## 2 Methods
### Laboratory Experiments and Mie Scattering Calculations to Evaluate LISST-VSF
#### 2.1.1 Instrumentation
\begin{array}{cccc}p_{11} (\psi)&p_{12}(\psi)&0&0\\ p_{12}(\psi)&p_{22}(\psi)&0&0\\ 0&0&p_{33}(\psi)&p_{34}(\psi)\\ 0&0&-p_{34}(\psi)&p_{44}(\psi)\end{array} \right]\left[ \begin{array}{c}I_{i} \\ Q_{i}\\ U_{i}\\ V_{i}\end{array} \right], \tag{1}\]  
where \(\lambda\) has been omitted for brevity, \(C\) is a constant factor (for a given sample, light wavelength, and measurement geometry), \(p_{11}(\psi)\) represents the scattering phase function, and the reference plane is the scattering plane containing the incident and scattered directions [20; 51; 52]. This form provides a reasonable description of the measured scattering matrix by suspensions of randomly-oriented marine particles, including various specific types of particles present in seawater [24; 29; 33; 36; 37; 42]. In the case of unpolarized incident light (i.e., \(Q_{i}\), \(U_{i}\), and \(V_{i}\) are all zero), the volume scattering function \(\beta(\psi)\) equals (to within a constant factor) \(p_{11}(\psi)\), and the degree of linear polarization \(DoLP(\psi)\) can be determined from [29; 36; 37; 53]  
\[DoLP(\psi)=\frac{-p_{12}(\psi)}{p_{11}(\psi)}=\frac{-Q_{s}(\psi)}{I_{s}(\psi)}. \tag{2}\]  
Positive values of \(DoLP(\psi)\) are for dominantly perpendicular polarization and negative values for dominantly parallel polarization. We note that this definition of \(DoLP(\psi)\) has been widely used for characterizing the inherent scattering properties of various types of particles beyond aquatic particles, such as aerosol particles and cosmic dust [30; 54; 55; 56; 57; 58]. The LISST-VSF measurements of forward scattering within the angular range 0.09-15.17\({}^{\circ}\) are made with two linear polarization states of the incident beam, but with no polarization analyzers of the ring detectors. For the ring detectors, the calibrated \(\beta(\psi)\) in absolute units is a standard output of the manufacturer's processing software. The absolute calibration is based on the manufacturer-provided conversion from ring detector counts to physical units using radiant sensitivity of ring detectors [59; 60]. Detection of scattered light within the angular range 14-155\({}^{\circ}\) using the Roving Eyeball sensor employs measurements made with two linear polarization states of the incident beam and the corresponding two linear polarization states of the scattered light. The four measurement configurations allow for the determination of relative values of \(p_{11}(\psi)\), \(p_{12}(\psi)\), and \(p_{22}(\psi)\). The calibrated \(\beta(\psi)\) values within the Roving Eyeball angular range are obtained by scaling the \(p_{11}(\psi)\) data from the Roving Eyeball sensor. Specifically, the scattering measurements from the first angles of the Roving Eyeball sensor are forced to match the calibrated \(\beta(\psi)\) values from the overlapping last ring detectors. The \(DoLP(\psi)\) values are obtained from Equation (2) using \(p_{11}(\psi)\) and \(p_{12}(\psi)\), and are also included in the standard output of the manufacturer's processing code. We also used a DAWN-EOS multi-angle light scattering instrument which provided independent measurements of \(\beta(\psi)\) and \(DoLP(\psi)\) of polystyrene beads suspended in water. These measurements were made with a sample placed in a 20 mL cylindrical glass vial. The DAWN-EOS instrument used in this study has been previously characterized and calibrated for such measurement configuration [61]. This instrument uses a diode-pumped frequency-doubled Nd-YAG laser at light wavelength 532 nm with a Gaussian beam profile of 62 \(\upmu\)m in diameter. The interrogated sample volume is on the order of 10 nL. The incident beam can be linearly polarized both parallel and perpendicular to the scattering plane. The intensity of scattered light is measured simultaneously with eighteen photodiode detectors and no polarization analyzers, enabling measurements within a range of scattering angles from 22.5 to 147\({}^{\circ}\).