激光频率波动对空间引力波探测激光干涉测量的影响分析
doi: 10.11728/cjss2025.01.2024-0020 cstr: 32142.14.cjss.2024-0020
-
刘宇 男, 1997年6月出生于山西省阳泉市, 现为中国科学院大学杭州高等研究院及中国科学院国家空间科学中心硕士研究生, 参与了空间引力波探测太极计划全链路动态数值仿真的工作. E-mail: liuyu21 a@mails.ucas.ac.cn -
张玉珠 女, 1983年11月出生于北京市, 现为中国科学院国家空间科学中心副研究员, 硕士生导师, 主要研究方向为复杂系统仿真、空间引力波探测任务仿真和基于模型的系统工程(MBSE)等. E-mail: zhangyuzhu@nssc.ac.cn
作者简介:
通讯作者:
Analysis of the Influence and Importance of Laser Frequency Fluctuation on Laser Interference Simulation System for Space Gravitational Wave Detection
-
摘要: 空间引力波探测激光干涉测量系统噪声是决定探测任务成败的关键因素. 激光频率噪声是最重要的噪声之一, 有必要分析激光频率波动对测量结果的影响和各参数的变化对测量结果影响的百分比 (重要程度). 由于在地面难以模拟空间环境, 仿真分析是理想的实验手段. 基于空间引力波探测激光干涉测量仿真系统, 分析了自由运行激光器激光频率波动对其中的科学干涉仪、参考干涉仪和TM干涉仪模型造成的测量误差, 并运用直接求导法和Sobol法两种灵敏度分析方法对三种干涉仪模型输出的影响和重要程度进行灵敏度分析. 结果表明自由运行激光器激光频率波动造成的干涉仪测量结果变化远大于皮米量级. 在本文实验条件下, 测量光频率波动对三种干涉仪输出的重要程度分别为100%, 56%, 54%, 参考光频率波动对三种干涉仪输出的重要程度分别为0%, 44%, 46%.Abstract: The laser interferometric measurement system for space gravitational wave detection is of great significance for detection tasks, the noise of the interferometric measurement system is the key factor determining the success or failure of the task. Laser frequency noise is one of the most important noises. Therefore, it is necessary to analyze the impact and importance of laser frequency fluctuations on measurement results. Due to the difficulty in simulating the environment in space, analyzing based on simulation systems is an ideal approach. Based on the simulation system of space gravitational wave detection laser interferometry measurement, the measurement errors caused by laser frequency fluctuations of free running laser on the measurement results of scientific interferometer, reference interferometer, and TM interferometer models was analyzed. Then, sensitivity analysis was conducted using the derivative method and Sobol method with interference laser wavelength as input parameter. The influence and importance of laser frequency fluctuations of reference beam and measurement beam on the output of three interferometer models were analyzed. The results indicate that: laser frequency fluctuations during free running stages, which will cause changes in the measurement results of the interferometer, these changes are far greater than the picometers. Additionally, under the experimental conditions of this paper, the importance of measurement beam frequency fluctuation on the outputs of the three interferometers is 100%, 56%, and 54% respectively. The importance of reference beam frequency fluctuation on the outputs of the three interferometers is 0%, 44%, and 46% respectively.
-
图 1 空间引力波探测编队系统链路
Figure 1. Detection system links of space gravitational wave detection
图 2 激光频率波动对激光干涉测量影响分析实验模型
Figure 2. Experimental model for analyzing the influence of laser frequency fluctuation on laser interferometry
图 4 科学干涉仪输入/输出关系散点图
Figure 4. Scatter plot of science interferometer input-output relationship
图 5 参考干涉仪输入/输出关系散点图
Figure 5. Scatter plot of reference interferometer input-output relationship
图 6 TM干涉仪输入/输出关系散点图
Figure 6. Scatter plot of TM interferometer input-output relationship
表 1 Sobol g-function的灵敏度指标对比
Table 1. Comparison of sensitivity index of Sobol g-function
变量 一阶灵敏度指标 总灵敏度指标 本文解 解析解 本文解 解析解 x1 0.7153 0.7165 0.7850 0.7871 x2 0.1787 0.1791 0.2408 0.2420 x3 0.0236 0.0237 0.0342 0.0340 x4 0.0074 0.0072 0.0104 0.0105 x5 0.0001 0.0001 0.0001 0.0001 x6 0.0001 0.0001 0.0001 0.0001 x7 0.0001 0.0001 0.0001 0.0001 x8 0.0001 0.0001 0.0001 0.0001 
下载: 导出CSV
表 2 仿真光学平台中各元件含义, 摆放位置及方向
Table 2. Description, position and orientation of each component in the optical bench simulation
符号 含义 摆放位置/m 摆放方向 LB 激光器 (0.1, 0.1, 0) (0, –1, 0) A 反射镜 (–0.1, 0.05, 0) (1, –1, 0) B 分束器 (–0.1, 0.03, 0) (–1, –1, 0) C 分束器 (–0.1, 0, 0) (–1, 1, 0) E 分束器 (0, 0.05, 0) (1, –1, 0) F 分束器 (0, 0, 0) (–1, –1, 0) H 分束器 (0.1, 0.05, 0) (–1, 1, 0) I 分束器 (0.1, 0, 0) (1, –1, 0) J 科学干涉仪QPD (0.1, 0.05, 0) (0, 1, 0) G 参考干涉仪QPD (0, –0.05, 0) (0, 1, 0) D TM干涉仪QPD (–0.1, 0.05, 0) (0, 1, 0) TM 测试质量 (–0.2, 0, 0) (1, 0, 0) Remote 远端激光入射/本地激光出射点 (0.2, 0, 0) (–1, 0, 0) Adj 临近光学平台激光入射点 (–0.2, 0.03, 0) (1, 0, 0)
下载: 导出CSV
表 3 仿真系统部分参数
Table 3. Parameters of the simulation system
参数 取值 臂长 3×106 km 外差干涉效率 1 QPD半径 1 mm QPD狭缝大小 25 μm 光速 299792458 m⋅s–1 激光功率 1 W 激光波长 1064 nm
下载: 导出CSV
表 4 干涉仪输入/输出的默认值
Table 4. Default values for input and output
干涉仪 λr/nm λm/nm $ {\phi ^{{\text{LPF}}}} $/rad 科学干涉仪 1064 1064 1.771574804774003×1016 参考干涉仪 1064 1064 1.771574738708464×105 TM干涉仪 1064 1064 1.771574738775967×105
下载: 导出CSV
表 5 自由运行激光器激光波长波动导致的测量误差
Table 5. Measurement errors caused by wavelength fluctuations in free running lasers
干涉仪 λm波动范围 λr波动范围 λr, λm同时波动范围 相位差/rad 光程差/m 相位差/rad 光程差/m 相位差/rad 光程差/m 科学干涉仪 ±9.99×108 ±169 0 0 ±9.99×108 ±169 参考干涉仪 ±9.32×10–2 ±1.58×10–8 ±8.33×10–2 ±1.41×10–8 ±0.176 ±2.98×10–8 TM干涉仪 ±0.127 ±2.14×10–8 ±0.117 ±1.97×10–8 ±0.243 ±4.11×10–8
下载: 导出CSV
表 6 直接求导法的结果
Table 6. Results of sensitivity analysis based on derivative method
模型 模型输入参数 一阶灵敏度指标 科学干涉仪 λr 832.5070 λm –16650139143445.3213 参考干涉仪 λr 1387.5116 λm –1554.0130 TM干涉仪 λr 1942.5162 λm –2109.0176
下载: 导出CSV
表 7 科学干涉仪Sobol方法的结果
Table 7. Results of sensitivity analysis based on Sobol method for Sci-interferometer
采样数 一阶灵敏度指标 总灵敏度指标 λr λm λr λm 2000 0.000000000 –34080.509401456 0.000000000 1.000038804 4000 0.000000000 8313.376740156 0.000000000 1.000011119 6000 0.000000000 –6926.120416902 0.000000000 0.999992183
下载: 导出CSV
表 8 参考干涉仪Sobol方法的结果
Table 8. Results of sensitivity analysis based on Sobol method for Ref-interferometer
采样数 一阶灵敏度指标 总灵敏度指标 λr λm λr λm 2000 398.732348967 –2031.565140266 0.443703735 0.556524900 4000 1084.355308514 496.053218558 0.443442013 0.556361816 6000 892.892434128 –412.482744570 0.443667763 0.556508727
下载: 导出CSV
表 9 TM干涉仪Sobol方法的结果
Table 9. Results of sensitivity analysis based on Sobol method for TM interferometer
采样数 一阶灵敏度指标 总灵敏度指标 λr λm λr λm 2000 294.825816488 –1455.380150762 0.459104781 0.541125987 4000 801.554373052 355.541338080 0.458833596 0.540966969 6000 660.049114648 –295.382471800 0.459067649 0.541110365
下载: 导出CSV
-
[1] DANZMANN K, PRINCE T A, BINETRUY P, et al. LISA: Unveiling a Hidden Universe: Assessment Study Report[R]. Hannover: ESA/SRE, 2011, 3 (2) [2] LUO Z R, WANG Y, WU Y L, et al. The Taiji program: a concise overview[J]. Progress of Theoretical and Experimental Physics, 2021, 2021(5): 05A108 doi: 10.1093/ptep/ptaa083 [3] LUO J, CHEN L S, DUAN H Z, et al. TianQin: a space-borne gravitational wave detector[J]. Classical and Quantum Gravity, 2016, 33(3): 035010 doi: 10.1088/0264-9381/33/3/035010 [4] HISCOCK B, HELLINGS R W. OMEGA: a space gravitational wave MIDEX mission[C]//American Astronomical Society, 191st AAS Meeting. Bulletin of the American Astronomical Society, 1997: 1312 [5] 吴岳良, 胡文瑞, 王建宇, 等. 空间引力波探测综述与拟解决的科学问题[J]. 空间科学学报, 2023, 43(4): 589-599 doi: 10.11728/cjss2023.04.yg08WU Yueliang, HU Wenrui, WANG Jianyu, et al. Review and scientific objectives of spaceborne gravitational wave detection missions[J]. Chinese Journal of Space Science, 2023, 43(4): 589-599 doi: 10.11728/cjss2023.04.yg08 [6] ZHAO M Y, PENG X D, YANG Z, et al. Preliminary simulation of intersatellite laser interference link for the Taiji program[J]. Journal of Astronomical Telescopes, Instruments, and Systems, 2022, 8(3): 038002 [7] SALTELLI A, RATTO M, ANDRES T, et al. Global Sensitivity Analysis: The Primer[M]. Hoboken: John Wiley & Sons, 2008 [8] SOBOL’ I M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[J]. Mathematics and Computers in Simulation, 2001, 55(1/2/3): 271-280 [9] 赵梦园. 空间引力波探测激光干涉测量链路光学仿真研究[D]. 北京: 中国科学院大学, 2023ZHAO Mengyuan. Research on optical simulation of laser interference link in space gravitational wave detection[D]. Beijing: University of Chinese Academy of Sciences, 2023 [10] WANNER G, HEINZEL G, KOCHKINA E, et al. Methods for simulating the readout of lengths and angles in laser interferometers with Gaussian beams[J]. Optics Communications, 2012, 285(24): 4831-4839 doi: 10.1016/j.optcom.2012.07.123 [11] SALTELLI A, ANNONI P. How to avoid a perfunctory sensitivity analysis[J]. Environmental Modelling & Software, 2010, 25(12): 1508-1517 [12] SOBOL’ I M. Sensitivity estimates for nonlinear mathematical models[J]. Mathematical Modelling and Computational Experiment, 1993, 1(4): 407-414 [13] HOMMA T, SALTELLI A. Importance measures in global sensitivity analysis of nonlinear models[J]. Reliability Engineering & System Safety, 1996, 52(1): 1-17 [14] SALTELLI A, ANNONI P, AZZINI I, et al. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index[J]. Computer Physics Communications, 2010, 181(2): 259-270 doi: 10.1016/j.cpc.2009.09.018 [15] 刘源远. 汽车转向机构运动精度的灵敏度分析及优化设计[D]. 长沙: 湖南大学, 2017LIU Yuanyuan. Sensitivity Analysis on the Kinematic Accuracy of Automotive Steering Mechanism and Optimization Design[D]. Changsha: Hunan University, 2017 [16] SALTELLI A, SOBOL I M. About the use of rank transformation in sensitivity analysis of model output[J]. Reliability Engineering & System Safety, 1995, 50(3): 225-239 [17] SHINOZUKA M, DEODATIS G. Simulation of stochastic processes by spectral representation[J]. Applied Mechanics Reviews, 1991, 44(4): 191-204 doi: 10.1115/1.3119501 [18] 罗子人, 白姗, 边星, 等. 空间激光干涉引力波探测[J]. 力学进展, 2013, 43(4): 415-447 doi: 10.6052/1000-0992-13-044LUO Ziren, BAI Shan, BIAN Xing, et al. Gravitational wave detection by space laser interferometry[J]. Advances in Mechanics, 2013, 43(4): 415-447 doi: 10.6052/1000-0992-13-044 -
-
下载:
计量
- 文章访问数: 394
- HTML全文浏览量: 95
- PDF下载量: 29
-
被引次数:
0(来源:Crossref)
0(来源:其他)
