Equal-arm detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms. This is because the noise in the laser light is common to both arms, experiencing exactly the same delay, and thus cancels when it is differenced at the photo detector. In this situation, much lower level secondary noises then set the overall performance. If, however, the two arms have different lengths (as will necessarily be the case with space-borne interferometers), the laser noise experiences different delays in the two arms and will hence not directly cancel at the photo detector. To solve this problem, a technique involving heterodyne interferometry with unequal arm lengths and independent phase-difference readouts has been proposed. It relies on properly time-shifting and linearly combining independent Doppler measurements, and for this reason it has been called time-delay interferometry (TDI). This article provides an overview of the theory, mathematical foundations, and experimental aspects associated with the implementation of TDI. Although emphasis on the application of TDI to the Laser Interferometer Space Antenna mission appears throughout this article, TDI can be incorporated into the design of any future space-based mission aiming to search for gravitational waves via interferometric measurements. We have purposely left out all theoretical aspects that data analysts will need to account for when analyzing the TDI data combinations.

重力辐射等臂探测器允许进行比将光注入其臂的激光的固有相位稳定性低多个数量级的相位测量。这是因为激光中的噪声对于两个臂来说是共同的，经历完全相同的延迟，因此当它在光电探测器处存在差异时就被抵消。在这种情况下，较低水平的二次噪声决定了整体性能。然而，如果两个臂具有不同的长度（星载干涉仪必然会出现这种情况），则激光噪声在两个臂中经历不同的延迟，因此不会在光电探测器处直接抵消。为了解决这个问题，提出了一种涉及不等臂长和独立相位差读数的外差干涉测量技术。它依赖于正确的时移和线性组合独立的多普勒测量，因此它被称为时延干涉测量（TDI）。本文概述了与 TDI 实施相关的理论、数学基础和实验方面。尽管本文始终强调 TDI 在激光干涉仪空间天线任务中的应用，但 TDI 可以纳入任何未来旨在通过干涉测量搜索引力波的天基任务的设计中。我们故意忽略了数据分析师在分析 TDI 数据组合时需要考虑的所有理论方面。