## 4 Optical Methods
### Streamer-to-Flame Transition Detection  
The discharge in an air-fuel medium eventually results in flames. Intuitively, if we consider the streamer evolution in terms of overall luminosity (binarized area), we would expect a change in slope after the combustion initiation. When luminosity is generated only by the discharge, the initial rise in binarized area is limited, as the streamer is a sort of filament that involves a small number of pixels. Conversely, when the combustion starts, the pixels close to the filament are also involved, and the propagation is substantially perpendicular to the main streamer direction, obtaining a sort of linceolate luminous area, which involves a large number of pixels. Thus, theoretically, a discrimination of the combustion initiation could be possible by simply observing the binarized area evolution. Actually, this is not simple, since such area evolution is wobbly, showing a number of peaks and valleys. For example, in Figure 8a (second combustion event at \(\lambda=1.0\), first quadrant), many occurrences of slope change can be found. The corresponding smoothed series (red curve, temporal moving average with span = 5) shows the first increase in slope somewhere between 10 and 15 frames after the start of discharge, but exact detection is not easy. For all these reasons, this method requires a comparison with the corresponding data in motored conditions. As the discharge is a stochastic phenomenon, a statistical analysis was necessary; the average of all the  
Figure 7: Example to explain the coefficient of variation (CoV) streamer calculation methodology. All pictures refer to the first quadrant. (**a**) Streamer penetration P detection. The red asterisk represents the igniter tip position, while the white cross represents the streamer’s farthest point. (**b**) Temporal evolution of the penetration P for a certain number of streamers. Each streamer sequence is defined by a different line type; circular colored markers represent the point of maximum penetration P\({}_{\text{max}}\) for each sequence of frames. All the streamers start at the same time, but the P\({}_{\text{max}}\) and trend can be fairly different. (**c**) Maximum streamer penetration P\({}_{\text{max}}\) trend over the series of 63 consecutive discharges. The red dashed line represents the average value (avg). Red dotted lines represent the series standard deviation (\(\pm\text{dev}_{\text{std}}\)) from the corresponding average value. discharge events in motored conditions was used to obtain the discharge trace for each tip (Figure 8b). Moreover, in many combustion cases, it was found that the streamer binarized area, before the flame kernel became visible, showed a sort of plateau, denoting that the maximum penetration was already reached (Figure 8a, frames in the range 11-13). Thus, the detection of the streamer-to-flame transition was developed as follows:  
* For each combustion and for each quadrant, the binarized area trend was smoothed by using a five-point moving average. The five-point choice was found to be a good trade-off between the wobbly raw data and an even stronger smooth curve, which loses responsiveness. * Once smoothed, the series was compared with the average trend in motored conditions (i.e., where no combustion occurs). * The point of transition was determined by looking for a non-negligible increase in binarized area slope, which should occur in close proximity to the intersection between the combustion curve and the motored average one. After such a point, a region of strong increase in binarized area, not necessarily monotonic, should occur. This procedure was applied and then visually tested on all the recorded series, for all the combustion events and all the quadrants. The visual test consisted of the observation of the streamer evolution frames, reported, as an example, in Figure 9 (second combustion, first quadrant, \(\lambda=1.0\)).