## 2 The Influence of the Driving Conditions on the Performance of a Phase-Only OASLM
This figure illustrates that the reduction of the PV value is 0.1\(\lambda\) with the frequency increases from 50 Hz to 200 Hz, which corresponds to a decrease in \(V_{LC}\) of 1 V in Figure 2b. In summary, the write-light irradiance and frequency of \(V_{AC}\) simultaneously affect the phase-change ability of the OALCLV in the form of change in \(V_{LC}\), the voltage of the LC layer. At the same time, Equation (3) is a reliable formula to simulate \(V_{LC}\) and, when it is combined with the voltage response of the LC, the theoretical phase distribution can be accurately derived when the OALCLV is under different driving conditions. The voltage across the LC layer affects the phase-modulation ability, which can be controlled by changing the write-light irradiance in the form of a grayscale image loaded on the LCOS in a practical application; therefore, we have experimentally verified the phase-modulation ability of the OASLM as a function of gray-level values when the LED is at different drive currents. Figure 4a depicts the relationship between the phase change and grayscale values when the OASLM is under a \(V_{AC}\) of 14 V at 100 Hz and separately loaded these single-value grayscale images with values from 0 to 0.79 (in the normalized 0-255 grayscale range, 0-0.79 is the linear region of write-light irradiance as a function of grayscale value); meanwhile, the driving current of the LED changes from 200 mA to 800 mA. The dashed line shows the simulated phase-change relation deduced from the voltage response of the LC and Equation (3). The average error-rate between the simulated and experimental values is 2.2%. The figure shows that, with an increase in current, the decrease in the PV value, which is the phase-change ability, is 0.23\(\lambda\), mainly because of the increase in the phase-change values corresponding to the gray level 0, implying that the corresponding \(V_{LC}\) is improved. In particular, we simulated the range of \(V_{LC}\), which corresponds to 0-0.79 gray level when the OASLM is subjected to different driving conditions; the results are depicted in Figure 4b. The marked points correspond to the experimental values, which are basically consistent with the simulated values. Figure 4b shows that, when the drive current changes from 200 mA to 800 mA, the write-light irradiance corresponding to the gray level of 0.79 increases from 3.25 mW/cm\({}^{2}\) to 9.50 mW/cm\({}^{2}\), the \(V_{LC}\) values at 100 Hz exceed the \(V_{sat}\) value, so all the phase-change values reach the maximum value of 0.97\(\lambda\) as depicted in Figure 4a; the increase in \(V_{LC}\) at 100 Hz is approximately 0.4 V as the write-light irradiance corresponding to the gray level of 0 increases from 0.131 mW/cm\({}^{2}\) to 0.388 mW/cm\({}^{2}\), and results in a decrease of the PV values of 0.23\(\lambda\) as depicted in Figure 4a. When the frequency is greater than 200 Hz, the values of the \(V_{LC}\) of the gray level 0 are all 0.5 V for different driving currents and do not change with increasing frequency. The current of the LED must be at least 400 mA at this time to ensure that the \(V_{LC}\) value for the gray level 0.79 exceeds the \(V_{sat}\) value, so we set the driving current at 400 mA, the corresponding dynamic range of the write-light irradiance is 0.235-5.75 mW/cm\({}^{2}\) to 0.388 mW/cm\({}^{2}\) when the grayscale value changes from 0 to 0.79 and the frequency is set at 200 Hz in practical applications. The above analysis reveals that the range of the \(V_{LC}\) values corresponding to 0-0.79 gray level directly affects the phase-modulation capability of the OASLM. The ideal driving condition is that when the OASLM is loaded with 0-0.79 grayscale images, the range of \(V_{thr}\)-\(V_{sat}\) is at least contained in the variation range of \(V_{LC}\) to obtain theoretical phase-change capability.