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

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.

💡 Research Summary

Tilt‑to‑length (TTL) noise, caused by angular jitter of the spacecraft and the test‑mass optical assemblies (MOSA), is a major limitation for space‑based gravitational‑wave detectors such as LISA, Taiji and TianQin in the 0.1 mHz–1 Hz band. While laser‑frequency noise can be suppressed by second‑generation time‑delay interferometry (TDI), TTL noise remains because the jitter couples into the interferometric phase through several mechanisms (transmitter‑side wavefront distortion, receiver‑side incidence‑angle changes, and test‑mass mirror jitter). In practice, the three‑spacecraft constellation together with two MOSAs per spacecraft generates twelve independent TTL contributions that must be calibrated and subtracted from the science data.

Current post‑processing approaches model TTL as a linear (≥24 coefficients) or quadratic (up to 60 coefficients) function of the measured angular motions obtained from differential wavefront sensing (DWS). Estimating such a high‑dimensional parameter set with conventional Bayesian tools (MCMC, nested sampling) is computationally prohibitive, often requiring thousands of CPU‑hours because the coefficients are strongly correlated and the parameter space is highly degenerate.

The authors propose two complementary strategies to accelerate the calibration. First, they construct a linear transformation matrix that maps the original coupling coefficients onto a new basis in which the covariance between parameters is minimized. By diagonalizing the Fisher information (or equivalently performing a principal‑component‑like rotation), the transformed parameters become nearly orthogonal, dramatically reducing the condition number of the fitting problem. Second, they replace the standard Michelson TDI combination with the PD4L second‑generation TDI observable. PD4L has been shown to be more robust against laser‑frequency noise leakage and to exhibit weaker coupling between TTL terms, especially on the receiver side, thereby further alleviating parameter degeneracies.

The simulation framework incorporates realistic noise sources: spacecraft attitude jitter (10 nrad/√Hz ×