Accelerating TTL noise post-processing via combined coefficients and alternative TDI configuration

TL;DR

This work tackles TTL noise calibration in space-based GW detectors, where angular jitter couples to optical-path length and contaminates measurements. It combines a transformed TTL coefficient parameterization with an alternative second-generation TDI (PD4L) to dramatically accelerate coefficient fitting, reducing degeneracies and improving conditioning. For linear TTL modeling, fitting can be ~10× faster, and for quadratic TTL modeling, up to ~18× faster, when using PD4L with the transformed parameters, while achieving residual TTL levels below the acceleration and OMS noise floors even under amplified coupling. The approach enables scalable TTL noise calibration for missions like LISA, Taiji, and TianQin, providing robust noise suppression and a practical path toward real-time data pre-processing pipelines.

Abstract

Tilt-to-length (TTL) noise induced by angular jitter of spacecraft and test masses can affect the sensitivity of space-based gravitational-wave detectors such as LISA, Taiji, and TianQin. Such angular jitter can be measured using the differential wavefront sensing technique, enabling the modeling and subtraction of TTL noise from the data. However, owing to the multiple degrees of freedom of the detector constellation, a linear TTL model requires at least 24 parameters, while a higher-fidelity quadratic model involves up to 60 coefficients, rendering parameter estimation computationally expensive. To accelerate parameter determination, we propose a modified parameter set obtained via a linear transformation of the original angular coupling coefficients, which effectively reduces correlations among TTL noise components. In addition, we perform parameter fitting using an alternative second-generation time-delay interferometry configuration, PD4L, rather than the fiducial Michelson configuration. These two improvements enhance the convergence speed of the fitting procedure by a factor of approximately 10 for the linear model and approximately 18 for the quadratic model. The proposed approach can therefore substantially improve the efficiency of TTL noise calibration in space-based gravitational-wave detectors.

Figures (10)

• Figure 1: A: TM interferometer TTL noise; B: LA interferometer receiver TTL noise; C: LA interferometer transmitter TTL noise.
• Figure 2: TTL noise due to far-field phase error.
• Figure 3: The constellation layout and notations of detector.
• Figure 4: Spacecraft coordinate system.
• Figure 5: TTL noise PSDs at the transmitters (left panel) and receivers (right panel). For each panel, six solid curves ($d_{ij}$) correspond to the simulated TTL noise of the six inter-spacecraft links. The dashed (res1$_{ij}$) and dotted (res2$_{ij}$) curves represent the residuals after linear and quadratic model fitting and subtraction, respectively, applied directly to the simulated noise. This procedure provides a direct validation of the consistency between the adopted coupling models and the injected TTL noise.