## 4 Conclusions  
A VSF meter (VSFlab) was established and achieved good backward volume scattering function between 1\({}^{\circ}\) and 178.5\({}^{\circ}\) with the novel prism that prevents the stray light induced by the specular reflection of the incident beam from re-entering the scattering volume. A rigorous calibration method and validation for the VSFlab instrument converted the output raw signal into geophysical units (i.e., m\({}^{-1}\) sr\({}^{-1}\)) and corrected the underestimation caused by the shadow effect of the prism. By comparison with [PERSON]'s POLVSM measurement, which was redrawn from his work and Mie theory calculated results, the new prism was proved to be workable in reducing stray light. Furthermore, the VSF results for 2, 5, and 11 \(\upmu\)m polystyrene beads at 520 nm were also in good agreement with the theoretical results. All these validations fully proved the reliability of VSFlab in measuring the VSFs.  
Field observations in the East China Sea exhibited a moderate increase in VSFs from 170\({}^{\circ}\) to 178.5\({}^{\circ}\), not more than five times, while the VSF results in other regions showed a relatively sharp increase. The measured VSF could provide a basis for the parameterization of VSF in the radiative transfer model. The variability of \(\chi_{p}\) factors increased with an angle larger than 155\({}^{\circ}\) and reached the maximum value of 42.3% at 178.5\({}^{\circ}\). Based on the different VSF shapes at angles greater than 155\({}^{\circ}\), two types of VSFs were found in the ECS. With the assistance of BT-3000, it could be found that these two types differed in particle size distribution and shape parameters. The variability of \(\chi_{p}\) in the backward direction has the potential to be used to characterize the particles in the ECS.  
Conceptualization, C.W. and B.T.; methodology, C.W. and B.T.; software, C.W. and B.T.; validation, C.W. and B.T.; formal analysis, C.W. and B.T.; investigation, C.W. and B.T.; resources, H.H., D.P. and Z.M.; data curation, Y.G. and H.S.; writing--original draft preparation, C.W. and B.T.; writing--review and editing, C.W. and B.T.; visualization, Y.G.; supervision, H.H., D.P. and Z.M.; project administration, H.H., D.P. and Z.M.; funding acquisition, B.T., D.P. and Z.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by \"The Key Special Project for Introduced Talents Team of Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou), grant number GMI2019 ZD0602\"; \"the Scientific Research Fund of the Second Institute of Oceanography, SOA, grant number QNYC201602\"; \"the National Natural Science Foundation of China, grant number 41876033 and 61991454\".  
Not applicable.  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study. Written informed consent has been obtained from the patient(s) to publish this paper.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Equivalent Diameter (\(\upmu\)m)**} & \multicolumn{3}{c}{**Circularity**} \\ \cline{2-7}  & **Avg.** & \(\sigma\) & **\%** & **Avg.** & \(\sigma\) & **\%** \\ \hline Type I & 14.85 & 6.29 & 42.34 & 0.77 & 0.04 & 4.53 \\  & 12.16 & 4.5 & 37.00 & 0.74 & 0.11 & 14.98 \\  & 10.53 & 2.5 & 23.74 & 0.72 & 0.1 & 13.55 \\ \hline Type II & 7.85 & 2.13 & 27.10 & 0.77 & 0.03 & 4.30 \\  & 8.07 & 2.08 & 25.76 & 0.79 & 0.02 & 2.66 \\  & 8.33 & 2.23 & 26.72 & 0.78 & 0.03 & 3.74 \\  & 6.83 & 3.26 & 47.63 & 0.78 & 0.03 & 4.24 \\  & 8.73 & 2.32 & 26.53 & 0.75 & 0.04 & 5.61 \\  & 7.75 & 2.84 & 36.65 & 0.75 & 0.04 & 5.23 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average, standard deviation (\(\sigma\)), and percent variability (\(\sigma\) as %) of equivalent diameter and circularity from the microscopic imaging analysis data of particles in water samples.