Six-degree-of-freedom coupling analysis for the test mass interferometer in spaceborne gravitational wave detection

Abstract In spaceborne gravitational wave detection, tilt-to-length (TTL) coupling in the test mass (TM) interferometer can compromise the measurement accuracy and thereby affect the precision of the spacecraft’s position control, ultimately impairing the system’s overall performance in displacement measurement. This paper investigates the six-degree-of-freedom (six-DoF) geometric TTL coupling in the TM interferometer. Since coupling terms involving three or more DoFs are negligible as higher-order infinitesimals, the overall six-DoF coupling can be decomposed into a superposition of single- and dual-DoF coupling components, whose analytical expressions are derived in detail. Based on the six-DoF model, simulation results demonstrate that the angular motions θ x and θ y must be precisely controlled to achieve the required displacement sensitivity, whereas the constraints on the other three non-sensitive DoFs ( Δ x , Δ y , and θ z ) can be moderately relaxed. Furthermore, the effects of non-ideal factors, including large-scale surface shape error, dihedral angle error, and laser pointing error, are also systematically examined. These results may provide a theoretical reference for future ground-based studies and in-orbit verifications of the TM interferometer.