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摘要: 时间延迟干涉技术（Time-delay Interferometry，TDI）对中国引力波探测项目及其它天基激光精密测量任务具有重要的参考价值。在天基引力波探测任务中，需利用激光干涉仪对无拖曳检验质量块间实现十皮米量级的位移测量精度。其中，激光源频率噪声和时钟频率噪声是两项主要噪声。在欧洲主导的LISA（Laser Interferometer Space Antenna）引力波探测项目中，利用TDI对三星上的十二组相位测量值进行延迟和线性组合，构造出臂长相等的干涉仪，从而消除了激光源噪声以及光学平台位移噪声。为了消除时钟噪声，将时钟信号倍频到GHz，再通过相位调制的方式加载到星间激光链路上，最终从时钟边带拍频信号中提取出时钟噪声，并在TDI的数据组合中将时钟噪声项消除。为了实现TDI的时间延迟处理，要求对星间绝对距离进行精确测量。因此，在TDI机制中，星间激光链路需要同时实现位移测量、时钟边带调制和绝对距离测量3个功能。其中，后两个功能分别大约消耗10%和1%的载波激光功率。LISA项目针对TDI技术的地面论证结果表明，TDI技术对激光源和时钟的噪声抑制分别达到了109和5.8×104倍。Abstract: The Time-delay Interferometry (TDI) technique is of important value for China’s gravitational wave detection program and other space-based laser interferometry missions. In space-based gravitational wave detection, laser interferometry is utilized to achieve ten-picometer precision in the displacement measurements between drag-free proof masses. Laser frequency noise and clock frequency noise are the two dominant noises in the measurement. In the European LISA (Laser Interferometer Space Antenna) program for gravitational wave detection, TDI technique is used to remove laser noise and displacement noise of optical platform by time-delaying and linearly combining the twelve phase measurement data of the three satellites and thus creating an interferometer with equal-length beams. For the cancellation of clock noise, the frequencies of onboard clocks are multiplied to GHz levels and then the GHz clock signals are added on inter-satellite laser links by phase modulation. Finally, the clock noise can be extracted from the generated clock-sideband beat note, eliminating the clock noise terms in the TDI data combination. For the time-delay operation in the data post-processing of the TDI, there is also a requirement for the precise measurement of the absolute distances between three satellites. Therefore, in the TDI scheme, there are three functions applicable to the inter-satellite laser links: displacement measurement, clock sideband modulation and absolute distance ranging. The latter two functions consume the power of the optical carrier by 10% and 1%, respectively. The TDI demonstration in the LISA’s ground-based testbed shows the laser noise and clock noise can be suppressed by the factor of 109 and 5.8×104, respectively.
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图 5 当星座旋转时，
${L'_i} \ne {L_i}$ Figure 5. In the case of the constellation rotation,
${L'_i} \ne {L_i}$ 
图 6 时钟边带调制示意图。EOM：电光调制器
Figure 6. Schematic diagram of clock sideband modulation. EOM: Electro-Optic Modulator
图 7 探测端信号处理示意图。NCO：数控振荡器
Figure 7. Signal processing illustration of photon detection. NCO: Numerically Controlled Oscillator
图 8 在载波相位上调制数据码和伪随机码用于星间数据传输和绝对距离测量示意图
Figure 8. The phase of the carrier is modulated by data codes and pseudo-random codes for the inter-satellite data transmission and absolute distance measurement
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