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A Gregorian telescope is a reflector telescope with a concave ellipsoid secondary mirror, a feature of a 17th-century telescope-design by James Gregory, who specified a parabolic primary mirror with a hole in the center such that a focal plane was formed behind the primary. An "unused" focal plane within the light path existed between the primary and secondary. The telescope produced an un-reversed image, and a small such telescope could be used much like a small refracting telescope. At the time of the design, its aspheric mirrors were not easily manufactured.
The adjective Gregorian is now used to indicate use of a concave ellipsoid secondary (as opposed to Cassegrain for use of a convex hyperboloid secondary) and is used even if the primary is spherical. Gregorian variants put the (second) focal plane either behind a hole in the primary (like the original design), or in front of the primary, or to the side of the incoming light path, reflected sideways by a tertiary fold mirror in the manner of a Newtonian telescope's secondary. Some radio telescopes and other radio antennas use the Gregorian ellipsoid secondary, including off-axis telescopes, that have the primary reflector forming a portion of the sphere or paraboloid to one side of the optical axis. Example research astronomical telescopes: