Misalignment-induced nodal aberration fields in two-mirror astronomical telescopes

We present the effects of misalignments on the field dependence of the third-order aberration fields of traditional, two-mirror astronomical telescopes in the context of nodal aberration theory, which we believe is the most general and extensible framework for describing and improving on-station performance. While many of the advantages of nodal aberration theory, compared to other, often power series expansion-based descriptions of misalignment effects on aberrations, become particularly important when analyzing telescopes with more than two mirrors, or in the presence of figure errors; this paper aims to provide and demonstrate the fundamental concepts needed to fully describe the state of correction of misaligned two-mirror telescopes. Importantly, it is shown that the assumption that perfect performance on axis ensures a fully aligned telescope is false, and we demonstrate that if Ritchey-Chrétien telescopes are aligned for zero coma on axis as the sole criterion, formidable misalignments will likely remain, leading to image quality degradation, particularly beyond midfield caused by astigmatism with binodal field dependence (i.e., astigmatism goes to zero at two points in the field).