## 2 Materials  
There are three optical properties, which characterize the light propagation in the scattering and absorption medium with \(\mu_{a}\) being the absorption coefficient [mm\({}^{-1}\)], \(\mu_{s}\) being the scattering coefficient [mm\({}^{-1}\)], and \(g\) being the anisotropic factor to decide the scattering phase function [16; 17]. When changing the absorption coefficient, it is necessary to consider a complex system that includes a wavelength spectrum because color has a great impact on visual perception. Here, we simply focus on the relation between the scattering coefficient and visual perception. The material was adjusted to have an absorption coefficient close to 0. The scattering properties of the scattering medium with particles vary not only with the constituents but also with the manufacturing process [14; 15; 18]. Among them, it is known that even with the same constituents, changes in the stirring speed can also change the scattering properties, along with changes in the particle size distribution. In this study, as shown in Tables 1 and 2, samples with variations in scattering properties were prepared using two types of particles (titanium dioxide and zinc oxide) and changing the stirring speed while keeping the other constituents the same. By changing the stirring speed 5 to 40 m/s (refer to Table 1) of the two particle types in five different ways, 10 different samples were prepared. In addition, the samples with high scattering coefficients containing a large number of particles or nearly the limit of particles just before becoming lumps with a paste-like formation were prepared, as shown in Tables 3 and 4. The prepared samples were stirred slowly several times with a stick before transferring them to the containers for sensory testing and scattering coefficient measurements. During this process, we confirmed that there was no change in the dispersion state of the sample, such as precipitation. A photograph of a sample created through these processes is shown in Figure 1.  
The particles used were titanium dioxide (MT-100 AQ, primary particle diameter of 15 nm, TAYCA CORPORATION, Osaka-shi, Osaka, Japan) and zinc oxide (FINEX-50W, primary particle diameter of 20 nm, Sakai Chemical Industry Co., Ltd., Sakai-shi, Osaka, Japan) with hydrophilic surfaces. A thin-film spin system high-speed mixer (FLIMIX(r)FM-40L, PRIMIX Corporation, Awaji-shi, Hyogo, Japan) was used for samples Nos. 1-11 and a Homodisper (Homogenizing Disper Model 2.5, PRIMIX Corporation, Awaji-shi, Hyogo, Japan) for sample No. 12. The relation between mixer stirring speed and particle size distribution has been reported previously, and it was also reported that the stirring process maintained dispersion condition and that little precipitation was observed even after one month of making the dispersion [14]. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Sample No.** & **1** & **2** & **3** & **4** & **5** \\ \hline Particle & TiO\({}_{2}\) & TiO\({}_{2}\) & TiO\({}_{2}\) & TiO\({}_{2}\) & TiO\({}_{2}\) \\ \hline Stirring speed [m/s] & 5 & 10 & 20 & 30 & 40 \\ \hline Sample No. & 6 & 7 & 8 & 9 & 10 \\ \hline Particle & ZnO & ZnO & ZnO & ZnO & ZnO \\ \hline Stirring speed [m/s] & 5 & 10 & 20 & 30 & 40 \\ \hline \end{tabular}
\end{table} 
Table 1: Particle material and velocity of samples (Nos. 1–10) to change the scattering coefficient with stirring speed. \begin{table}
\begin{tabular}{c c c} \hline
**Sample No.** & **11** & **12** \\ \hline Stirring machine & Filmix-40 (FM-40) & Homogenizing Disper Model 2.5 (DH-2.5) \\ \hline Stirring speed & 40 m/s & 3000 r/min \\ \hline Stirring time [s] & 300 & 300 \\ \hline \end{tabular}
\end{table} 
Table 4: Components of the sample Nos. 11–12. Figure 1: Photographs for examples of scattering medium used in sensory test. \begin{table}
\begin{tabular}{c c} \hline
**Material** & **Mass Concentration [wt\%]** \\ \hline Purified water & 96.2 \\ \hline Particle & 3.0 \\ \hline Thickener, carboxymethyl cellulose & 0.8 \\ \hline \end{tabular}
\end{table}