# Reducing the Power Consumption of VR Displays with a Field Sequential Color LCD
## 2 Experiment
### Temperature-Dependent Physical Properties  
A pancake optical system [15; 16; 17] dominates VR headsets because of its compactness; however, its optical efficiency is reduced by 4\(\times\) because of the employed half mirror. A lower optical efficiency requires a brighter light engine to achieve the same brightness. Thus, the working temperature of the light engine can easily reach 50-60 \({}^{\circ}\)C by the thermal effect. The LCD light engine using an LC mixture with high clearing point is desirable. Therefore, it is necessary to systematically measure the temperature-dependent birefringence, visco-elastic constant, and figure of merit (FoM), which greatly impact the transmittance and response time of the AMLCD light engines. To measure the temperature-dependent birefringence, we filled a commercial homogeneous cell with a cell gap of 5.37 \(\upmu\)m with the LC mixture. Next, we used a Linkam heating stage (Linkam TMS94) to control the operating temperature. The test cell was sandwiched between two crossed polarizers. The probing beam was a He-Ne laser (\(\lambda\) = 633 nm). The temperature-dependent birefringence can be calculated from the measured voltage-dependent transmittance at each temperature. Results are shown as the black dots in Figure 1. The solid line represents [PERSON]'s semi-empirical equation [18]:  
\[\Delta n(T)=\Delta n_{0}S=\Delta n_{0}(1-T/T_{c})^{\beta}, \tag{1}\]  
where _Tc_ is the clearing temperature, \(\beta\) is the material constant, \(S\) is the order parameter, and \(\Delta n_{0}\) is the extrapolated birefringence at \(T\) = 0. Using Equation (1) to fit the experimental data, we obtained \(\Delta n_{0}\) = 0.277 and \(\beta\) = 0.237. As Figure 1 depicts, the experimental data agree well with the fitting curve. As the temperature (\(T\)) approaches _Tc_ (-96 \({}^{\circ}\)C), \(\Delta n\) decreases rapidly. High clearing temperature plays an important role in maintaining a high birefringence for the AMLCD to operate at an elevated temperature (50-60 \({}^{\circ}\)C) while the viscosity is reduced substantially. The temperature-dependent visco-elastic constant directly impacts the LC response time. The visco-elastic constant (\(\gamma_{1}/K_{11}\)) can be extracted from the measured time-dependent relaxation process of a homogenous cell. As the temperature increases, \(\gamma_{1}/K_{11}\) decreases rapidly and then saturates, as described below [19]:  
\[\frac{\gamma_{1}}{K_{11}}=A\frac{\exp(E_{a}/k_{B}T)}{(1-T/T_{c})^{\beta}}, \tag{2}\]  
where \(A\) is the proportionality constant, \(E_{a}\) is the activation energy, and \(k_{B}\) is the Boltzmann constant. Using Equation (2) to fit the experimental data indicated by black squares in Figure 2, we found \(A\) = 1.54 \(\times\) 10\({}^{-5}\) ms/\(\upmu\)m\({}^{2}\) and \(Ea\) = 334 meV. As shown in Figures 1 and 2, both birefringence and visco-elastic constant vary with temperature but at different rates. To find an optimal operating temperature, a figure of merit is defined as FoM = \(\Delta n^{2}/(\gamma_{1}/K_{11})\) to take both factors into account [20]. According to Figure 3, the optimal operating temperature occurs at -70 \({}^{\circ}\)C, and the FoM at \(T\) = 50 \({}^{\circ}\)C is 2.3\(\times\) higher than that at \(T\) = 22 \({}^{\circ}\)C. A more comprehensive FoM also includes the effect  
Figure 1: Temperature-dependent birefringence at \(\lambda\) = 633 nm and \(f\) = 1 kHz (the frequency of driving voltage applied on the LC cell). Dots are measured data and the solid line is the fitting curve with Equation (1). Figure 2: Temperature-dependent visco-elastic constant. Squares are measured data and the solid line is the fitting curve with Equation (2). of dielectric anisotropy \(\Delta\varepsilon\). A larger \(\Delta\varepsilon\) enables a lower threshold voltage and operating voltage, but the viscosity may inevitably increase. For this LC mixture, there is a good balance between viscosity and dielectric anisotropy. \(\Delta\varepsilon\) = 6.9 at \(T\) = 25 \({}^{\circ}\)C and \(f\) = 1 kHz.