Calculating the precision of tilt-to-length coupling estimation and noise subtraction in LISA using Fisher information

TL;DR

This paper models tilt-to-length noise in LISA, uses Fisher information to estimate the precision of TTL coupling coefficients, and assesses the residual noise after subtraction, highlighting the impact of angular jitter and sensor noise.

Contribution

It introduces a frequency domain model for TTL noise in LISA and applies Fisher analysis to quantify the estimation uncertainties and their effect on residual noise.

Findings

Residual TTL noise limited to 8 pm/√Hz with ideal angular jitter

Realistic jitter increases TTL uncertainties by 70 times

Residual noise after subtraction depends on sensor noise and jitter models

Abstract

Tilt-to-length (TTL) noise from angular jitter in LISA is projected to be the dominant noise source in the milli-Hertz band unless corrected in post-processing. The correction is only possible after removing the overwhelming laser phase noise using time-delay interferometry (TDI). We present here a frequency domain model that describes the effect of angular motion of all three spacecraft on the interferometric signals after propagating through TDI. We then apply a Fisher information matrix analysis to this model to calculate the minimum uncertainty with which TTL coupling coefficients may be estimated. Furthermore, we show the impact of these uncertainties on the residual TTL noise in the gravitational wave readout channel, and compare it to the impact of the angular witness sensors' readout noise. We show that the residual TTL noise post-subtraction in the TDI variables for a case using the LISA angular jitter requirement and integration time of one day is limited to the 8\,pm/$\sqrt{\rm Hz}$ level by angular sensing noise. However, using a more realistic model for the angular jitter we find that the TTL coupling uncertainties are 70 times larger, and the noise subtraction is limited by these uncertainties to the 14\,pm/$\sqrt{\rm Hz}$ level.