Aberration fields of off-axis two-mirror astronomical telescopes induced by lateral misalignments

This paper presents a systematic and in-depth discussion for the aberration fields of off-axis two-mirror astronomical telescopes with an offset pupil that is induced by lateral misalignment. Based on the framework of nodal aberration theory and a system level pupil coordinate transformation, the aberration function for misaligned off-axis telescopes is derived. Some general descriptions for the misalignment-induced aberrations are presented. The specific astigmatic and coma aberration field characteristics in off-axis two-mirror telescopes are then discussed. The precision of the presented aberration expressions is demonstrated. The discrepancies between the ray tracing data and aberration expressions are explicated. Then the inherent relationships between the astigmatism and coma aberration fields are revealed and explicated. Based on this knowledge, some quantitative discussions are further presented for determining the misalignments used to compensate for the effects of primary mirror astigmatic figure errors as well as separating these two effects when coupled. Other effects of lateral misalignments are also presented, especially the field-constant focal shift, which is only sensitive to the lateral misalignments in the symmetry plane of the nominal off-axis system. A quantitative discussion is also presented which explains the reason why trefoil aberration in off-axis telescopes is more sensitive to lateral misalignments. Most of the results presented in this paper can be extended to the other off-axis astronomical telescopes with more freedoms.