Alignment algorithm for three-mirror anastigmatic telescopes based on nodal aberration theory

For most of the alignment algorithms, alignment errors and figure errors cannot be separated due to the coupling effect among optical elements. We present an alignment algorithm for TMA telescopes on the framework of nodal aberration theory (NAT). Based on NAT, we firstly determine the axial misalignments of secondary (SM) and tertiary (TM) mirrors. Then we decouple the lateral misalignments and angular misalignments of SM and TM. Finally, we decouple the figure errors of primary mirror (PM) from the alignment errors of SM and TM. To validate the algorithm, a TMA telescope is designed for simulation. In the simulation, modulation transfer function (MTF) is chosen to evaluate the telescope before and after correction. It is found that the algorithm presented in this paper maintains high precision. In the end, a Monte Carlo simulation is conducted to further demonstrate the accuracy of the presented alignment algorithm even in poor conditions.