Structural aberration coefficients for freeform imaging systems

Abstract

Freeform imaging systems are a subject of current interest. To aid in the design of such systems, we introduce structural aberration coefficients for plane symmetric imaging with XY-polynomial freeform surfaces that may also be tilted. Further, we extend the coefficients to systems with an arbitrary number of components and specifically provide analytical equations for two-mirror systems. Distinguishing between system configuration and structural parameters enhances clarity, which we highlight by deriving new conditions for minimum root-mean-square (RMS) spot size and minimum RMS wavefront error in aplanatic two-mirror telescopes.