## 6 Conclusions  
In this work, an optical method was presented to characterize the radio-frequency corona streamer penetration variability and the transition from streamer to flame in an optical engine. For this purpose, a high-speed camera able to record the natural luminosity of discharge and combustion in the visible range was used. Framerate and frame area were set to ensure high temporal resolution (79 kHz) and high magnification, respectively, to properly analyze such phenomena. Engine speed and throttle position, together with corona electrical parameters, were fixed to ensure high repeatability in terms of in-cylinder conditions and power supply at the igniter electrode. Streamer penetration was calculated in motored conditions, while streamer-to-flame transition was recorded with three different fueling levels, to ensure a relative air-fuel ratio \(\lambda\) of 1.0, 1.2, and 1.4.  
The main findings are as follows:  
* A stable preprocessing method was determined, based on in-house MATLAB scripts together with built-in functions. It consisted of average background removal, equalization, Gaussian filtering, and thresholding. The threshold level was defined manually, frame by frame, but the threshold level to discriminate dark and light pixels belonged to an easily detectable narrow range. The procedure continued with binarization, hole filling, and boundary recognition. Finally, the frame area was divided into four quadrants, in order to analyze the discharge events from the corona tips independently from each other.
* A method to evaluate streamer repeatability in motored conditions was reported. For each discharge event, the maximum penetration (i.e., the maximum distance between streamer and tip) over time was detected. The maxima values, one for each consecutive discharge, were compared, and a statistical analysis was carried out, where the average value, standard deviation, and coefficient of variation were computed. This procedure was carried out separately for each igniter tip.
* A method to discriminate frames with pure streamer from combustion frames was reported. It was based on the evolution of the binarized area, evaluated separately for each electrode tip. The first significant increase in slope that generated a deviation between the binarized area trend and the corresponding motored one was defined as the detection condition for the flame presence.
* For the motored test case, as an example, the streamer penetration parameters were calculated. According to the nomenclature used in this work, the highest streamer penetration, on average, was found for the fourth tip (more than 7 mm), while the second and third tips featured with the lowest penetration (about 4 mm). Standard deviation, on the contrary, was not so different among the four tips (0.9-1.0 mm).
* By applying the method to detect the transition between streamer and flames, it was found that all visible flames were always present at the end of the discharge. On average, at fixed lambda, it was not possible to find a tip-dependent trend. Focusing on the tip, instead, a lower lambda resulted in more advanced early flame detection. Nevertheless, the average gap in the first frame with combustion between the three lambda values was small (at most three frames, i.e., about 0.2 crank angle degrees).  
Conceptualization, C.N.G. and V.C.; methodology, V.C. and G.D.; software, V.C.; validation, S.P.; formal analysis, V.C.; investigation, L.P.; resources, G.D.; data curation, F.R.; writing--original draft preparation, V.C.; writing--review and editing, G.D.; visualization, V.C.; supervision, C.N.G.; project administration, C.N.G.; funding acquisition, C.N.G. All authors read and agreed to the published version of the manuscript.  
This research activity was partially granted by the Basic Research Funds supplied by the Department of Engineering of the University of Perugia.  
The authors declare no conflict of interest.