Experimental Demonstration of Geometric Tilt-to-Length Noise Model in Test Mass Interferometer

Area of Science:

• Astrophysics and Space Science
• Optical Physics and Interferometry

Background:

• Space-based gravitational wave detectors require ultra-precise laser interferometry.
• Tilt-to-length coupling noise is a significant performance-limiting factor in these systems.

Purpose of the Study:

• To develop and experimentally validate a theoretical model for geometric tilt-to-length noise in test mass interferometers.
• To understand the coupling mechanisms of system parameters to tilt-to-length noise.

Main Methods:

• Derived an analytical expression for optical path length variation due to test mass angular jitter using geometrical optics.
• Performed numerical simulations to compare with the theoretical model.
• Designed and constructed an experimental system using laser heterodyne interferometry and differential wavefront sensing, simulating angular jitter with a fast steering mirror.

Main Results:

• The theoretical model showed excellent agreement with numerical simulations.
• Experimental data validated the theoretical prediction of the first-order tilt-to-length coupling coefficient with a low linear fitting error of 1.5%.
• Observed independence of second-order and zero-order terms from lateral displacement, consistent with theoretical expectations.

Conclusions:

• Presented the first experimental verification of the geometric tilt-to-length coupling model.
• The validated model is essential for mitigating noise and enhancing measurement precision in future gravitational wave missions.