Single-step alignment of a two-mirror telescope using sigma vectors in nodal aberration theory

We present a single-step telescope alignment method based on the sigma vectors in nodal aberration theory (NAT) for high-precision telescope systems. Field dependency investigation of aberrations is crucial for precise alignment campaigns of modern, complex telescope systems. Since NAT is a surface-based theory, the contribution of a specific surface to the net aberration field is distinguishable and identifiable. Sigma vectors provide the foundation for a deterministic and precise telescope alignment. They successfully describe and quantify aberration field centers for aberrations in misaligned optical systems. Here, we demonstrate the use of sigma vectors for a deterministic, accurate, and fast telescope alignment on a 490 mm entrance pupil diameter Cassegrain telescope. From an arbitrary state of misalignment, the telescope is aligned to within 4 microns of decenter and 0.001 deg of tilt error by a single-step secondary mirror misalignment correction with a five-axis stage. (c) 2025 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.