Global alignment of a segmented space telescope based on the stitched sensitivity matrix

As the demand for astronomical observations continues to grow, the aperture of telescopes is increasing, with segmented primary mirrors becoming a prevailing trend. However, segmented telescopes require a series of complex steps to ensure precise alignment between the individual segments, achieving diffraction-limited imaging performance. Among these steps, global alignment mainly focuses on placing the secondary mirror (SM) and primary mirror (PM) in the best possible positions, thus laying the foundation for subsequent alignments. This paper simulates the global alignment process using a stitched sensitivity matrix model for the segmented telescope to calculate the misalignments of optical elements. The specific formulation of the stitched sensitivity matrix model and the segment tilt misalignment calculation model has been explicitly derived in this paper. Furthermore, to the best of our knowledge, the sensitivity matrix is constructed based on the first nine fitted Zernike coefficients. Incorporating the piston and tip/tilt terms introduces additional constraints to the matrix, thereby improving the solution accuracy. During the alignment process, the segment tilt misalignment calculation model is employed to constrain the positions of the spots, ensuring their stability. These combined constraints collectively guarantee that the spot positions remain fixed throughout the global alignment, while enabling high-precision wavefront correction. The alignment process for global alignment is described in detail, and the correction results are analyzed under no error and measurement error conditions. Monte Carlo simulations indicate that the proposed method is effective in solving misalignments during global alignment. The research presented in this paper provides valuable insights for the development of large-aperture segmented telescopes.