## 3 Results and Discussion
### New Procedure for Beam-Steering Correction  
In Figure 6, the new procedure for beam-steering correction in droplet size distributions is described. As an example, the drop size distribution measurement already depicted in Figure 4 (\(\mu\) = 0.69 Pa\(\cdot\)s; \(\mathrm{p_{G}}\) = 0.8 MPa; \(V_{L}\) = 20 L/h; GLR = 0.35), was selected. The different steps are marked by the letters A-C.  
1. Firstly, a multimodal log-normal distribution (see Section 2.6) is fitted to the droplet size distribution, calculated by the mathematical inversion procedure of the measurement device. According to Equation (2), the method allows the application of an infinite number of modalities. However, as the number of fit parameters increases with the number of modalities, their amount should be reduced to a minimum value that still represents the full distribution sufficiently. In the presented study, trimodal log-normal fits are used for this purpose. Therefore, nine coefficients have to be fitted (\(x_{501-3}\), \(\sigma_{1-3}\), A\({}_{1-3}\)). It must be mentioned that different multimodal probability functions, like Rosin-Rammler or Nukiyama-Tansawa, could deliver better results when other laser diffraction spectroscopes are used. 2. The trimodal log-normal curve is split into its single modalities. The 3 rd modality, representing the largest droplets, is considered to represent the apparent droplet size distribution caused by the beam steering effect (see Section 3.1). 3. A modified distribution is formed by the combination of the 1 st and 2 nd modality to a bimodal log-normal distribution. The area under the curve (AUC) is re-standardized to a value of 1 by balancing the ratio indicators A\({}_{1}\) and A\({}_{2}\) in the following way: \[A_{1;2\ mod}\ =\ \frac{A_{1;2}}{(1-A_{3})}\] (2)  
The results of all performed measurements were fitted by a trimodal log-normal distribution with R\({}^{2}\) values above 0.99. In this example, a measurement with overlapping real and apparent droplet size distributions was used, as in this case the standard procedure of detector deactivation cannot be applied. In Figure 7, uncorrected and modified distributions are compared to each other. The modified distribution is much narrower than that of the uncorrected measurement. The characteristic plateau, caused by the beam-steering effect, is successfully removed. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\mathbf{d_{exit\ orifice}}\) & \(\mathbf{P_{gas}}\) & \(\mathbf{x_{10,3}}\) & \(\mathbf{u_{r}(\mu)}\) & \(\mathbf{x_{50,3}}\) & \(\mathbf{u_{r}(\sigma)}\) & \(\mathbf{x_{90,3}}\) & \(\mathbf{u_{r}(\phi)}\) \\ (mm) & (MPa) & (\(\mu\)m) & (\%) & (\(\mu\)m) & (\%) & (\(\mu\)m) & (\%) \\ \hline
1 & 0.3 & 953 & 3. Still, it must be ensured that the mode of the apparent droplet size distribution is detectable by the applied multimodal probability function. This means that the method cannot be applied when the  
Figure 6: Procedure of beam-steering correction, exemplarily presented at a measurement with overlapping real and apparent droplet size distribution (\(\mu\) = 0.69 Pa-s; p\({}_{\rm G}\) = 0.8 MPa; \(V_{L}\) = 20 L/h; GLR = 0.35): (**A**) Trimodal log-normal fit of the measured droplet size distribution. (**B**) Split in single modalities. (**C**) Formation of modified droplet size distribution. Figure 7: Comparison of uncorrected and modified distributions (\(\mu\) = 0.69 Pa-s; p\({}_{\rm G}\) = 0.8 MPa; \(V_{L}\) = 20 L/h; GLR = 0.35). overlap of real and apparent droplet size distribution exceeds a certain extent. Moreover, the method does not include final evidence of exact droplet size distribution measurements. However, it delivers the most probable interpretation of gained measurement results when log-normal fits with R\({}^{2}\) values above 0.99 are applicable. For further validation, gained results could be compared to results of other measurement techniques, like shadowgraphic imaging or Phase Doppler Anemometry (PDA).