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| [[File:RitcheyTelescope.jpg|thumb|right|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]]
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| A '''Ritchey–Chrétien telescope''' ('''RCT''' or simply '''RC''') is a specialized [[Cassegrain telescope]] invented in the early 20th century that has a [[hyperboloid|hyperbolic]] [[primary mirror]] and a hyperbolic [[secondary mirror]] designed to eliminate optical errors ([[Coma (optics)|coma]]). They have large field of view free of optical errors compared to a more conventional [[reflecting telescope]] configuration. Since the mid 20th century most large professional research telescopes have been Ritchey–Chrétien configurations.
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| ==History==
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| [[File:NOFS 40inch03.jpg|thumb|right|The 40-inch (1.0 m) Ritchey at [[United States Naval Observatory Flagstaff Station]]]]
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| 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 {{convert|60|cm|in|abbr=on}} in 1927 (e.g. 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]].
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| The Ritchey–Chrétien design is free of third-order [[coma (optics)|coma]] and [[spherical aberration]],<ref name = "Sacek1">
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| {{cite web
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| | last = Sacek | first = Vladimir
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| | date = 14 July 2006
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| | title = Classical and aplanatic two-mirror systems
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| | url = http://www.telescope-optics.net/classical_and_aplanatic.htm
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| | work = Notes on Amateur Telescope Optics
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| | accessdate = 2010-04-24
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| }}</ref> although it does suffer from fifth-order coma, severe large-angle [[astigmatism]], and comparatively severe [[Field curvature#Curvature of the field of the image|field curvature]].<ref name = "Rutten67">
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| {{cite book
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| | author = Rutten, Harrie; van Venrooij, Martin
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| | year = 2002
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| | title = Telescope Optics
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| | page = 67
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| | publisher = [[Willmann-Bell]]
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| | isbn = 0-943396-18-2
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| }}</ref> 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 examples are relatively rare due to the high cost of hyperbolic primary mirror fabrication; Ritchey–Chrétien configurations are most commonly found on high-performance professional telescopes.
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| 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 (optics)|coma]] and [[astigmatism]]. With two curved 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]]. 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.
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| ==Mirror parameters==
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| [[File:Diagram Reflector RitcheyChretien.svg|thumb|Diagram of a Ritchey-Chrétien reflector telescope]]
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| The [[radius of curvature (optics)|radii of curvature]] of the primary and secondary mirrors, respectively, in a two-mirror Cassegrain configuration are
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| :<math>R_1 = -\frac{2DF}{F - B}</math>
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| and
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| :<math>R_2 = -\frac{2DB}{F - B - D}</math>
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| where
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| * <math>F</math> is the effective [[focal length]] of the system,
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| * <math>B</math> is the back focal length (the distance from the secondary to the focus), and
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| * <math>D</math> is the distance between the two mirrors.
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| 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>.
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| 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
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| :<math>K_1 = -1 - \frac{2}{M^3}\cdot\frac{B}{D}</math>
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| and
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| :<math>K_2 = -1 - \frac{2}{(M - 1)^3}\left[M(2M - 1) + \frac{B}{D}\right]</math>
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| where <math>M = F/f_1 = (F - B)/D</math> is the secondary magnification.<ref>
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| {{cite book
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| |last=Smith |first=Warren J.
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| |year=2008
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| |title=Modern Optical Engineering
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| |pages=508–510 |edition=4th
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| |publisher=[[McGraw-Hill Professional]]
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| |isbn=978-0-07-147687-4
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| }}</ref> 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.)
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| 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>
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| {{Cite book
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| |author=Allen, Lew
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| |coauthors=''et al.''
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| |year=1990
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| |title=The Hubble Space Telescope Optical Systems Failure Report
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| |url=http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19910003124_1991003124.pdf
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| |publisher=[[NASA]]
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| |id=NASA-TM-103443
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| }}</ref> Incorrect null correctors have led to other mirror fabrication errors as well, such as in the [[New Technology Telescope]].
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| ==Examples of large Ritchey–Chrétien telescopes==
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| [[Image:Prompt.jpg|thumb|right|16 in (41 cm) [[RC Optical Systems]] truss telescope, part of the [[PROMPT Telescopes]] array]]
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| * The 10.4 m [[Gran Telescopio Canarias]] at [[Roque de los Muchachos Observatory]]
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| * The two 10.0 m telescopes of the [[Keck telescope|Keck Observatory]]
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| * The four 8.2 m telescopes comprising the [[Very Large Telescope]] in [[Chile]]
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| * The 8.2 m [[Subaru (telescope)|Subaru telescope]] at [[Mauna Kea Observatory]]
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| * The two 8.0 m telescopes comprising the [[Gemini Observatory]]
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| * The 4.1 m [[VISTA (telescope)|Visible and Infrared Survey Telescope for Astronomy]] at the [[Paranal Observatory]] (Chile)
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| * The 3.9 m [[Anglo-Australian Telescope]] at [[Siding Spring Observatory]] ([[Australia]])
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| * The 3.58 meter [[New Technology Telescope]] at the [[European Southern Observatory]]
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| * The 3.58 meter [[Telescopio Nazionale Galileo]] at [[Roque de los Muchachos Observatory]]
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| * The 3.5 m ARC telescope at [[Apache Point Observatory]], [[New Mexico]], [[U.S.A.]]
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| * The 3.5 m [[Calar Alto Observatory]] telescope at mount Calar Alto (Spain)
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| * The 3.5 m [[Herschel Space Observatory]] currently operating in orbit at the [[L2 point]] 1.5 million km from Earth
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| * The 3.50 m [[WIYN Observatory]] at [[Kitt Peak National Observatory]]
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| * The 2.56 m effective f/11 [[Nordic Optical Telescope]] on La Palma, Canary Islands.
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| * The 2.50 m [[Sloan Digital Sky Survey]] telescope (modified design) at [[Apache Point Observatory]], [[New Mexico]], [[U.S.A.]]
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| * The 2.4 m [[Hubble Space Telescope]] currently in orbit around the Earth
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| * The 2.2 m [[Calar Alto Observatory]] telescope at mount [[Calar Alto]] (Spain)
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| * The 2.1 m telescope at San Pedro Martir, [[National Astronomical Observatory (Mexico)]]
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| * The 2.0 m telescope at [[Rozhen Observatory]]
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| * The 2.0 m Himalayan Chandra Telescope of the [[Indian Astronomical Observatory]], Hanle, India
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| * The 1.8 m [[Pan-STARRS]] telescopes at [[Haleakala]] on [[Maui]], [[Hawaii]]
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| * The 1.6 m [[Mont Mégantic Observatory|Mont-Mégantic Observatory]] telescope on [[Mont Mégantic|Mont-Mégantic]] in [[Quebec]], [[Canada]]
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| * The 1.5 m telescope at Loiano Observatory, Italy
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| * The 1.3 m telescope at Skinakas Observatory, Crete, Greece
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| * 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).
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| * The 85 cm [[Spitzer Space Telescope]], infrared space telescope currently operating in Earth-trailing orbit
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| Ritchey intended the 100 inch [[Mount Wilson Observatory#100 inch (2.5 m) Hooker Telescope|Hooker telescope]] 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. |year=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
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| |author=Wilson, R.N.
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| |publisher=Springer-Verlag: Berlin, Heidelberg, New York
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| |volume=1
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| |year=1996}} P. 454</ref> have allowed the RCT design to take over - the Hale telescope 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
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| |author=Zirker, J.B.
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| |year=2005
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| |publisher=Johns Hopkins Univ Press}}, p. 317.</ref>
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| ==See also==
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| {{Commons category|Ritchey–Chrétien telescopes}}
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| *[[List of largest optical reflecting telescopes]]
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| *[[List of telescope types]]
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| *[[Reflecting telescope]]
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| *[[Schmidt–Cassegrain telescope]]
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| *[[Maksutov telescope]]
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| ==References==
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| {{reflist|1}}
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| {{DEFAULTSORT:Ritchey-Chretien telescope}}
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| [[Category:Telescope types]]
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| [[nl:Spiegeltelescoop#Ritchey-Chrétientelescoop]]
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