Alignment algorithm for reflective telescopes based on nodal aberration theory and the real-ray-tracing method

Nodal aberration theory (NAT) serves as a potent tool for investigating the misalignment of reflective telescopes and is commonly employed in alignment algorithms. A vital parameter in NAT is the sigma vector. The traditional method of calculating this vector is based on paraxial ray tracing, which is relatively complicated and faces the challenge in extending NAT to multi-mirror reflective telescopes. A method for calculating the sigma vector based on real-ray-tracing data provides a convenient solution for locating the aberration field center in a misaligned system. In this paper, we propose an aberration field simulation procedure and alignment algorithm for reflective telescopes. The proposed method combines NAT with real-ray-tracing data and a numerical iteration algorithm that overcomes the limitations of traditional methods, successfully extending this approach to address misalignment issues in multi-mirror systems. The algorithm was applied to a co-axis four-mirror reflective telescope with misalignments, demonstrating its capability to address alignment challenges in multi-mirror systems while significantly reducing computational complexity. The simulation results validate the feasibility of the proposed method, offering flexibility for integrating alignment algorithms with ray data from commercial software or other ray-tracing methods.