We present a general optical design survey of two-mirror unobstructed plane-symmetric freeform (FF) telescopes to provide a standardized framework and reference for further developments in the field of FF optics. We find that there are fundamentally two main design forms: those that use a positive tilt of the secondary and those that employ a negative rotation to achieve the unobstructed condition. Utilizing this survey, results can be categorized into simple groups of two-mirror unobstructed FF telescopes, analogous to the distinction between a Gregorian-type telescope and Cassegrain-type telescope. Allowing FF surfaces in optical design can enable more compact telescopes while potentially improving the image quality and allowing wider fields of view (FOVs). We define a FF optic as a nonrotationally symmetric mirror or lens, typically with large departures from a best-fit spherical surface (many microns or even millimeters). New manufacturing and testing methods have enabled the production of these types of surfaces. The telescopes we present maintain a 4∶1 aspect ratio of the FOV and utilize X-Y polynomials for mirror surface description. We impose a plane symmetric constraint on the system and an accessible entrance pupil. We generate charts documenting the relationship between FOV and F/# for the presented optical design forms. We also compare our results to a baseline rotationally symmetric system. These results provide a general method of evaluating baseline designs for two-mirror unobstructed FF telescopes.
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