Approximate model for the coupling of far-field wavefront errors and jitter in space-based gravitational wave laser interferometry

TL;DR

This paper develops an approximate noise model for space-based gravitational wave detectors that accounts for wavefront errors and jitter, aiding system simulation and optimization.

Contribution

It introduces a comprehensive, efficient model based on Nijboer-Zernike diffraction theory to analyze coupling noise in laser interferometry systems.

Findings

Derived an approximate expression for far-field WFE with minimal error.

Identified that correcting certain optical aberrations can worsen WFE.

Provided insights for active suppression of specific Zernike modes.

Abstract

Space-based gravitational wave observatories, such as LISA, Taiji, and TianQin, employ long-baseline laser interferometry, necessitating displacement measurement sensitivity at 1 pm/$\sqrt{Hz}$ level. A significant challenge in achieving this precision is the coupling noise arising from far-field wavefront errors (WFE) and laser pointing jitter. This paper presents a comprehensive noise model that incorporates three critical factors: transmitted WFE, static pointing angle, and laser beam jitter. Utilizing the Nijboer-Zernike diffraction theory, we derive an approximate expression for far-field WFE, ensuring minimal error and efficient computational performance. The approximate expression has convincing physical interpretability and reveals how various Zernike aberrations and their coupling impact far-field WFE. Furthermore, the study identifies that correcting optical axis deviations induced by $Z_3^{\pm1}$ through beam tilt exacerbates far-field WFE, underscoring the necessity for active suppression of $Z_3^{\pm1}$. The proposed model facilitates detailed system simulations of the laser link, evaluates Tilt-to-Length (TTL) noise, and offers theoretical insights for system optimization.