a 2 mm grid. (**b**) Interpolation method “nearest”. (**c**) Interpolation method “linear”. (**d**) Interpolation method “cubic”. (**e**) Interpolation method “spline”. (**f**) Interpolation method “makima”. These images are depicted in Figure 12. The difference is so small that it is not recognizable on the \(-20\) dB scale (that was used in all other figures) a \(-50\) dB scale was used instead. These images depict that there are significant differences. With the interpolation method \"nearest\" a large error at around \(y=170\), \(x=90\). Using the interpolation method \"linear\", the largest error is seen in the area of the \(20\) mm flaw. Figure 12c-e depict similarity in errors. All images present a large part of their errors in the area of the flaw, but previous images (see Figure 11) show that these are not decisive in the flaw identification. To decide which of the images in Figure 11 are the best reproduction of the \"default\" image, the sum of all pixel values in Figure 12 are calculated, and the largest absolute value is determined to be the best reproduction. In this case, the \"spline\" interpolation is the best reproduction (see Figures 11e and 12d). In Figure 13, these values depicted are related to the best reproduction. It can be seen that all methods have similar accuracy values. It is shown that the interpolation method \"linear\" is the worst reproduction. Since time efficiency is a main objective, the computation time for the interpolation is given in Figure 14. Figure 14 depicts the needed time for the evaluation of the measurement results related to the \"default\" time. It can be seen in Figure 14 that each interpolation method needs approximately 500% evaluation time related to the \"default\" time. Only the \"makima\" interpolation method needs 1200% extra time for the evaluation; in comparison to Figure 13, this is not the best reproduction. The presented example has a measurement time reduction of 98%, equivalent to up to 10 hours of time saved. An extra evaluation time of 1200% is approximately 1 min. Figure 12: Error images of the different interpolation methods for the refining of the measurement values related to the “default” image.