## 3 Results and Discussions
### Validation of the VSFlab and Comparison with LISST-VSF  
To further validate our improvement on measurement of backward scattering, experiments on various sizes of polystyrene beads at 532 nm and 520 nm were carried out. Calibration for the VSFlab at 520 nm had been done using the same method mentioned in Section 2.3. The phase function for 3 \(\upmu\)m polystyrene beads at 532 nm was obtained according to Equation (3) for the comparison with POLVSM measurement which was redrawn from [PERSON]'s work [23] and Mie theory calculated result (see Figure 6). Both results of VSFlab and POLVSM showed good agreement with Mie theory in 1\({}^{\circ}\) to 170\({}^{\circ}\). Notable differences were observed in the backward scattering range between 170\({}^{\circ}\) and 178.5\({}^{\circ}\) (see Figure 6b), that the VSFlab result was closer to the theoretical result while the POLVSM result showed overestimations. The mean relative errors between 170\({}^{\circ}\) and 178.5\({}^{\circ}\) were 56.76% and 16.53% for POLVSM and VSFlab results, respectively. VSF results for 2, 5, and 11 \(\upmu\)m polystyrene beads at 520 nm also revealed good agreement with theoretical results from 170\({}^{\circ}\) to 178.5\({}^{\circ}\) (see Figure 7d-f). The mean relative errors from 170\({}^{\circ}\) to 178.5\({}^{\circ}\) for 2, 5, and 11 \(\upmu\)m beads were 21.5%, 45.3%, and 34.07%, respectively. It indicated that the customized new prism could reduce the stray light returning to the basin efficiently and such design could avoid manufacturing flaws. Figure 5: **(a)** Scatterplot between raw signal voltage measured by VSFlab and calculated VSF for 0.203 \(\upmu\)m bead solutions with various concentrations at four scattering angles of 6\({}^{\circ}\) (blue dots), 90\({}^{\circ}\) (red dots), 177\({}^{\circ}\) (green dots) and 178.5\({}^{\circ}\) (dark dots). The values (voltage and \(\beta\)) at 90\({}^{\circ}\), 177\({}^{\circ}\), and 178.5\({}^{\circ}\) are multiplied by 10, 30, and 30 for an unambiguous presentation. The four lines are the results of applying a robust linear regression model. \(R^{2}\) for the four angles are 0.9764, 0.9835, 0.9791, and 0.9851 respectively. Horizontal and vertical error bars represent standard deviations estimated, respectively, from the 30 measurements of Voltage (\(\theta\)) at each concentration and \(\widetilde{\beta}_{Mie}\) calculated by accounting for uncertainties in the mean diameter of the beads and measured \(c\). **(b)** Calibration coefficients \(k\) for each angle at 532 nm. **(c)** Comparison of VSFs for 3 \(\upmu\)m beads before amplitude calibration and after amplitude calibration. In order to facilitate comparison with the calibrated scattering signal, the scattering signal before calibration was multiplied by the average \(k\) between 3\({}^{\circ}\) and 177\({}^{\circ}\). **(d)** A schematic of the shadow effect. The blue region represents the scattering volume from which the scattering light is shadowed by prism 1. The green region represents the scattering volume from which the scattering light is received by the PMT. At the scattering angles between 1\({}^{\circ}\) and 150\({}^{\circ}\), VSFlab was proved to be workable by comparison with LISST-VSF (see Figure 7a-c). The mean relative percentage difference of 2 \(\upmu\)m polystyrene beads between VSF measured by LISST-VSF and theoretical values was 11.4% from 1\({}^{\circ}\) to 150\({}^{\circ}\) and that between VSF measured by VSFlab and theoretical values was 9.8% from 1\({}^{\circ}\) to 178.5\({}^{\circ}\). For 5 and 11 \(\upmu\)m polystyrene beads, the magnitude of the minima or maxima from VSFlab differed by a few tens of percent from the Mie scattering values. These deviations were due to the large angular acceptance of the detector in VSFlab relative to that in LISST-VSF. However, the angular acceptance of VSFlab was acceptable since the VSFs of the natural samples usually show smoother angular distributions, which could be confirmed in experimental results on natural samples.