Adapting time-delay interferometry for LISA data in frequency

Abstract

Time-delay interferometry (TDI) is a post-processing technique used to reduce laser noise in heterodyne interferometric measurements with unequal armlengths, a situation characteristic of space gravitational detectors such as the Laser Interferometer Space Antenna (LISA). This technique consists in properly time-shifting and linearly combining the interferometric measurements in order to reduce the laser noise by several orders of magnitude and to detect gravitational waves. In this communication, we show that the Doppler shift due to the time evolution of the armlengths leads to an unacceptably large residual noise when using interferometric measurements expressed in units of frequency and standard expressions of the TDI variables. We also present a technique to mitigate this effect by including a scaling of the interferometric measurements in addition to the usual timeshifting operation when constructing the TDI variables. We demonstrate analytically and using numerical simulations that this technique allows one to recover standard laser noise suppression which is necessary to measure gravitational waves.

Geometric approach for the modified second generation time delay interferometry

“…The latter two physical quantities, namely, the laser frequency and phase noise, are by and large equivalent, but in the case of the laser frequency noise, there will be an additional Doppler shift, and the delay operator needs to be corrected (also see the discussions in Ref. [35]). In the remainder of the present paper, the calculations will be carried out by considering the laser frequency noise, which perturb around the center frequency ν i ≈ 282 THz.…”

Bayesian time delay interferometry

“…TDI is reviewed extensively in Ref. [5] and recent developments include new TDI combinations using spacecraft velocities and accelerations that numerically solve for delays [6], a Doppler shift scaling operation on TDI combinations for implementation of frequency domain phase measurements [7] and demonstration of the coupling between the on-board anti-aliasing filter and the time dependence of the delays in TDI performance [8].…”