Alignment analysis of four-mirror spherical aberration correctors

Telescopes use primary mirrors with spherical shape to reduce the cost of the mirror fabrication and to allow the mirror to operate at fixed elevation. These advantages become significant as the size of the telescope grows. However, the disadvantage of the spherical primary is a large amount of spherical aberration which needs to be corrected. We present an analysis of alignment issues for four-mirror spherical aberration correctors for spherical primary mirror telescopes. The sensitivities of image quality across the field (in terms of spot size) to mirror misalignments are found. These sensitivities are useful in choosing the tolerances for the mechanical assembly holding the corrector. A singular value decomposition of the sensitivity matrix shows the combination of element motions that result in orthogonal aberration modes. Studying these combinations of modes and misalignments can lead to a conceptual understanding of the system, which aids in the initial and operational alignment of the spherical aberration corrector.