LISA Non-Linear Dynamics and Tilt-To-Length Coupling

TL;DR

This work analyzes Tilt-To-Length (TTL) coupling in the LISA interferometer by embedding non-linear, time-varying closed-loop dynamics of spacecraft and benches into a detailed simulation. TTL coefficients (24 in total) are inferred from simulated measurements using a time-domain least-squares estimator, with regularization to mitigate bias and ill-conditioning. The study finds TTL contributions are limited within the 8–200 mHz band for nominal coefficients, yet estimator bias and channel correlations can affect accuracy; sinusoidal maneuvers dramatically improve inference to about 0.1% and allow near-perfect subtraction of TTL noise, validating the maneuver design. These results provide practical TTL calibration strategies and demonstrate that TTL noise can be mitigated to the level of other instrumental noises, supporting robust science operation for LISA.

Abstract

For the LISA mission, Tilt-To-Length (TTL) coupling is expected to be one of the dominant instrumental noise contributions after laser frequency noise is suppressed based, on assumptions on the size of the coupling and angular jitter levels. This work uses for the first time a closed-loop, non-linear, and time-varying dynamics implementation to simulate detailed angular jitters for the spacecraft and optical benches. In turn, this gives an improved expectation of the TTL contribution to the interferometric output. It is shown that the TTL coupling impact is limited given current estimates on the size of coupling coefficients. A time-domain Least Squares estimator is used to infer the TTL parameters from the simulated measurements. The bias and correlations limit the estimator in the case of regular datasets with amplified TTL coefficients to a relative error of $10\%$, but the subtraction of the TTL signal still works well. For lower readout noises, the estimation error diverges, which can be mitigated using a regularization term. Alternatively, using sinusoidal maneuvers improves the inference to a high accuracy of $0.1\%$ for TTL coefficients around the expected level, removing all correlations in the inferred parameters. This validates the maneuver design by Wegener et al. (2025) in this closed-loop setting.

Figures (22)

• Figure 1: Figure cut of constellation geometry of in the triangle plane. The scheme for numbering , , light travel times $\tau$, and opening angles $\varphi_b$ are defined.
• Figure 2: Figure cut of geometry. The definition of the $\mathcal{B}$, $\mathcal{H}_{1}$, and $\mathcal{H}_2$ frames is illustrated. The center-of-mass of the satellite forms the origin of the $\mathcal{B}$ frame, while the centers of the housings form the origin of the $\mathcal{H}_1$ and $\mathcal{H}_2$ frames. Additionally to the basis vectors, the Cardan angles are defined, following the right-hand rule for their direction of rotation.
• Figure 3: Representative and jitter shapes are shown. The left subplots show the of the internal states of the simulator in terms of radians. The right subplots show the later used time derivatives. The are calculated from a e5 dataset with $N_\text{avg.}=5$ (c.f. App. \ref{['app:lisanode']}). Reference lines show jitters used in another publication hartig2025tilt: solid lines in black or lighter colors are white jitter references with a low frequency roll off, while the dashed black lines are colored jitter. Note that for the colored jitter case, $\eta$ is set to zero. Additionally, for the jitter the dash-dotted reference lines have been added from case B in george2023fisher. Their are defined in Eqs. \ref{['eq:ref_white_sc_jitter']}--\ref{['eq:ref_col_mosa_jitter2']}. The top left subplot has a plateau for low frequencies, which exactly corresponds to the white readout noise ([power-half-as-sqrt,per-mode=symbol]0.20.5). The fall-off towards higher frequencies is a result of the moment-of-inertia. Without noise, the fall-off would be a power law; but with the noise present, there is a change in the fall-off. The thruster noise widens the peak.
• Figure 4: Representative outputs for 12. The left subplots show the of the output in terms of radians over time, the right subplots show the later used derivatives. The upper subplots show the result of a simulation with the standard noise settings of [power-half-as-sqrt,per-mode=symbol]0.20.5, and the lower subplots with half the noise. The are calculated from a e5 dataset with $N_\text{avg.}=5$ (c.f. App. \ref{['app:lisanode']}). The left subplots show two peaks for the $\phi_{12}$ sensing output. The low-frequency peak comes from the contribution of the jitter, and the medium-frequency peak from the contribution of the jitter. The $\eta_{12}$ sensing output only sees the jitter contributions, as the jitter is subdominant, resulting in only one peak. The plateau towards higher frequencies corresponds directly to the level of readout noise.
• Figure 5: of -X (second-generation Michelson variables) for different simulation scenarios. These include different settings for the coefficients and different noise levels (low readout noise means half of the nominal settings). 'Random' refers to the coefficients being sampled from a uniform distribution. The black line gives the noise requirement of paczkowski_postprocessing_2022 (c.f. Eqs.\ref{['eq:req-tm-displacement']},\ref{['eq:req-tm-acc']}). The vertical dashed line gives the drag-free frequency bandwidth inchauspe23_dynamics. The variation in readout noise only has an impact on frequencies around 100m. For equal coefficients of [per-mode=symbol]2.3 the shape of the is very close to the simulation with no contribution. The are calculated from a e6 dataset with $N_\text{avg.}=50$ (c.f. App. \ref{['app:lisanode']}).