## 1 Introduction  
The volume scattering function (VSF), which describes the angular distribution of the scattered light resulting from an incident beam interacting with an infinitesimally small volume of water, is a fundamental inherent optical property (IOP) of the ocean [1; 2; 3; 4]. It is generally defined as the radiant intensity \(I\) scattered from a volume element at scattering angle \(\theta\) per unit of incident irradiance \(E\) and per unit of scattering volume \(V\):  
\[\beta(\theta)=\frac{dI(\theta)}{EdV} \tag{1}\]  
Based on Equation (1), the scattering coefficient, \(b\), can be directly related to the VSF through Equation (2):  
\[b=2\pi\int_{0}^{\pi}\beta(\theta)\sin(\theta)d\theta \tag{2}\]The VSF is often normalized by \(b\) to yield the phase function,  
\[\overline{\beta}(\theta)=\beta(\theta)/b \tag{3}\]  
which provides information about the relative angular distribution of the scattering. The knowledge of the VSFs is of central importance for understanding the full radiative flux balance of the ocean [5; 6; 7; 8]. The VSF in the backward direction is critical to interpreting ocean color remote sensing as the bidirectional distribution of the upwelling radiance has been shown to be largely governed by the shape of the VSF in the backward direction [9]. The VSF's measurements can be traced back to the 1950s-1980s [10; 11; 12; 13; 14; 15; 16]. Measurement of the scattered light is made between 10\({}^{\circ}\) and 170\({}^{\circ}\) as the projector containing the light source rotates around the sample volume in [PERSON]'s instrument [13]. Such a design in which either a light source or another component (i.e., a single detector) rotates around the sample volume was commonly applied for wide-angle VSF detection and generally has advantages of high angular resolution and convenient calibration procedure [17; 18; 19; 20; 21; 22; 23]. [PERSON] et al. proposed a novel optical design that the photomultiplier (PMT) rotates around the scattering sample to measure the VSF from 3\({}^{\circ}\) to 171\({}^{\circ}\) with an angular resolution of 1\({}^{\circ}\)[18]. Similarly, [PERSON] et al. [19] and [PERSON] et al. [20] installed the rotatable detector in their instruments to measure the VSF from 1\({}^{\circ}\) to 170\({}^{\circ}\) (angular resolution of 1\({}^{\circ}\)) and full Muller matrix measurements from 16\({}^{\circ}\) to 160\({}^{\circ}\) (angular resolution of 2\({}^{\circ}\)), respectively. Measuring the signal at high backscattering angles (>170\({}^{\circ}\)) is hard for the above instruments. That is because the detector is performed in the same plane as the plane which contains the light source, the shadow of the light source masks the detector when this latter is positioned to the high backscattering angles. To distinguish between the plane of the light source from the plane of the detector, [PERSON] and [PERSON] [21] proposed a periscopic optical system to change the propagation direction of scattered light and thus the detector and the light source are not in the same plane. For measurement at general angles, the periscopic prism rotates around the photodetector assembly axis that extends through the center of the scattering volume. For measurement at angles near 0\({}^{\circ}\), the periscopic prism was designed with a parallel shift such that the beam edge slides along the prism boundary and no direct light is received. MVSM utilized two strategies to measure VSF between 0.5\({}^{\circ}\) and 179\({}^{\circ}\). The rotatable periscopic prism increases more instability of the optical path compared with the structure of the fixed prism and rotatable detector. Recently, [PERSON] et al. [23] proposed a new instrument called Polarized Volume Scattering Meter (POLVSM). Only one strategy based on the rotating-detector principle realized the VSF measurement between 1\({}^{\circ}\) and 179\({}^{\circ}\). Two customized prisms called \"P1\" and \"P2\" were used to form a double periscopic optical system.