Error modeling of polarization devices in simultaneous phase-shifted lateral shearing interferometry
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摘要:
为了对同步相移横向剪切干涉系统中偏振器件的选型、装调以及误差补偿提供可靠的理论依据，本文根据琼斯矩阵原理，构建了系统中1/4波片和偏振片阵列误差对测量结果影响程度的误差模型，对四分之一波片的相位延迟误差、快轴方位角误差以及偏振片阵列透光轴方位角误差对测量结果的影响进行了定量分析。仿真结果表明：1/4波片的相位延迟误差在±1°以内时，波面测量误差为0.00002λ(PV)和0.000062λ(RMS)；1/4波片的调整精度在±2°以内时，波面测量误差为0.0001λ(PV)和0.00006λ(RMS)；偏振片阵列方位角误差在±1°以内时，测量误差为0.003λ(PV)和0.001λ(RMS)。根据仿真结果对测量系统中偏振元器件进行选型，同时选择两种不同精度的偏振元器件进行对比实验。实验结果的残差值与仿真结果的残差值的PV以及RMS值偏差均小于λ/20，可以在一定程度上验证模型的有效性。本文提出的数学模型可以为同步相移横向剪切干涉系统中偏振器件的选型提供可靠的理论依据。
Abstract:To provide a reliable theoretical basis for the selection, mounting, and error compensation of the polarization device in the synchronous phase-shift transverse shear interference system, based on the Jones matrix principle, we construct an error model reflecting the degree of influence of the errors of quarter-waveplate and polarizer array on the measurement results in the system. Then, we quantitatively analyze how the measurement results are influenced by the following factors: the phase delay error of quarter-waveplate, fast-axis azimuthal angle error, and transmission-axis azimuthal angle error of the polarizer array. The simulation results show that the wavefront measurement errors are 0.00002λ(PV) and 0.000062λ(RMS) when the phase delay error of the quarter-waveplate is within ±1°, 0.0001λ(PV) and 0.00006λ(RMS) when the adjustment accuracy of the quarter-waveplate is within ±2°, and 0.003λ(PV) and 0.001λ(RMS) when the azimuthal angle error of the polarizer array is within ±1°. According to the simulation results, the polarization components in the measurement system were selected. At the same time, two polarization components with different levels of accuracy were chosen for comparison experiments. The experimental results indicate the following conclusions: the deviations of the residual values of the experimental results from the residual values of the simulation results in terms of the PV and the RMS values are less than λ/20, and the validity of the model can be verified to a certain extent. The mathematical model proposed in this paper can provide a reliable theoretical basis for the selection of polarization devices in synchronous phase-shifted transverse shear interference systems.
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图 1 同步相移横向剪切干涉原理图
Figure 1. Schematic diagram of simultaneous phase shift lateral shearing interferometry
图 2 重建面形残差随相位延迟误差变化曲线
Figure 2. Residual surface shape varying with waveplate phase delay error
图 3 重建面形残差随快轴方位角误差变化曲线
Figure 3. Residual surface shape varying with waveplate fast axis azimuth error
图 4 重建面形残差随偏振片阵列方位角误差变化曲线
Figure 4. Residual surface shape varying with polarizer array azimuth error
图 5 同步相移横向剪切干涉测量系统
Figure 5. Synchronous phase-shift transverse shear interferometry system
表 1 残差对比结果
Table 1. Comparative analysis of residual (Unit: λ)
PV RMS 实验结果残差 0.0058 0.0026 仿真结果残差 0.0040 0.0015 
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