On the Non-Paraxial Diffraction of the Set of All Possible Stigmatic Pairs of Mirrors

We present a comprehensive vector diffraction analysis of stigmatic pairs of mirrors derived from closed-form equations that describe all possible aplanatic two-mirror systems. Using a vectorial generalized version of Richards-Wolf integral, we evaluate the focal field distributions, accounting for polarization effects, high numerical apertures, and deviations from the scalar approximation. Numerical simulations based on the derived mirror profiles demonstrate diffraction-limited performance free of spherical aberration, with agreement to geometric ray-tracing results.