## Materials and Methods
### Post-Processing and Calibration
Briefly, a calibration plate is installed in the test section at the same optical setting like for the actual spray measurements. Two exchangeable glass plates are used with numerous opaque circles, which mimic droplets of a wide range of diameters between 1 \(\upmu\)m and 300 \(\upmu\)m. The calibration plates are manufactured by an etching process with an absolute accuracy of 0.1 \(\upmu\)m. In this context, it should be pointed out that the numerical aperture of the optical setup \(\text{NA}\approx 0.1\), which means that only a small part of the off-axis light contributes to the image. Hence, images of liquid droplets and opaque circles are very similar with the exception of a bright spot (glare point) at the centre of a droplet [38]. This calibration technique was proven to be feasible at several occasions [29; 34]. In this study, the DoF correction is enabled since the calibration plate can be moved in the direction perpendicular to the image plane with an accuracy of 1 \(\upmu\)m by means of a traverse system. This is necessary to obtain quantitative data from blurred droplets, which are located outside the focal plane. In the calibration procedure, this situation can be simulated by blurred circles on the calibration plate at a known distance from the focal plane. The criterion to correct blurry droplets is the average intensity gradient at the outer contour of the droplet. Finally, the measured diameter of one droplet is corrected based on the known diameter from the calibration plate. It is of great importance that, in this step of the calibration, the smallest detectable droplet size and the size of the acceptable measurement volume is determined because larger droplets can be detected at a larger distance out of the focal plane than smaller droplets. The smallest detectable droplet size of the experimental setup presented in this paper was set to 4 \(\upmu\)m, which could be detected consistently at a distance out of the focal plane of \(\pm\) 200 \(\upmu\)m. Based on the fixed measurement volume, the minimum intensity gradient of larger droplets was directly derived and the bias on the number distribution of the spray, due to the size-dependent detectability, could be corrected. Another parameter that has to be considered for microscopic imaging is the diffraction limit. According to [PERSON] [15], the smallest resolvable length scale \(d_{\text{diff}}\) of the presented optical setup is given by  
\[d_{\text{diff}}=\frac{\lambda}{2\,\text{NA}}=2.9\,\upmu\text{m}, \tag{1}\]  
with the wavelength of the light source \(\lambda\)= 587 nm and the numerical aperture \(\text{NA}\approx 0.1\). This result confirms that the smallest detectable droplet size of 4 \(\upmu\)m is selected reasonably, even though it is close to the estimated diffraction limit. In the final step of the processing routine, the droplet velocity is determined. First, a regular Particle Image Velocimetry (PIV) algorithm is applied to all droplets of one image in order to obtain  
Figure 8: Exemplary raw image at \(T_{\text{IB}}=773\,\text{K}\) and at \(x=50\,\text{mm}\) with enhanced contrast for better visualisation of the highly inhomogeneous background: (**a**) global threshold of 80%; (**b**) local threshold of 80%. an estimate of the velocity vector for each droplet. Based on this result, a least square fitting algorithm is used to detect the identical droplets on both images taken by the double frame camera. Then, the velocity can be calculated for each droplet using the inter framing time [8]. For the discussion of the measurement accuracy, it is important to note that only droplets with a valid velocity assignment were taken into account. Furthermore, the difference between the measured volume distribution of droplets and the flux density distribution had to be taken into account [1]. Therefore, the knowledge about the velocity of each individual droplet was used to correct for this bias. The characteristics of the presented diagnostics are defined by the optical components and the processing routine as summarised in Table 1.