## 3 Results and Discussion  
Table 2 presents the resulting signal-to-noise ratios (SNRs) from the simulation results for each scenario. The results were obtained from an L9 orthogonal array, which was constructed by using [PERSON]'s design of experiments method. Figure 3 shows the average calculated SNRs according to the levels of each factor in Table 2. Figure 3 illustrates the relative influence of the levels of each factor on the performance characteristics. The slopes connecting the average values indicate the sensitivity of \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multirow{2}{*}{**Description**} & \multicolumn{3}{c}{**Levels**} \\ \cline{3-5}  & & **1** & **2** & **3** \\ \hline A & Applied voltage & 15 V & 20 V & 25 V \\ B & Width of driving & 1 \(\upmu\)m & 2 \(\upmu\)m & 4 \(\upmu\)m \\ C & Cell gap & 38 \(\upmu\)m & 40 \(\upmu\)m & 42 \(\upmu\)m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Levels of each control factor. Figure 2: Modeling for ELC diffuser analysis. The LC layer is divided into grids. The behavior of LC molecules and the corresponding refractive index are calculated in each grid. each level to the performance characteristic. As the slope increases, the correlation to the performance characteristic also increases. The factor levels of A1, B2, and C3 had the highest average Taguchi SNR. The corresponding applied voltage, driving electrode width, and liquid crystal thickness were 15 V, 2 and 42 \(\upmu\)m, respectively. However, the SNR may increase if the control factor A is set to 15 V or below (level 1) and factor C is 42 \(\upmu\)m or above (level 3). As a result, the performance is improved. Hence, it is necessary to conduct additional simulations for factors A and C.  
In the case of factor C, the response time of the liquid crystal is seriously delayed if the thickness of the LC layer is excessively larger than the width of the diffusing unit, and the applied voltage becomes higher. Therefore, factor C was restricted to level 3. After factors B and C were fixed to levels 2 and 3, respectively, factor A was set to 15, 14, and 13 V, which correspond to level 1 and below. Each performance characteristic and SNR were calculated to identify the optimal values of factor A. The SNRs for 15, 14, and 13 V were \(-\)28.32, \(-\)31.23, and \(-\)33.31 dB, respectively. The SNR was highest when factor A was 15 V. Accordingly, the optimal design conditions for the applied voltage, electrode width, and cell gap of the ELC diffusing unit were 15 V, 2 and 42 \(\upmu\)m, respectively. Under these conditions, the SNR of the performance characteristic for the retardation distribution was calculated as \(-\)28.32 dB. Figure 4 shows the simulation results for the director distribution of the LC molecules on the cross-section of the ELC diffusing unit. The LC molecules homogeneously aligned with the same pre-tilt angle by rubbing process change to the vertical direction by applying a voltage above the threshold. In this case, the LC directors near one of the electrodes of the ELC unit are aligned in the opposite direction to the pre-tilt angle due to the mirror symmetry of the electric field distribution. As a result, the alignment of the LC molecules at the corresponding position becomes unstable, thereby leading to the disclination of the LC directors, as shown in Figure 4. Since the electrodes of the ELC unit