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

Space-based gravitational wave detection missions impose extremely stringent requirements on the measurement precision of the laser interferometer, where tilt-to-length coupling noise emerges as a critical factor degrading performance. This paper focuses on geometric tilt-to-length noise in the test mass interferometer, conducting both theoretical modeling and experimental validation. First, based on the principles of geometrical optics, an analytical expression is derived for the optical path length difference variation induced by test mass angular jitter, clarifying the coupling mechanisms of the various system parameters to the tilt-to-length coupling. Numerical simulations demonstrate an excellent agreement between the theoretical model and simulation results. To further validate the theoretical model, an experimental system combining laser heterodyne interferometry and differential wavefront sensing technique is designed and constructed, with a fast steering mirror employed to simulate test mass angular jitter, enabling precise measurement of both the optical path and angular variations. By varying the lateral displacement dlat of the fast steering mirror, the experimental data exhibit strong consistency with the theoretical prediction of the first-order tilt-to-length coupling coefficient, with a linear fitting error as low as 1.5%. Moreover, the independence of the second-order and zero-order terms relative to dlat also aligns with the theoretical expectation. Thus, the first experimental verification of the geometric tilt-to-length coupling model is presented in this paper.