Interferometric measurement of thermal deformation for ultra-stable structural support frame of gravitational wave spacecraft
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摘要:
为满足空间引力波探测用陶瓷基超稳结构的热形变测试需求，解决该类构件制备完成前测量链路难以验证的工程难题，本文搭建了一套适用于1mHz~0.1 Hz频段的地面真空热形变干涉测量系统。选用几何构型、安装接口及测量光路均与陶瓷基构件等效的 4J32 殷钢样件作为试验件，完成系统综合热膨胀系数标定、长期位移稳定性测试与低频噪声分析。试验将被测结构、光纤测量头、反射镜与温度传感器整体置于真空环境，利用腔体自然降温实现测量链路整体热响应标定；在mK级稳态温控下，采用Welch法获取位移噪声幅值谱密度，对比分析干涉仪本征噪声、热等效噪声与系统综合噪声。实验结果表明：系统综合热膨胀系数与殷钢本征值相对偏差约8.3%，可有效表征测量链路整体热响应；系统在mHz频段位移噪声幅值谱密度26.6 nm/√Hz，长周期测量稳定性较好；干涉仪本征噪声较系统综合噪声低约两个数量级，温度波动转换的热等效位移噪声仅占系统噪声的7.8%~14.1%，二者均远低于系统综合测量噪声，并非系统测量误差的主要来源。该系统与方法完成了全测量链路验证与噪声基准建立，可为后续陶瓷基超稳结构热形变测试提供等效验证基础与可复用技术方案。
Abstract:To satisfy the thermal deformation testing requirements of ceramic-based ultra-stable structures for space gravitational wave detection, and address the difficulty of verifying the measurement link prior to component fabrication, a ground-based vacuum interferometric measurement system operating within 1 mHz–0.1 Hz is developed in this paper. We use an equivalent 4J32 Invar sample for tests. It matches ceramic parts in geometry, interfaces and optical path. We calibrate thermal expansion and test displacement stability. We also decompose low-frequency noise systematically. In the experiment, the tested structure, fiber-optic measuring probe, reflector and temperature sensors are placed in a vacuum environment, and the natural cooling of the cavity is utilized to realize the overall thermal response calibration of the measurement link. Under mK-level steady-state temperature control, the Welch method is employed to acquire the amplitude spectral density of displacement noise, and a comparative analysis is conducted on the intrinsic noise of the interferometer, thermal equivalent noise and system comprehensive noise. The experimental results show that the relative deviation between the system comprehensive thermal expansion coefficient and the intrinsic value of Invar is about 8.3%, which can effectively characterize the overall thermal response of the measurement link. The amplitude spectral density of displacement noise of the system in the mHz band is approximately 26.6 nm/√Hz, and the consistency of long-period multi-segment steady-state measurement results is high, demonstrating high reliability. The intrinsic noise of the interferometer is about two orders of magnitude lower than the system comprehensive noise, and the thermal equivalent displacement noise converted from temperature fluctuation only accounts for 7.8%~14.1% of the system noise; both of them are far lower than the comprehensive measurement noise and do not constitute major interference. The proposed system and method complete the full measurement link verification and noise benchmark establishment, and can provide an equivalent verification foundation and reusable technical scheme for subsequent thermal deformation testing of ceramic-based ultra-stable structures.
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图 1 光纤双频干涉位移测量原理示意图
Figure 1. Schematic of fiber dual-frequency interferometric displacement measurement
图 2 热形变测量系统总体组成示意图
Figure 2. Overall schematic of thermal deformation measurement system
图 12 温度与位移时域变化及系统综合热膨胀系数标定结果a) 平均温度-位移变化 b) 位移-温度线性回归
Figure 12. Temperature–displacement evolution and system thermal expansion coefficient calibration a) Mean temperature-displacement variation b) Displacement-temperature linear regression
图 13 干涉仪本征噪声与系统位移噪声ASD对比
Figure 13. Intrinsic interferometer noise vs. System displacement noise
图 14 热等效位移噪声与系统位移噪声ASD对比
Figure 14. Thermal-equivalent noise vs. System displacement noise
图 15 温度波动与位移波动的散点图及线性拟合结果
Figure 15. Temperature vs. displacement fluctuation (linear fit)
图 16 热等效位移噪声占系统实测噪声的频率依赖比例
Figure 16. Frequency-dependent ratio of thermal-equivalent displacement noise to measured system noise
表 1 FDS-02光纤双频激光干涉仪主要技术参数
Table 1. Main technical parameters of the FDS-02 fiber dual-frequency laser interferometer
参数 数值 激光波长（20 °C，
标准大气压）1550 nm波长精度 <±0.1 ppm 波长稳定性 <±20 ppb（1 h）；<±50 ppb（24 h） 光束直径 3 mm ± 0.2 mm 测量量程 0～1 m 光学信号周期 λ/4（387.5 nm） 测量分辨率 0.38 nm（4 倍光学细分） 系统非线性误差（SDE） <±2 nm（速度 <50 mm/s，信号强度 >70%） 测量头热漂移系数 <30 nm/ °C 最大测量速度 1 m/s 
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