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[[File:Nikon 1 V1 + Fisheye FC-E9 01.jpg|right|thumb|upright=1.3|A fisheye lens on a  [[Nikon 1 V1]]]]
http://support.groupsite.com/entries/49040760-Hostgator-Favicon - [http://support.groupsite.com/entries/49040760-Hostgator-Favicon http://support.groupsite.com/entries/49040760-Hostgator-Favicon]; Let's take a look on world's webhosting business: Thousands and thousands of internet hosts spread around the world and their company objective is simple - to obtain acknowledged and make profit. With so much sound around the webhosting market, it is a challenging job for us to get the right hosting. Nevertheless, it's not too difficult for me to find Hostgator - a hosting service that stood out from the rest with impressive functions. What I am going to perform in this short article is to assess Hostgator hosting as well as disclosing the technique of Hostgator success.<br><br><br><br>[http://www.google.de/url?url=https://www.facebook.com/HostgatorCoupons2015&rct=j&q=&esrc=s&sa=U&ei=fNnuVIqCCcW5Ub3IgfgO&ved=0CE8QFjAH&usg=AFQjCNEMyrnB89Oa8BC7GvJN-2QnwyZRNA google.de]In any web company, we rely on good internet hosts to provide stable and trusted web hosting services. Hostgator provides timely and promising qualities.<br><br>Hostgator provides a lot of plans to customers. Virtually all the packages provided are cost effective. Hostgator shared hosting are charged $4.95 monthly for the standard shared hosting packaged. At charges which begin from $9.95 yearly, you can take pleasure in even more compact bundles which really come with a great deal of things. Although there still have a lot packages which providing less expensive rates, however if you start to research and try Hostgator, you will feel that every dollar and cent you invested is just not lost. Do your very own study on the features included in every plans Hostgator providing, then you can differentiate the differences with others bundles offered by various other host.<br><br>Hostgator also offers a lot of various other attributes. For exaple, Hostgator assists you to back up the website immediately and securely. Furthermore, you have the option to host unrestricted domains, sub domains and FTP accounts. Of source, the function which discussed just now will not be available if you are the standard hosting bundle subscriber. For fundamental package, Hostgator still offers you single domain which packaged together with twenty sub domains. In my opinion, you can start your trial with Hostgator's fundamental bundle. When company gets mature and thinking for development, you can anytime update your package to more advance one.<br><br>Hostgator provides control panel. Out of so many web hosts around the world, Hostgator's cpanel can be said succeeding the top ranking amongst them.<br><br>In term of customer supports, Hostgator has a really strong consumer care team which working 24/7 to assist you tackle all kinds of issues relevant to their items. This is why till now, Hostgator still the finest option for consumers.<br><br>A last words for those who are getting began - don't be scare by exactly what you are checking out as constructing a great website is not that difficult. The work is in reality pretty simple and direct as long as you're getting the right details. To obtain started, you'll initially need a domain and a trusted hosting service.
 
A '''fisheye lens''' is an [[wide-angle lens|ultra wide-angle lens]] that produces strong [[Distortion_(optics)|visual distortion]] intended to create a wide panoramic or [[Sphere#Hemisphere|hemispherical]] image.<ref name="bare_url_a">{{cite book|url=http://books.google.com/?id=3zljhHdWO2IC&pg=PA55&dq=%22a+fisheye+lens+is%22#v=onepage&q=%22a%20fisheye%20lens%20is%22&f=false|author=Henry Horenstein|title=Black and White Photography: A Basic Manual|page=55|isbn=9780316373050|date=2005-04-20}}</ref><ref name="bare_url">{{cite book|url=http://books.google.com/?id=OJrJrEJ-r9QC&dq=kingslake+fisheye+lens+invented+by&q=fish+eye#v=snippet&q=fish%20eye&f=false|author=Rudolf Kingslake|title=A history of the photographic lens|page=145|isbn=9780124086401|date=1989-10-28}}</ref> Fisheye lenses achieve extremely wide [[angle of view|angles of view]] by forgoing producing images with straight lines of perspective ([[rectilinear lens|rectilinear images]]), opting instead for a special mapping (for example: equi[[solid angle]]), which gives images a characteristic convex non-rectilinear appearance.
 
The term ''fisheye'' was coined in 1906 by American physicist and inventor [[Robert W. Wood]] based on how a fish would see an ultra-wide hemispherical view from beneath the water (a phenomenon known as [[Snell's window]]).<ref name="bare_url" /><ref>{{cite magazine|url=http://books.google.com/books?id=DdDPLGzgHoIC&pg=PA159&dq=fisheye+lens+wood&hl=en&sa=X&ei=knFwT_joHqPL0QG5-fHdBg&ved=0CHsQ6AEwCA#v=onepage&q=fisheye%20lens%20wood&f=false|magazine=Philosophical Magazine|volume=12|issue=6|year=1906|chapter=Fish-Eye Views, and Vision under Water|author=RW Wood, Professor of Experimental Physics|publisher=Johns Hopkins University|page=159}}</ref> Their first practical use was in the 1920s for use in [[meteorology]]<ref>{{cite book|url=http://books.google.com/?id=_gqwwMWZm84C&q=first+practical+fisheye+lens&dq=first+practical+fisheye+lens|author=David Brooks|title=Lenses and lens accessories: a photographer's guide|page=29|isbn=9780930764340|year=1982}}</ref><ref>Hill, R. 1924. A lens for whole sky photographs. ''Quarterly Journal of the Royal Meteorological Society'' 50:227-235.</ref>{{Citation needed|date=March 2012}} to study cloud formation giving them the name "whole-sky lenses". The angle of view of a fisheye lens is usually between 100 and 180 degrees<ref name="bare_url_a" /> while the [[focal length]]s depend on the [[film format]] they are designed for.
 
[[Mass production|Mass-produced]] fisheye lenses for [[photography]] first appeared in the early 1960s<ref>[http://books.google.com/books?id=u4rXBqSmjPAC&pg=PA209&dq=first+practical+fisheye+lens&hl=en&sa=X&ei=ZXVwT87_Nsa00QGVr6X-Bg&ved=0CHYQ6AEwCA#v=onepage&q=first%20practical%20fisheye%20lens&f=false Simon Stafford, Rudi Hillebrand, Hans-Joachim Hauschild, The new Nikon compendium: cameras, lenses & accessories since 1917, page 209]</ref> and are generally used for their unique, distorted appearance. For the popular [[135 film|35 mm film]] format, typical focal lengths of fisheye lenses are between 8&nbsp;mm and 10&nbsp;mm for circular images, and 15–16&nbsp;mm for full-frame images.  For digital cameras using smaller electronic imagers such as 1/4" and 1/3" format CCD or CMOS sensors,  the focal length of "miniature" fisheye lenses can be as short as 1 to 2mm.
 
These types of lenses also have other applications such as re-projecting images filmed through a fisheye lens, or created via computer generated graphics, onto hemispherical screens. Fisheye lenses are also used for scientific photography such as recording of [[Aurora (astronomy)|aurora]] and [[meteor]]s, and to study plant canopy geometry and to calculate near-ground [[solar radiation]]. They are also used as [[peephole]] door viewers to give the user a wide field of view.
 
==Uses in photography==
 
In a '''circular fisheye lens''', the [[image circle]] is ''[[inscribed]] in'' the film or sensor area; in a '''full-frame fisheye lens''' the image circle is ''[[circumscribed]] around'' the film or sensor area.
 
Further, different fisheye lenses distort images differently, and the manner of distortion is referred to as their '''[[#Mapping function|mapping function]].''' A common type for consumer use is ''equi[[solid angle]].''
 
Although there are digital fisheye effects available both in-camera and as computer software they can't extend the angle of view of the original images to the very large one of a true fisheye lens.
 
===Circular fisheye===
[[File:Imagine being a fly VLT.jpg|thumb|alt=Image taken using a circular fisheye lens|[[ESO]]'s [[Very Large Telescope|VLT]] image taken with a circular fisheye lens.]]
The first types of fisheye lenses to be developed were "circular fisheye"&nbsp;— lenses which took in a 180° hemisphere and projected this as a circle within the film frame. Some circular fisheyes were available in [[orthographic projection (cartography)|orthographic projection]] models for scientific applications.  These have a 180° ''vertical'' [[angle of view]], and the horizontal and diagonal angle of view are also 180°.  Most circular fisheye lenses cover a smaller image circle than rectilinear lenses, so the corners of the frame will be completely dark.
 
===Full-frame fisheye===
[[File:Vlg shop.jpg|thumb|right|An example of full-frame fisheye used in a closed space ([[Nikkor]] 10.5mm)]]
As fisheye lenses gained popularity in general photography, camera companies began manufacturing fisheye lenses that enlarged the image circle to cover the entire rectangular frame, called a "full-frame fisheye".<ref>[http://books.google.com/books?id=P39ysk_UwZcC&pg=PA33&dq=%22full+frame+fisheye%22&hl=en&sa=X&ei=D3-iT6CSGYb30gHUgp3VDA&ved=0CEkQ6AEwAA#v=onepage&q=%22full%20frame%20fisheye%22&f=false Rob Sheppard, The Magic of Digital Nature Photography, page 33]</ref>
 
The picture angle produced by these lenses only measures 180 degrees when measured from corner to corner: these have a 180° ''diagonal'' [[angle of view]], while the horizontal and vertical angles of view will be smaller; for an equisolid angle-type 15&nbsp;mm full-frame fisheye, the horizontal FOV will be 147°, and the vertical FOV will be 94°.<ref>The formula is <math>\text{FOV} = 4 \cdot \arcsin \left(\frac{\text{frame size}}{4\cdot \text{focal length}}\right)</math> which comes from [[inverse function|inverting]] the [[#Mapping function|mapping function]]; [http://www.dyxum.com/columns/articles/lenses/Takumar-17f4/Takumar_17mmF4_fisheye_review.asp Dyxum, Gustavo Orensztajn]</ref>
 
The first full-frame fisheye lens to be mass-produced was a 16&nbsp;mm lens made by [[Nikon]] in the early 1970s. Digital cameras with [[APS-C]] sized sensors require a 10.5&nbsp;mm lens (or, for Canon APS-C cameras, a 10&nbsp;mm lens) to get the same effect as a 16&nbsp;mm lens on a camera with full-frame sensor.<ref>[http://www.nikonusa.com/template.php?productNr=2148&cat=1&grp=5 AF DX Fisheye-NIKKOR 10.5 mm f/2.8G ED specification]</ref>
 
===Focal length===
Sigma currently makes a 4.5mm fisheye lens that captures a 180 degree field of view on a crop body.<ref>http://www.sigma-photo.com/lenses/lenses_all_details.asp?id=3336&navigator=6 4.5mm F2.8 EX DC Circular Fisheye HSM</ref>
Sunex also makes a 5.6mm fisheye lens that captures a circular 185 degree field of view on a 1.5x Nikon and 1.6x Canon DSLR cameras.
 
[[Nikon]] produced a 6&nbsp;mm circular fisheye lens that was initially designed for an expedition to [[Antarctica]].  It featured a 220-degree field of view, designed to capture the entire sky and surrounding ground when pointed straight up. This lens is no longer manufactured by Nikon,<ref>{{cite web|url=http://www.mir.com.my/rb/photography/companies/nikon/nikkoresources/fisheyes/6mmf28.htm|title=Additional Information on Fisheye-Nikkor 6mm f/2.8 lens|publisher=Malaysian Internet Resources|accessdate=2008-11-11}}</ref> and is used nowadays to produce interactive virtual-reality images such as [[QuickTime VR]] and [[IPIX]]. Because of its very wide field of view, it is  very large and cumbersome&nbsp;— weighing {{convert|5.2|kg|lb}} and having a diameter of {{convert|236|mm|in}}.  It dwarfs a regular 35&nbsp;mm SLR camera<ref>{{cite web|url=http://www.mir.com.my/rb/photography/companies/nikon/nikkoresources/late70nikkor/fisheyes/6mmf28.htm|title=Additional Information on Fisheye-Nikkor 6mm f/2.8 lens: Late 70s|publisher=Malaysian Internet Resources|accessdate=2008-11-11}}</ref> and has its own tripod mounting point, a feature normally seen in large [[Long focus lens|long-focus]] or [[telephoto lens]]es to reduce strain on the [[lens mount]] because the lens is heavier than the camera. The lens is extremely rare.<ref>{{cite journal|last=Laurent|first=Olivier Laurent|title=Rare extreme wide-angle Nikkor lens goes on sale|journal=British Journal of Photography|date=23 April 2012|url=http://www.bjp-online.com/british-journal-of-photography/news/2169615/rare-extreme-wide-angle-nikkor-lens-goes-sale|accessdate=24 April 2012}}</ref>
 
An 8&nbsp;mm fisheye lens, also made by [[Nikon]], has proven useful for scientific purposes because of its equidistant (equiangular) projection, in which distance along the radius of the circular image is proportional to [[zenith angle]].
 
===Fisheye lenses for APS-C cameras===
* [[Pentax DA 10-17mm lens]] (F3.5-4.5) / [[Tokina AF 10-17mm f/3.5-4.5 AT-X DX]]
* [[Samyang 8mm f3.5 fisheye]]. Notable for its [[stereographic projection]].
* [[Sigma 10mm F2.8 EX DC Fisheye HSM lens]]
* [[Nikon AF DX Fisheye-Nikkor 10.5mm f/2.8G ED]]
* [[Sigma 4.5mm F2.8 EX DC Circular Fisheye HSM lens|Sigma 4.5&nbsp;mm {{f/}}2.8 EX DC Circular Fisheye HSM]] for [[APS-C]] sensors
 
===Fisheye lenses for 35 mm cameras===
 
====Circular fisheye====
 
* [[Peleng lens|Peleng]] 8&nbsp;mm {{f/}}3.5
* [[Sigma 8mm f/4 EX DG lens|Sigma 8&nbsp;mm {{f/|4.0}} EX DG]]
* [[Sigma 8mm f/3.5 EX DG lens|Sigma 8&nbsp;mm {{f/}}3.5 EX DG]] - replaces the Sigma 8&nbsp;mm {{f/|4.0}} EX DG
 
====Full-frame fisheye====
* [[Canon EF 15mm lens|Canon EF 15&nbsp;mm {{f/}}2.8]] (discontinued)
* Canon Fisheye FD 15mm {{f/}}2.8 (old lens, does not work on EF mount)
* [[Minolta AF 16mm f/2.8 Fisheye lens]]
* Sigma 15mm {{f/}}2.8 EX DG Diagonal Fisheye
* Fisheye-Nikkor AF 16mm {{f/}}2.8 D
 
==== Zoom fisheye ====
*[[Canon EF 8-15mm lens|Canon EF 8–15mm f/4L Fisheye USM]]{{spaced ndash}}lens can be used as both a full-frame fisheye and a circular fisheye on a 35&nbsp;mm full-frame film or DSLR such as the canon 5d (Mark I{{spaced ndash}}III) cameras, it can only be used as a cropped circular or as a full-frame fisheye on EOS DSLRs with APS-C/H size sensors (a zoom lock is included).
 
* [[Pentax SMC Pentax-F Fish-Eye 1:3.5–4.5 17–28mm]]{{spaced ndash}}lens was born for full-frame film cameras, to take the place of the 16mm f/2.8 in the AF era. It starts from a 17mm full-frame fisheye and reaches the end of the excursion as an overdistorted 28mm. Was intended as a "special effect" lens and never had big sales.<ref>http://panopticus.altervista.org/fishlist/pentax/17-28pkaf.htm</ref>{{citation needed|date=January 2013}}
 
===Miniature fisheye lenses===
[[Miniature digital camera]]s, especially when used as [[security camera]]s, often tend to have such lenses for similar reasons. Miniature fisheye lenses are designed for small-format CCD/CMOS imagers commonly used in consumer and security cameras.<ref>[http://www.omnitech.com/fisheye.htm 190 Degree FOV Miniature Fisheye Lens]</ref><ref>[http://www.optics-online.com/dsl_fisheye.asp Miniature fisheye lenses]</ref> Popular format sizes are 1/4" (active area 3.6mmx2.7mm), 1/3" (active area 4.8mmx3.6mm) and 1/2" (active area 6.6mmx4.8mm). Depending on the imager active area, the same lens can form a circular image on one imager (e.g. 1/2"), and a full frame on the other (e.g. 1/4").
 
<gallery widths="200" heights="190">
Museumfisheye.jpg|An image of the [[Louvre]] museum entry taken with the 7.5&nbsp;mm {{f/|5.6}} circular fisheye Nikkor lens
Car Fisheye.jpg|Canon 8–15mm zoom at 8mm of BMW M3
Panotools5618.jpg|Image shot with a 16mm full-frame fisheye lens before and after remapping to [[rectilinear lens|rectilinear]] perspective.{{refn|group=n|Camera: a 35mm-format digital SLR, editing tool: [[Panorama Tools]]}}
</gallery>
 
==Other applications==
* Many [[planetarium]]s now use fisheye projection lenses to project the night sky or other digital content onto the interior of a dome.
* [[Flight simulators]] and visual combat simulators use fisheye projection lenses in order to create an immersive environment for pilots, air traffic controllers, or military personnel to train in.
* Similarly, the [[IMAX#IMAX Dome/OMNIMAX|IMAX Dome]] (previously 'OMNIMAX') motion-picture format involves photography through a circular fisheye lens, and projection through the same onto a hemispherical screen.
* Scientists and resource managers (e.g., biologists, foresters, and meteorologists) use fisheye lenses for [[hemispherical photography]] to calculate plant canopy indices and near-ground solar radiation. Applications include evaluation of forest health, characterization of [[monarch butterfly]] winter roosting sites, and management of [[vineyards]].
* Astronomers use fisheye lenses to capture cloud cover and [[light pollution]] data.
* Photographers and videographers use fisheye lenses so they can get the camera as close as possible for action shots whilst also capturing context, for example in [[skateboarding]] to focus on the board and still retain an image of the skater.
* The first music video to be shot completely with fisheye lens was for the [[Beastie Boys]] song "[[Shake Your Rump]]" in 1989.
* In [[Computer Graphics]], circular fisheye images can be used to create [[environment map]] from physical world. One complete 180-degree wide angle fisheye image will fit to half of cubic mapping space if proper algorithm applies on. Environment maps can be used to render 3D object and virtual panoramic scene.
 
==Mapping function==
The mapping of a sideways object leads to a picture position displacement from the image center.  The manner of this conversion is the mapping function.  The distance of a point from the image center 'r' is dependent on the focal length of the optical system 'f', and the angle from the optical axis 'θ', where 'θ' is in [[radian]]s.
 
[[File:Fisheye mapping function crop.png|thumb|upright=1.6|Illustration of the conceptual significance of the ''r'', ''f'', and ''θ'' variables used in the mapping function specification.]]
 
<gallery widths="220" heights="150px">
File:PeterW zt 1.svg|Original tunnel to be photographed, with camera looking from inside center to left wall.
</gallery>
 
===Normal (non-fisheye) lens===
 
<gallery widths="220" heights="150px">
File:PeterW zt 2.svg|Gnomonical
File:PeterW zt 3.svg|Gnomonical, 40° right pan
</gallery>
 
* Gnomonical (perspective): <math>r = f \tan(\theta)</math>. Works like the pinhole camera. Straight lines remain straight (distortion free). <math>\theta</math> has to be smaller than 90°. The aperture angle is gaged symmetrically to the optical axis and has to be smaller than 180°. Large aperture angles are difficult to design and lead to high prices.
 
===Fisheye lens===
 
Fisheye lenses can have many different mapping functions:<ref>[http://www.lenstip.com/index.php?test=obiektywu&test_ob=160 Samyang 8 mm f/3.5 Aspherical IF MC Fish-eye]</ref>
<gallery widths="220" heights="150px">
File:PeterW zt 4.png|Stereographic
File:PeterW zt 5.png|Equidistant
File:PeterW zt 6.png|Equisolid angle
File:PeterW zt 7.png|Orthographic
</gallery>
 
* Stereographic (conform): <math>r = 2 f \tan(\theta / 2)</math>. Maintains angles. This mapping would be ideal for photographers because it doesn't compress marginal objects as much. [[Samyang Optics|Samyang]] is the only manufacturer to produce this kind of fisheye lens, but it is available under different brand names. This mapping is easily implemented by software.
* Equidistant (linear scaled): <math>r = f \cdot \theta</math>. Maintains angular distances. Practical for angle measurement (e.g., star maps). [[Panorama Tools (software)|PanoTools]] uses this type of mapping.
* Equisolid angle (equal area): <math>r = 2 f \sin(\theta / 2)</math>. Maintains surface relations. Every pixel subtends an equal [[solid angle]], or an equal area on the [[unit sphere]]. Looks like a mirror image on a ball, best special effect (unsophisticated distances), suitable for area comparison (clouds grade determination). This type is popular but it compresses marginal objects. The prices of these lenses are high, but not extreme.
* Orthographic: <math>r = f \sin(\theta)</math>. Maintains planar illuminance. Looks like an orb with the surroundings lying on < max. 180° aperture angle.
 
* Other mapping functions (for example [[Panomorph]] Lenses) are also possible for enhancing the off-axis resolution of fisheye lenses.
 
With appropriate software, the curvilinear images produced by a fisheye lens can be remapped to a conventional [[rectilinear lens|rectilinear]] projection. Although this entails some loss of detail at the edges of the frame, the technique can produce an image with a field of view greater than that of a conventional rectilinear lens. This is particularly useful for creating [[Panoramic photography|panoramic images]].
 
All types of fisheye lens bend straight lines. Aperture angles of 180° or more are possible only with large amounts of [[barrel distortion]].
 
==See also==
{{Views}}
* [[Azimuthal equidistant projection]], the [[Map projection|projection]] that a fisheye lens creates.
* [[Stereographic projection]]
 
==Notes==
{{Reflist|group=n}}
 
==References==
{{Reflist}}
 
==External links==
{{Commons category|Fisheye lenses}}
* [http://wiki.panotools.org/Fisheye_Projection Fisheye projection theory]
* [http://panopticus.altervista.org/fishlist/fishlist.htm A list of fisheye lenses]
* [http://www.car.nuigalway.ie/documents/chughes_ietautomotivefisheye.pdf Overview of fish-eye distortion effects]
 
{{Photography}}
 
[[Category:Photographic lenses]]

Latest revision as of 12:18, 6 December 2014

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