## 1 Introduction
The volume scattering function provides incomplete information, in the sense that it does not contain information about polarization effects associated with light scattering. A complete characterization of elastic incoherent interactions of light at arbitrary wavelength \(\lambda\) with a sample volume of seawater is provided by a 4 \(\times\) 4 scattering matrix, often referred to as the phase matrix or Mueller matrix [20; 21; 22; 23]. This matrix describes a linear transformation of irradiance and polarization of an incident beam described by a 4-component Stokes vector into the intensity and polarization of the scattered beam that is also described by its corresponding Stokes vector. \(\beta(\psi,\ \lambda)\) is related to the first element of the scattering matrix, \(p_{11}(\psi,\lambda)\), and can be obtained from a measurement using unpolarized light for illumination of sample and measuring the total scattered intensity. The degree of linear polarization of scattered light, \(DoLP(\psi,\lambda)\), describes the proportion of linearly polarized light relative to total intensity of the scattered light beam. As described in greater detail below, for various assemblages of particles including suspended marine particles and when the incident light beam is unpolarized, this quantity can be derived from the first two elements of the scattering matrix, which requires measurements involving linear polarization [29; 36; 37]. Despite the relative importance of \(\beta(\psi,\lambda)\) and \(DoLP(\psi,\lambda)\) of seawater and the associated particulate components \(\beta_{p}(\psi,\lambda)\) and \(DoLP_{p}(\psi,\lambda)\), the ocean optics community has historically relied mostly on simplified theoretical models (such as Mie scattering theory for homogenous spheres) and a limited dataset of measurements made with custom-built light scattering instruments. For example, over the past several decades, a limited dataset of \(\beta(\psi,\lambda)\) measurements made by [PERSON] [38] was widely used as a standard input for the particulate scattering phase function for radiative transfer modeling in the ocean. Comprehensive determinations of the scattering matrix for natural seawater have been very scarce [39; 40; 41; 42]. These determinations showed that the off-diagonal matrix elements for seawater are very small or negligible, indicating very small effects associated with optical activity or orientational anisotropy of seawater scatterers [37; 42]. More recently, several light scattering sensors have been developed for in situ deployments or laboratory use [43; 44; 45; 46], but to our knowledge, none of these sensors are commercially available. While measurements with these new sensors have already significantly contributed to the increase of available datasets of \(\beta(\psi,\lambda)\) (or \(\beta_{p}(\psi,\lambda)\) which can usually be satisfactorily estimated by subtracting the contribution associated with water molecules) in various oceanic environments [44; 47; 48], the determinations of \(DoLP_{p}(\psi,\lambda)\) for natural assemblages of marine particles remain very scarce, as indicated by the rarity of scattering matrix measurements of seawater. Recently, a new light scattering instrument, the LISST-VSF (Sequoia Scientific, Inc., Bellevue, WA, USA), has become commercially available, and provides the capability of determining both the volume scattering function and the degree of linear polarization of scattered light at a single light wavelength (532 nm) with high angular resolution over the range \(\sim\)0.1\({}^{\circ}\) to 155\({}^{\circ}\)[49]. It is capable of both in situ and benchtop measurements on water samples. This commercial instrument is expected to enable routine measurements by different groups of investigators, so it has the potential to enhance our understanding of light scattering properties of seawater and marine particles and advance the related applications.