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The Ritchey–Chrétien reflector follows the same folded path as a Cassegrain reflector, but both the concave primary and convex secondary are hyperbolic. Their conic constants and separation are chosen to cancel third-order spherical aberration and coma. The focal plane is behind the perforated primary.

The absence of third-order coma gives a much more useful wide field than a classical Cassegrain reflector, making this design attractive for research imaging. It retains astigmatism and field curvature, so a large flat detector generally needs corrective optics; higher-order optical aberrations are not all removed. Both aspheric mirrors are more demanding to manufacture and align, and the usual secondary obstruction remains. The sketch illustrates the beam routing and mirror types; its conics are not an optimized aplanatic prescription.

A Gregorian telescope has a concave parabolic primary and a concave ellipsoidal secondary. Unlike the Cassegrain reflector, the secondary is beyond the primary focus: the rays cross that focus before reaching it. The two foci of the secondary’s ellipse are the intermediate focus and final rear focus, so the reflected rays return through the primary hole to the detector.

The real intermediate focus permits a field stop to reject unwanted light, and the two image inversions give an erect image. The rear focus is convenient and the effective focal length can be large. The secondary beyond prime focus makes the tube longer than the corresponding Cassegrain reflector, often with a larger secondary obstruction. The classical design retains off-axis coma, astigmatism and field curvature, and needs careful alignment.