Tilt error’s characteristic analysis of dual liquid crystal polarization grating system
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摘要:
为了精确控制激光光束指向，本文基于双液晶偏振光栅系统的光束指向算法，分析了系统中因光栅倾斜产生的误差。首先，采用一种基于衍射光栅方程的光线追迹方法求解出射光束指向，引入了入射光束指向和光栅倾斜角，通过与仿真结果进行对比，验证了该方法的正确性和精度。其次，通过对光栅不同倾斜情况的分析，本文给出了不同倾斜情况下光栅姿态的表达式，并结合光线追迹法得到了相应的出射光束指向表达式，并进一步分析了光栅倾斜产生的调零误差和旋转误差。研究结果表明，在0°~0.3°光栅倾斜角范围内，调零误差分别在0.25 mrad和2 mrad以内，旋转误差分别在85 mrad和430 mrad左右。本文方法可实现对双液晶偏振光栅系统中出射光束指向和光栅倾斜误差的精确计算。
Abstract:In order to precisely control the direction of laser beams, we analyze the error caused by the grating tilt in the system based on the optical beam pointing algorithm of the dual liquid crystal polarization grating system. Firstly, a ray tracing method based on the diffraction grating equation is used to solve the outgoing beam pointing, introducing the incident beam pointing and grating tilt angle. The correctness and accuracy of this method are verified through comparison with simulation results. Secondly, by analyzing different cases of grating tilt, we provide expressions of the grating attitude under different tilt conditions, and in combination with the ray tracing method, obtain the expressions for the outgoing beam pointing for corresponding situations, analyzing the zeroing error and rotation error caused by grating tilt. The research results indicate that within the 0° to 0.3° grating tilt angle range, the zeroing errors are within 0.25 mrad and 2 mrad respectively, and the rotation errors are around 85 mrad and 430 mrad, respectively. We propose a method for accurately calculating the pointing direction and grating tilt errors in the exit beam of a dual liquid crystal polarization grating system.
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表 1 光栅旋转角为变量时的验证结果
Table 1. Verification results when the grating’s rotation angle is variable
光栅1
旋转角
$ {\theta _1} $（°）光栅2
旋转角
$ {\theta _2} $（°）关系式（rad） 仿真（rad） $ \varTheta $ $ \varPhi $ $ \varTheta $ $ \varPhi $ 0 0 0 0.0873 0 0.0873 30 0 5.5260 0.0959 5.5260 0.0959 60 0 4.9022 0.1159 4.9022 0.1159 90 0 4.3944 0.1380 4.3944 0.1380 120 0 3.9514 0.1563 3.9514 0.1563 150 0 3.5401 0.1680 3.5401 0.1680 180 0 3.1416 0.1720 3.1416 0.1720 0 30 0.5585 0.1242 0.5585 0.1242 0 60 0.6339 0.1919 0.6339 0.1919 0 90 0.5331 0.2569 0.5331 0.2569 0 120 0.3733 0.3086 0.3733 0.3086 0 150 0.1907 0.3415 0.1907 0.3415 0 180 0 0.3528 0 0.3528 
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表 2 光栅倾斜角为变量时的验证结果
Table 2. Verification results when the grating’s tilt angle is variable
光栅1
倾斜角
$ {t_1} $（°）光栅2
倾斜角
$ {t_2} $（°）关系式（rad） 仿真（rad） $ \varTheta $ $ \varPhi $ $ \varTheta $ $ \varPhi $ 0 0 0.50004 0.22072 0.50004 0.22072 1 0 0.49900 0.22101 0.49900 0.22101 2 0 0.49784 0.22134 0.49784 0.22134 3 0 0.49656 0.22170 0.49656 0.22170 4 0 0.49515 0.22210 0.49515 0.22210 5 0 0.49363 0.22254 0.49363 0.22254 0 1 0.50007 0.22072 0.50007 0.22072 0 2 0.50028 0.22073 0.50028 0.22073 0 3 0.50065 0.22076 0.50065 0.22076 0 4 0.50119 0.22080 0.50119 0.22080 0 5 0.50190 0.22086 0.50190 0.22086
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表 3 入射光束指向为变量时的验证结果
Table 3. Verification results when the pointing of the incident light beam is variable
入射光束
指向方位角
$ {\varTheta _0} $（°）入射光束
指向俯仰角
$ {\varPhi _0} $（°）关系式（rad） 仿真（rad） $ \varTheta $ $ \varPhi $ $ \varTheta $ $ \varPhi $ 45 1 0.6639 0.1512 0.6639 0.1512 90 1 0.6908 0.1382 0.6908 0.1382 135 1 0.7807 0.1322 0.7807 0.1322 180 1 0.8705 0.1378 0.8705 0.1378 225 1 0.8966 0.1506 0.8966 0.1506 270 1 0.8559 0.1626 0.8559 0.1626 315 1 0.7794 0.1676 0.7794 0.1676 360 1 0.7035 0.1631 0.7035 0.1631 0 1 0.7035 0.1631 0.7035 0.1631 0 2 0.6387 0.1771 0.6387 0.1771 0 3 0.5835 0.1918 0.5835 0.1918 0 4 0.5363 0.2070 0.5363 0.2070 0 5 0.4955 0.2227 0.4955 0.2227
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