Research on pointing accuracy of liquid crystal phase array based on the 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，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，本文重点研究了工作波长、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，仿真分析了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 phase array (LC OPA) is widely used in lidar, laser communication and laser weapons to scan and control laser beams. In order to optimize the design of LC OPA and high-precision laser beam control, we study the influence of working wavelength, number of pixels, pixel size, and effective grey levels on beam pointing accuracy. Firstly, according to the liquid crystal phase modulation principle , 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 to be 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. The multivariable universal formula is also 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. Working principle of kinoform. (a) Modulus; (b) quantization
图 3 周期光栅法和变周期光栅法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 gratings 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 modulation amount 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
Figure 5. The pointing error caused by the discrete phase of the 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时的相位分布
Figure 6. Quantitation phase distribution at θ=2.06′. The red and blue lines represent the ideal phase distribution and the phase distribution for NG=32, respectively
图 7 相位等分的指向误差随偏转角度的变化关系
Figure 7. Relationship between the pointing error of uniform phase and the rotation angle
图 8 指向误差随波长的变化情况：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情况。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情况。λ=1.064 μm，NG=32，PN=
1024 Figure 10. Pointing error as a function of pixel size at the condition of λ=1.064 μm, 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 sets of data. The left ordinate represents the pointing errors of simulation and computation and the right ordinate represents the deviation
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 errors between uniform and nonuniform phase at different rotation angles
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 images. (a) Without the driving voltage; (b) NG=32; (c) NG=64; (d) NG=128; (e) NG=256
图 20 实验测量的水平偏转50次光斑质心
Figure 20. Experimental measurement results of the centroid of the light spot with 50 horizontal deflections
图 22 像素数分别为 (a)
1024 , (b) 702, (c) 512, (d) 320, (e) 200时采集的光斑图像Figure 22. Acquired optical spot images when the pixel number are (a)
1024 , (b) 702, (c) 512, (d) 320 and (e) 200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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