Pointing accuracy research of liquid crystal phase array based on variable period grating method
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摘要:
液晶光学相控阵被广泛应用于激光雷达、激光通信以及激光武器中，进行激光光束的扫描控制。为了实现液晶相控阵的最优设计和激光光束高精度控制，本文重点研究工作波长、像素数、像素尺寸及有效灰度数对光束指向精度的影响规律。首先，根据液晶相位调制原理，仿真分析了周期光栅法和变周期光栅法的有效扫描角度和衍射效率；然后基于驱动电压灰度等分相位调制量，仿真分析指向误差随工作波长、像素数、像素尺寸以及有效灰度数的变化规律，推导出多变量普适公式；接着，仿真分析了驱动电压灰度非等分相位调制量时的指向精度，并和等分相位调制量的结果进行对比分析；最后，实验验证了有效灰度数、像素数和指向误差的关系，初步证实了经验公式的有效性。本文的研究结果可为液晶相控阵的设计提供理论依据。
Abstract:Liquid crystal optical phased array (LC OPA) is widely used in lidar, laser communication and laser weapons to scan and control laser beams. In order to realize the optimal design of LC OPA and high-precision control of laser beam, this paper focuses on the influence of working wavelength, number of pixels, pixel size and effective grey levels on beam pointing accuracy. Firstly, according to the principle of liquid crystal phase modulation, the effective scanning angle and diffraction efficiency of the period grating and the variable period grating methods are simulated and analyzed. Secondly, assuming the phase modulation is equally divided by the driving voltage, the variation law of the pointing error with the working wavelength, the number of pixels, the pixel size and the effective grey levels is simulated and analyzed, and the multivariable universal formula is derived. Thirdly, the pointing accuracy of the nonuniform phase modulation is simulated, analyzed, and compared with the results of the uniform phase modulation. Finally, the relationship between the effective grey levels and the pointing error is verified by experiments, and the validity of the empirical formula is preliminarily confirmed. The research results can provide a theoretical basis for the design of LC OPA.
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图 1 相息图工作原理：(a)取模；(b)量化
Figure 1. Principle of kinoform: (a) Modulus; (b) Quantization
图 3 周期光栅和变周期光栅的衍射效率随衍射角度的变化
Figure 3. Diffraction efficiency as a function of diffraction angle for period and variable period gratings
图 4 NG=32时等分相位调制量和有效电压灰度的关系
Figure 4. Uniform phase as a function of grey level for NG=32
图 5 液晶相控阵离散相位产生指向误差示意图
Figure 5. Schematic diagram of the pointing error caused by discrete phase for liquid crystal phase array
图 6 θ=2.06′的量化相位分布：红色实线代表理想分布，蓝色实线代表NG=32时相位分布
Figure 6. Quantitation phase distribution at θ=2.06′: the red and blue line represent the distribution of ideal and NG=32 respectively
图 7 指向误差随偏转角度的变化关系
Figure 7. Relation between the pointing error and the rotation angle
图 8 指向误差随波长的变化关系：PS=17 μm，PN=
1024 ，NG =32Figure 8. Pointing error as a function of wavelength at the condition of PS=17 μm, PN=
1024 and NG =32
图 9 指向误差随有效灰度数的变化：λ=1.064 μm，PS=17 μm，PN=
1024 Figure 9. Pointing error as a function of effective grey levels at the condition of λ=1.064 μm, PS=17 μm and PN=
1024 
图 10 指向误差随像素尺寸的变化：λ=1.064μm，NG=32，PN=
1024 Figure 10. Pointing error as a function of pixel size at the condition of λ=1.064μm, NG=32 and PN=
1024 
图 11 指向误差随像素数的变化：λ=1.064 μm，NG=32，PS=17 μm
Figure 11. Pointing error as a function of pixel number at the condition of λ=1.064 μm, NG=32 and PS=17 μm
图 12 10组数据的仿真和计算结果：左侧纵坐标表示仿真值和计算值，右侧纵坐标表示二者的偏移量
Figure 12. Simulation and calculation results for 10 groups data: the left and right ordinates represent the pointing error of simulation and computation and the deviation respectively
图 13 非等分相位调制量和有效灰度数的关系
Figure 13. Nonuniform phase modulation as a function of effective grey levels
图 14 θ=0.41′时的等分和非等分量化相位分布
Figure 14. Uniform and nonuniform quantitation phase distribution at θ=0.41′
图 15 非等分相位的指向误差随偏转角度的变化
Figure 15. Pointing error of nonuniform phase as a function of rotation angle
图 16 不同偏转角度下等分相位和非等分相位的指向误差的差值
Figure 16. Difference of pointing error between uniform and nonuniform phase at different rotation angle
图 17 θ=−0.02′处等分相位和非等分相位的量化相位分布
Figure 17. Quantitation phase distributions for uniform and nonuniform phase at θ=−0.02′
图 19 采集的光斑图像：(a)没有施加电压， (b) NG=32， (c) NG=64， (d) NG=128，(e) NG=256
Figure 19. Acquired optical spot image: (a) Without the driving voltage, (b) NG=32, (c) NG=64, (d) NG=128, and (e) NG=256
图 20 实验测量的水平偏转50次光斑质心
Figure 20. Measured center of gravity of light spot at horizontal direction with 50 times
图 21 指向误差随有效灰度数的变化
Figure 21. Experiment measured pointing error as a function of effective grey levels
图 22 采集的光斑图像：像素数= (a)
1024 , (b) 702, (c) 512, (d) 320, (e) 200Figure 22. Acquired optical spot image: pixel number= (a)
1024 , (b) 702, (c) 512, (d) 320, (e) 200
图 23 指向误差随像素数的变化
Figure 23. Experiment measured pointing error as a function of pixel number
表 1 随机选取的液晶相控阵多变量数据
Table 1. Random selection data for the multivariable of liquid crystal phase array
组别 PS/μm PN NG λ/μm 1 10.0 1000 50 1.000 2 5.0 800 40 0.800 3 8.0 900 60 0.500 4 12.0 512 80 0.635 5 15.0 700 32 0.444 6 9.2 600 64 0.900 7 16.0 888 76 0.456 8 14.0 666 86 0.707 9 18.0 500 90 1.180 10 9.0 1200 100 1.300 
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