Aberrations of plane-symmetrical mirror systems with freeform surfaces. Part I: generalized ray-tracing equations.

The aberrations of reflective optical systems with one plane of symmetry are investigated in the most general case, with freeform surfaces and possibly different locations of the tangential and sagittal object and image. In this first paper in a series of two, we establish generalized ray-tracing equations including transverse aberrations up to the third order in ray coordinates. The ray-tracing treatment allows us to overcome difficulties linked to the non-existence of a suitable astigmatic wavefront reference. The obtained expressions can describe multi-mirror systems and include all induced aberration terms. As an illustration, a simple freeform off-axis mirror is analyzed.