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Two-mirror telescopes possess an agreeable tradeoff between performance and complexity that suits the needs of many scientific tasks, and recent developments in manufacturing technology have enabled unobscured two-mirror designs with freeform surfaces. We illustrate how structural aberration coefficients reveal the fundamental aberration characteristics of such systems and provide a summary table of general solutions that prescribe freeform surface shapes and tilts. Two unobscured design forms with remarkable aberration cancellation, inspired by well-known on-axis anastigmatic solutions, are presented. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]