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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.

In a classical Cassegrain reflector, a concave parabolic primary sends light toward an intermediate focus, but a convex hyperbolic secondary intercepts it before it reaches that focus. The secondary returns the beam through a central hole in the primary to a focal plane behind the primary. The two relevant foci of the secondary’s hyperbola are the primary’s would-be focus and the final focus.

The secondary magnifies the effective focal length, giving a compact tube and convenient rear-mounted instruments. The classical conics correct on-axis spherical aberration, but not the off-axis coma, astigmatism or field curvature. There is secondary obscuration, diffraction from its supports, and sensitivity to mirror alignment. A long effective focal length is useful for a small angular image scale per detector pixel, but yields a small field for a fixed detector size.