A Cassegrain telescope in which both the primary and secondary mirrors have hyperboloidal surfaces. This has the advantage over the standard Cassegrain system of giving images free from coma and spherical aberration over wide fields. Typically the primary mirror has a focal ratio of about 2.5, giving a final focal ratio of about 8. The short tube length and good optical performance make the Ritchey–Chrétien very popular for modern large instruments; the Keck Telescopes and the Very Large Telescope are of this design. It is named after its co-inventors, G. W. Ritchey and the French optician Henri Chrétien (1879–1956).