Research on high-speed measurement of Mueller matrix based on overdriving technique
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摘要:
为实现穆勒矩阵的高速测量，本文提出一种基于过压驱动的穆勒矩阵高速测量方法。首先，建立基于液晶的穆勒矩阵仿真模型，仿真分析了待测物穆勒矩阵测量的可行性。其次，给出液晶相位延迟器的过压驱动方法，并利用过压驱动技术缩短了偏振态的切换时间。最后，实验测量了空气、偏振片及1/4波片的穆勒矩阵。实验结果表明：6个偏振态的生成频率从71 Hz提升到417 Hz，穆勒矩阵的测量频率从10 Hz提升到60 Hz，提升约6倍；同时，穆勒矩阵测量均方误差（MSE）优于
0.0004 ，消光比优于750∶1，椭偏度低于1.06%。因此，过压驱动方法能够实现穆勒矩阵的高速测量，进一步推动其在动态偏振分析、光学元件在线质检、生物医学成像等实时检测领域的应用。Abstract:This paper proposes a high-speed Mueller matrix measurement method based on an overdriving technique exerted on a liquid crystal variable retarder. First, a liquid crystal-based simulation model of the Mueller matrix measurement system is established, which helps to confirm the feasibility of the system. Next, an overdriving scheme for the liquid crystal variable retarder is introduced to shorten the polarization-state switching time. Finally, the Mueller matrices of air, a polarizer, and a quarter-wave plate are measured experimentally. The results show that the generation frequency of six polarization states increases from 71 Hz to 417 Hz, and the Mueller matrix measurement frequency increases from 10 Hz to 60 Hz, representing approximately a sixfold improvement. Furthermore, the mean squared error (MSE) of the measurements is below 0.0004. The extinction ratio exceeds 750:1. And the ellipsometric error is below 1.06%. These results demonstrate that the overdriving method enables high-speed Mueller matrix measurements, thereby facilitating applications in real-time inspection fields such as dynamic polarization analysis, online quality inspection of optical components, and biomedical imaging.
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图 2 检偏器检测的各偏振态透过率仿真结果
Figure 2. Simulated transmittance for each polarization state passed through the polarizer
图 4 待测物穆勒矩阵仿真结果：(a) 90°偏振片；(b) 90°1/4波片
Figure 4. Simulated Mueller matrix of sample: (a) 90° polarizer; (b) 90° quarter wave plate
图 6 液晶相位延迟量测量光路
Figure 6. Optical configuration for of liquid crystal phase delay measurement
图 10 相位延迟量从0.25 λ切换到1 λ的过压驱动：(a)正常驱动；(b)过压驱动
Figure 10. Overdriving for the phase delay switched from 0.25 λ to 1 λ: (a) Normal; (b) Overdriving
图 12 偏振态产生实验光路
Figure 12. Experimental optical setup for polarization state generation
图 17 测量的待测物穆勒矩阵：(a) 90°偏振片；(b) 90°1/4波片
Figure 17. Measured Mueller matrix of sample: (a) 90° polarizer; (b) 90° 1/4 waveplate
表 1 偏振态与液晶相位延迟量对应关系
Table 1. Relation between polarization state and liquid crystal phase delay
δ1/λ δ2/λ Stokes矢量 偏振态 0.5 1 (1 1 0 0) 0°线偏振(H) 0.25 0.25 (1 0 1 0) 45°线偏振(P) 1 1 (1 −1 0 0) 90°线偏振(V) 0.25 0.75 (1 0 −1 0) 135°线偏振(M) 0.75 0.5 (1 0 0 1) 左旋圆偏振(L) 0.25 0.5 (1 0 0 −1) 右旋圆偏振(R) 
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表 2 穆勒矩阵仿真测量的光强
Table 2. Simulated light intensity for Mueller matrix test
H P V M L R H 1 0.5 0 1 0.5 0.5 P 0.5 1 0.5 0 0.5 0.5 V 0 0.5 1 0.5 0.5 0.5 M 0.5 0 0.5 1 0.5 0.5 L 0.5 0.5 0.5 0.5 1 0 R 0.5 0.5 0.5 0.5 0 1
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表 3 偏振态切换时间
Table 3. Switch time of polarization state
偏振态 LCVR-1/λ 时间/ms LCVR-2/λ 时间/ms ①H→P 0.5→0.25 0.6 1→0.25 0.6 ②P→V 0.25→1 3.5 0.25→1 3.5 ③V→M 1→0.25 0.6 1→0.75 0.8 ④M→L 0.25→0.75 4.2 0.75→0.5 0.7 ⑤L→R 0.75→0.25 0.7 0.5→0.5 0 ⑥R→H 0.25→0.5 3.8 0.5→1 4.3
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表 4 偏振态产生实验结果
Table 4. Experimental results for Polarization generation
偏振态 最小值(μw) 最大值(mw) 消光比 椭偏度 H 10.1 7.987 790∶1 P 10.5 7.975 759∶1 V 10.4 7.962 765∶1 M 10.2 7.976 781∶1 L 3.941 3.982 1.03% R 3.936 3.978 1.06%
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表 5 穆勒矩阵的测量光强
Table 5. Measured intensity for Mueller matrix
H P V M L R H 5.52 2.55 0.055 2.68 2.65 2.78 P 2.66 5.49 2.53 0.063 2.62 2.74 V 0.056 2.58 5.51 2.45 2.62 2.73 M 2.54 0.058 2.61 5.57 2.79 2.65 L 2.75 2.83 2.94 2.64 5.48 0.069 R 2.69 2.65 2.72 2.74 0.058 5.51
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