Phase-extracting method of optical frequency scanning interference signals based on the CEEMD-HT algorithm
doi: 10.37188/CO.2022-0173
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摘要:
光频扫描非线性会影响光频扫描干涉（FSI）信号的相位提取精度，进而降低扫频干涉测距精度。针对这一问题，本文提出了一种基于互补集合经验模态分解结合希尔伯特变换（CEEMD-HT）算法的干涉信号相位提取方法。在CEEMD-HT算法进行理论推导和仿真分析的基础上，通过仿真验证了该算法对非平稳扫频干涉信号相位求解的有效性。进一步采用FSI实验系统中的真实输出光频率作为仿真条件进行了仿真实验，仿真结果表明CEEMD-HT算法对干涉信号相位的求解精度以及FSI测距精度都有显著的改善。最后，通过FSI测距系统的测距实验对所提出的干涉信号相位提取方法进行验证。结果表明：在2 m自由空间测量范围内，基于CEEMD-HT算法的重复测距精度为2.79 μm，相较于EMD-HT和直接测量法分别提高了5.19倍和8.28倍。
Abstract:Aiming at the problem that the optical frequency scanning nonlinearity affects the phase extracting accuracy of the optical Frequency Scanning Interferometry (FSI) signal, and thus reduces the FSI ranging accuracy, a phase-extracting method based on the Complementary Ensemble Empirical Mode Decomposition and Hilbert Transform (CEEMD-HT) algorithm is proposed in this paper. Based on theoretical derivation and simulation analysis of the CEEMD-HT algorithm, the effectiveness of the algorithm in solving the phase of the non-stationary interference signal in scanning-frequency is verified by simulation. Further simulation experiments were implemented by using the real output optical frequency obtained with FSI ranging system as the simulation conditions. The simulation results showed that the CEEMD-HT algorithm significantly improved the phase extracting accuracy of the interference signal and the FSI ranging accuracy. Finally, the proposed interference signal phase-extracting method was verified via the experiment of the FSI ranging system. The results showed that the ranging repeatability of the measurement system based on the CEEMD-HT algorithm was 2.79 μm in the free space measurement range of 2 m. Compared with EMD-HT and direct measurement methods, the ranging repeatability was improved by 5.19 times and 8.28 times, respectively.
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图 2 干涉信号的相位分解示意图
Figure 2. Schematic diagram of the interferometric phase decomposition
图 3 EMD对非稳干涉信号的分解重构示意图
Figure 3. Schematic diagram of the EMD decomposition and reconstruction of the non-stationary interference signal
图 5 CEEMD对干涉信号的分解重构示意图
Figure 5. Schematic diagram of the decomposition and reconstruction of the interference signal via CEEMD
图 7 单周期相位差提取仿真结果对比图
Figure 7. Comparison of simulation results of single cycle phase difference extraction
图 8 测距仿真结果对比图
Figure 8. Comparison of the ranging simulation results of different phase extracting methods
图 10 实测干涉信号处理对比图
Figure 10. Comparison of measured interference signal processing results
表 1 Simulation parameters of the scanning nonlinearity
Table 1. Simulation parameters of the scanning nonlinearity
Parameters Parameter name Value/unit a Interference signal amplitude 1 V ${\upsilon _0}$ ECDL initial optical frequency 0 Hz $\Delta \upsilon $ Optical frequency scanning range 2 THz L Measured distance 10 m n Air refractive index 1 c Velocity of light 3×108 m/s t Scan cycle 5 s SNR Signal to noise ratio of
interference signal25, 20, 15, 10 dB S Interference signal sampling frequency 10 MHz 
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