The principal applications of off-axis optical systems are to avoid obstruction of the primary aperture by secondary optical elements, instrument packages, or sensors, and to provide ready access to instrument packages or sensors at the focus.
The engineering tradeoff of an off-axis optical system is an increase in image aberrations.
There are various theoretical models for aberration in off-axis optical systems.
[1] This involves various techniques including different types of equations for ray-tracing, and a goal can be optimizing the design.
[3] This article incorporates public domain material from Federal Standard 1037C.