Time-delay interferometry for space-based gravitational wave detection

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.