## 2 Experimental Setup and Methods
### Experimental Setup  
In our experimental setup, as shown in Figure 2, the airflow of particulate matter is collected from the real environment or the aerosol generator and then passes through the optical detection area from an optimally designed sheath nozzle. The velocity of flow of the collected particle sample is limited to 1.2 L/min composed of 0.6 L/min sample flow and 0.6/min sheath flow by two flow controllers and a gas pump. In Figure 2, two red arrows are used to mark the particle inlet and the sheath gas inlet. The sample inlet is at the top of the sample airflow. When the particles to be measured enter the flow channel from the inlet, they will be wrapped in the sheath flow and then dispersed and diluted. In the optical system, a horizontally polarized laser beam (532 nm, 100 mW, MSL-III-532, Changchun New Industries Optoelectronics Technology Co., Ltd.) passes through a polarization state generator that can modulate the incident light to horizontal (H), 45\({}^{\circ}\) (P) linear polarization state, and right (R) circular polarization state, respectively. The polarized light is focused to form a light sheet by a cylindrical lens and then incident on the airflow channel of the aerosol particles. The width and height of the laser spot are 1 mm and 0.04 mm, respectively. To reduce the influence of stray lights, the scattering chamber is coated with high absorption material, and the forward non-scattered beam is absorbed by an optical trap at the end of the chamber. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Shape**} & \multicolumn{1}{c}{**Aerosol Type**} & \multicolumn{1}{c}{**Manufacturer**} & \multicolumn{1}{c}{**Complex Refractive**} & \multicolumn{1}{c}{**Generator**} \\ \hline \multicolumn{1}{c}{Sphere} & \multicolumn{1}{c}{PSL (1, 2, 2.5 μm)} & Sigma-Aldrich & 1.590–0.000i & Met-one 255 \\ \hline \multirow{4}{*}{Quasi-spherical} & Na\({}_{2}\)SO\({}_{4}\) & Hong-Meng Beijing & 1.480–0.001i [26] & Met-one 255 \\  & NaCl & Hong-Meng Beijing & 1.540–0.001i [26] & Met-one 255 \\  & NaNO\({}_{3}\) & Hong-Meng Beijing & 1.587–0.001i [26] & Met-one 255 \\  & Fly ash & AIOFM & 1.570–0.010i [27] & TSI-3400A \\  & Carbon sphere & Nano-Micro Tech & 1.670–0.270i [28] & TSI-3400A \\ \hline \multirow{4}{*}{Highly irregular shape} & Arizona dust & Power Technology & 1.540–0.020i [29] & TSI-3400A \\  & Carbon nanochip & Sigma-Aldrich & 1.670–0.270i [28] & TSI-3400A \\ \cline{1-1}  & Mesoporous carbon & XFNANO & 1.670–0.270i [28] & TSI-3400A \\ \cline{1-1}  & Hollow carbon sphere & XFNANO & 1.670–0.270i [28] & TSI-3400A \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of the aerosol types included in this paper. Figure 1: Size distribution of particles measured by an aerodynamic particle size. The scattered light is measured by four polarization detection channels at the scattering angle 30\({}^{\circ}\) (P1), 60\({}^{\circ}\) (P2), 85\({}^{\circ}\) (P3), and 115\({}^{\circ}\) (P4), respectively, and the intensity detected at the scattering angle 10\({}^{\circ}\) (I) is the reference channel. Each polarization detection channel is equipped with a spatial filtering module and fiber bundles are connected to the detection module, which is composed of a silicon photomultiplier tubes (SiPMT) array. The signal-processing unit mainly includes a current-to-voltage converter and a signal amplifier. Then, signals of 17 channels (including 16 polarization-integrated signals and 1 intensity signal) were collected by an acquisition device (DAQ) (FCFR-USB2068, Fectec Technology, China) with a sampling rate of 1 M/s simultaneously. The scattering response pulse width for each aerosol is about 5-10 us and the Stokes vectors of 10,000 particles per minute are recorded. In experiments, three instruments with different polarization states of incident light (horizontal (H), 45\({}^{\circ}\) (P) linear polarization, and right (R) circular polarization, respectively) worked simultaneously to form a set of multidimensional polarization online analysis systems.