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| [[Image:EightInchTelescope.JPG|thumb|right|200px|Eight Inch refracting telescope ([[Chabot Space and Science Center]])]]
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| An '''optical telescope''' is a [[telescope]] that gathers and [[Focus (optics)|focuses]] light, mainly from the [[Visible spectrum|visible]] part of the [[electromagnetic spectrum]] create a [[magnification|magnified]] image for direct view, making a [[photograph]], or collecting data through electronic [[image sensor]]s.
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| There are three primary types of optical telescope:
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| * [[Refracting telescope|refractors]], which use [[lens (optics)|lenses]] ([[dioptrics]])
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| * [[Reflecting telescope|reflectors]], which use [[mirror]]s ([[catoptrics]])
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| * [[catadioptric system#Catadioptric telescopes|catadioptric telescopes]], which combine lenses and mirrors
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| A telescope's light gathering power and ability to resolve small detail is directly related to the diameter (or aperture) of its [[Objective (optics)|objective]] (the primary lens or mirror that collects and focuses the light). The larger the objective, the more light the telescope collects and the finer detail it resolves.
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| People use telescopes and [[binoculars]] for activities such as [[observational astronomy]], [[ornithology]], [[pilotage]] and [[reconnaissance]], and watching sports or performance arts.
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| ==History==
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| {{Further|History of the telescope}}
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| The telescope is more a discovery of optical craftsmen than an invention of scientist.<ref>[http://galileo.rice.edu/sci/instruments/telescope.html galileo.rice.edu '''The Galileo Project > Science > The Telescope''' by Al Van Helden – “the telescope was not the invention of scientists; rather, it was the product of craftsmen.”]</ref><ref name="LZZginzib4C page 55">[http://books.google.com/books?id=2LZZginzib4C&pg=PA62&vq=dutch&dq=intitle:Stargazer+digges+coins&lr=&as_brr=0&source=gbs_search_s&cad=0#PPA55,M1 Fred Watson, '''Stargazer''' (page 55)]</ref> The [[Lens (optics)|lens]] and the properties of refracting and reflecting light had been known since [[Ancient history|antiquity]] and theory on how they worked were developed by ancient [[Greek philosophy|Greek]] philosophers, preserved and expanded on in the [[Islamic Golden Age|medieval Islamic world]], and had reached a significantly advanced state by the time of the telescope's invention in [[early modern Europe]].<ref>[http://books.google.co.uk/books?hl=en&lr=&id=KAWwzHlDVksC&oi=fnd&pg=PR1&dq=alhazen+and+the+telescope&ots=0GOT5dCTU8&sig=U-uj1p9TvkAW12XFz8mkfI6TWMg#PPA27,M1 '''The History of the Telescope''' By Henry C. King, Page 25-29]</ref><ref>progression is followed through [[Robert Grosseteste]] [[Witelo]], [[Roger Bacon]], through [[Johannes Kepler]], D. C. Lindberg, Theories of Vision from al-Kindi to Kepler, (Chicago: Univ. of Chicago Pr., 1976), pp. 94-99</ref> But the most significant step cited in the invention of the telescope was the development of lens manufacture for [[Glasses|spectacles]],<ref name="LZZginzib4C page 55"/><ref>[http://galileo.rice.edu/sci/instruments/telescope.html galileo.rice.edu '''The Galileo Project > Science > The Telescope''' by Al Van Helden]</ref><ref>[http://books.google.com/books?id=peIL7hVQUmwC&pg=PA218&dq=invention+of+the+telescope&lr=#PPA26,M1 '''Renaissance Vision from Spectacles to Telescopes''' By Vincent Ilardi], page 210</ref> first in Venice and Florence in the thirteenth century,<ref>[http://galileo.rice.edu/sci/instruments/telescope.html galileo.rice.edu '''The Galileo Project > Science > The Telescope''' by Al Van Helden '']</ref> and later in the spectacle making centers in both the [[Netherlands]] and Germany.<ref>[http://books.google.co.uk/books?hl=en&lr=&id=KAWwzHlDVksC&oi=fnd&pg=PR1&dq=alhazen+and+the+telescope&ots=0GOT5dCTU8&sig=U-uj1p9TvkAW12XFz8mkfI6TWMg#PPA27,M1 '''The History of the Telescope''' By Henry C. King, Page 27 "''(spectacles) invention, an important step in the history of the telescope''"]</ref> It is in the Netherlands in 1608 where the first recorded optical telescopes ([[refracting telescope]]s) appeared. The invention is credited to the spectacle makers [[Hans Lippershey]] and [[Zacharias Janssen]] in Middelburg, and the instrument-maker and optician [[Jacob Metius]] of [[Alkmaar]].<ref>[http://galileo.rice.edu/sci/instruments/telescope.html galileo.rice.edu '''The Galileo Project > Science > The Telescope'''] by Al Van Helden ''"The Hague discussed the patent applications first of Hans Lipperhey of Middelburg, and then of Jacob Metius of Alkmaar... another citizen of Middelburg, Sacharias Janssen had a telescope at about the same time but was at the Frankfurt Fair where he tried to sell it"''</ref>
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| [[Galileo Galilei|Galileo]] greatly improved on these designs the following year, and is generally credited as the first to use a telescope for astronomy. Galileo's telescope used Hans Lippershey's design of a convex [[Objective (optics)|objective lens]] and a concave [[Eyepiece|eye lens]], and this design is now called a [[Galilean telescope]]. [[Johannes Kepler]] proposed an improvement on the design<ref>See his books ''[[Johannes Kepler#Prague (1600–1612)|Astronomiae Pars Optica]]'' and ''[[Johannes Kepler#Prague (1600–1612)|Dioptrice]]''</ref> that used a convex [[eyepiece]], often called the [[Keplerian Telescope]].
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| The next big step in the development of refractors was the advent of the [[Achromatic lens]] in the early 18th century,<ref>[http://www.mhs.ox.ac.uk/sphaera/index.htm?issue8/articl5 Sphaera - Peter Dollond answers Jesse Ramsden] - A review of the events of the invention of the achromatic doublet with emphasis on the roles of Hall, Bass, John Dollond and others.</ref> which corrected the [[chromatic aberration]] in Keplerian telescopes up to that time—allowing for much shorter instruments with much larger objectives.
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| For [[reflecting telescope]]s, which use a [[curved mirrors|curved mirror]] in place of the objective lens, theory preceded practice. The theoretical basis for [[curved mirrors]] behaving similar to lenses was probably established by [[Alhazen]], whose theories had been widely disseminated in Latin translations of his work.<ref>[http://books.google.com/books?id=2LZZginzib4C&pg=PA40&dq=intitle:Stargazer+digges+coins&lr=&as_brr=0&ei=BIwrSc6pB4OClQT4zfyxBg#PPA108,M1 Stargazer - By Fred Watson, Inc NetLibrary, Page 108]</ref> Soon after the invention of the refracting telescope Galileo, [[Giovanni Francesco Sagredo]], and others, spurred on by their knowledge that curved mirrors had similar properties as lenses, discussed the idea of building a telescope using a mirror as the image forming objective.<ref>[http://books.google.com/books?id=2LZZginzib4C&pg=PA40&dq=intitle:Stargazer+digges+coins&lr=&as_brr=0&ei=BIwrSc6pB4OClQT4zfyxBg#PPA108,M1 Stargazer - By Fred Watson, Inc NetLibrary, Page 109]</ref> The potential advantages of using [[parabolic reflector|parabolic mirrors]] (primarily a reduction of [[spherical aberration]] with elimination of [[chromatic aberration]]) led to several proposed designs for reflecting telescopes,<ref>works by [[Bonaventura Cavalieri]] and [[Marin Mersenne]] among others have designs for reflecting telescopes</ref> the most notable of which was published in 1663 by [[James Gregory (astronomer and mathematician)|James Gregory]] and came to be called the [[Gregorian telescope]],<ref>[http://books.google.com/books?id=2LZZginzib4C&pg=PA62&vq=dutch&dq=intitle:Stargazer+digges+coins&lr=&as_brr=0&source=gbs_search_s&cad=0#PPA121,M1 Stargazer - By Fred Watson, Inc NetLibrary, Page 117]</ref><ref>[http://books.google.co.uk/books?hl=en&lr=&id=KAWwzHlDVksC&oi=fnd&pg=PR1&dq=alhazen+and+the+telescope&ots=0GOT5dCTU8&sig=U-uj1p9TvkAW12XFz8mkfI6TWMg#PPA71,M1 '''The History of the Telescope''' By Henry C. King, Page 71]</ref> but no working models were built. [[Isaac Newton]] has been generally credited with constructing the first practical reflecting telescopes, the [[Newtonian telescope]], in 1668<ref name="books.google.com">[http://books.google.com/books?id=32IDpTdthm4C&pg=PA67&lpg=PA67&dq=newton+reflecting+telescope++1668+letter+1669&source=bl&ots=PKABaGwPaN&sig=rPS8w23_nAp3kH5YMYGZ7JHhOaI&hl=en&ei=0QC1Svf7AsWb8Aa3nqGTDw&sa=X&oi=book_result&ct=result&resnum=5#v=onepage&q=newton%20reflecting%20telescope%20%201668%20letter%201669&f=false '''Isaac Newton: adventurer in thought''', by Alfred Rupert Hall, page 67]</ref> although due to their difficulty of construction and the poor performance of the [[speculum metal]] mirrors used it took over 100 years for reflectors to become popular. Many of the advances in reflecting telescopes included the perfection of [[parabolic reflector|parabolic mirror]] fabrication in the 18th century,<ref>Parabolic mirrors were used much earlier, but [[James Short (mathematician)|James Short]] perfected their construction. See {{cite web |url=http://www.astro.lsa.umich.edu/undergrad/Labs/optics/Reflectors.html |title=Reflecting Telescopes (Newtonian Type) |publisher=Astronomy Department, University of Michigan}}</ref> silver coated glass mirrors in the 19th century, long-lasting aluminum coatings in the 20th century,<ref>Silvering was introduced by [[Léon Foucault]] in 1857, see [http://www.madehow.com/inventorbios/39/Jean-Bernard-L-on-Foucault.html madehow.com - Inventor Biographies - Jean-Bernard-Léon Foucault Biography (1819-1868)], and the adoption of long lasting aluminized coatings on reflector mirrors in 1932. [http://www.cambridge.org/uk/astronomy/features/amateur/files/p28-4.pdf Bakich sample pages Chapter 2, Page 3 ''"John Donavan Strong, a young physicist at the California Institute of Technology, was one of the first to coat a mirror with aluminum. He did it by thermal vacuum evaporation. The first mirror he aluminized, in 1932, is the earliest known example of a telescope mirror coated by this technique."'']</ref> [[segmented mirror]]s to allow larger diameters, and [[active optics]] to compensate for gravitational deformation. A mid-20th century innovation was [[catadioptric system|catadioptric]] telescopes such as the [[Schmidt camera]], which uses both a lens (corrector plate) and mirror as primary optical elements, mainly used for wide field imaging without spherical aberration.
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| The late 20th century has seen the development of [[adaptive optics]] and [[space telescope]]s to overcome the problems of [[astronomical seeing]].
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| ==Principles==
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| ''For detailed information on specific designs of reflecting, refracting, and catadioptric telescopes: see the main articles on [[Reflecting telescope]]s, [[Refracting telescope]]s, and [[Catadioptric]]s.''
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| The basic scheme is that the primary light-gathering element the [[objective (optics)|objective]] (1) (the [[convex lens]] or [[concave mirror]] used to gather the incoming light), focuses that light from the distant object (4) to a focal plane where it forms a [[real image]] (5). This image may be recorded or viewed through an [[eyepiece]] (2), which acts like a [[magnifying glass]]. The eye (3) then sees an inverted [[magnification|magnified]] [[virtual image]] (6) of the object.
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| [[Image:Kepschem.png|thumb|350px|right|Schematic of a [[Keplerian telescope|Keplerian]] [[refracting telescope]]]]
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| ===Inverted images===
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| Most telescope designs produce an inverted image at the focal plane; these are referred to as ''inverting telescopes''. In fact, the image is both inverted and reverted, or rotated 180 degrees from the object orientation. In astronomical telescopes the rotated view is normally not corrected, since it does not affect how the telescope is used. However, a mirror diagonal is often used to place the eyepiece in a more convenient viewing location, and in that case the image is erect but everted (reversed left to right). In terrestrial telescopes such as [[Spotting scope]]s, [[monocular]]s and [[binoculars]], prisms (e.g., [[Porro prism]]s), or a relay lens between objective and eyepiece are used to correct the image orientation. There are telescope designs that do not present an inverted image such as the [[Refracting telescope#Refracting telescope designs|Galilean refractor]] and the [[Gregorian telescope|Gregorian reflector]]. These are referred to as ''erecting telescopes''.
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| ===Design variants===
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| Many types of telescope fold or divert the optical path with secondary or tertiary mirrors. These may be integral part of the optical design ([[Newtonian telescope]], [[Cassegrain reflector]] or similar types), or may simply be used to place the eyepiece or detector at a more convenient position. Telescope designs may also use specially designed additional lenses or mirrors to improve image quality over a larger field of view.
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| <!--no special reason to mention a Maksutov telescope here, it is a rare type; the Cassegrain is the "grandfather" of all these designs. Also, folding the optical path alone, ''e.g.'' by flat mirrors, should not reduce the field of view-->
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| ==Characteristics==
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| Design specifications relate to the characteristics of the telescope and how it performs optically. Several properties of the specifications may change with the equipment or accessories used with the telescope; such as [[Barlow lens]]es, [[star diagonal]]s and [[eyepiece]]s. These interchangeable accessories don't alter the specifications of the telescope, however they alter the way the telescopes properties function, typically [[magnification]], [[angular resolution]] and [[field of view|FOV]].
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| ===Surface resolvability===
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| The smallest resolvable surface area of an object, as seen through an optical telescope, is the limited physical area that can be resolved. It is analogous to [[angular resolution]], but differs in definition: instead of separation ability between point-light sources it refers to the physical area that can be resolved. A familiar way to express the characteristic is the resolvable ability of features such as [[Moon]] craters or [[Sun]] spots. Expression using the formula is given by the sum of twice the resolving power <math>R</math> over [[aperture]] diameter <math>D</math> multiplied by the objects diameter <math>D_{ob}</math> multiplied by the constant <math>\Phi</math> all divided by the objects [[apparent diameter]] <math>D_{a}</math>.<ref name="SaharaSkyObservatory">{{cite web|url=http://www.saharasky.com/saharasky/formula.html|title=Telescope Formulae|date=3 July 2012|publisher=SaharaSky Observatory}}</ref><ref name="RyukyuAstronomyClub">{{cite web|url=http://www.nexstarsite.com/_RAC/form.html|title=Optical Formulae|date=2 January 2012|publisher=Ryukyu Astronomy Club}}</ref>
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| ''Resolving power <math>R</math> is derived from the [[wavelength]] <math>{\lambda}</math> using the same unit as [[aperture]]; where 550 [[nanometers|nm]] to [[millimeters|mm]] is given by: <math>R = \frac{\lambda}{10^6} = \frac{550}{10^6} = 0.00055</math>.''
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| <br/>''The constant <math>\Phi</math> is derived from [[radians]] to the same unit as the objects [[apparent diameter]]; where the [[Moon]]s [[apparent diameter]] of <math>D_{a} = \frac{313\Pi}{10800}</math> [[radians]] to [[arcseconds|arcsecs]] is given by: <math>D_{a} = \frac{313\Pi}{10800}*206265 = 1878</math>.''
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| An example using a telescope with an [[aperture]] of 130 [[millimeters|mm]] observing the [[Moon]] in a 550 [[nanometer|nm]] [[wavelength]], is given by: <math>F = \frac{\frac{2R}{D}*D_{ob}*\Phi}{D_{a}} = \frac{\frac{2*0.00055}{130}*3474.2*206265}{1878} \approx 3.22</math>
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| The unit used in the object diameter results in the smallest resolvable features at that unit. In the above example they are approximated in [[kilometers]] resulting in the smallest resolvable [[Moon]] craters being 3.22 [[kilometers|km]] in diameter. The [[Hubble|Hubble Space Telescope]] has a primary mirror [[aperture]] of 2400 [[millimeters|mm]] that provides a surface resolvability of [[Moon]] craters being 174.9 [[meters]] in diameter, or [[Sun]] spots of 7365.2 [[kilometers|km]] in diameter.
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| ===Angular resolution===
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| Ignoring blurring of the image by turbulence in the atmosphere ([[astronomical seeing|atmospheric seeing]]) and optical imperfections of the telescope, the [[angular resolution]] of an optical telescope is determined by the diameter of the [[primary mirror]] or lens gathering the light (also termed its "[[aperture]]")
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| The [[Rayleigh criterion]] for the resolution limit <math>\alpha_R</math> (in [[radian]]s) is given by
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| :<math>\sin(\alpha_R) = 1.22 \frac{\lambda}{D}</math>
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| where <math>\lambda</math> is the [[wavelength]] and <math>D</math> is the aperture. For [[visible light]] (<math>\lambda</math> = 550 nm) in the [[small-angle approximation]], this equation can be rewritten:
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| :<math>\alpha_R = \frac{138}{D}</math>
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| Here, <math>\alpha_R</math> denotes the resolution limit in [[arcsecond]]s and <math>D</math> is in millimeters.
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| In the ideal case, the two components of a [[double star]] system can be discerned even if separated by slightly less than <math>\alpha_R</math>. This is taken into account by the [[Dawes limit]]
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| :<math>\alpha_D = \frac{116}{D}</math>
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| The equation shows that, all else being equal, the larger the aperture, the better the angular resolution. The resolution is not given by the maximum [[magnification]] (or "power") of a telescope. Telescopes marketed by giving high values of the maximum power often deliver poor images.
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| For large ground-based telescopes, the resolution is limited by [[astronomical seeing|atmospheric seeing]]. This limit can be overcome by placing the telescopes above the atmosphere, e.g., on the summits of high mountains, on balloon and high-flying airplanes, or [[space telescope|in space]]. Resolution limits can also be overcome by [[adaptive optics]], [[speckle imaging]] or [[lucky imaging]] for ground-based telescopes.
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| Recently, it has become practical to perform [[aperture synthesis]] with arrays of optical telescopes. Very high resolution images can be obtained with groups of widely spaced smaller telescopes, linked together by carefully controlled optical paths, but [[List of astronomical interferometers at visible and infrared wavelengths|these interferometers]] can only be used for imaging bright objects such as stars or measuring the bright cores of [[active galaxies]].
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| ===Focal length and focal ratio===
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| The [[focal length]] of an [[optics|optical]] system is a measure of how strongly the system converges or diverges [[light]]. For an optical system in air, it is the distance over which initially [[collimated]] rays are brought to a [[focus (optics)|focus]]. A system with a shorter focal length has greater [[optical power]] than one with a long focal length; that is, it bends the [[ray (optics)|ray]]s more strongly, bringing them to a focus in a shorter distance. In astronomy, the f-number is commonly referred to as the ''focal ratio'' notated as <math>N</math>. The [[f-number|focal ratio]] of a telescope is defined as the [[focal length]] <math>f</math> of an [[Objective (optics)|objective]] divided by its diameter <math>D</math> or by the diameter of an [[aperture]] stop in the system. The [[focal length]] controls the [[field of view]] of the instrument and the scale of the image that is presented at the focal plane to an [[eyepiece]], film plate, or [[Charge-coupled device|CCD]].
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| An example of a telescope with a [[focal length]] of 1200 [[millimeters|mm]] and [[aperture|aperture diameter]] of 254 [[millimeters|mm]] is given by:
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| <math>N = \frac {f}{D} = \frac {1200}{254} \approx 4.7</math>
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| Numerically large [[f-number|Focal ratios]] are said to be ''long'' or ''slow''. Small numbers are ''short'' or ''fast''. There are no sharp lines for determining when to use these terms, an individual may consider their own standards of determination. Among contemporary astronomical telescopes, any telescope with a [[f-number|focal ratio]] slower (bigger number) than f/12 is generally considered slow, and any telescope with a focal ratio faster (smaller number) than f/6, is considered fast. Faster systems often have more [[optical aberrations]] away from the center of the [[field of view]] and are generally more demanding of eyepiece designs than slower ones. A fast system is often desired for practical purposes in [[astrophotography]] with the purpose of gathering more [[photons]] in a given time period than a slower system, allowing time lapsed [[photography]] to process the result faster.
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| Wide-field telescopes (such as [[astrograph]]s), are used to track [[satellite]]s and [[asteroid]]s, for [[cosmic ray|cosmic-ray]] research, and for [[astronomical survey]]s of the sky. It is more difficult to reduce [[optical aberrations]] in telescopes with low f-ratio than in telescopes with larger f-ratio.
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| ===Light-gathering power===
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| The light-gathering power of an optical telescope, also referred to as aperture gain is the ability of a telescope to collect a lot more light than the human eye. Its light-gathering power, is probably its most important feature. The telescope acts as a ''light bucket'', collecting all of the photons that come down on it from a far away object, where a larger bucket catches more [[photons]] resulting in more received light in a given time period, effectively brightening the image. This is why the pupils of your eyes enlarge at night so that more light reaches the retinas. The gathering power <math>P</math> compared against a human eye is the squared result of the division of the [[aperture]] <math>D</math> over the observer's pupil diameter <math>D_{p}</math>,<ref name="SaharaSkyObservatory"/><ref name="RyukyuAstronomyClub"/> with an average adult having a [[pupil]] diameter of 7mm. Younger persons host larger diameters, typically said to be 9mm, as the diameter of the pupil decreases with age.
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| An example gathering power of an [[aperture]] with 254 [[millimeters|mm]] compared to an adult pupil diameter being 7 [[millimeters|mm]] is given by: <math>P = (\frac {D}{D_{p}})^2 = (\frac {254}{7})^2 \approx 1316.7</math>
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| Light-gathering power can be compared between telescopes by comparing the [[area|area's]] <math>A</math> of the two different [[aperture]]s.
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| As an example, the light-gathering power of a 10 [[meter]] [[telescope]] is 25x that of a 2 [[meter]] [[telescope]]: <math>p = \frac {A_{1}}{A_{2}} = \frac {\pi5^2}{\pi1^2} = 25</math>
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| For a survey of a given area, the [[field of view]] is just as important as raw light gathering power. Survey telescopes such as the [[Large Synoptic Survey Telescope]] try to maximize the product of mirror area and [[field of view]] (or [[etendue]]) rather than raw light gathering ability alone.
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| ===Magnification===
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| The magnification through a telescope magnifies a viewing object while limiting the [[Field of view|FOV]]. Magnification is often misleading as the optical power of the telescope, its characteristic is the most misunderstood term used to describe the observable world. At higher magnifications the image quality significantly reduces, usage of a [[Barlow lens]]—which increases the effective focal length of an optical system—multiplies image quality reduction.
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| Similar minor effects may be present when using [[star diagonal]]s, as light travels through a multitude of lenses that increase or decrease effective focal length. The quality of the image generally depends on the quality of the optics (lenses) and viewing conditions—not on magnification.
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| Magnification itself is limited by optical characteristics. With any telescope or microscope, beyond a practical maximum magnification, the image looks bigger but shows no more detail. It occurs when the finest detail the instrument can resolve is magnified to match the finest detail the eye can see. Magnification beyond this maximum is sometimes called ''empty magnification''.
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| To get the most detail out of a telescope, it is critical to choose the right magnification for the object being observed. Some objects appear best at low power, some at high power, and many at a moderate magnification. There are two values for magnification, a minimum and maximum. A wider [[field of view]] [[eyepiece]] may be used to keep the same [[focal length|eyepiece focal length]] whilst providing the same magnification through the telescope. For a good quality telescope operating in good atmospheric conditions, the maximum usable magnification is limited by diffraction.
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| ====Visual====
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| The visual magnification <math>M</math> of the field of view through a telescope can be determined by the telescopes [[focal length]] <math>f</math> divided by the [[eyepiece]] [[focal length]] <math>f_{e}</math> (or diameter).<ref name="SaharaSkyObservatory"/><ref name="RyukyuAstronomyClub"/> The maximum is limited by the diameter of the [[eyepiece]].
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| An example of visual [[magnification]] using a [[telescope]] with a 1200 [[millimeters|mm]] [[focal length]] and 3 [[millimeters|mm]] [[eyepiece]] is given by: <math>M = \frac {f}{f_{e}} = \frac {1200}{3} = 400</math>
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| ====Minimum====
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| There is a lowest useable [[magnification]] on a telescope. The increase in brightness with reduced magnification has a limit related to something called the [[exit pupil]]. The [[exit pupil]] is the cylinder of light coming out of the eyepiece, hence the lower the [[magnification]], the larger the [[exit pupil]]. The minimum <math>M_{m}</math> can be calculated by dividing the [[telescope]] [[aperture]] <math>D</math> over the exit pupil diameter <math>D_{ep}</math>.<ref name="RocketMime">{{cite web|url=http://www.rocketmime.com/astronomy/Telescope/telescope_eqn.html|date=17 November 2012|publisher=RocketMime|title=Telescope Equations}}</ref> Decreasing the magnification past this limit cannot increase brightness, at this limit there is no benefit for decreased magnification. Likewise calculating the [[exit pupil]] <math>D_{ep}</math> is a division of the [[aperture]] diameter <math>D</math> and the visual magnification <math>M</math> used. The minimum often may not be reachable with some telescopes, a telescope with a very long [[focal length]] may require a ''longer-focal-length'' eyepiece than is possible.
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| An example of the lowest usable magnification using a 254 [[millimeters|mm]] [[aperture]] and 7 [[millimeters|mm]] [[exit pupil]] is given by: <math>M_{m} = \frac {D}{D_{ep}} = \frac {254}{7} \approx 36</math>, whilst the [[exit pupil]] diameter using a 254 [[millimeters|mm]] [[aperture]] and 36x [[magnification]] is given by: <math>D_{ep} = \frac {D}{M} = \frac {254}{36} \approx 7</math>
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| ====Optimum====
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| A useful reference is:
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| *For small objects with low surface brightness (such as [[galaxies]]), use a moderate magnification.
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| *For small objects with high surface brightness (such as [[planetary nebulae]]), use a high magnification.
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| *For large objects regardless of surface brightness (such as [[diffuse nebulae]]), use low magnification, often in the range of minimum magnification.
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| Only personal experience determines the best optimum magnifications for objects, relying on observational skills and seeing conditions.
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| ===Field of View===
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| [[Field of view]] is the extent of the observable world seen at any given moment, through an instrument )e.g., [[telescope]] or [[binoculars]]), or by naked eye. There are various expressions of [[field of view]], being a specification of an [[eyepiece]] or a characteristic determined from and [[eyepiece]] and [[telescope]] combination. A physical limit derives from the combination where the [[field of view|FOV]] cannot be viewed larger than a defined maximum, due to [[diffraction]] of the optics.
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| ====Apparent====
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| Apparent [[field of view|FOV]] is the observable world observed through an ocular [[eyepiece]] without insertion into a [[telescope]]. It is limited by the barrel size used in a telescope, generally with modern telescopes that being either 1.25 or 2 inches in diameter. A wider [[field of view|FOV]] may be used to achieve a more vast observable world given the same [[magnification]] compared with a smaller [[field of view|FOV]] without compromise to magnification. Note that increasing the [[field of view|FOV]] lowers [[surface brightness]] of an observed object, as the gathered light is spread over more area, in relative terms increasing the observing area proportionally lowers surface brightness dimming the observed object. Wide [[field of view|FOV]] [[eyepiece]]s work best at low magnifications with large [[apertures]], where the relative size of an object is viewed at higher comparative standards with minimal magnification giving an overall brighter image to begin with.
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| ====True====
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| True [[field of view|FOV]] is the observable world observed though an ocular [[eyepiece]] inserted into a [[telescope]]. Knowing the true [[field of view|FOV]] of [[eyepiece]]s is very useful since it can be used to compare what is seen through the [[eyepiece]] to printed or computerized [[star chart]]s that help identify what is observed. True [[field of view|FOV]] <math>v_{t}</math> is the division of apparent [[field of view|FOV]] <math>v_{a}</math> over [[magnification]] <math>M</math>.<ref name="SaharaSkyObservatory"/><ref name="RyukyuAstronomyClub"/>
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| An example of true [[field of view|FOV]] using an [[eyepiece]] with 52° apparent [[field of view|FOV]] used at 81.25x [[magnification]] is given by: <math>v_{t} = \frac {v_{a}}{M} = \frac {52}{81.25} = 0.64^\circ</math>
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| ====Maximum====
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| Max [[field of view|FOV]] is a term used to describe the maximum useful true [[field of view|FOV]] limited by the optics of the [[telescope]], it is a physical limitation where increases beyond the maximum remain at maximum. Max [[field of view|FOV]] <math>v_{m}</math> is the sum of barrel size <math>B</math> by the division of 1 [[radian]] <math>\frac{180}{\pi}</math> over the [[telescope]]s [[focal length]] <math>f</math>.<ref name="SaharaSkyObservatory"/><ref name="RyukyuAstronomyClub"/>
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| An example of max [[field of view|FOV]] using a [[telescope]] with a barrel size of 31.75 [[millimeters|mm]] (1.25 [[inches]]) and [[focal length]] of 1200 [[millimeters|mm]] is given by: <math>v_{m} = B*\frac {\frac {180}{\pi}}{f} \approx 31.75*\frac {57.2958}{1200} \approx 1.52^\circ</math>
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| ==Observing through a telescope==
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| There are many properties of optical telescopes and the complexity of observation using one can be a daunting task, experience and experimentation are the major contributors to understanding how to maximize your observations. In practice, only two main properties of a telescope determine how observation differs: the [[focal length]] and [[aperture]]. These relate as to how the optical system views an object or range and how much light is gathered through an ocular [[eyepiece]]. [[Eyepiece]]s further determine how the [[field of view]] and [[magnification]] of the observable world change.
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| ===Observable world===
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| This term describes what can be seen using a telescope, when viewing an object or range the observer may use many different techniques. Understanding what can be viewed and how to view it depends on the [[field of view]]. Viewing an object at a size that fits entirely in the [[field of view]] is measured using the two telescope properties—[[focal length]] and [[aperture]], with the inclusion of an ocular [[eyepiece]] with suitable [[focal length]] (or diameter). Comparing the observable world and the [[angular diameter]] of an object shows how much of the object we see. However, the relationship with the optical system may not result in high [[surface brightness]]. Celestial objects are often dim because of their vast distance, and detail may be limited by [[diffraction]] or unsuitable optical properties.
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| ===Field of view and magnification relationship===
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| Finding what can be seen through the optical system begins with the [[eyepiece]] providing our [[field of view]] and [[magnification]], the [[magnification]] is given by the division of the telescope and [[eyepiece]] [[focal length]]s. Using an example of an amateur telescope such as a [[Newtonian telescope]] with an [[aperture]] <math>D</math> of 130 mm (5") and [[focal length]] <math>f</math> of 650mm (25.5"), we use an [[eyepiece]] with a [[focal length]] <math>d</math> of 8 mm and [[field of view|apparent field of view]] <math>v_{a}</math> of 52°.'' The [[magnification]] at which the observable world is viewed at is given by: <math>M = \frac {f}{d} = \frac {650}{8} = 81.25</math>. The [[field of view|true field of view]] <math>v_{t}</math> requires the [[magnification]], which is formulated by its division over the [[field of view|apparent field of view]]: <math>v_{t} = \frac {v_{a}}{M} = \frac {52}{81.25} = 0.64</math>. Our resulting [[field of view|true field of view]] is 0.64°, allowing an object such as the [[Orion nebula]], which appears [[elliptical]] with an [[angular diameter]] of 65 x 60 [[arcminutes]] to be viewable through the telescope in it's entirety, where the whole of the [[nebula]] is within the observable world. Using methods such as this, can greatly increase your viewing potential ensuring the observable world can contain the entire object, or whether to increase/decrease magnification viewing the object in a different aspect.
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| ===The brightness factor===
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| Note that the [[surface brightness]] at such a magnification significantly reduces, resulting in a far dimmer appearance. A dimmer appearance results in less visual detail of the object. Details such as matter, rings, spiral arms, and gases may be completely hidden from the observer, giving a far less ''complete'' view of the object or range. Physics dictates that at the theoretical minimum magnification of the telescope, the surface brightness is at 100%. Practical, however, various factors prevent 100% brightness. These include telescope limitations ([[focal length]], [[eyepiece]] focal length,etc.) and the age of the observer.
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| Age plays a role in brightness, as a contributing factor is the observer's [[pupil]]. With age the [[pupil]] naturally shrinks in diameter, generally accepted a young adult may have a 7 mm diameter [[pupil]], an older adult as little as 5 mm and a younger person larger at 9 mm. The [[magnification|minimum magnification]] <math>m</math> can be expressed as the division of the [[aperture]] <math>D</math> and [[pupil]] <math>p</math> diameter given by: <math>m = \frac {D}{d} = \frac {130}{7} \approx 18.6</math>. A problematic instance may be apparent achieving a theoretical surface brightness of 100%, as the required [[focal length|effective focal length]] of the optical system may require an [[eyepiece]] with too large a diameter.
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| Some telescopes cannot achieve the theoretical surface brightness of 100%, while some telescopes can achieve it using a very small diameter [[eyepiece]]. To find what [[eyepiece]] is required to get our [[magnification|minimum magnification]] we can rearrange the magnification formula, where its now the division of the telescopes [[aperture]] over the [[magnification|minimum magnification]]: <math>d = \frac {D}{m} = \frac {130}{18.6} \approx 35</math>. An [[eyepiece]] of 35 mm is a non-standard size and would not be purchasable, in this scenario
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| to achieve 100% we would required a standard manufactured [[eyepiece]] size of 40 mm. As the [[eyepiece]] has a larger [[focal length]] than our [[magnification|minimum magnification]], an abundance of wasted light isn't received through our eyes.
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| ===Exit pupil===
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| [[File:Comparison of exit pupils for astronomy.png|200x100px|framed|right|These eyes represent a scaled figure of the [[human eye]] where 15 px = 1 mm, they have a [[pupil]] diameter of 7 mm. ''Figure A'' has an [[exit pupil]] diameter of 14mm, for [[astronomy]] purposes results in 50% loss of light. ''Figure B'' has an exit pupil of 6.4mm, which allows the full 100% of observable light to be perceived by the observer.]]
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| The increase in [[surface brightness]] as you reduce magnification is limited, that limitation is what we describe as the [[exit pupil]]; a cylinder of light that projects out the eyepiece to the observer. An [[exit pupil]] much match or be smaller in diameter than our [[pupil]] to receive the full amount of projected light, a larger [[exit pupil]] results in the wasted light. The [[exit pupil]] <math>e</math> can be derived with from division of the telescope [[aperture]] <math>D</math> and the [[magnification|minimum magnification]] <math>m</math>, derived by: <math>e = \frac {D}{m} = \frac {130}{18.6} \approx 7</math>. The [[pupil]] and [[exit pupil]] are almost identical in diameter giving no wasted observable light with the optical system. A 7mm [[pupil]] falls slightly short of 100% brightness, where the [[surface brightness]] <math>B</math> can be measured from the product of the constant 2, by the square of the [[pupil]] <math>p</math> resulting in: <math>B = 2*p^2 = 2*7^2 = 98</math>. The limitation here is the [[pupil]] diameter, it's an unfortunate result and degrades with age. Some observable light loss is expected and decreasing the magnification cannot not increase surface brightness once the system has reached its minimum usable magnification, hence why the term is referred to as ''usable''.
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| ==Imperfect images==
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| No telescope can form a perfect image. Even if a reflecting telescope could have a perfect mirror, or a refracting telescope could have a perfect lens, the effects of aperture diffraction are unavoidable. In reality, perfect mirrors and perfect lenses do not exist, so image [[Aberration in optical systems|aberrations]] in addition to aperture diffraction must be taken into account. Image aberrations can be broken down into two main classes, monochromatic, and polychromatic. In 1857, [[Philipp Ludwig von Seidel]] (1821–1896) decomposed the first order monochromatic aberrations into five constituent aberrations. They are now commonly referred to as the five Seidel Aberrations.
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| ===The five Seidel aberrations===
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| {{main|Optical aberration}}
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| ; [[Spherical aberration]] : The difference in focal length between paraxial rays and marginal rays, proportional to the square of the objective diameter.
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| ; [[Coma (optics)|Coma]] : A defect by which points appear as comet-like asymmetrical patches of light with tails, which makes measurement very imprecise. Its magnitude is usually deduced from the [[optical sine theorem]].
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| ; [[Astigmatism]] : The image of a point forms focal lines at the sagittal and tangental foci and in between (in the absence of coma) an elliptical shape.
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| ; Curvature of Field: The [[Petzval field curvature]] means that the image, instead of lying in a plane, actually lies on a curved surface, described as hollow or round. This causes problems when a flat imaging device is used e.g., a photographic plate or CCD image sensor.
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| ; Distortion: Either barrel or pincushion, a radial distortion that must be corrected when combining multiple images (similar to stitching multiple photos into a [[Panoramic photography|panoramic photo]]).
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| Optical defects are always listed in the above order, since this expresses their interdependence as first order aberrations via moves of the exit/entrance pupils. The first Seidel aberration, Spherical Aberration, is independent of the position of the exit pupil (as it is the same for axial and extra-axial pencils). The second, coma, changes as a function of pupil distance and spherical aberration, hence the well-known result that it is impossible to correct the coma in a lens free of spherical aberration by simply moving the pupil. Similar dependencies affect the remaining aberrations in the list.
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| ===The chromatic aberrations===
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| : Longitudinal [[chromatic aberration]]: As with spherical aberration this is the same for axial and oblique pencils.
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| : Transverse chromatic aberration (chromatic aberration of magnification)
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| ==Astronomical research telescopes==
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| [[File:Two Unit Telescopes VLT.jpg|thumb|Two of the four Unit Telescopes that make up the [[ESO]]'s [[Very Large Telescope|VLT]], on a remote mountaintop, 2600 metres above sea level in the Chilean Atacama Desert.]]
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| Optical telescopes have been used in astronomical research since the time of their invention in the early 17th century. Many types have be constructed over the years depending on the optical technology, such as refracting and reflecting, the nature of the light or object being imaged, and even where they are placed, such as [[space telescope]]s. Some are classified by the task they perform such as [[Solar telescope]]s.
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| ===Large reflectors===
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| Nearly all large research-grade astronomical telescopes are reflectors. Some reasons are:
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| *In a lens the entire volume of material has to be free of imperfection and inhomogeneities, whereas in a mirror, only one surface has to be perfectly polished.
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| *Light of different colors travels through a medium other than vacuum at different speeds. This causes [[chromatic aberration]].
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| *Reflectors work in a wider [[spectrum]] of light since certain wavelengths are absorbed when passing through glass elements like those found in a refractor or catadioptric.
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| *There are technical difficulties involved in manufacturing and manipulating large-diameter lenses. One of them is that all real materials sag in gravity. A lens can only be held by its perimeter. A mirror, on the other hand, can be supported by the whole side opposite to its reflecting face.
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| Most large research reflectors operate at different focal planes, depending on the type and size of the instrument being used. These including the [[Reflecting telescope#Prime focus|prime focus]] of the main mirror, the [[Cassegrain telescope|cassegrain focus]] (light bounced back down behind the primary mirror), and even external to the telescope all together (such as the [[Reflecting telescope#Nasmyth and coudé focus|Nasmyth and coudé focus]]).<ref>[http://books.google.com/books?id=FGHhZf-k8SkC&pg=PA91&dq=large+telescopes+can+use+prime+code+focus&hl=en&sa=X&ei=h0A0T-uYN8j40gHZ3unlAg&sqi=2&ved=0CGEQ6AEwAw#v=onepage&q=large%20telescopes%20can%20use%20prime%20code%20focus&f=false S. McLean, Electronic imaging in astronomy: detectors and instrumentation, page 91]</ref>
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| [[Image:USA harlan j smith telescope TX.jpg|thumb|[[Harlan J. Smith Telescope]] reflecting telescope at [[McDonald Observatory]], Texas]]
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| A new era of telescope making was inaugurated by the [[Multiple Mirror Telescope]] (MMT), with a mirror composed of six segments synthesizing a mirror of 4.5 [[metre|meter]]s diameter. This has now been replaced by a single 6.5 m mirror. Its example was followed by the [[Keck telescope]]s with 10 m segmented mirrors.
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| The largest current ground-based telescopes have a [[primary mirror]] of between 6 and 11 meters in diameter. In this generation of telescopes, the mirror is usually very thin, and is kept in an optimal shape by an array of actuators (see [[active optics]]). This technology has driven new designs for future telescopes with diameters of 30, 50 and even 100 meters.
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| Relatively cheap, mass-produced ~2 meter telescopes have recently been developed and have made a significant impact on astronomy research. These allow many astronomical targets to be monitored continuously, and for large areas of sky to be surveyed. Many are [[robotic telescope]]s, computer controlled over the internet (see ''e.g.'' the [[Liverpool Telescope]] and the [[Faulkes Telescope North]] and [[Faulkes Telescope South|South]]), allowing automated follow-up of astronomical events.
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| Initially the [[detector]] used in telescopes was the [[human eye]]. Later, the sensitized [[photographic plate]] took its place, and the [[spectrograph]] was introduced, allowing the gathering of spectral information. After the photographic plate, successive generations of electronic detectors, such as the [[charge-coupled device]] (CCDs), have been perfected, each with more sensitivity and resolution, and often with a wider wavelength coverage.
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| Current research telescopes have several instruments to choose from such as:
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| *imagers, of different spectral responses
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| *spectrographs, useful in different regions of the spectrum
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| *polarimeters, that detect light [[Polarization (waves)|polarization]].
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| The phenomenon of optical [[diffraction]] sets a limit to the resolution and image quality that a telescope can achieve, which is the effective area of the [[Airy disc]], which limits how close two such discs can be placed. This absolute limit is called the [[diffraction limit]] (and may be approximated by the [[Rayleigh criterion]], [[Dawes limit]] or [[Sparrow's resolution limit]]). This limit depends on the wavelength of the studied light (so that the limit for red light comes much earlier than the limit for blue light) and on the [[diameter]] of the telescope mirror. This means that a telescope with a certain mirror diameter can theoretically resolve up to a certain limit at a certain wavelength. For conventional telescopes on Earth, the diffraction limit is not relevant for telescopes bigger than about 10 cm. Instead, the [[Astronomical seeing|seeing]], or blur caused by the atmosphere, sets the resolution limit. But in space, or if [[adaptive optics]] are used, then reaching the diffraction limit is sometimes possible. At this point, if greater resolution is needed at that wavelength, a wider mirror has to be built or [[aperture synthesis]] performed using an array of nearby telescopes.
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| In recent years, a number of technologies to overcome the distortions caused by [[Earth's atmosphere|atmosphere]] on ground-based telescopes have been developed, with good results. See [[adaptive optics]], [[speckle imaging]] and [[Optical interferometry#Astronomical optical interferometry|optical interferometry]].
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| ==See also==
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| * [[Astronomy]]
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| * [[Astrophotography]]
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| * [[Amateur telescope making]]
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| * [[Depth of field]]
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| * [[Dipleidoscope]]
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| * [[Globe effect]]
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| * [[Bahtinov mask]]
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| * [[Carey mask]]
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| * [[Hartmann mask]]
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| * [[History of optics]]
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| * [[List of optical telescopes]]
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| * [[List of largest optical reflecting telescopes]]
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| * [[List of largest optical refracting telescopes]]
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| * [[List of largest optical telescopes historically]]
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| * [[List of solar telescopes]]
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| * [[List of space telescopes]]
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| * [[List of telescope types]]
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| ==Notes==
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| {{reflist}}
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| ==External links==
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| * [http://www.telescope-optics.net/index.htm Notes on AMATEUR TELESCOPE OPTICS]
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| * [http://www.stargazing.net/naa/scopemath.htm Online Telescope Math Calculator]
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| * [http://www.licha.de/astro_article_mtf_telescope_resolution.php The Resolution of a Telescope]
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| * [http://media.skyandtelescope.com/documents/AboutScopes.pdf skyandtelescope.com - What To Know (about telescopes)]
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| {{Astronomy navbox}}
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| {{DEFAULTSORT:Optical Telescope}}
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| [[Category:Telescopes]]
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| [[Category:Dutch inventions]]
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| [[ja:天体望遠鏡#光学望遠鏡]]
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