## 2 Measurement Approach
### Determination of the Positions of the Blade Edges and the Natural Transition Line  
Turbulence wedges are located in the region between the leading edge and the natural transition line. In order to focus the turbulence wedge detection on this region, the natural transition line and the leading edge need to be located in the thermogram first. To detect the \(y\)-positions of the blade edges and the natural transition line, a chord-wise gradient approach is chosen: for each image column, which corresponds to the chord-wise \(y\)-direction, the spatial derivative \(\text{d}I/\text{d}y\) of the pixel intensities \(I\) is calculated and then normalized with its maximum value:  
\[\left(\frac{\text{d}I}{\text{d}y}\right)_{\text{norm}}=\left|\frac{\text{d}I} {\text{d}y}\right|\cdot\left(\text{max}\!\left(\left|\frac{\text{d}I}{\text{ d}y}\right|\right)\right)^{-1}. \tag{1}\]  
After the normalization, all local maxima above a threshold value of \(0.1\,\text{pixel}^{-1}\) are located. This threshold value is heuristically based as it suppresses noise but allows the local maxima due to the natural transition to be detected. A lower threshold value would lead to more false detections due to noise; a higher value would miss more actual transition points. To illustrate how the local maxima correspond to the \(y\)-positions of the blade edges and the natural transition, a simulated thermogram with a single turbulence wedge is shown in Figure 2a, for which the gradient is calculated for two different image columns. The studied image columns are chosen so that one (marked with a blue dotted line) intersects the turbulence wedge and therefore contains a premature transition. The other (marked with a dashed orange line) does not intersect a turbulence wedge and thus contains a natural flow transition.  
According to Figure 2a, the pixel intensities of the background and the blade differ significantly, which leads to large local maxima in the gradient at the positions of the leading and the trailing edge, respectively. The natural transition also leads to a local maximum of the intensity gradient due to a large difference in pixel intensities between the laminar and the turbulent flow regions. Therefore, three local maxima can be present in the intensity gradient, corresponding to the trailing edge, the natural transition and the leading edge, see Figure 2b, at the top. The \(y\)-positions of the maxima are set as the \(y\)-positions of the blade edges and the natural transition line. In cases where only two maxima exist, see Figure 2b, at the bottom, the maxima are assigned to the trailing and leading edges. This case occurs when the chord-wise intensity profile contains a premature transition, which leads to intensity gradients that are below the threshold. Hence, the natural transition is not detectable in image columns where a premature transition exists. Therefore, the detected points of the natural transition are fitted with a linear regression so that the \(y\)-position \(y_{\text{NT}}\) of the natural transition is defined for each \(x\)-position of the thermogram and also for the region of the premature flow transition.  
With the extracted \(y\)-positions of the natural transition line and the leading edge, the wedge detection algorithm can now be applied to the thermogram.