## 2 Methods
### Laboratory Experiments and Mie Scattering Calculations to Evaluate LISST-VSF
#### 2.1.4 Determination of Correction Functions
Finally, by combining Equations (5) and (8), \(CF(\psi)\) can be determined for each LISST-VSF measurement as  
Figure 2: Comparison of measurements of the particulate beam attenuation coefficient, \(c_{p}\), at 532 nm obtained with a spectrophotometer with measurements from the LISST-VSF. The comparison is depicted for suspensions of polystyrene beads of six different diameters as indicated in the legend, and the 1:1 line is plotted for reference (dotted black line). Appropriate dilution factors have been applied to account for the different particle concentrations used in measurements with each instrument. The presented values correspond to samples measured with the LISST-VSF. \[CF(\psi)=\frac{\widetilde{\beta}_{p}^{Mie}(\psi)\ c_{p}^{LISST*}\frac{Q^{Mie}_{0}}{Q ^{Mie}_{0}}}{\beta_{p}^{LISST*}(\psi)}. \tag{9}\]  
The application of this protocol to every individual measurement of \(\beta_{p}^{LISST*}(\psi)\) helps to better capture the variability between individual measurements during a given series of LISST-VSF measurements on a given sample, for example due to imperfect mixing in the 2 L sample chamber or potential electronic fluctuations in the instrument. The smaller-sized particle standards (<500 nm in diameter) appear as the best candidates for determination of \(CF(\psi)\) because they produce a relatively featureless pattern of angular scattering (see the results for 200 nm beads in Figure 1). The measurements with larger beads (500 nm to 2000 nm) were not used in these determinations because the angular scattering pattern includes multiple maxima and minima (see the results for 2000 nm beads in Figure 1), which render the comparison of \(\beta_{p}^{LISST*}(\psi)\) and \(\beta_{p}^{REF}(\psi)\) particularly sensitive to even small uncertainties in measurements or theoretical calculations. The results obtained with beads of 100, 200, and 400 nm in diameter were considered in the determinations of final correction function \(CF_{f}(\psi)\) within four angular ranges, as described below:  
\[CF_{f}(\psi)=(CF_{100}(\psi)+CF_{200}(\psi)+CF_{400}(\psi))/3\ \text{for}\ \psi=0.09\text{--}60^{\circ} \tag{10a}\]  
\[CF_{f}(\psi)=CF_{200}(\psi)\ \text{for}\ \psi=61\text{--}128^{\circ} \tag{10b}\]  
\[CF_{f}(\psi)=(CF_{200}(\psi)+CF_{400}(\psi))/2\ \text{for}\ \psi=129\text{--}150^{\circ} \tag{10c}\]  
\[CF_{f}(\psi)=(CF_{100}(\psi)+CF_{200}(\psi)+CF_{400}(\psi))/3\ \text{for}\ \psi=151\text{--}155^{\circ}. \tag{10d}\]  
The \(CF_{200}(\psi)\) data obtained with 200 nm beads provide the main contribution to the determination of \(CF_{f}(\psi)\). The \(CF_{100}(\psi)\) data obtained with 100 nm beads are used partially because of increased uncertainty in the PSD of these beads (\(CV\) of nominal mean diameter is 7.8%, see Table 1). The \(CF_{400}(\psi)\) data obtained with 400 nm beads are also used partially and cover the backscattering angles, where these particular data are useful for correction of an apparent artifact near 130-140\({}^{\circ}\), which is rather minor but has been consistently observed with our LISST-VSF instrument for various natural particle assemblages. The calculations of \(CF_{100}(\psi)\), \(CF_{200}(\psi)\), and \(CF_{400}(\psi)\) were made using data for particle concentrations and PMT gains which ensured sufficient signal for the ring detectors while avoiding PMT saturation of the Roving Eyeball sensor (see dilution factors in italic font in Table 1). For a given bead standard, the final values of correction function at different angles were determined as the median values of all the relevant determinations. The final \(CF_{f}(\psi)\) was smoothed in the angular range 2.56-155\({}^{\circ}\) with a 3-point and then a 5-point moving average. In addition, \(CF_{f}(\psi)\) within the near-forward angular range 0.09-4.96\({}^{\circ}\) was set to a constant value of \(CF_{f}(\psi_{32})\), where \(\psi_{32}=15.17^{\circ}\) corresponds to the last ring detector.