## 3 Results and Discussion
### Polarization Characteristics of Particle Size  
Our experiments start with aerosol samples with different particle sizes. Figure 5 shows 12 two-dimensional scatterplots with 24 polarization indices, corresponding to three kinds of monodisperse polystyrene spheres with different sizes. For each polarization index, the mean value, PFR, and Wilk's Lambda of the measured data are shown in Figure 6 and can be thought of as quantitative evaluation of the experimental results in Figure 5. Herein Wilk's Lambda is calculated as the ratio of intraclass variance and the population variance. The smaller ratio of intraclass variance means better interclass discrimination:  
\[Wilk^{\prime}s-Lambda=\frac{\sigma_{\text{intra}}^{2}}{\sigma_{\text{total}}^{2}} \tag{3}\]  
Figure 5 shows the different intraclass dispersion and class separation distances of different PSL aerosols. Although all the scatter plots can separate three types of PSL samples, the discrimination ability of polarization indices is different. Figure 6 shows the mean values, PFR, and Wilk's Lambda parameters of multidimensional polarization results, respectively. The horizontal axis represents the numbering order of polarization indices listed in Table 2.  
Figure 4: (**a**) Intensity channel at 10\({}^{\circ}\) (each measurement point represents a particle); (**b**) 85-degree R-Pdop of different PSLs (each point in the figure is averaged over 300 particles); (**c**) relationship between standard deviation and average number at R-Pdop (85\({}^{\circ}\)) (each measurement point represents a particle). Generally, for some specific polarization indices, the difference of mean value points out the distinction between classes and also implies the sensitivity of this index to some microphysical feature of aerosol samples. For samples shown in Figure 5, the main difference between these three types of samples is particle size. So it can be seen that P-Hdop (60\({}^{\circ}\)), R-Pdop (60\({}^{\circ}\)), P-Pdop (115\({}^{\circ}\)), and R-Pdop (85\({}^{\circ}\)) can be used to distinguish three kinds of PSL samples from Figure 5. However, the PFR parameters show the data dispersion of many single aerosol measurements, corresponding to the resolution of measurement results. Considering the definition of the Wilk's Lambda parameter, the proper polarization parameters among the whole index group suitable for aerosol identification should have a larger mean difference and a smaller Wilk's Lambda. For the experiments shown in Figure 6a, P-Hdop (60\({}^{\circ}\)) is a better indicator than P-Pdop (115\({}^{\circ}\)) (marked by the red inverted triangle). On the other hand, whether based on mean value or Wilk's Lambda, we can see that H-Hdop (60\({}^{\circ}\)) and H-Pdop (60\({}^{\circ}\)) are not usable in classifying the three types of samples in Figure 6a, and it seems that the two parameters are possibly less sensitive to aerosol size (marked by the blue inverted triangle). Figure 5: 24-dimensional polarization indices distribution of PSL samples with different sizes. Figure 6: (**a**) Mean values of multidimensional polarization indices; (**b**) PFR indices; (**c**) Wilk’s Lambda indices. The red triangles mark index 11 (P-Hdop (60\({}^{\circ}\))) and index 16 (P-Pdop (115\({}^{\circ}\))), and the blue triangles are index 3 (H-Hdop (60\({}^{\circ}\))) and index 4 (H-Pdop (60\({}^{\circ}\))). Because we have recorded the polarization scattering indices of aerosols one by one in the experiments, we can extract not only the average measurement results of aerosol samples but also statistical indicators such as PFR and Wilk's Lambda parameters. Through a comprehensive analysis of single-particle polarization scattering signals, we can reasonably understand the feasibility and possibility of various polarization indices applied to field measurements.