View source for Ritchey–Chrétien telescope

{{Short description|Specialized Cassegrain telescope}}
[[File:RitcheyTelescope.jpg|thumb|right|George Willis Ritchey's original 24-inch (0.6 m) reflecting telescope with a parabolic mirror and two foci: Newtonian and Cassegrain. Part of the Smithsonian's collection, it has been on loan to the Chabot Space and Science Center since 2004.]]

A '''Ritchey–Chrétien telescope''' ('''RCT''' or simply '''RC''') is a specialized variant of the [[Cassegrain telescope]] that has a [[hyperboloid|hyperbolic]] [[primary mirror]] and a hyperbolic [[secondary mirror]] designed to eliminate off-axis optical errors ([[Coma (optics)|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==
[[File:NOFS 40inch03.jpg|thumb|right|The 40-inch (1.0 m) Ritchey at [[United States Naval Observatory Flagstaff Station]].]]

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 an aperture diameter of {{convert|60|cm|in|abbr=on}} in 1927 (Ritchey 24-inch reflector). The second RCT was a {{convert|102|cm|in|abbr=on}} instrument constructed by Ritchey for the [[United States Naval Observatory]]; that telescope is still in operation at the [[United States Naval Observatory Flagstaff Station|Naval Observatory Flagstaff Station]].

==Design==
As with the other Cassegrain-configuration reflectors, the Ritchey–Chrétien telescope (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 its mirrors require sophisticated techniques to manufacture and test.  Hence the Ritchey–Chrétien configuration is most commonly found on high-performance professional telescopes.

===Two-mirror foundation===
A telescope with only one curved mirror, such as a [[Newtonian telescope]], will always have aberrations. If the mirror is spherical, it will suffer primarily from [[spherical aberration]]. If the mirror is made parabolic, to correct the spherical aberration, then it still suffers from [[coma (optics)|coma]] and [[Astigmatism (optical systems)|astigmatism]], since there are no additional design parameters one can vary to eliminate them. With two non-spherical mirrors, such as the Ritchey–Chrétien telescope, coma can be eliminated as well, by making the two mirrors' contribution to total coma cancel. This allows a larger useful field of view. However, such designs still suffer from astigmatism.

The basic Ritchey–Chrétien two-surface design is free of third-order [[coma (optics)|coma]] and [[spherical aberration]].<ref name="Sacek1">
{{cite web
 |last=Sacek |first=Vladimir
 |date=14 July 2006
 |title=Classical and aplanatic two-mirror systems
 |series=Notes on amateur telescope optics
 |website=telescope-optics.net
 |url=http://www.telescope-optics.net/classical_and_aplanatic.htm
 |access-date=2010-04-24
}}
</ref> However, the two-surface design does suffer from fifth-order coma, severe large-angle [[Astigmatism (optical systems)|astigmatism]], and comparatively severe [[Field curvature#Curvature of the field of the image|field curvature]].<ref name="Rutten67">
{{cite book
 |last1=Rutten |first1=Harrie
 |last2=van Venrooij |first2=Martin
 |year=2002
 |title=Telescope Optics
 |page=67
 |publisher=Willmann-Bell
 |isbn=0-943396-18-2
}}
</ref>

===Further corrections by a third element===
When focused midway between the sagittal and tangential focusing planes, stars appear as circles, making the Ritchey–Chrétien well suited for wide field and photographic observations.
The remaining aberrations of the two-element basic design may be improved with the addition of smaller optical elements near the focal plane.<ref>
{{cite journal
 |first1=I.S. |last1=Bowen 
 |first2=A.H. |last2=Vaughan
 |year=1973
 |title=The optical design of the 40&nbsp;in. telescope and of the Irenee DuPont telescope at Las&nbsp;Campanas Observatory, Chile
 |journal=Applied Optics
 |volume=12  |issue=77  |pages=1430–1435
 |bibcode=1973ApOpt..12.1430B
 |doi=10.1364/AO.12.001430
 |pmid=20125543 
 |url=https://www.osapublishing.org/ao/abstract.cfm?uri=ao-12-7-1430
}}
</ref><ref>
{{cite journal
 |last1=Harmer |first1=C.F.W.
 |last2=Wynne  |first2=C.G.   |author2-link=Charles Gorrie Wynne
 |date=October 1976
 |title=A simple wide-field Cassegrain telescope
 |journal=[[Monthly Notices of the Royal Astronomical Society]]
 |volume=177  |pages=25–30
 |doi=10.1093/mnras/177.1.25P  |bibcode=1976MNRAS.177P..25H
 |url=http://adsabs.harvard.edu/full/1976MNRAS.177P..25H
 |access-date=29 August 2017
|doi-access=free
 }}
</ref> 

Astigmatism 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 RCT 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 [[Sloan Digital Sky Survey|SDSS]] telescope and the [[VISTA (telescope)|VISTA telescope]]; this can allow a field-of-view up to around 3° diameter.

The [[Schmidt camera]] can deliver even wider fields up to about 7°.  However, the Schmidt requires a full-aperture corrector plate, which restricts it to apertures below 1.2&nbsp;meters, while a Ritchey–Chrétien can be much larger. Other telescope designs with front-correcting elements are not limited by the practical problems of making a multiply-curved Schmidt corrector plate, such as the [[Lurie–Houghton telescope|Lurie–Houghton design]].

===Aperture obstruction===
In a Ritchey–Chrétien design, as in most Cassegrain systems, the secondary mirror blocks a central portion of the aperture. This ring-shaped entrance aperture significantly reduces a portion of the [[modulation transfer function]] (MTF) over a range of low spatial frequencies, compared to a full-aperture design such as a refractor.<ref>
{{cite web
 |url=http://www.telescope-optics.net/obstruction.htm
 |title=Effects of the aperture obstruction
}}
</ref> This MTF notch has the effect of lowering image contrast when imaging broad features. In addition, the support for the secondary (the spider) may introduce diffraction spikes in images.

===Mirrors===
[[File:Diagram Reflector RitcheyChretien.svg|thumb|Diagram of a Ritchey–Chrétien reflector telescope]]

The [[radius of curvature (optics)|radii of curvature]] of the primary and secondary mirrors, respectively, in a two-mirror Cassegrain configuration are:

:<math>R_1 = -\frac{2DF}{F - B} = -\frac{2F}{M}</math>
and

:<math>R_2 = -\frac{2DB}{F - B - D} = -\frac{2B}{M-1}</math>,

where
* <math>F</math> is the effective [[focal length]] of the system,
* <math>B</math> is the back focal length (the distance from the secondary to the focus),
* <math>D</math> is the distance between the two mirrors and
* <math>M = (F - B)/D</math> is the secondary magnification.<ref>
{{cite book
 |last=Smith |first=Warren J.
 |year=2008
 |title=Modern Optical Engineering
 |edition=4th |pages=508–510
 |publisher=[[McGraw-Hill Professional]]
 |isbn=978-0-07-147687-4
}}
</ref>

If, instead of <math>B</math> and <math>D</math>, the known quantities are the focal length of the primary mirror, <math>f_1</math>, and the distance to the focus behind the primary mirror, <math>b</math>, then <math>D = f_1(F - b)/(F + f_1)</math> and <math>B = D + b</math>.

For a Ritchey–Chrétien system, the [[conic constant]]s <math>K_1</math> and <math>K_2</math> of the two mirrors are chosen so as to eliminate third-order spherical aberration and coma; the solution is:

:<math>K_1 = -1 - \frac{2}{M^3}\cdot\frac{B}{D}</math>
and
:<math>K_2 = -1 - \frac{2}{(M - 1)^3}\left[M(2M - 1) + \frac{B}{D}\right]</math>.

Note that <math>K_1</math> and <math>K_2</math> are less than <math>-1</math> (since <math>M>1</math>), 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 [[interferometer]]s. 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.<ref>
{{cite report
 |last1=Allen |first1=Lew
 |display-authors=etal
 |year=1990
 |title=The Hubble Space Telescope Optical Systems Failure Report
 |publisher=[[NASA]]
 |id=NASA-TM-103443
 |url=https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19910003124_1991003124.pdf
}}
</ref>

Incorrect null correctors have led to other mirror fabrication errors as well, such as in the [[New Technology Telescope]].

===Additional flat mirrors===
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. This article only discusses the mirrors required for forming an image, not those for placing it in a convenient location.

==Examples of large Ritchey–Chrétien telescopes==
Ritchey intended the 100-inch [[Mount Wilson Observatory#Hooker Telescope|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<ref>{{Cite journal|title=Advanced Techniques for Measuring Primary Mirrors for Astronomical Telescopes|author= Burge, J.H.|date=1993|publisher=Ph.D. Thesis, University of Arizona |url=http://www.loft.optics.arizona.edu/documents/journal_articles/1993_James_Burge.pdf}}</ref> and fabrication<ref>{{cite book|title=Reflecting Telescope Optics I. Basic Design Theory and its Historical Development|author=Wilson, R.N.|publisher=Springer-Verlag: Berlin, Heidelberg, New York|volume=1|date=1996|bibcode=1996rtob.book.....W}} P. 454</ref> 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.<ref>{{cite book|title=An acre of glass: a history and forecast of the telescope|author=Zirker, J.B.|date=2005  |publisher=Johns Hopkins Univ Press}}, p. 317.</ref>

[[File:Prompt.jpg|thumb|right|A 41 cm [[RC Optical Systems]] truss telescope, part of the [[PROMPT Telescopes]] array.]]

* The 10.4 m [[Gran Telescopio Canarias]] at [[Roque de los Muchachos Observatory]] on [[La Palma]], [[Canary Islands]], ([[Spain]]).
* The two 10.0 m telescopes of the [[Keck telescope|Keck Observatory]] at [[Mauna Kea Observatory]], ([[United States]]).
* The four 8.2 m telescopes comprising the [[Very Large Telescope]], ([[Chile]]).
* The 8.2 m [[Subaru (telescope)|Subaru telescope]] at [[Mauna Kea Observatory]], ([[United States]]).
* The two 8.0 m telescopes comprising the [[Gemini Observatory]] at [[Mauna Kea Observatory]], ([[United States]]) and [[Chile]].
* The 4.1 m [[VISTA (telescope)|Visible and Infrared Survey Telescope for Astronomy]] at the [[Paranal Observatory]], ([[Chile]]).
* The 4.1 m [[Southern Astrophysical Research Telescope]] at [[Cerro Pachón]], ([[Chile]]).
* The 4.0 m [[Mayall Telescope]] at [[Kitt Peak National Observatory]], ([[United States]]).
* The 4.0 m [[Blanco telescope]] at the [[Cerro Tololo Inter-American Observatory]], ([[Chile]]).
* The 3.94 m telescope at [[Eastern Anatolia Observatory|Eastern Anatolia Observatory (DAG)]] in [[Erzurum]], [[Turkey]].
* The 3.9 m [[Anglo-Australian Telescope]] at [[Siding Spring Observatory]], ([[Australia]]).
* The [[3.6 m Devasthal Optical Telescope]] of [[Aryabhatta Research Institute of Observational Sciences]], Nainital, ([[India]]).
* The 3.58 m [[Telescopio Nazionale Galileo]] at [[Roque de los Muchachos Observatory]] on [[La Palma]], [[Canary Islands]], ([[Spain]]).
* The 3.58 m [[New Technology Telescope]] at the [[European Southern Observatory]], ([[Chile]]).
* The 3.5 m ARC telescope at [[Apache Point Observatory]], [[New Mexico]], ([[United States]]).
* The 3.5 m [[Calar Alto Observatory]] telescope at mount Calar Alto, ([[Spain]]).
* The 3.50 m [[WIYN Observatory]] at [[Kitt Peak National Observatory]], ([[United States]]).
* The 3.4 m INO340 Telescope at [[Iranian National Observatory]], ([[Iran]]).
* The 2.65 m [[VLT Survey Telescope]] at [[ESO]]’s [[Paranal Observatory]], ([[Chile]]).
* The 2.56 m effective {{f/}}11 [[Nordic Optical Telescope]]  on [[La Palma]], [[Canary Islands]], ([[Spain]]).
* The 2.50 m [[Sloan Digital Sky Survey]] telescope (modified design) at [[Apache Point Observatory]], [[New Mexico]], U.S.
* The 2.4 m [[Hubble Space Telescope]] currently in orbit around the Earth.
* The 2.4 m [[Thai National Observatory]] telescope on [[Doi Inthanon]], ([[Thailand]]).
* The 2.3 m [[Aristarchos Telescope]] at [[Chelmos Observatory]], [[Greece]].
* The 2.2 m [[Calar Alto Observatory]] telescope at mount [[Calar Alto]], ([[Spain]]).
* The 2.15 m [[Leoncito Astronomical Complex]] telescope on [[San Juan Province, Argentina|San Juan]], [[Argentina]].
* The 2.12 m telescope at [[Sierra de San Pedro Mártir|San Pedro Martir]], [[National Astronomical Observatory (Mexico)]].
* The 2.1 m telescope at [[Kitt Peak National Observatory]], ([[United States]]). 
* The 2.08 m [[Otto Struve Telescope]] at [[McDonald Observatory]], ([[United States]]).
* The 2.0 m [[Liverpool Telescope]] ([[robotic telescope]]) on [[La Palma]], [[Canary Islands]], ([[Spain]]).
* The 2.0 m telescope at [[Rozhen Observatory]], [[Bulgaria]].
* The 2.0 m Himalayan Chandra Telescope of the [[Indian Astronomical Observatory]], Hanle, ([[India]]).
* The 1.8 m [[Pan-STARRS]] telescopes at [[Haleakala]] on [[Maui]], [[Hawaii]].
* The 1.65 m telescope at [[Molėtai Astronomical Observatory]], ([[Lithuania]]).
* The 1.6 m [[Mont Mégantic Observatory|Mont-Mégantic Observatory]] telescope on [[Mont Mégantic|Mont-Mégantic]] in [[Quebec]], [[Canada]].
* The 1.6 m [[PerkinElmer|Perkin-Elmer]] telescope on [[Pico dos Dias Observatory]] in [[Minas Gerais]], [[Brazil]].
*The 1.3 m telescope at [[Skinakas Observatory]], in the island of [[Crete]], [[Greece]].
* The 1.0 m [[George Ritchey|Ritchey Telescope]] at the [[United States Naval Observatory Flagstaff Station]] (the final telescope made by G. Ritchey before his death).
* The 1.0 m [[DFM Engineering]] {{f/}}8 at [[Embry-Riddle Observatory]] in [[Daytona Beach, Florida]], ([[United States]]).
* The four 1.0 m [[SPECULOOS]] telescopes at the [[Paranal Observatory]] in [[Chile]] dedicated to the search for Earth-sized [[exoplanets]].
* The 0.85&nbsp;m [[Spitzer Space Telescope]], infrared space telescope in an Earth-trailing orbit (retired by [[NASA]] on 30 January 2020).
* The 0.8 m [[ASTELCO|Astelco Systems]] design Perren Telescope at the [[UCL Observatory|University College London Observatory]] in Mill Hill, London, ([[UK]]).
* The 0.8 m [[DFM Engineering]] CCT-32 telescope at the [[University of Victoria]] in Victoria, British Columbia
* The 0.208&nbsp;m LOng Range Reconnaissance Imager (LORRI) camera on board the [[New Horizons]] space craft, currently beyond Pluto.

==See also==
{{Commons category|Ritchey-Chrétien telescopes}}
* [[List of largest optical reflecting telescopes]]
* [[List of telescope types]]
* [[Lurie–Houghton telescope]]
* [[Maksutov telescope]]
* [[Reflecting telescope]]
* [[Schmidt–Cassegrain telescope]]

==References==
{{reflist|25em}}

{{DEFAULTSORT:Ritchey-Chretien telescope}}
[[Category:Telescope types]]