## 2 Materials and Methods
### Description of New Prism Design  
The prism P2 used in POLVSM (Figure 2a) is a specially customized prism that creates an air gap to prevent reflected light from entering the basin. As the backward scattered light near 180\({}^{\circ}\) is weak and easily overestimated, creating an air gap is an important and necessary way to reduce stray light. However, in our practice, this structure is relatively expensive and tends to easily break during manufacturing. More importantly, making the top surface of this air gap smooth and flat enough in practice is a challenge because the polishing process is implemented via a small customized mold in a limited space where the checking process is difficult to carry out. Therefore, flaws likely occur, and light usually diffuses and brings undesired stray light. For convenient manufacturing, we propose a relatively simple prism design, as shown in Figure 2b. The new prism sticks a single prism and an ND filter together instead of creating an air gap. The surfaces around the prism, except for the top surface, are coated with black paint, which has an absorption greater than 99.75%. The ND filter in this prism has a low transmittance of 1% and a surface roughness of 1/4 \(\lambda\). Theoretically, the forward light intensity experiences a loss of at least 99% when the light propagates through the filter for the first time. Then, more than 98% of the transmitted forward light escapes from the  
Figure 1: (**a**) Schematic of the measurement principle of the VSF instrument. The wavelength of the laser source is 532 nm (as an alternative, the 520 nm CW laser module of MatchBoxTM is available). The pinhole is used to block the divergent stray light of the laser source. The adjustor is set for the adjustment of the laser source’s tilt angle. The beam splitter separates the laser into two beams: reflected beam and transmitted beam. The reflected beam is detected by the reference photodetector. The transmitted beam enters the sample via the mirror and prism 1, leaves the sample via the new prism, and is detected by the transmittance photodetector. Scattered light is detected by the photomultiplier tube (PMT) that spins along with the rotating device and basin. (**b**) Schematic of the rotatable component. The basin is used to store the sample where scattering occurs. The detector is rotated following the direction of the yellow arrow together with the basin driven by the rotating device. (**c**) Exhibition of VSFlab. top surface of the prism for \(c\) measurements, and only nearly 2% of the transmitted forward light is reflected back to the prism. This reflected light undergoes another loss of at least 99% when propagating the ND filter back to the basin. As the transmittance of the light passing through the ND filter is even lower than 1% because the filter is put aslant, the amount of reflected light back to the basin is much less than 10\({}^{-6}\) of the forward light. To ensure that the interface between the ND filter and the prism is thin enough to guarantee good transmittance and negligible refraction, we use an interferometer in checking whether the surfaces of the ND filter and prism are polished such that their roughness reaches 1/4 \(\lambda\). Benefiting from mature manufacturing and efficient optical glue, our ND filter and prism could be seamlessly integrated. As this prism is designed to ensure that the transmitted light is vertical to the top surface of the prism for the correct measurement of \(c\), the determination of each angle, including \(\theta_{1},\theta_{2}\), and \(\theta_{3}\) marked in Figure 2c, follows Equation (4). \[\left\{ \begin{array}{l}\frac{\sin\left(90^{\circ}-\theta_{3}\right)}{\sin \left(180^{\circ}-2\theta_{2}-\theta_{3}\right)}=\frac{n_{2}}{n_{1}}\\ \theta_{1}-\theta_{3}=90^{\circ}\end{array} \right. \tag{4}\]  
where \(n_{2}\) represents the refractive index of the prism and \(n_{1}\) represents the refractive index of the sample. An optical simulation is implemented in the TracePro simulation platform to verify the rationality of the prism design.