Progress in Aberration Theory for Freeform Off-Axis Mirror Systems

In this invited paper, a simple and efficient matrix formalism is presented for computing aberrations in plane-parallel freeform mirror systems. The approach is flexible and can be easily generalized to arbitrary aberration orders and/or to systems with different symmetries. As an illustration, we derive analytical expressions for all second- and third-order image and pupil aberrations in plane-parallel confocal N-mirror systems. Some design examples are also presented and discussed.