## 3 Results and Discussion
### Correction Functions for LISST-VSF
These median values indicate no overall bias in the corrected measurements of \(\beta_{p}^{LISST}(\psi)\) relative to the reference values of \(\beta_{p}^{REF}(\psi)\) and small statistical differences between \(\beta_{p}^{LISST}(\psi)\) and \(\beta_{p}^{REF}(\psi)\). Table 2 also includes the statistical parameters for a subset of data presented in Figure 7a. In this subset, the forward scattering measurements with ring detectors were excluded, so the angular range is 16-150\({}^{\circ}\). The statistical parameters for this subset are generally improved compared with the dataset covering the angular range 3.02-150\({}^{\circ}\). For example, the root mean square difference (\(RMSD\)) is smaller (0.015 m\({}^{-1}\) sr\({}^{-1}\) vs. 0.21 m\({}^{-1}\) sr\({}^{-1}\)) and the slope of linear regression is closer to 1 (0.958 vs.  
Figure 6: Comparison of \(\beta_{p}(\psi)\) measurements on suspensions of polystyrene beads of varying diameter with reference values, \(\beta_{p}^{REF}(\psi)\). The \(\beta_{p}^{LISST}(\psi)\) data represent \(CF_{f}\)-corrected median values obtained from a series of measurements with the LISST-VSF. Independent measurements of \(\beta_{p}(\psi)\) obtained with the DAWN-EOS instrument are also shown as diamonds in panels a, b, c and e. The bead diameters are indicated in the legend. 0.723). The improvements in the statistical parameters after removing the ring detector data are related primarily to much larger values of volume scattering function at forward scattering angles compared with larger angles, and a tendency to negative bias in \(\beta_{p}^{LIST}(\psi)\) relative to \(\beta_{p}^{REF}(\psi)\) at forward angles. To further validate the correction of LISST-VSF measurements with the \(CF_{f}(\psi)\) function, we performed comparisons for approximate scattering and backscattering coefficients, \(b_{p,150}\) and \(b_{bp,150}\), respectively. The approximate scattering coefficient \(b_{p,150}\) was obtained by integrating the volume scattering function within the angular range from 0.09\({}^{\circ}\) to 150\({}^{\circ}\). The approximate backscattering coefficient \(b_{bp,150}\) was obtained by the integration from 90\({}^{\circ}\) to 150\({}^{\circ}\). These calculations were made for the uncorrected measured \(\beta_{p}^{LIST*}(\psi)\), \(CF_{f}\)-corrected measured \(\beta_{p}^{LIST}(\psi)\), and reference \(\beta_{p}^{REF}(\psi)\). We also used Mie scattering calculations to estimate the underestimation of the scattering and backscattering coefficients for the examined polystyrene beads caused by the integration of \(\beta_{p}^{REF}(\psi)\) up to 150\({}^{\circ}\) as opposed to 180\({}^{\circ}\). We found that the approximate scattering coefficient, \(b_{p,150}^{REF}\), can be lower by as much as 7% compared with the \"true\" scattering coefficient \(b_{p}^{REF}\). This result was observed for 100 nm beads. For backscattering the approximate coefficient \(b_{bp,150}^{REF}\) was found to be lower by as much as 24% for the 500 nm beads. Although the LISST-VSF measurements extend to 150\({}^{\circ}\) rather than 180\({}^{\circ}\), the approximate coefficients are still useful for our validation exercise because most of the angular range and magnitude of total scattering and backscattering coefficients are included in the integration up to 150\({}^{\circ}\). In addition, this validation analysis includes all 20 experiments conducted in this study, and not just the six example experiments presented in Figures 6 and 7. Figure 8 compares the reference values of \(b_{p,150}^{REF}\) and \(b_{bp,150}^{REF}\) with LISST-VSF values determined from uncorrected \(\beta_{p}^{LIST*}(\psi)\) and \(CF_{f}\)-corrected \(\beta_{p}^{LIST}(\psi)\).