## 3 Results and Discussion
### Correction Functions for LISST-VSF
In these calculations we used the median values of \(\beta_{p}^{LIST*}(\psi)\) and \(\beta_{p}^{LIST}(\psi)\) for each measurement series from all 20 experimental combinations of bead sizes, concentrations, and PMT gains listed in Table 1. For all experiments, the approximate coefficients, \(b_{p,150}^{LIST*}\) and \(b_{bp,150}^{LIST*}\), derived from uncorrected \(\beta_{p}^{LIST*}(\psi)\) are nearly half of the reference values of \(b_{p,150}^{REF}\) and \(b_{bp,150}^{REF}\). After \(CF_{f}(\psi)\) correction the approximate coefficients \(b_{p,150}^{LIST}\) and \(b_{bp,150}^{LIST}\) exhibit a nearly 1:1 relationship with \(b_{p,150}^{REF}\) and \(b_{bp,150}^{REF}\). The statistical parameters that quantify the overall good agreement between \(b_{p,150}^{LIST}\) and \(b_{bp,150}^{REF}\) and between \(b_{bp,150}^{LIST}\) and \(b_{bp,150}^{REF}\) are listed in Table 2.  
Figure 7: (**a**) Scatter plot of \(\beta_{p}^{LIST}\) vs. \(\beta_{p}^{REF}\) for polystyrene beads of varying diameters as indicated. Data obtained with the ring detectors and Roving Eyeball sensor are plotted separately, and the 1:1 line is plotted for reference (dotted black line). (**b**) Residuals expressed as percentages between \(\beta_{p}^{LIST}\) and \(\beta_{p}^{REF}\) for each bead size as a function of scattering angle. Similarly to the validation analysis of \(CF_{f}(\psi)\), the performance of the correction function \(BF_{f}(\psi)\) was evaluated by comparing the corrected LISST-VSF measurements of the degree of linear polarization, \(DoLP_{p}^{LIST}(\psi)\), with reference values of \(DoLP_{p}^{REF}(\psi)\) for six samples of polystyrene beads (100, 200, 400, 500, 700, 2000 nm in diameter). Figure 9 depicts these comparisons. The values of \(DoLP_{p}^{\text{DAWN}}(\psi)\) measured with DAWN-EOS are also depicted for the 100, 200, 400, and 700 nm beads. For all bead sizes, the magnitude and angular dependence of \(DoLP_{p}^{LIST}(\psi)\) exhibits generally a very good agreement with both the reference values and DAWN-EOS measurements. For larger beads, notable differences occur within the minima of the degree of linear polarization, for example near the angle of 80\({}^{\circ}\) for the 400 nm beads (Figure 9c). \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Data** & **R** & **_A_ & **B** & **MB** & **MR** & **RMSD** & **MAPD** & **N** \\ \hline \(\beta_{p}^{LIST}\) (w/ rings) & 0.987 & 0.72 & 0.031 m\({}^{-1}\) sr\({}^{-1}\) & \(-\)0.028 m\({}^{-1}\) sr\({}^{-1}\) & 1.00 & 0.210 m\({}^{-1}\) sr\({}^{-1}\) & 3.94\% & 876 \\ \(\beta_{p}^{LIST}\) (w/o rings) & 0.998 & 0.96 & 0.002 m\({}^{-1}\) sr\({}^{-1}\) & \(-\)0.002 m\({}^{-1}\) sr\({}^{-1}\) & 1.00 & 0.015 m\({}^{-1}\) sr\({}^{-1}\) & 3.39\% & 810 \\ \(b_{p_{150}^{LIST}}^{LIST}\) & 0.995 & 1.04 & \(-\)0.048 m\({}^{-1}\) & \(-\)0.007 m\({}^{-1}\) & 1.00 & 0.043 m\({}^{-1}\) & 2.30\% & 20 \\ \(b_{p_{150}^{LIST}}^{LIST}\) & 0.999 & 0.99 & 0.0001 m\({}^{-1}\) & \(-\)0.001 m\({}^{-1}\) & 1.00 & 0.006 m\({}^{-1}\) & 3.70\% & 20 \\ \(DoLP_{p}^{LIST}\) & 0.989 & 0.91 & 0.046 & 0.016 & 0.99 & 0.065 & 5.00\% & 810 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical results evaluating the comparison of corrected data from the LISST-VSF measurements with reference values obtained from Mie scattering calculations. For \(\beta_{p}^{LIST}\), the results are shown for the angular range 3.02-150\({}^{\circ}\) which includes the ring data and for the range 16-150\({}^{\circ}\) without the ring data. \(R\) is the Pearson correlation coefficient and the coefficients \(A\) and \(B\) are the slope and \(y\)-intercept, respectively, determined from a type II linear regression between individual pairs of \(X_{i}\) and \(Y_{i}\) values where \(Y_{i}\) represents measured values and \(X_{i}\) reference values. The mean bias (\(MB\)) was calculated as \(1/N\times\sum_{i=1}^{N}\left(Y_{i}-X_{i}\right)\) and \(MR\) represents the median ratio of \(Y_{i}\) /\(X_{i}\).