Tilt-To-Length Coupling in LISA -- Uncertainty and Biases

TL;DR

This paper analyzes the accuracy of estimating tilt-to-length coupling coefficients in LISA, highlighting biases introduced by readout noise and comparing estimators to improve noise mitigation strategies.

Contribution

It provides a detailed comparison of least squares and instrumental variables estimators for TTL coupling, including a bias prediction equation for least squares.

Findings

Least squares estimator is biased by angular readout noise.

Instrumental variables estimator converges to an unbiased estimate with more data.

An equation predicting the bias of the least squares estimator is derived.

Abstract

The coupling of the angular jitter of the spacecraft and their sub-assemblies with the optical bench and the telescope into the interferometric length readout will be a major noise source in the LISA mission. We refer to this noise as tilt-to-length (TTL) coupling. It will be reduced directly by realignments, and the residual noise will then be subtracted in post-processing. The success of these mitigation strategies depends on an accurate computation of the TTL coupling coefficients. We present here a thorough analysis of the accuracy of the coefficient estimation under different jitter characteristics, angular readout noise levels, and gravitational wave sources. We analyze in which cases the estimates degrade using two estimators, the common least squares estimator and the instrumental variables estimator. Our investigations show that angular readout noise leads to a systematic bias of the least squares estimator, depending on the TTL coupling coefficients, jitter and readout noise level, while the instrumental variable estimator converges to an unbiased result as the data set length increases. We present an equation that predicts the estimation bias of the least squares method due to angular readout noise.