Active alignment of complex perturbed pupil-offset off-axis telescopes using the extension of nodal aberration theory

This paper presents an optical alignment strategy for complex perturbed pupil-offset off-axis reflective telescopes, based on the extension of nodal aberration theory (NAT). First, the direct expansion of the wave aberration function in the vector form for perturbed off-axis systems is given, which is especially convenient for the expansion of the corresponding higher-order terms. The inherent vector relationships between the contributions generated by the aberrations of the on-axis parent systems through pupil transformation are disclosed in detail, which is helpful to understand the aberration behavior of off-axis systems. Then, according to the inherent vector relationships, an analytical alignment model based on NAT for complex cases of perturbed off-axis telescopes is established. It can quantitatively separate the effects of misalignments and surface figure errors from the total aberration fields. The alignment model is solved by using particle swarm optimization algorithm. Then, an optical alignment example of the off-axis three-mirror anastigmatic telescope with misalignments and complex surface figure errors based on the proposed method is demonstrated. After correction, the perturbed telescope can be nearly restored to the nominal states. Finally, Monte Carlo simulations are carried out to show the effectiveness and accuracy of the proposed method.