## 3 Results and Discussion
### Signal Processing  
To obtain a characteristic signature in the photodiode signal that unambiguously identifies a cutting interruption, as a first step, we apply a digital two-element high pass filter (\(y_{\mathrm{k}}=x_{\mathrm{k}}-x_{\mathrm{k-1}}\)) to the measured signals, as shown in Figure 4. The resulting filtered signals are depicted in Figure 5 for a complete cut (top) and an incomplete cut (bottom). Distinctive points in the filtered signal are found at, firstly, 0.1 s (pronounced peak) indicating the piercing; secondly, at 1.2 s the onset of the laser cut is indicated by a pronounced signal with strong fluctuations; and thirdly, the end of the laser cut is noticeable by a high negative peak at second 3.0. Figure 4: Voltage signal delivered by the Si and InGaAs diodes of a complete (**top**) and incomplete (**bottom**) cut. The time of the cutting interruption is marked by dashed lines. The comparison of the signals with and without cutting interruption reveals distinctive differences in the fluctuation range. During cutting (second 1.2 to second 3.0), the fluctuation range of the InGaAs diode is always higher as compared to the fluctuation range of the Si diode. When a cutting interruption occurs, as shown in Figure 5 (bottom), the fluctuation range of the InGaAs diode falls below the fluctuation range of the Si diode. At the end of the cutting interruption, controversially, the fluctuation range of the InGaAs signal exceeds that of the Si signal, _i.e.,_ the degree of the filtered signal fluctuation can be utilized to discriminate a complete cut from a cutting interruption. We, therefore, calculate a measure of the degree for the fluctuation by determining the standard error from 50 sequent data points of the high pass filtered signal (Figure 5). The results of this calculation are summarized in Figure 6 for the complete cut (top) and the incomplete cut (bottom). In this representation of the processed data, the signal of the complete cut is identified by the derived data from the InGaAs diode being continuously higher than that of the Si photodiode. Contrary to that, during the cutting interruption (marked by dashed lines in the lower part of Figure 6), the derived data from the InGaAs diode falls below that of the Si diode. To gain a digital value indicating whether a cutting interruption occurs or not, _i.e.,_ discriminating the two regimes, the signal of both diodes must be compared. The calculation of this discriminating value is described in Equation (1), where _Ct_ describes the binary value for a cutting interruption and _fr_ the fluctuation range of the particular diode signal. The if constraint returns a \"1\" whether the greater than condition in the square bracket is true and a \"0\" in case of a false condition. This digital value expresses a \"1\" for cutting interruption and a \"0\" for complete cutting. Further, _cf_ describes a correction factor for the fine tuning to achieve a high detection rate and low beta error late. In a series of 20 cuts, a correction factor of 0.85 results is determined to detect all cutting interruptions without any false reports. With a  
Figure 5: High pass filtered signal of a complete (**top**) and incomplete cut (**bottom**). The time domain in which the cutting interruption occurs is marked by the two grey shaded rectangular with dashed lines. significantly higher correction factor, not all cutting interruptions were detected and a much lower correction factor errors are also indicated in faultless cuts. \[Ct=\text{if}[\text{fr}(\text{Si})>\big{(}\text{cf}\times\text{fr}(\text{InGaAs}) \big{)}] \tag{1}\]  
When Equation (1) is applied to the signals shown in Figure 6, a digital signal is calculated, which is only 1 in case of a cutting interruption (_cf._ Figure 7). For the complete cut the signal is always 0 except from the end of the cut, _i.e._, the sensor system even identifies the end of a cut, interpreted as a cutting interruption.