Single-field-of-view misalignment solution method based on map sensitivity matrix

As scientific demands advance, future astronomical telescopes will require larger apertures to improve precision and detection depth. However, larger apertures pose greater alignment challenges for monolithic and segmented telescopes. Accurately and efficiently solving the misalignment of each optical element has become a critical factor in determining the final imaging performance. This paper proposes a method for solving misalignment parameters by constructing a sensitivity matrix using a wavefront map of a single field of view. The method based on wavefront map sensitivity has been derived to be equivalent to the method based on the sensitivity of the infinite-order aberration coefficients. To validate the method's accuracy, simulation alignment processes are conducted for both monolithic and segmented telescopes. Simulation results demonstrate that by constructing the sensitivity matrix for a single field of view and performing three iterations, the misaligned optical system can be well-corrected. This method can significantly improve the alignment efficiency. This study provides an effective method for solving misalignments in large-aperture astronomical telescopes.