Design method of large-aperture tilted three-mirror astronomical telescopes with boresight adjustment based on the nodal aberration theory

This paper proposes an analytical design method for tilted three-mirror astronomical telescopes with boresight adjustment. Based on the local coordinate system (LCS) paraxial ray trace and nodal aberration theory (NAT), combined with Seidel coefficient expressions, we derive analytical formulas for the induced linear with field astigmatism and image plane displacement (boresight error) induced by the tilt and decenter of the primary mirror (PM), secondary mirror (SM), and tertiary mirror (TM). On this basis, the design method is introduced. This design method simultaneously considers minimizing the induced coma and astigmatism along with boresight adjustment, enabling the generation of initial tilted three-mirror configurations that either eliminate obscuration or achieve optimal structural compactness. To demonstrate the feasibility of the method, we conduct tilted designs for two three-mirror anastigmat (TMA) systems as examples, yielding several promising tilted three-mirror configurations. The design results validate the effectiveness of this method.