液晶可变延迟器对不同入射角度的精确标定

孔泉慧子; 张瑞; 薛鹏; 王志斌; 景宁

doi:10.37188/CO.EN-2025-0035

液晶可变延迟器对不同入射角度的精确标定

孔泉慧子^{1, 2,},
张瑞^{1, 2, ,},
薛鹏¹,
王志斌¹,
景宁²

1.
中北大学山西省智能微波光电技术创新中心, 山西太原 030051
2.
中北大学信息与通信工程学院, 山西太原 030051

详细信息

中图分类号: O436.3
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出版历程
- 收稿日期: 2025-07-11
- 录用日期: 2025-09-03
- 网络出版日期: 2025-09-20

Precise calibration of liquid crystal variable retarder for various incident angles

doi: 10.37188/CO.EN-2025-0035

KONG Quan-hui-zi^{1, 2
,},
ZHANG Rui^{1, 2
, ,},
XUE Peng¹,
WANG Zhi-bin¹,
JING Ning²

1.
Technology Innovation Center of Shanxi Provincial for Intelligent Microwave Photoelectric, North University of China, Taiyuan, Shanxi 030051, China
2.
School of Information and Communication Engineering, North University of China, Taiyuan, Shanxi 030051, China

Funds: Supported by National Natural Science Foundation of China (No. 62105302)

More Information

Author Bio:
KONG Quan-hui-zi (2003—), female, from Xingping, Shaanxi Province, master student. She obtained her bachelor's degree from North University of China in 2025. She is mainly engaged in the research of polarization measurement and photoelastic modulation measurement technology. E-mail: kongquanhuizi@163.com

ZHANG Rui (1987—), male, from Changzhi, Shanxi Province, Ph.D., professor and doctoral supervisor. He obtained his Ph.D. from North University of China in 2017. He is mainly engaged in the research of photoelastic modulation, spectral measurement, and photoelectric detection. E-mail：zhangrui@nuc.edu.cn

Corresponding author: zhangrui@nuc.edu.cn

摘要

摘要:
针对液晶可变相位延迟器（LCVR）入射角变化引起的偏振测量精度下降问题，本文探讨了液晶可变相位延迟器的相位延迟特性，重点分析了不同入射角对相位延迟量的影响。在垂直入射LCVR的延迟量标定基础上，推导了LCVR在不同入射角度和不同驱动电压下的相位延迟标定方程，建立相位延迟量与二维入射角（方位角α和俯仰角β）之间的关系。实验在α = 20° β = 0°，α = 0° β = 20°，及任意角度α = 15° β = 5°三种情况进行验证，结果表明，相位延迟量理论计算值与实验测量值之间的最大平均误差不超过0.059 rad，所提标定方法准确可行。本文所提方法为LCVR在偏振成像等光学应用中的参数标定及性能提升提供了有力的支撑。
- 液晶可变相位延迟器(LCVR) /
- 二维入射角 /
- 驱动电压 /
- 相位延迟标定
Abstract:
This study investigates the reduction in polarization measurement accuracy caused by varying incident angles in a liquid crystal variable retarder (LCVR). The phase delay characteristics of the LCVR were examined, with particular emphasis on the influence of different two-dimensional incident angles on phase delay behavior. Building upon the calibration of phase delay under normal incidence, a phase delay calibration model was developed to account for variations in incident angle and driving voltage. A mathematical relationship was established between phase delay and the azimuth angle (α) and pitch angle (β). Experimental validation was conducted under three conditions: α = 20°, β = 0°; α = 0°, β = 20°; and an arbitrary angle where α = 5°, β = 15°. The results demonstrated that the maximum average deviation between theoretical predictions and experimental measurements did not exceed 0.059 rad. The proposed calibration method proved to be both accurate and practical. This approach offers robust support for LCVR parameter calibration and performance optimization in optical systems, particularly in polarization imaging applications.
- liquid crystal variable retarder (LCVR) /
- two-dimensional incident angles /
- drive voltage /
- phase delay calibration

HTML全文

图 1 LCVR作为偏振调制器的调制原理图

Figure 1. Modulation schematic diagram of the LCVR as a polarization modulator.

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图 2 LCVR驱动电压与折射率椭球偏转角关系示意图 (a)二维角度入射LCVR原理图；(b) U≤U_L的折射率椭球；(c) U>U_L的折射率椭球

Figure 2. LCVR drive voltage and refractive index ellipsoid deflection angle diagram. (a) Schematic diagram of the two-dimensional angle incident LCVR. (b) Refractive index ellipsoid for U≤U_L; (c) Refractive index ellipsoid for U>U_L.

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图 3 (a) LCVR相位延迟测量光路原理图；(b)相位延迟测量装置图

Figure 3. (a) Schematic diagram of the optical path principle for LCVR phase delay measurement; (b)Phase delay measuring device diagram.

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图 4 λ=532 nm时 (a)垂直入射下的出射光强T-U关系图；(b)不同入射角度下δ-U关系图

Figure 4. At λ= 532 nm. (a) T-U diagram under normal incidence; (b) δ-U diagram at different azimuth incidence angles.

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图 5 不同入射角情况下δ-U曲线分析图 (a) α=0°，β=0°；(b) α<0°，β=0°；(c) α>0°，β=0°

Figure 5. Analysis diagram of δ-U curves for different incidence angles. (a) α = 0°, β = 0°; (b) α<0°, β = 0°; (c) α>0°, β = 0°.

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图 6 不同驱动电压下δ-α-β的三维关系 (a) U=0V (b) U=2.2V (c) U=10V

Figure 6. 3D relationship of δ-α-β at different driving voltages. (a) U = 0 V (b) U = 2.2 V (c) U = 10 V.

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图 7 理论与实验结果对比图 (a) α= 20°, β= 0°;(b) α= 0°, β= 20°;(c) α= 15°, β= 5°

Figure 7. Comparison of the theoretical and experimental results. (a) α= 20°, β= 0°; (a) α= 0°, β= 20°; (a) α= 15°, β= 5°.

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