# Ritchey–Chrétien telescope

George Ritchey's 24-inch (0.6 m) reflecting telescope, the first RCT to be built, later on display at the Chabot Space and Science Center in 2004

A Ritchey–Chrétien telescope (RCT or simply RC) is a specialized variant of the Cassegrain telescope that has a hyperbolic primary mirror and a hyperbolic secondary mirror designed to eliminate off-axis optical errors (coma). The RCT has a wider field of view free of optical errors compared to a more traditional reflecting telescope configuration. Since the mid 20th century, a majority of large professional research telescopes have been Ritchey–Chrétien configurations; some well-known examples are the Hubble Space Telescope, the Keck telescopes and the ESO Very Large Telescope.

## History

The Ritchey–Chrétien telescope was invented in the early 1910s by American astronomer George Willis Ritchey and French astronomer Henri Chrétien. Ritchey constructed the first successful RCT, which had a diameter aperture of 60 cm (24 in) in 1927 (e.g. Ritchey 24-inch reflector). The second RCT was a 102 cm (40 in) instrument constructed by Ritchey for the United States Naval Observatory; that telescope is still in operation at the Naval Observatory Flagstaff Station.

The basic Ritchey–Chrétien two-surface design is free of third-order coma and spherical aberration,[1] although it does suffer from fifth-order coma, severe large-angle astigmatism, and comparatively severe field curvature.[2] The remaining aberrations of the basic design may be improved with the addition of smaller optical elements near the focal plane.[3][4] When focused midway between the sagittal and tangential focusing planes, stars are imaged as circles, making the RCT well suited for wide field and photographic observations. As with the other Cassegrain-configuration reflectors, the RCT has a very short optical tube assembly and compact design for a given focal length. The RCT offers good off-axis optical performance, but the Ritchey–Chrétien configuration is most commonly found on high-performance professional telescopes.

A telescope with only one curved mirror, such as a Newtonian telescope, will always have aberrations. If the mirror is spherical, it will suffer from spherical aberration. If the mirror is made parabolic, to correct the spherical aberration, then it must necessarily suffer from coma and astigmatism. With two non-spherical mirrors, such as the Ritchey–Chrétien telescope, coma can be eliminated as well. This allows a larger useful field of view. However, such designs still suffer from astigmatism. This too can be cancelled by including a third curved optical element. When this element is a mirror, the result is a three-mirror anastigmat. Alternatively, a Ritchey-Chrétien may use one or several low-power lenses in front of the focal plane as a field-corrector to correct astigmatism and flatten the focal surface, as for example the SDSS telescope and the VISTA telescope; this can allow a field-of-view up to around 3 degrees diameter.

(Although the Schmidt camera can deliver even wider fields up to about 7 degrees, the Schmidt requires a full-aperture corrector plate which restricts it to apertures below 1.2 metres, while a Ritchey-Chrétien can be much larger).

In practice, each of these designs may also include any number of flat fold mirrors, used to bend the optical path into more convenient configurations.

## Mirror parameters

Diagram of a Ritchey-Chrétien reflector telescope

The radii of curvature of the primary and secondary mirrors, respectively, in a two-mirror Cassegrain configuration are

${\displaystyle R_{1}=-{\frac {2DF}{F-B}}}$

and

${\displaystyle R_{2}=-{\frac {2DB}{F-B-D}}}$

where

• ${\displaystyle F}$ is the effective focal length of the system,
• ${\displaystyle B}$ is the back focal length (the distance from the secondary to the focus), and
• ${\displaystyle D}$ is the distance between the two mirrors.

If, instead of ${\displaystyle B}$ and ${\displaystyle D}$, the known quantities are the focal length of the primary mirror, ${\displaystyle f_{1}}$, and the distance to the focus behind the primary mirror, ${\displaystyle b}$, then ${\displaystyle D=f_{1}(F-b)/(F+f_{1})}$ and ${\displaystyle B=D+b}$.

For a Ritchey–Chrétien system, the conic constants ${\displaystyle K_{1}}$ and ${\displaystyle K_{2}}$ of the two mirrors are chosen so as to eliminate third-order spherical aberration and coma; the solution is

${\displaystyle K_{1}=-1-{\frac {2}{M^{3}}}\cdot {\frac {B}{D}}}$

and

${\displaystyle K_{2}=-1-{\frac {2}{(M-1)^{3}}}\left[M(2M-1)+{\frac {B}{D}}\right]}$

where ${\displaystyle M=F/f_{1}=(F-B)/D}$ is the secondary magnification.[5] Note that ${\displaystyle K_{1}}$ and ${\displaystyle K_{2}}$ are less than ${\displaystyle -1}$ (since ${\displaystyle M>1}$), so both mirrors are hyperbolic. (The primary mirror is typically quite close to being parabolic, however.)

The hyperbolic curvatures are difficult to test, especially with equipment typically available to amateur telescope makers or laboratory-scale fabricators; thus, older telescope layouts predominate in these applications. However, professional optics fabricators and large research groups test their mirrors with interferometers. A Ritchey–Chrétien then requires minimal additional equipment, typically a small optical device called a null corrector that makes the hyperbolic primary look spherical for the interferometric test. On the Hubble Space Telescope, this device was built incorrectly (a reflection from an un-intended surface leading to an incorrect measurement of lens position) leading to the error in the Hubble primary mirror.[6] Incorrect null correctors have led to other mirror fabrication errors as well, such as in the New Technology Telescope.

## Examples of large Ritchey–Chrétien telescopes

Ritchey intended the 100-inch Mount Wilson Hooker telescope (1917) and the 200-inch (5 m) Hale Telescope to be RCTs. His designs would have provided sharper images over a larger usable field of view compared to the parabolic designs actually used. However, Ritchey and Hale had a falling-out. With the 100-inch project already late and over budget, Hale refused to adopt the new design, with its hard-to-test curvatures, and Ritchey left the project. Both projects were then built with traditional optics. Since then, advances in optical measurement[7] and fabrication[8] have allowed the RCT design to take over - the Hale telescope, dedicated in 1948, turned out to be the last world-leading telescope to have a parabolic primary mirror.[9]

16 in (41 cm) RC Optical Systems truss telescope, part of the PROMPT Telescopes array