## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & \multicolumn{3}{c}{**L9**} & \multirow{2}{*}{**Performance Characteristic**} & \multirow{2}{*}{**SNR (dB)**} \\ \cline{2-2} \cline{4-5}  & **A** & & & & **B** & **C** \\ \hline
1 & 1 & 1 & 1 & 51.18335 & \(-\)34.1826 \\
2 & 1 & 2 & 2 & 27.07782 & \(-\)28.6523 \\
3 & 1 & 3 & 3 & 54.52134 & \(-\)34.7313 \\
4 & 2 & 1 & 2 & 33.20978 & \(-\)30.4253 \\
5 & 2 & 2 & 3 & 33.11352 & \(-\)30.4001 \\
6 & 2 & 3 & 1 & 98.72268 & \(-\)39.8883 \\
7 & 3 & 1 & 3 & 42.44344 & \(-\)32.5562 \\
8 & 3 & 2 & 1 & 68.32977 & \(-\)36.6922 \\
9 & 3 & 3 & 2 & 118.7621 & \(-\)41.4936 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance characteristics and signal-to-noise ratios (SNRs) in each simulation. Figure 3: Average SNR according to the levels of each factor. are located just above the black matrix, however, the optical distortion caused by the unstable behavior of the LC molecules near the edge of the unit is blocked by the black matrix and can be ignored. Figure 5 illustrates the retardation distributions of the ideal diffusing unit and the optimally designed ELC diffusing unit according to the positions. The retardation between both driving electrodes and the center of the ELC diffusing unit is lower than the ideal retardation. This occurs because the strong vertical component of the electric field heading from the driving electrodes at both ends to the common electrode makes the LC molecules excessively arranged in the vertical direction with respect to the surface. There is an inflection of the retardation distribution near the edge of a driving electrode, which is about 18 \(\upmu\)m from the center of the unit. The inflection is caused by the distorted behaviors of LC molecules, which is attributable to the generation of the horizontal component in the electric field heading from the edge of the driving electrode to the common electrode. Figure 6 shows the normalized intensity of the exiting light at different viewing angles in wide-view mode. The results were calculated by ray tracing for an LCD system with the optimally designed ELC diffuser. The intensity of the exiting light was calculated by counting the number of rays that passed through the LC panel and the ELC diffuser according to the exit angles. The resulting intensity distribution was similar to the Lambertian distribution. However, the intensity of the exiting light was higher than the ideal one at a viewing angle of 50\({}^{\circ}\) or less but was lower at higher viewing angles. Figure 4: LC directors in a cross section of the ELC diffusing unit under the optimum conditions obtained by [PERSON]’s method. Figure 5: Retardation distributions of the ELC diffusing unit and the ideal diffusing unit. This occurred because the discrepancy in the retardation distributions (Figure 4) results in deviation of the wavefront and direction of the exiting light from the ideal case. As shown in Figure 6, the intensity is higher than the ideal one at some viewing angles because the rays that are expected to exit at a viewing angle of at least 50\({}^{\circ}\) actually exit at lower angles. Figure 7 presents the normalized luminance of the exiting light according to the viewing angles, including the Lambertian distribution, wide-view mode of the LCD system with the ELC diffuser, the conventional IPS-LCD, and the calculation of the narrow-view mode with the ELC diffuser turned off. Similar to Figure 6, the luminance of the wide-view mode in Figure 7 \"(b)\" is generally lower than the ideal case in Figure 7 \"(a)\" at a viewing angle of 50\({}^{\circ}\) and above. However, in comparison with the IPS-LCD, a very high luminance is shown at almost all the viewing angles except in a few sections near 70\({}^{\circ}\). The IPS-LCD is known to have the best wide-viewing characteristics among LCD modes. Even in comparison with the ideal Lambertian distribution, the similarity was 84.3%.