Optical pupil localization method and experimental validation of active segmented mirror based on local wavefront sensitivity analysis

Segmented deployable space imaging systems represent a promising solution for future ultra-large aperture space optical systems. With the proposal of larger aperture segmented telescope designs, ultra-lightweight primary mirror (PM) segments with lower areal density have become a research hotspot. However, the lightweight structure poses more stringent challenges in maintaining a high-precision surface figure of PM segments. Active deformable PM segments with surface shape adjustment capability serve as an effective approach to address these challenges. To achieve surface figure control at the PM segments scale, accurate determination of the PM segments' surface figure error magnitude is fundamentally required. After in-orbit deployment of segmented mirror systems, deviations between the actual position and ideal position of PM segments will induce optical pupil localization errors in the system's overall pupil plane. The optical pupil localization error (OPLE) of PM segments leads to an inaccurate decoupling of wavefront errors into individual PM segments, thereby compromising the accuracy of surface figure correction. This paper proposes an active segmented mirror optical pupil localization method based on local wavefront sensitivity analysis. By utilizing the deformation capability of active optics, we establish sensitivity equations through wavefront variations within the PM segments' pupil region before and after surface shape adjustments, enabling the inverse solution for the OPLE of PM segments. The proposed method achieves micrometer-level positioning accuracy of PM segments' positional errors solely relying on focal plane information, while avoiding the introduction of additional mechanisms. Experimental validations were designed to verify the feasibility of the method.