Aberrational interactions between axial and lateral misalignments in pupil-offset off-axis two-mirror astronomical telescopes.

Abstract

Due to the absence of rotational symmetry, the effects of axial and lateral misalignments couple tightly together, which leads to special aberration field characteristics. This paper will present an in-depth and systematic discussion on the interactions between the effects of axial and lateral misalignments in pupil-offset off-axis two-mirror astronomical telescopes. The aberration function of this class of telescopes in the presence of axial and lateral misalignments is derived. The specific expressions of two dominant non-rotationally symmetric aberrations, i.e., astigmatism and coma, are obtained and the aberration field characteristics are discussed. Importantly, it is shown that under certain conditions, a node will arise in the field of view for these two kinds of aberrations. Then the aberrational compensation mechanisms between axial and lateral misalignments are quantitatively explicated, and it is shown that the non-rotationally symmetric aberrations induced by axial misalignments can well be compensated by lateral misalignments. However, we also find that in this process, the defocus aberration induced by these two kinds of misalignments will accumulate (rather than cancel out). Therefore, in practice, it is better to separate these two kinds of misalignment. Finally, we propose a simple method to decouple axial misalignments from lateral misalignments with wavefront measurement at one field position. Most of this work can be extended to other kind of pupil-offset off-axis astronomical telescopes, such as off-axis three-mirror anastigmatic telescopes.