## 3 Results & Discussion
### Detection of Incomplete Cuts  
To sense and discriminate complete and incomplete cuts, we developed and evaluated an algorithm based on the observation and interpretation of the geometric parameters and properties in the blue and green melt pool areas. A flowchart specifying the algorithm is shown in Figure 11. As an initial step, the image processing step is performed as described above (cf. Section 2.3) to obtain the area, length, width, ferret diameter, and the center position of the melt pool for the green and blue color channels, respectively. The algorithm for detection of a cutting error was first tested with different thresholds on eight cutting samples, four complete and four incomplete cuts each, for stainless steel, zinc-coated steel, and aluminum, and then applied to all cutting samples. The threshold value for the detection depends on the exposure time, the binarization method of the image processing as well as on the material of the sheet and must also be adjusted for stainless steel, zinc-coated steel, and aluminum. In the first selection, the blue melt pool area is checked if it is larger than a selected threshold value, which is based on the previously described experimental results and set according to the maximum detection limit. The upper threshold TH1 and lower threshold TH2 are used as preselection to sort out unambiguous incomplete and complete cuts for which incorrect geometries are calculated. This applies to the upper threshold, e.g., for plasma formation, where the images are heavily overexposed for the green and blue color channel, and also for the case where the area for incomplete cuts is significantly larger and extends beyond the field of view of the nozzle. In these cases, a cut is considered incomplete. For complete cuts with low feed rates, where the material is molten only at the laser cut front and immediately expelled out of the kerf, where consequently low process radiation is emitted, the camera is less exposed, and the geometries cannot always be calculated from the melt pool area. In these cases, a complete cut always occurs. Specifically, for the stainless steel, we selected a threshold greater than TH1 = 1600 pixels or less than TH2 = 500 pixels for the preselection of complete and incomplete cuts. For zinc-coated steel, the threshold value for TH1 changes to 900 and TH2 to 450 pixels. These specific threshold values are determined from the comparison of the melt pool areas shown in Figure 8.  
Figure 10: Comparison of the distribution of the melt pool area for complete and incomplete cuts in aluminum. The second selection is to check whether the blue melt pool area equals or exceeds the green melt pool area with a threshold value of TH3 = 90% for stainless steel and 95% for zinc-coated steel. In the third selection, it is then checked whether the ellipse enlarges in the direction of the fed rate and meanwhile, the blue melt pool area of the horizontal axis, the vertical axis of the ellipse, or the minimum or maximum ferret diameter passes TH4 and TH5 of 98% of the green melt pool area for stainless steel, respectively TH4 and TH5 of 100% for zinc coated steel. This is the case when the melt collects in the whole kerf and cannot be driven downward and out or expelled upward because the bottom edge of the sheet remains united. Finally, in the fourth selection, it is controlled if the center of the blue and green melt pool area is in the center of the nozzle or the direction of the feed rate since the center point also shifts when the ellipse is enlarged in the feed rate direction. For aluminum, solely the first selection of the algorithm is applied to distinguish a complete cut from an incomplete cut. The blue melt pool area is checked if it is larger than the threshold TH1 = 2000 pixels. This threshold is determined from the comparison of the melt pool areas for aluminum shown in Figure 9 and refers to the overexposure of the high-speed camera image, where an incomplete cut always occurs for aluminum.