Phase-extracting Method of Optical Frequency Scanning Interference Signals Based on the CEEMD-HT Algorithm
doi: 10.37188/CO.2022-0173
-
摘要:
针对光频扫描非线性对光频扫描干涉（FSI）信号相位提取精度存在影响，进而降低扫频干涉测距精度这一问题，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，测量结果表明：在2米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和直接测量法重复测量精度分别提高了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 curve 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 that of the FSI ranging. 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.
-
Key words:
- interferometry /
- ranging /
- frequency scanning /
- nonlinearity in frequency scanning /
- phase extracting
-
图 3 EMD对干涉信号的分解重构示意图
Figure 3. Schematic of the EMD decomposition and reconstruction of the interference signal
图 5 CEEMD对干涉信号的分解重构示意图
Figure 5. Schematic 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 with different phase extracting methods
表 1 Simulation parameters of the scanning nonlinearity
Table 1. Simulation parameters of the scanning nonlinearity
参数
Parameters参数描述
Parameter name数值/单位
Value/unita 干涉信号幅值
Interference signal amplitude1 v ${\upsilon _0}$ ECDL初始光频率
ECDL initial optical frequency0 Hz $\Delta \upsilon $ 光频扫描范围
Optical frequency scanning range2 THz L 被测距离
Measured distance10 m n 空气折射率
Air refractive index1 c 光速
Velocity of light3×108 m/s t 扫描周期
Scan cycle5 s SNR 干涉信号信噪比
Signal to noise ratio of interference signal25, 20, 15, 10 dB S 干涉信号采样频率
Interference signal sampling frequency10 MHz 
下载: 导出CSV
-
[1] LU CH, LIU G D, LIU B G, et al. Absolute distance measurement system with micron-grade measurement uncertainty and 24 m range using frequency scanning interferometry with compensation of environmental vibration[J]. Optics Express, 2016, 24(26): 30215-30224. doi: 10.1364/OE.24.030215 [2] SHI G, ZHANG F M, QU X H, et al. High-resolution frequency-modulated continuous-wave laser ranging for precision distance metrology applications[J]. Optical Engineering, 2014, 53(12): 122402. doi: 10.1117/1.OE.53.12.122402 [3] SHI G, WANG W, ZHANG F M. Precision improvement of frequency-modulated continuous-wave laser ranging system with two auxiliary interferometers[J]. Optics Communications, 2018, 411: 152-157. doi: 10.1016/j.optcom.2017.11.062 [4] WANG ZH Y, LIU ZH G, DENG ZH W, et al. Phase extraction of non-stationary interference signal in frequency scanning interferometry using complex shifted Morlet wavelets[J]. Optics Communications, 2018, 420: 26-33. doi: 10.1016/j.optcom.2018.03.032 [5] CHENG X R, LIU J CH, JIA L H, et al. Precision and repeatability improvement in frequency-modulated continuous-wave velocity measurement based on the splitting of beat frequency signals[J]. Optics Express, 2021, 29(18): 28582-28596. doi: 10.1364/OE.433637 [6] DALE J, HUGHES B, LANCASTER A J, et al. Multi-channel absolute distance measurement system with sub ppm-accuracy and 20 m range using frequency scanning interferometry and gas absorption cells[J]. Optics Express, 2014, 22(20): 24869-24893. doi: 10.1364/OE.22.024869 [7] LIU G D, XU X K, LIU B G, et al. Dispersion compensation method based on focus definition evaluation functions for high-resolution laser frequency scanning interference measurement[J]. Optics Communications, 2017, 386: 57-64. doi: 10.1016/j.optcom.2016.10.052 [8] XU X K, LONG K, XU J X, et al. The method of dispersion cancellation based on the forward and reverse tuning of a laser frequency-modulated continuous wave system[J]. Journal of Infrared and Millimeter Waves, 2021, 40(2): 243-247. (in Chinese) [9] WANG D F, YAO X, JIAO ZH K, et al. Time-delay interferometry for space-based gravitational wave detection[J]. Chinese Optics, 2021, 14(2): 275-288. (in Chinese) doi: 10.37188/CO.2020-0098 [10] GONG H, LIU ZH G, ZHOU Y L, et al. Mode-hopping suppression of external cavity diode laser by mode matching[J]. Applied Optics, 2014, 53(4): 694-701. doi: 10.1364/AO.53.000694 [11] DENG ZH W, LIU ZH G, LI B, et al. Precision improvement in frequency-scanning interferometry based on suppressing nonlinear optical frequency sweeping[J]. Optical Review, 2015, 22(5): 724-730. doi: 10.1007/s10043-015-0134-1 [12] GONG H, LIU ZH G, ZHOU Y L, et al. Extending the mode-hop-free tuning range of an external-cavity diode laser by synchronous tuning with mode matching[J]. Applied Optics, 2014, 53(33): 7878-7884. doi: 10.1364/AO.53.007878 [13] YÜKSEL K, WUILPART M, MÉGRET P. Analysis and suppression of nonlinear frequency modulation in an optical frequency-domain reflectometer[J]. Optics Express, 2009, 17(7): 5845-5851. doi: 10.1364/OE.17.005845 [14] AHN T J, LEE J Y, KIM D Y. Suppression of nonlinear frequency sweep in an optical frequency-domain reflectometer by use of Hilbert transformation[J]. Applied Optics, 2005, 44(35): 7630-7634. doi: 10.1364/AO.44.007630 [15] ROOS P A, REIBEL R R, BERG T, et al. Ultrabroadband optical chirp linearization for precision metrology applications[J]. Optics Letters, 2009, 34(23): 3692-3694. doi: 10.1364/OL.34.003692 [16] DENG W, LIU ZH G, DENG ZH W, et al. Extraction of interference phase in frequency-scanning interferometry based on empirical mode decomposition and Hilbert transform[J]. Applied Optics, 2018, 57(9): 2299-2305. doi: 10.1364/AO.57.002299 [17] BEDROSIAN E. A product theorem for Hilbert transforms[R]. Santa Monica: RAND Corporation, 1962. [18] RILLING G, FLANDRIN P, GONÇALVES P. On empirical mode decomposition and its algorithms[C]. Proceedings of IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing NSIP-03, IEEE, 2003: 8-11. [19] WU ZH H, HUANG N E. Ensemble empirical mode decomposition: a noise-assisted data analysis method[J]. Advances in Adaptive Data Analysis, 2009, 1(1): 1-41. doi: 10.1142/S1793536909000047 [20] YEH J R, SHIEH J S, HUANG N E. Complementary ensemble empirical mode decomposition: A novel noise enhanced data analysis method[J]. Advances in Adaptive Data Analysis, 2010, 2(2): 135-156. doi: 10.1142/S1793536910000422 -
下载:
点击查看大图
计量
- 文章访问数: 71
- HTML全文浏览量: 22
- PDF下载量: 93
- 被引次数: 0
