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Hubble, as well as numerous other professional telescopes, use the Ritchey–Chrétien design. What optical and instrumental advantages does this kind of telescope have for professional astronomy?

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I think the first sentence from the Wikipedia article on Ritchey–Chrétien telescopes is one of the major compelling reasons:

A Ritchey–Chrétien telescope (or RCT) is a specialized Cassegrain telescope designed to eliminate coma, thus providing a large field of view compared to a more conventional configuration.

Elimination of optical abberations is very important in the RC design. In addition to eliminating spherical abberations, which all cassegrain telescopes do, a RCT eliminates coma. This helps to maintain image quality across a larger field of view allowing for larger detectors.

In addition, it has a flat focal plane. This too is important for large field imagers since a lack of a flat focal plane means that if you focus the central area the edges will be out of focus and vice versa. This was an issue for old photographic plate systems as you would actually have to bend the glass of the plates to get the entire image in focus. Clyde Tombaugh used to tell a story about observing while looking for Pluto where he was out in the dome putting in a new photographic plate, and it shattered just after he finished applying the pressure to curve the plate into the focal plane of the telescope he was using. It was a cold night and he was afraid something more important had shattered.

The RCT design still suffers from astigmatism and field distortion as you move off-axis but it does manage to correct three of the five major abberations. So this type of telescopes is preferred for professional systems because it has a better optical image compared to other designs and allows for larger field of view.

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Indeed curved focal planes make installing modern-day CCDs something of a challenge, as they are finding while upgrading the 48" at Palomar. – Chris White Jan 7 '13 at 13:34

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