为了分析液晶相控阵空间光调制特性与驱动电压之间的关系, 根据液晶连续体弹性形变理论, 提出一种基于非线性最小二乘差分迭代求解液晶指向矢空间分布的方法。该方法利用液晶材料的电光特性, 以阈值电压时的液晶指向矢分布作为初始值, 通过非线性最小二乘法推导在驱动电场的作用下液晶指向矢的空间分布情况, 以及稳定状态时液晶相位延迟与驱动电压之间的相位调制特性曲线。最终通过实验完成了理论验证, 控制液晶相控阵的驱动电压, 实现对远场光束指向的偏转控制。利用驱动电压直接求解电位移矢量, 为后续指向矢与电位移耦合迭代提供初始值, 不仅减少了计算量, 而且更加符合液晶分子在实际电场作用下的运动过程, 减少了模型误差。结果表明: 在系统的终止误差为1.0×10-8时, 不同电压下的迭代时间均值为0.33 s; 在驱动电压为5 V的情况下, 该算法与差分迭代相比, 液晶分子倾斜角的角度误差精度提高了0.09 rad。

To analyze the relationship between the spatial light modulation characteristics of a liquid crystal phased array and the driving voltage using the liquid crystal continuous elastic deformation theory, in this paper, a method for solving the spatial distribution of a differential iteration liquid crystal director was proposed based on nonlinear least squares. Based on the electro-optical properties of the liquid crystal material, the distribution of the liquid crystal director at the threshold voltage was used as the initial value. For the direct calculation of the component of the potential shift vector along the Z axis with the driving voltage, the director space distribution of the liquid crystal was deduced under the action of an applied electric field. The phase modulation characteristic curve of the liquid crystal phase delay versus the applied voltage in the steady state was plotted. Finally, the theory was verified experimentally. Far-field beam pointing deflection control was achieved by controlling the driving voltage of the liquid crystal phased array. Using the driving voltage to directly solve the electric displacement vector, the initial value of the coupling between the director and potential shift was provided. This not only simplified the calculation but also accords with the motion process of the liquid crystal molecule under the action of the actual electric field as well as reduced the model error. The simulation results show that when the system error is 1.0×10-8, the mean time of iteration is 0.33 s under different voltages. When the driving voltage is 5 V, the angular error precision of the tilt angle of the liquid crystal molecules is improved by 0.09 rad compared to that achieved with the direct difference iteration method.