Model-based alignment method for segmented space telescopes using extended beacon

The segmented space telescopes like James Webb Space Telescope require precise alignment of their segmented primary mirrors and secondary mirrors to achieve diffraction-limited performance. Traditional phase retrieval methods, while accurate, are computationally intensive and prone to local minima. The proposed model-based approach in this paper offers rapid convergence, low computational cost, and compatibility with extended targets. The method employs specific image-quality metrics: the second moment of image intensity for correcting SM position errors, PM segment figure errors, and tip/tilt errors; and the power spectral density at modulation transfer function sidelobe peaks for piston error detection. An end-to-end alignment procedure is introduced, comprising four sequential steps: SM alignment via multi-field balancing, segment figure error correction, segment tip/tilt error correction, and segment piston error correction. Simulations using a JWST-like optical model demonstrate the effectiveness of the method, verifying its capability to correct coupled misalignments between the SM and PM segments.