## 2 Methods
### Laboratory Experiments and Mie Scattering Calculations to Evaluate LISST-VSF
#### 2.1.1 Instrumentation
To encompass the large dynamic range of scattered intensity, three selectable gain settings are available for each detector (gain factors of 1, 21, or 101). As the DAWN-EOS detectors have no polarization analyzers, they only measure the first parameter of Stokes vector of the scattered light, \(I_{s}(\psi)\). Here we define \(I_{s\parallel}(\psi)\) for the parallel polarization of the incident beam and \(I_{s\perp}(\psi)\) for the perpendicular polarization of the incident beam. The matrix elements \(p_{11}(\psi)\) and \(p_{12}(\psi)\) can be obtained (to within a constant factor) from DAWN-EOS measurements as  
\[p_{11}(\psi)=\frac{I_{s\parallel}(\psi)+I_{s\perp}(\psi)}{2} \tag{3}\]  
\[p_{12}(\psi)=\frac{I_{s\parallel}(\psi)-I_{s\perp}(\psi)}{2}, \tag{4}\]  
which allows for determination of \(DoLP(\psi)\) from Equation (2). The calibration procedure described in [PERSON] et al. [61] allows for determination of \(\beta(\psi)\) in absolute units. Importantly, the calibration procedure of DAWN-EOS is fundamentally different from the calibration procedure of LISST-VSF. The manufacturer's calibration of LISST-VSF is based on a nominal radiant sensitivity of ring detectors (amperes of photoelectric current per watt of optical power) traceable to the National Institute of Standards and Technology [59; 60]. In contrast, the calibration of DAWN-EOS is based on measurements of light scattered at 90\({}^{\circ}\) by pure toluene with the incident beam having a linear perpendicular polarization [61]. This calibration relies on the known magnitude of molecular scattering by toluene. The two different methods employed in calibration of LISST-VSF and DAWN-EOS allow for comparisons of independent estimates of \(\beta(\psi)\) obtained by these instruments. We also recall that the \(DoLP(\psi)\) estimates obtained with the two instruments within the common range of scattering angles are based on different polarization measurement configurations used by these instruments. A Lambda 18 spectrophotometer was used to collect independent measurements of the spectral beam attenuation coefficient, \(c(\lambda)\), of polystyrene beads suspended in water. These measurements were made for comparisons with the beam attenuation data obtained with LISST-VSF, and also to aid in the preparation of samples with appropriate concentrations of polystyrene beads to ensure that measurements with LISST-VSF and DAWN-EOS were made within the single scattering regime. The spectrophotometric measurements were made in the spectral range from 290 nm to 860 nm with 1 nm interval, but only data at 532 nm are used in this study. The general applicability of laboratory spectrophotometers with proper modifications to enable measurements of beam attenuation of particle suspensions, including colloidal samples, has long been recognized [62; 63]. In our study, a sample of particle suspension was measured in a 1-cm quartz cuvette placed at a significant distance from the detector (~25 cm from the entrance of the integrating sphere), and field stops were aligned within the light path to reduce the size of the beam and acceptance angle of the detector to less than 1\({}^{\circ}\). This measurement geometry has been used in our previous studies of spectral beam attenuation by various particle assemblages [64; 65].