## 3 Results and Discussion  
### Correction Functions for LISST-VSF  
The results for \(CF_{100}(\psi)\), \(CF_{200}(\psi)\), \(CF_{400}(\psi)\), and \(CF_{f}(\psi)\) are plotted in Figure 4. The final correction function \(CF_{f}(\psi)\) indicates that \(\beta_{p}^{LISST*}(\psi)\) is lower than \(\beta_{p}^{REF}(\psi)\) by a factor of about 2, and also exhibits some angular variability. One consistent feature in the forward scattering region, which is independent of the bead size, is a sharp increase in \(CF_{f}(\psi)\) with a peak at ring 26 (\(\psi=5.84^{\circ}\)). We observed a similar but inverse feature consistently in natural seawater samples, which suggests that the behavior of the correction function at these angles is credible. Within the angular range of data from the Roving Eyeball sensor (16-150\({}^{\circ}\)), the \(CF_{f}(\psi)\) values remain generally in the range between  
Figure 3: Measured values of the particulate volume scattering function \(\beta_{p}(\psi)\) obtained with the LISST-VSF after correction (circles) for scattering angles 90–150\({}^{\circ}\) and illustration of the results of two model relationships ([PERSON] and Zaneveld [75], [PERSON] et al. [76]) fitted to the data. The illustrated example measurement was made on a natural sample collected from the San Diego River estuary. 1.7 and 1.9. For angles larger than 150\({}^{\circ}\), we did not obtain consistent results of the correction function for different bead sizes (not shown), so this angular range is omitted from our analysis of LISST-VSF measurements. Note also that CF\({}_{400}(\psi)\) differs greatly from CF\({}_{100}(\psi)\) and CF\({}_{200}(\psi)\) within the angular range between about 65\({}^{\circ}\) and 120\({}^{\circ}\). This can be attributed to the uncertainty in the determinations of \(CF_{400}(\psi)\) associated with a well-pronounced minimum in the volume scattering function for the 400 nm beads in this angular range. Therefore, the CF\({}_{400}(\psi)\) data in this angular range were not used in the determination of final CF\({}_{f}(\psi)\). The results for \(BF_{100}(\psi)\), \(BF_{200}(\psi)\), \(BF_{400}(\psi)\), and \(BF_{f}(\psi)\), are shown in Figure 5. As seen, \(BF_{f}(\psi)\) is negative within the examined angular range and varies within a relatively narrow range of values between about \(-0.02\) and \(-0.04\). Similar to the results for CF\({}_{400}(\psi)\), the distinct feature of positive bias observed in the \(BF_{400}(\psi)\) data around the scattering angle of 80\({}^{\circ}\) can be attributed to the uncertainty associated with a minimum in the volume scattering function for the 400 nm beads in this angular range. This portion of \(BF_{400}(\psi)\) data was not used in the determination of final \(BF_{f}(\psi)\). The performance of the final correction function \(CF_{f}(\psi)\) within the range of scattering angles from 0.09\({}^{\circ}\) to 150\({}^{\circ}\) was evaluated by comparing the corrected LISST-VSF measurements of volume scattering function, \(\beta_{p}^{LISST}(\psi)\), with reference values of \(\beta_{p}^{REF}(\psi)\) for six samples of polystyrene beads (100, 200, 400, 500, 700, and 2000 nm in diameter; see the dilution factors for these samples indicated in boldface in Table 1). The beads with diameters of 500, 700, and 2000 nm were not used in the generation of the final correction function, so they provide completely independent data for evaluating the performance of CF\({}_{f}(\psi)\). The evaluation with the data for 100, 200, and 400 nm beads is also useful because the final CF\({}_{f}(\psi)\) was determined by averaging the results obtained with multiple bead sizes and concentrations of these samples, and not from a single bead size and concentration. Results of independent measurements obtained with the DAWN-EOS on four bead suspensions (100, 200, 400, and 700 nm) are also included in the evaluation analysis for additional comparisons.