thumb|A circular fisheye lens for [[Nikon F-mount|alt=a camera lens with a spherical glass top standing upright on a wood table]]
A fisheye lens is an ultra wide-angle lens that produces strong visual distortion intended to create a wide panoramic or hemispherical image. Fisheye lenses achieve extremely wide angles of view, well beyond any rectilinear lens. Instead of producing images with straight lines of perspective (rectilinear images), fisheye lenses use a special mapping ("distortion"; for example: equisolid angle, see below), which gives images a characteristic convex non-rectilinear appearance.
thumb|Circular fisheye photograph of Oude Kerk Amsterdam. [[Chromatic aberration can clearly be seen toward the outer edges.]]
The term fisheye was coined in 1906 by American physicist and inventor Robert W. Wood based on how a fish would see an ultrawide hemispherical view from beneath the water (a phenomenon known as Snell's window). 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, and are generally used for their unique, distorted appearance. For the popular 35mm film format, typical focal lengths of fisheye lenses are for circular images, and for diagonal images filling the entire frame. For digital cameras using smaller imagers such as and format CCD or CMOS sensors, the focal length of "miniature" fisheye lenses can be as short as .
Fisheye lenses also have other applications, such as re-projecting images originally filmed through a fisheye lens, or created via computer-generated graphics, onto hemispherical screens. They are also used for scientific photography, such as recordings of aurora and meteors, and to study plant canopy geometry, and to calculate near-ground solar radiation. In everyday life, they are perhaps most commonly encountered as peephole door viewers to give a wide field of view.
History and development
Panoramas with fisheye distortion predate photography and the fisheye lens. In 1779, Horace Bénédict de Saussure published his downward-facing fisheye view of the Alps: "All the objects are drawn in perspective from the centre".
<gallery mode="packed" heights="200px">
File:Vue circulaire des montagnes qu ‘on decouvre du sommet du Glacier de Buet, from Horace-Benedict de Saussure, Voyage dans les Alpes, précédés d'un essai sur l'histoire naturelle des environs de Geneve. Neuchatel, l779-96, pl. 8.jpg|"Vue circulaire des montagnes qu'on découvre du sommet du Glacier de Buet", Horace-Benedict de Saussure
File:Wood-1906 - Fig 1.jpg|Wood's pail (top) and improved (bottom) camera (1906)
File:Wood-1906 - Fig 2.jpg|First known fisheye image recorded in 1905 using Wood's pail apparatus (1906)
File:Bond-1922 - Fig 1.png|Bond's hemispherical lens (1922)
</gallery>
In 1906, Wood published a paper detailing an experiment in which he built a camera in a water-filled pail starting with a photographic plate at the bottom, a short focus lens with a pinhole diaphragm located approximately halfway up the pail, and a sheet of glass at the rim to suppress ripples in the water. The experiment was Wood's attempt "to ascertain how the external world appears to the fish" and hence the title of the paper was "Fish-Eye Views, and Vision under Water". Bond's hemispheric lens also reduced the need for a pinhole aperture to ensure sharp focus, so exposure times were also reduced.
Hill Sky Lens
[[File:Hill Sky Lens (1924).svg|thumb|right|Hill/Beck Sky Lens (1923, GB 225,398) Distortion is unavoidable in a lens that encompasses an angle of view exceeding 125°, but Hill and Beck claimed in the patent that stereographic or equidistant projection were the preferred mapping functions.
The Hill Sky Lens was fitted to a whole sky camera, typically used in a pair separated by for stereo imaging, and equipped with a red filter for contrast; in its original form, the lens had a focal length of and cast an image in diameter at . Conrad Beck described the camera system in an article published in 1925. At least one has been reconstructed.
German and Japanese development
thumb|right|Schulz/AEG Weitwinkelobjektiv (1932, DE 620538) Compared to the 1923 Hill Sky Lens, the 1932 Weitwinkelobjektiv featured two diverging meniscus elements ahead of the stop and used a cemented achromatic group in the converging section. and [[Otto Umbehr|Umbo used the AEG lens for artistic purposes, with photographs published in a 1937 issue of Volk und Welt.
The AEG Weitwinkelobjektiv formed the basis of the later Nippon Kogaku (Nikon) Fisheye-Nikkor 16 mm lens of 1938, which was used for military and scientific (cloud cover) purposes. Nikon, which had a contract to supply optics to the Imperial Japanese Navy, possibly gained access to the AEG design under the Pact of Steel. which was used for aerial surveillance during World War II. The converging rear group of the Pleon was symmetrical, derived from the 4-element Topogon lens designed by Richter for Zeiss in 1933. Testing on a captured lens after the war showed the Pleon provided an equidistant projection to cover a field of approximately 130°, and negatives were printed using a special rectifying enlarger to eliminate distortion.
35 mm development
thumb|right|upright=0.7|Merté/Zeiss Sphaerogon (1935, DE 672 393 Unlike the Weitwinkelobjektiv, Merté's Sphaerogon was not limited to medium format cameras; prototype versions of the Sphaerogon were constructed for the [[Contax I miniature format camera. The first prototype Sphaerogon lenses constructed had a maximum aperture of , but later examples were computed half a stop faster, to . Several prototype examples of Sphaerogon lenses were recovered as part of the Zeiss Lens Collection seized by the Army Signal Corps as war reparations in 1945; the collection, which the Zeiss firm had retained as a record of their designs, was later documented by Merté, the former head of optical computation for CZJ, working under Signal Corps officer Edward Kaprelian.
After the war, the Fisheye-Nikkor lens was mated to a medium format camera and was produced in slightly modified form (focal length increased slightly to 16.3 mm) as the "Sky-image Recording Camera" in March 1957 for the Japanese government, followed by a commercial release as the Nikon Fisheye Camera (also known as the "Nikon Sky Camera" or "Nikon Cloud Camera") in September 1960, which had a retail price of . The revised lens created a circular image in diameter and covered a complete hemispherical field of 180°. Only 30 examples of the Nikon Fisheye Camera were manufactured, and of those, 18 were sold to customers, mainly in the United States; Nikon likely destroyed the remaining stock to avoid tax penalties. Photographs taken with the Fisheye Camera that were published in Life in 1957 marked the first wide exposure of the public to fisheye distortion; including a photograph of the United States Senate caucus room, taken by Ed Clark and published in an April 1957 issue, and a photograph of pole vaulter Bob Gutowski taken by Ralph Crane, published in July 1957.
thumb|left|[[Album cover of Are You Experienced (1967) by The Jimi Hendrix Experience, featuring the trio photographed using a fisheye lens]]
The Nikon Fisheye Camera was discontinued in September 1961, which required the reflex mirror on its Nikon F and Nikkormat cameras to be locked up prior to mounting the lens. Prior to the early 1960s, fisheye lenses were used primarily by professional and scientific photographers, but the advent of the fisheye for the 35 mm format increased its popular use. The Fisheye-Nikkor 8 mm has a field of view of 180° and uses 9 elements in 5 groups; it has a fixed focus and built-in filters intended for black-and-white photography. Research indicates that fewer than 1,400 lenses were built. As fisheye lenses became more widely available, the distinctive distortion grew in popularity, especially for album covers. For example, British fashion photographer Tim Walker used a fisheye lens to capture the cover of Harry Styles' 2019 pop/rock album, Fine Line. Other genres that have taken advantage of the fisheye lens look include punk rock, hip-hop, and skateboarding videos.
- 6 mm (1969), the first fisheye to feature a 220° field of view; A 6.2 mm SAP fisheye was later produced in limited numbers with an aspherical surface, encompassing a 230° field of view.
- 8 mm (1970), the first circular fisheye with variable focus, automatic aperture, and reflex viewing (mirror lock-up no longer required). followed by the slightly faster UW Rokkor-PG 18 mm from Minolta in 1966. Both of these were reflex-viewing and fixed-focus. Both Pentax and Minolta followed up with faster lenses with variable focus in 1967 (Super Fish-eye-Takumar 17 mm ) and 1969 (Rokkor-OK 16 mm ), respectively. The 16 mm Rokkor was later adopted by Leica as the Fisheye-Elmarit-R (1974) for its SLRs and then converted to autofocus (1986) for the Alpha system. , the same basic optical design is still sold as the Sony SAL16F28.
Design
Unlike rectilinear lenses, fisheye lenses are not fully characterised by focal length and aperture alone. Angle of view, image diameter, projection type, and sensor coverage all vary independently of these.
Image diameter and coverage
{| style="float:right; margin-left:1em; border:solid 1px #cccccc; text-align:center;"
|+ style="text-align:left; font-weight:bold;" | Types of using format
|-
! colspan="2" style="width:135px;" | Circular
! style="width:135px;" | Cropped circle
! style="width:135px;" | Full-frame
|- style="vertical-align:top;"
| colspan="2" | 134px
| 134px || 134px
|- style="vertical-align:top; font-size:85%;"
| style="width:20px; font-weight:bold;" | 3:2
| style="width:104px;" | 52% sensor
| 78% FOV, 92% sensor || 59% FOV
|- style="vertical-align:top; font-size:85%;"
| style="font-weight:bold;" | 4:3
| 59% sensor || 86% FOV, 90% sensor || 61% FOV
|- style="vertical-align:middle; font-size:85%;"
| colspan="3" | 134px<br />Circular fisheye for 35 mm<br />
| 134px<br />Full-frame fisheye with rudimentary lens hood<br />
|- style="vertical-align:top; font-size:85%;"
| colspan="2" | 134px<br />ESO's VLT image taken with a circular fisheye lens.
| 134px<br />35 mm circular fisheye with DX-format-camera<br /> || 134px<br />Diagonal fisheye used in a closed space (Nikkor 10.5 mm)
|}
In a circular fisheye lens, the image circle is inscribed in the film or sensor area; in a diagonal ("full-frame") fisheye lens, the image circle is circumscribed around the film or sensor area. This implies that using a fisheye lens for a different format than it was intended for is easy (as opposed to a rectilinear lens), and may change its characteristic.
Further, different fisheye lenses map ("distort") images differently, and the manner of distortion is referred to as their mapping function. A common type for consumer use is equisolid angle.
Although there are digital fisheye effects available both in-camera and as computer software, neither can extend the angle of view of the original images to the very large one of a true fisheye lens.
Focal length
The focal length is determined by the angular coverage, the specific mapping function used, and the required dimensions of the final image. Focal lengths for popular amateur camera sizes are computed as:
{|class="wikitable" style="text-align:center;"
|+ Calculated fisheye focal lengths, (millimeters)
|-
! scope="row" rowspan=2 colspan=2 | Inverse mapping function Sunex also makes a 5.6mm fisheye lens that captures a circular 185° field of view on a 1.5x Nikon and 1.6x Canon DSLR cameras.
thumb|left|upright=1.5|Fisheye-Nikkor 6mm mounted on a [[Nikon F2 in the Nikon Museum.]]
Nikon produced a 6 mm circular fisheye lens for 35 mm film that was initially designed for an expedition to Antarctica. It featured a 220° field of view, designed to capture the entire sky and surrounding ground when pointed straight up. This lens is no longer manufactured, 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 — weighing , having a diameter of , a length of and an angle of view of 220 degrees. It dwarfs a regular 35 mm SLR camera and has its own tripod mounting point, a feature normally seen in large long-focus or telephoto lenses to reduce strain on the lens mount. The lens is extremely rare.
thumb|The fish eye lens Laowa 4mm of the manufacturer [[Venus Optics]]
More recently, the Japanese manufacturer Entaniya offers several fisheye lenses with angles of view up to 250° on 35 mm full frame, and up to 280° on smaller sensors (see list below), intended for use in virtual reality applications. In 2018, Venus Optics introduced a 210° fisheye lens for the Micro Four Thirds system.
The 8 mm and 7.5 mm circular fisheye lenses made by Nikon have proven useful for scientific purposes because of their equidistant (equiangular) projection, in which distance along the radius of the circular image is proportional to the zenith angle.
Diagonal fisheyes (a.k.a. full-frame or rectangular)
As fisheye lenses gained popularity in general photography, camera companies began manufacturing fisheye lenses with an enlarged image circle to cover the entire rectangular film frame. They are called diagonal, or sometimes "rectangular" or "full-frame", fisheyes. (This was well before digital photography, so the use of the term "full frame" with respect to fisheyes has nothing to do with the use of the term to designate a digital sensor measuring 36x24 mm).
The angle of view produced by diagonal fisheyes only measures 180° from corner to corner: they have a 180° diagonal angle of view (AOV), while the horizontal and vertical angles of view will be smaller. For an equisolid angle 15 mm full-frame fisheye, the horizontal AOV will be 147°, and the vertical AOV will be 94°.
One of the first diagonal fisheye lenses to be mass-produced was the Nikon Fisheye-Nikkor F 16mm , made in the early 1970s.
To obtain the same effect on digital cameras with smaller sensors, shorter focal lengths are required. Nikon makes a 10.5 mm fisheye for their APS DX SLRs. Several other companies make "full frame", i.e. diagonal, fisheyes for APS and m43 cameras, see next paragraph.
Portrait or cropped-circle fisheyes
An intermediate between a diagonal and a circular fisheye consists of a circular image optimised for the width of the film format rather than the height. As a result, on any non-square film format, the circular image will be cropped at the top and bottom, but still show black edges on the left and right. This format is called a "portrait" fisheye; historically, it has been rather rareonly the 12 mm Accura lens (see list below) directly follows the portrait principle. Today however, a portrait fisheye effect is easily achieved by using a fisheye lens intended for full coverage of a smaller sensor format, like an APS diagonal fisheye on a 35 mm full frame camera, or an m43 diagonal fisheye on APS.
Miniature fisheye lenses
Miniature digital cameras, especially when used as security cameras, often tend to have fisheye lenses to maximize coverage. Miniature fisheye lenses are designed for small-format CCD/CMOS imagers commonly used in consumer and security cameras. Popular image sensor format sizes used include ", ", and ". Depending on the active area of the image sensor, the same lens can form a circular image on a larger image sensor (e.g. "), and a full frame on a smaller one (e.g. ").
Examples and specific models
For a comprehensive list of all current and all past fisheye lenses, see External Links below.
Noteworthy fisheye lenses for APS-C cameras
The APS-C image sensor used in Canon cameras is , or on the diagonal, which is slightly smaller than the sensor size used by other popular manufacturers of cameras with APS-C sensors, such as Fuji, Minolta, Nikon, Pentax, and Sony. The other common APS-C sensors are on the long dimension and on the shorter side, for a diagonal dimension of .
Circular APS-C fisheye lenses
- Sigma
- Lensbaby
Diagonal APS-C fisheye lenses
- Nikon for Nikon F DSLRs
- Samyang for various APS DSLRs. Notable for its stereographic projection.
- Samyang for various mirrorless mounts. Notable for its stereographic projection.
- Sigma for various APS DSLRs.
Zoom APS-C fisheye lenses
- Pentax / Tokina (jointly developed) for various APS DSLRs.
Noteworthy fisheye lenses for 35 mm full frame cameras
Circular fisheye lenses
thumb|The Peleng 8 mm circular fisheye lens
- Accura 12 mm (180° portrait fisheye lens, i.e. optimised for the height rather than the width of the frame, thus giving a circular image of larger diameter, i.e. cropped at the top and bottom. 1968. Sold as Beroflex, Berolina, Panomar, Sigma, Spiratone, Universa, Upsilon, Vemar etc. Very bad.)
- C-4 Optics Hyperfisheye 4.9 mm (270°, 2020, for mirrorless camera only, 13 kg)
- Canon FD 7.5 mm (180°, 1971, three versions: initial version with silver bayonet ring, 1973 S.S.C. version with silver bayonet ring, 1979 NewFD version with the same SSC coating, black bayonet ring; all have inbuilt, wheel-selectable colour filters)
- Entaniya HAL 200 6 mm (200°, 19.9 mm image diameter, for mirrorless camera only)
- Entaniya HAL 250 6 mm (250°, 23.7 mm image diameter, for mirrorless camera only, fixed aperture, 2 kg (the company also makes a 280° model with however only 5mm image diameter))
- Nikon F 6 mm (220°, 1972)
- Nikon F 6 mm (220°, 1970)
- Nikon F 7.5 mm (220°, 1966)
- Samyang 12 mm ED AS NCS Diagonal Fisheye (famous for its stereographic projection; available in several SLR and mirrorless camera mounts)
- Sigma 15 mm EX DG Diagonal Fisheye
- TTArtisan 11mm Fisheye (notable as the first fisheye lens marketed, among others, in Leica M rangefinder mount and for Fuji GFX (the lens does not cover the full GFX frame, though!). An expert found it is actually 15 mm in focal length and has an angle of view of only 176°.)
- Zenitar 16 mm Fisheye lens
Zoom fisheye lenses
- Canon EF 8–15mm L Fisheye USM180° at all focal lengths, but turning from a circular to a diagonal fisheye on a 35 mm full-frame camera, i.e. changing in vertical angle of view. On a crop camera with APS-C/H size sensors, it only yields a cropped circular and full-frame image. A zoom lock is included which avoids leaving the focal length range of full coverage on crop sensor cameras.
- Nikon AF-S Fisheye Nikkor 8–15mm E EDdesigned for full-frame and FX cameras, this lens behaves identically to the Canon.
- Tokina AT-X AF DX = Pentax DA ED IF 10–17 mm a fisheye zoom lens designed for APS-C sensor cameras, also sold as an NH version without integrated lens hood: then, it is usable on full frame cameras.
- Pentax F 17–28mm FisheyeThis lens was born for 35 mm 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 (diagonal) fisheye. When it reaches 28mm, the fisheye effect is almost gone, leaving an overdistorted wideangle image. It was intended as a "special effect" lens and is claimed not to have sold too many copies.
Curiosities
- Canon 5.2 mm f/2.8 RF L (a 190° stereographic fisheye with two fisheye lens systems: for 3D virtual reality shooting onto a single 35 mm full-frame image sensor, and less relevant for photography: fitting two image circles onto one frame of 36 mm width means that each can only be 18 mm in diameter, wasting quite a bit of resolution)
- Pentax K "Bird's eye" 8.4 mm (prototype, 1982, rendition not quite the same as a fisheye)
Sample images
<gallery widths="200" heights="190">
Museumfisheye.jpg|An image of the Louvre museum entry taken with the 7.5 mm circular fisheye Nikkor lens
WellsCathedral-28F12wyrdlight.jpg| Fisheye used to capture entire Wells Cathedral Chapter House room
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 perspective.
File:Fisheye 16mm vs Ultra Wide Angle 11mm.jpg|Comparison of rectilinear 11mm lens and fisheye 16mm lens on a full frame DSLR
File:Fisheye mapping function (animation).gif|Comparison of conventional (rectilinear) mapping function with four different fisheye mapping functions, given a constant focal length.
</gallery>
Other applications
thumb|The curves of [[ESO's headquarters through a fish-eye lens. ]]
- Many planetariums now use fisheye projection lenses to project the night sky or other digital content onto the interior of a dome.
- Fish-eye lenses are used in POV pornography to make things right in front of the camera look bigger.
- 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 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 "eye" of the HAL 9000 computer from 2001: A Space Odyssey was constructed using a Fisheye-Nikkor 8 mm lens. HAL's point-of-view was filmed using a Fairchild-Curtis 'bug-eye' lens originally designed for films in the Cinerama 360 dome format.
- The first music video to be shot near completely with fisheye lens was for the Beastie Boys song "Hold It Now, Hit It" in 1987.
- In Computer Graphics, circular fisheye images can be used to create environment maps from the physical world. One complete 180-degree wide angle fisheye image will fit to half of cubic mapping space using the proper algorithm. Environment maps can be used to render 3D objects and virtual panoramic scenes.
- Many personal weather station online cameras around the world upload fisheye images of the current local sky conditions as well as a previous day time-lapse sequence with climate conditions such as temperature, humidity, wind and rainfall amounts.
- In door's peepholes, to allow the viewer inside to see a wider view from the outside.
Mapping function
The subject is placed in the image by the lens according to the mapping function of the lens. The mapping function gives , the position of the object from the center of the image, as a function of , the focal length, and , the angle from the optical axis, in radians.
{|class=wikitable style="text-align:center;"
|+ Comparison of mapping functions
!Subject
|colspan=5 | 300px<br/>Original tunnel to be photographed, with camera looking from inside center to left wall.<br/>
|-
! rowspan=2 style="width:10%;" | !! Normal !! colspan=4 | Fisheye
|-
! style="width:18%;" |Rectilinear
! style="width:18%;" |Stereographic
! style="width:18%;" |Equidistant
! style="width:18%;" |Equisolid angle
! style="width:18%;" |Orthographic
|-
! scope="row" | Other names
| gnomonic, perspective, conventional
| panoramic, conform, planisphere
| linear, linear-scaled
| equal-area
| orthogonal
|-
! scope="row" Image
|130px
|130px
|130px
|130px
|130px
|-
! scope="row" | Mapping function
|
|
- Samyang 8 mm
- Samyang 12 mm
|
- Canon FD 7.5 mm
- Coastal Optical 7.45 mm
- Nikkor 6 mm
- Nikkor 7.5 mm
- Nikkor 8 mm
- Nikkor 8 mm
- Peleng 8 mm
- Rokkor 7.5 mm
- Sigma 8 mm
- Samyang 7.5 mm
|
- Canon EF 15 mm (1988)
- Minolta 16 mm (1971)
- Nikkor 10.5 mm
- Nikkor 16 mm (1995)
- Sigma 4.5 mm
- Sigma 8 mm EX DG
- Sigma 8 mm