# Pursuing High Quality Phase-Only Liquid Crystal on Silicon (LCoS) Devices
## 6 Phase Stability  
Phase stability in terms of time-fluctuation is the major weakness in PWM devises [60; 61; 62]. The different working principles of digital and analog driving schemes are shown in Figure 7[63].  
\(V_{rms}\) can be calculated between the voltages (\(v_{1}\) and \(v_{2}\)) applied in a short period of time (\(t_{1}\) and \(t_{2}\)), as shown in the following equation:  
\[V_{rms}=\sqrt{\frac{t_{1}v_{1}^{2}+t_{2}v_{2}^{2}}{t_{1}+t_{2}}} \tag{7}\]  
Briefly, the digital driving scheme maintains a constant voltage (\(\Delta\)V) while changing the pulse width to achieve the various \(V_{rms}\) values. The flicker yields from charging and discharging phenomenon within the sub-millisecond because the instantaneous voltage recognized by liquid crystal is the time ratio between the pulses at constant voltage (\(\Delta\)V) in the driving cycle. On the other hand, the analog driving scheme achieves its \(V_{rms}\) values by changing the applied voltages at constant frequency. There is no obvious flicker in the analog driving scheme because the instantaneous voltage resembling \(V_{rms}\) is perceived by the liquid crystals without a noticeable charging and discharging phenomenon. Figure 8 shows the phase flicker generated from digital drive at gray level 70 using a LETO panel.  
Figure 6: The phase precision measurements of 3 different LCoS-SLMs. The inserts are the enlarged figure from gray level 100 to 150. The values in a. is the phase linearity error (APAE%); and b. is the mSTD of phase precision error.  
Figure 7: The schemes of digital and analog driving waveforms.  
Two measurements with different photodetector settings are performed to show the phase shift and phase flicker in each gray scale. The digital color light sensor (TCS-3404 from TAOS) is adopted as a photodetector for the phase linearity and phase precision measurements. The data are taken every 100 ms for each gray level, which is presented as a red line for measured phase shift in Figures 9 and 10. Temporal fluctuation is measured by a polarization interferometer (PIF) with a polarizer and an analyzer aligned at 45 \({}^{\circ}\) with respect to the rubbing direction. The photodetector is connected to a high-resolution oscilloscope (300 MHz 2.5 GS/s from Tektronix TDS3034B). The data are taken every few \(\upmu\)s for each gray level. The phase flicker is determined by the maximum and minimum phase values of each gray level. The \(\Delta\)V values of these three panels are 5.00V, 2.12V and 1.10V for PCM-2-01-633, PCU-3-01-633, and LETO, respectively. Their LC response times are 3.8, 2.8, and 20.7 ms, and their resulting mean standard deviations (mSTD) are 0.14 \(\pi\), 0.12 \(\pi\), and 0.04 \(\pi\), respectively. The small \(\Delta\)V setting in the digital driving scheme is able to minimize the flicker, as suggested in the data. To validate the assumption, the thicker cell gap of PCU-3-01-633 LCoS-SLM filled with the same LC was prepared to achieve 2\(\pi\) radius phase shift at lower \(\Delta\)V = 1.04 V. The mSTD of the thicker LCoS-SLM (named PCU-3-01-633-2) is only 0.04 \(\pi\). The response time, regrettably, slows considerably from 2.8 to 9.6 ms. To summarize the phase stability in the digital drive LCoS-SLM, it is able to minimize the flicker when smaller \(\Delta\)V is applied for 2 \(\pi\) radius phase shift modulation. The slower LC response, however, is inevitable with this approach.  
Figure 8: The digital drive waveform and its corresponding phase flicker measured in the high-resolution oscilloscope.  
Figure 9: The phase stability measurements of PCM-2-01-633, and LETO LCoS-SLMs at 633 nm.