## 2 Description of the Experiment
### Calibration of SLIPI-LIF/Mie Ratio and Extinction Cross-Section (\(\sigma_{\rm e}\)) Images  
Figure 4 is an example of results at layer number \(m\) = 30 which corresponds to the depth position \(Z\) = 15 mm. In (a) the SLIPI-LIF image of the spray is shown together with the transmitted light from the fluorescing liquid in the cuvette. The Mie image and the intensity ratio, SLIPI-LIF/Mie are given in (b) and (c), respectively. These images are recorded using the experiments described in Section 2.1. Some residual stripes are seen on the processed SLIPI images. These artifacts can be reduced by averaging the data over a larger number of images, effectively reducing the intensity variations between the three sub-images. Other reasons for their occurrence are given in [16; 20] together with some suppression strategy.  
The black dashed line in Figure 4 corresponds to the location where PDA measurements are performed. For each location, 20,000 validated droplet size measurements are recorded by the PDA instrument. In all measurements, the percentage of validation rate was above 96%, confirming a good sphericity of the droplets at a distance 7.5 cm below the nozzle tip without unwanted multi-occupancy effects. Figure 4 shows the SLIPI-LIF/Mie ratio and various mean diameters, D\({}_{10}\), D\({}_{30}\), and D\({}_{32}\) plotted against the PDA measurement position. Those mean diameters are calculated by using the droplet distribution histogram shown in Figure 4 for measurement positions X = 1 and X = 10. From mean diameters, it is seen that arithmetic mean diameter (D\({}_{10}\)) is the lowest mean diameter while SMD, D\({}_{32}\), is the largest. The size distribution histograms are shown in Figure 4e or a similar distribution can also be utilized for deducing several other mean diameters, as given in reference [13; 27].  
Figure 5a shows the plots of SLIPI-LIF/Mie ratio against droplets D\({}_{32}\) and D\({}_{30}\). Both the experimental data and the calibration fit for correlating the ratio with mean diameters are seen. In a recent study, [PERSON] et al. [37] extensively investigated the SLIPI-LIF/Mie ratio and the PDA calibration in a simple pressure atomizer. A calibration curve similar to Figure 5a in this study is also reported by the authors in [37]. Figure 5b shows the plot of calibrated SLIPI-ratio (droplets SMD) against the corresponding droplets \(\sigma_{\rm e}\). To deduce the averaged \(\sigma_{\rm e}\), the histogram of the droplets size distribution (see Figure 4e) for each measured SMD value is used as input data to the Lorenz-Mie calculator software developed by the authors. The input incident wavelength is set, here, to 447 nm, while the refractive indices are set to 1 for air and 1.33 for the water droplets. The entire medium is assumed to  
be non-absorbing. Figure 5c shows the calibrated SLIPI-LIF/Mie ratio maps representing droplet SMD extracted using the calibration curve given in Figures5a, while 5d shows the droplets \(\sigma_{\rm e}\) maps obtained from the calibration curve shown in Figure 5b. It is observed in Figure 5c that the largest droplets corresponding to approximately SMD = 60 \(\upmu\)m are located at the spray edge, while the smallest droplets of approximately SMD = 25 \(\upmu\)m are in the spray center. It is seen in Figure 5d that the \(\sigma_{\rm e}\) varies from \(0.5\times 10^{-3}\) mm\({}^{2}\) in the center of the spray to \(3\times 10^{-3}\) mm\({}^{2}\) at the outermost edges of the spray.  
Figure 4: (**a**) SLIPI-LIF image of the spray and the dye cuvette; (**b**) SLIPI-Mie image; (**c**) SLIPI-LIF/Mie ratio image of the spray; the PDA measurements are plotted in (**d**) against the SLIPI-LIF/Mie ratio and droplet mean diameters; (**e**) histograms of droplet size distributions measured using PDA.