A unique astigmatic nodal property in misaligned Ritchey-Chrétien telescopes with misalignment coma removed

We present the aberration field response of Ritchey-Chrétien telescopes, with the aperture stop on the primary mirror, to secondary mirror misalignments. More specifically, we derive a general condition for the geometry of the binodal astigmatic aberration field for a telescope that has been aligned to remove field-constant coma. It has been observed that when the coma caused by secondary mirror misalignments is removed the astigmatic field is typically not symmetric around the periphery, but, significantly, it is always effectively zero on-axis. This observation is a manifestation of binodal astigmatism where one of the astigmatic nodes remains near the field center. Here, we show how the condition to remove field-constant coma simultaneously creates a constraint whereby one of the astigmatic nodes must remain effectively on-axis. This result points to why the alignment of a large telescope based on axial imagery is insufficient and demonstrates exactly the geometry of the remaining misalignment aberration field, which dominates the performance of the telescope, providing insights into more complete alignment approaches.