Active optical alignment of off-axis telescopes based on nodal aberration theory.

Our paper mainly separates the specific aberration contributions of third-order astigmatism and third-order coma from the total aberration fields, on the framework of the modified nodal aberration theory (NAT), for the perturbed off-axis telescope. Based on the derived aberration functions, two alignment models for the same off-axis two-mirror telescope are established and compared. Among them, one is based on third-order NAT, the other is based on fifth-order NAT. By comparison, it is found that the calculated perturbations based on fifth-order NAT are more accurate. It illustrates that third-order astigmatism and third-order coma contributed from fifth-order aberrations can't be neglected in the alignment process. Then the fifth-order NAT is used for the alignment of off-axis three-mirror telescopes. After simulation, it is found that the perturbed off-axis three-mirror telescope can be perfectly aligned as well. To further demonstrate the application of the alignment method based on fifth-order NAT (simplified as NAT method), Monte-Carlo simulations for both off-axis two-mirror telescope and off-axis three-mirror telescope are conducted in the end. Meantime, a comparison between NAT method and sensitivity table method is also conducted. It is proven that the computation accuracy of NAT method is much higher, especially in poor conditions.