Analysis and verification on multi-DOF optical path sensitivity of an off-axis four-mirror telescope

The structural stability of the optical system in an off-axis four-mirror space telescope is critical to maintaining its optical performance and avoiding potential system failure. Structural deformation can cause variations of the optical path within the telescope, with different degrees of freedom (DOFs) of mirror displacement exerting varying degrees of influence on the optical path. This study develops a model to analyze the impact of multi-DOF rigid body displacements of mirrors on the optical path and predicts the sensitivity of each DOF. The findings are validated through simulations using Zemax, identifying the sensitive DOFs, which are further confirmed through experiments. The results reveal that the effects of displacements vary across different mirrors and DOFs. For instance, in the primary mirror, translation along the Z-axis, translation along the Y-axis, and rotation around the X-axis have the most significant impacts on the optical path and are identified as sensitive directions. In the rotation direction around the X axis, the optical path variation caused by the primary mirror's displacement is significantly greater than that of the secondary mirror. These sensitive directions should receive special attention during the design and testing phases of the telescope. This research provides essential technical support and methodological references for ultra-high-precision multi-DOF structural stability measurements in gravitational wave telescopes. It also offers valuable guidance for the design of ultra-stable structures.