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

**Authors:** Marie-Sophie Hartig, Joshua Marmor, Daniel George, Sarah Paczkowski, Jose Sanjuan  
**arXiv:** [2410.16475](https://arxiv.org/abs/2410.16475)  
**Date:** 2024-10-21  
**Summary page:** https://www.summarizepaper.com/en/paper/2410.16475v1/

## Key points

- Study on Tilt-To-Length (TTL) Coupling in LISA mission
- Significance of spacecraft angular jitter and its coupling with optical bench and telescope
- Noise source affecting interferometric length readouts
- Importance of mitigating noise through realignments and post-processing
- Crucial role of accurately computing TTL coupling coefficients for mitigation strategies
- Use of least squares estimator and instrumental variables estimator to evaluate coefficient estimation accuracy
- Bias introduced by angular readout noise in least squares estimator, while instrumental variable estimator remains unbiased
- Presentation of equation predicting estimation bias in least squares method due to angular readout noise
- Insights provided for enhancing measurement accuracy and optimizing post-processing techniques in LISA missions
- Consideration of extreme mass ratio inspirals as astrophysical phenomena within analysis framework for addressing challenges related to TTL coupling in future space missions

## Summary

In the study "Tilt-To-Length Coupling in LISA — Uncertainty and Biases," researchers Marie-Sophie Hartig, Joshua Marmor, Daniel George, Sarah Paczkowski, and Jose Sanjuan investigate the intricate relationship between spacecraft angular jitter and their sub-assemblies with the optical bench and telescope in the context of the LISA mission. This coupling poses a significant noise source that can affect interferometric length readouts. The team highlights the importance of mitigating this noise through realignments and subtracting residual noise during post-processing. However, accurately computing TTL coupling coefficients is crucial for the success of these mitigation strategies. To address this challenge, two estimators - least squares estimator and instrumental variables estimator - are employed to evaluate coefficient estimation accuracy under varying jitter characteristics, angular readout noise levels, and gravitational wave sources. The investigations reveal that angular readout noise can introduce bias in the least squares estimator based on TTL coupling coefficients, jitter levels, and readout noise intensity. In contrast, the instrumental variable estimator remains unbiased in these scenarios. Additionally, an equation predicting estimation bias in the least squares method due to angular readout noise is presented by the researchers. By shedding light on uncertainties and biases associated with TTL coupling in LISA missions, this study provides valuable insights for enhancing measurement accuracy and optimizing post-processing techniques. Furthermore,<Organization>, by considering factors such as extreme mass ratio inspirals as astrophysical phenomena within their analysis framework,<Organization> offers a holistic perspective on addressing challenges related to tilt-to-length coupling in future space missions like LISA.