## Materials and Methods
### Post-Processing and Calibration  
The processing of images is performed by means of a MATLAB(r) (R2017b, The MathWorks, Inc.) routine that has previously been developed at the institute [8; 36]. This post-processing routine was successfully used for multiple experiments in the past [29; 37]. The first step of the routine is the separation of droplets from the background by means of an intensity threshold. This threshold is dynamically set to 80% of the median value of the intensity distribution of each individual image. In the first place, the choice of the threshold level is empirical. However, it has been proven to be a robust criterion for various test images and different experimental setups. In general, the choice of the threshold level is a trade-off between the correct detection of small droplets and the incorrect assignment of droplets to the background noise. In the present study, the threshold level was mainly chosen in order to prevent the incorrect assignment of droplets to the background noise. In other words, the threshold level was not optimised for detecting droplets as small as possible. This is a feasible setting, since the chosen size of the smallest detectable droplets of 4 um in diameter can be spatially resolved by a fair amount of pixels (4 um \(\approx\) 5 pixels). Ideally, the choice of the threshold level should be validated by an estimation of the overall noise level. However, this requires a comprehensive investigation, which is beyond the scope of this study. We are well aware that the selected threshold level will affect the directly derived droplet size. Therefore, a suitable calibration of the optical setup was necessary for determining the droplet size with high accuracy, which will be elucidated in detail subsequently. Furthermore, the routine was complemented by a local threshold technique in order to enable the measurement close to the atomiser, where an inhomogeneous illumination due to the spray cloud was inevitable. In this work, the image was simply subdivided into twelve segments of equal dimensions, and a local threshold was set for each of the segments. The result of the first step of the processing routine is illustrated for a raw image with a highly inhomogeneous background in Figure 8a,b using the global threshold and the described local threshold, respectively. The global threshold yielded many incorrectly detected droplets in the dark areas of the image, while in the bright areas some droplets were not detected at all. In contrast, the result when using the local threshold was more sensible since the number of incorrectly detected droplets was drastically reduced. It should be noted that this simple segmentation of the image is not ideal, but feasible in this case since only round droplets of a certain size range are present in the spray. In summary, quantitative droplet data could be obtained at very low distances downstream of the atomiser nozzle at the cost of a higher computational effort for image processing. In addition, the accuracy of detected droplets was improved due to the fact that a slightly inhomogeneous background was present in many spray images, while the calibration of droplet size, which will be elaborated in the next paragraph, was conducted with a homogeneous background. By separation of droplets from the background by means of an intensity threshold, the outer contour of each droplet can be identified directly. However, a suitable calibration is necessary since the chosen threshold level of 80% is arbitrary and the determination of droplet size is dependent on the droplet position relative to the focal plane and the droplet size itself [7]. In other words, a robust procedure is required for determining the actual droplet diameter from the detected droplet diameter while considering defocused droplets in the measurement volume. In order to address this issue, a Depth of Field (DoF) calibration is performed, which is discussed in detail by [PERSON] et al. [34].