Nonrotationally symmetric aberrations of off-axis two-mirror astronomical telescopes induced by axial misalignments.

In unobscured off-axis astronomical telescopes with an offset pupil, the effects of axial misalignments are very different from those in on-axis ones. Specifically, a series of nonrotationally symmetric aberrations with characteristic field dependence will be induced by axial misalignments. This paper takes off-axis two-mirror astronomical telescopes as an example to discuss the field characteristics of several important nonrotationally symmetric aberrations (including astigmatism, coma, and trefoil aberration) induced by axial misalignments in off-axis astronomical telescopes. The expressions of these aberrations are derived under some approximations. The accuracy of the proposed expressions is demonstrated. The specific field characteristics of these aberrations are presented and explicated. It is shown that the effects of axial misalignments bear strong similarities to the effects of the lateral misalignments in the symmetry plane of the off-axis system. On the other hand, the inherent relationships between astigmatism and coma induced by axial misalignments are further revealed, which are different from those induced by lateral misalignments. This fact presents the possibility of separating the effects of axial misalignments and lateral misalignments. Most of this work can be extended to other off-axis astronomical telescopes with more freedom.