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Encyclopedia > Fisheye lens
Fisheye 15 mm (type: equisolid angle), 35 mm-film, cropped by slide-frame. Complete room (4 walls, ceiling and floor).

In photography, a fisheye lens is a wide-angle lens that takes in an extremely wide, hemispherical image. Originally developed for use in meteorology and astronomy and called "whole-sky lenses", fisheye lenses quickly became popular in general photography for their unique, distorted appearance. They are often used by photographers shooting broad landscapes to suggest the curve of the Earth. Hemispherical photography is used for various scientific purposes to study plant canopy geometry and to calculate near-ground solar radiation. Fisheye 15mm (type: equisolid angle), 35mm-Film, cropped by slide-frame. ... Fisheye 15mm (type: equisolid angle), 35mm-Film, cropped by slide-frame. ... Photography [fÓ™tÉ‘grÓ™fi:],[foÊŠtÉ‘grÓ™fi:] is the process of recording pictures by means of capturing light on a light-sensitive medium, such as a film or electronic sensor. ... One of Canons most popular wide-angle lenses - 17-40 mm f/4 L retrofocus zoom lens. ... For other uses, see Sphere (disambiguation). ... // Meteorology (from Greek: Î¼ÎµÏ„Î­Ï‰ÏÎ¿Î½, meteoron, high in the sky; and Î»ÏŒÎ³Î¿Ï‚, logos, knowledge) is the interdisciplinary scientific study of the atmosphere that focuses on weather processes and forecasting. ... For other uses, see Astronomy (disambiguation). ... Solar irradiance spectrum at top of atmosphere. ...

The focal lengths of fisheye lenses depend on the film format. For the popular 35 mm film format, typical focal lengths of fisheye lenses are between 8 mm and 10 mm for circular lenses, and 15-16 mm for full-frame lenses. This article is about focal length related to lenses and systems of lenses. ... // Movie film formats Amateur formats: 8 mm Single-8 Super 8 mm Polavision 9,5 mm film 17. ... 135 Film Size, Kodak Tri-X 400 speed 135 (ISO 1007) is a film format for still photography. ...

All the ultra-wide angle lenses suffer from some amount of barrel distortion. While this can easily be corrected for moderately wide angles of view, rectilinear ultra-wide angle lenses with angles of view greater than 90 degrees are difficult to design. Fisheye lenses achieve extremely wide angles of view by foregoing a rectilinear image, opting instead for a special mapping (for example: equisolid angle), which gives images a characteristic convex appearance. A panorama by rotating lens or stitching images (cylindrical perspective) is not a fisheye photo. Barrel Simulation Barrel distortion is a divergence from the rectilinear projection in geometric optics where image magnification decreases with increasing distance from the optical axis. ... A cameras angle of view can be measured horizontally, vertically, or diagonally. ... In photography, a rectilinear lens is a photographic lens that yields images where straight features, such as the walls of buildings, appear with straight lines, as opposed to being curved. ... This article is an overview of the term Panorama. ... Cylindrical perspective is caused by fisheye and panoramic lenses which reproduce straight horizontal lines above and below the lens axis level as curved while reproducing straight horizontal lines on lens axis level as straight. ...

## Types of fisheye lenses GA_googleFillSlot("encyclopedia_square");

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. In geometry, an inscribed planar shape or solid is one that is enclosed by and fits snugly inside another geometric shape or solid. ... Circles circumscribed about several polygons In geometry, a circumscribed planar shape or solid is one that encloses and fits snugly around another geometric shape or solid. ...

Further, different fisheye lenses distort images differently, and the manner of distortion is referred to as their mapping function. A common type for consumer use is equisolid angle.

### Circular

The picture using a circular fish eye lens

These have a 180° vertical angle of view, and the horizontal and diagonal angle of view are also 180°. A cameras angle of view can be measured horizontally, vertically, or diagonally. ...

### Full-frame

Fisheye 10.5 mm Nikkor (type: equisolid angle), APS-C sized sensor, cropped to rectangle.

As fisheye lenses gained popularity in general photography, camera companies began manufacturing fisheye lenses that enlarged the image circle to cover the entire 35 mm film frame, and this is the type of fisheye most commonly used by photographers. Nikkor is the brand of the lenses produced by Nikon Corporation, Japan. ...

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 mm full-frame fisheye, the horizontal FOV will be 147°, and the vertical FOV will be 94°.[1] A cameras angle of view can be measured horizontally, vertically, or diagonally. ...

The first full-frame fisheye lens to be mass-produced was a 16 mm lens made by Nikon in the late 1960s. Digital cameras with APS-C sized sensors require a 10.5 mm lens to get the same effect as a 16 mm lens on a camera with full-frame sensor.[2] For other uses, see Nikon (disambiguation). ... The 1960s decade refers to the years from 1960 to 1969. ... Advanced Photo System type-C (APC-C) is a type of sensor used in digital Single Lens Reflex cameras, also called dSLRs. ...

## Focal length

The widest lens ever produced was a 6 mm circular fisheye made by Nikon. 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 still manufactured by Nikon upon special order[1], 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 - weighing 5.2 kg (11.5 lb) and having a diameter of 236 mm (9.3 in). It dwarfs a regular 35mm SLR camera[2] 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 because the lens is heavier than the camera. For other uses, see Nikon (disambiguation). ... QuickTime VR (virtual reality) (also known as QTVR) is a type of image file format supported by Apples QuickTime. ... IPIX (Interactive Picture, Inc. ... 500 mm telephoto lens with extension tube. ... A Leica R series teleconverter, with the female side of the Leica R bayonet mount. ...

An 8mm fisheye lens, also made by Nikon, has proven useful for various scientific uses because of its equidistant (equiangular) projection, in which distance along the radius of the circular image is proportional to zenith angle. For other uses, see Nikon (disambiguation). ...

## Other uses

• Some planetariums use a form of fisheye lens to project a two-dimensional film image of the night sky onto the interior of a dome.
• 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.
• Photographers and videographers use fisheye lenses so they can get the camera as close as possible for action shots, for example in skateboarding to focus on the board and still retain an image of the skater.
• The peepholes used in doors contain fisheye lenses.
• The first music video to be shot completely with fisheye lens was for the Beastie Boys song "Shake Your Rump" in 1989.

For the song by Ai Otsuka, see Planetarium (song) // A planetarium is a theatre built primarily for presenting educational and entertaining shows about astronomy and the night sky, or for training in celestial navigation. ... IMAX theatre at the Melbourne Museum complex, Australia BFI London IMAX by night LHemisferic (Ciutat de les Arts i les CiÃ¨ncies) Valencia, Spain IMAX (short for Image Maximum) is a film format created by Canadas IMAX Corporation that has the capacity to display images of far greater... Binomial name (Linnaeus, 1758) The butterfly species Danaus plexippus is commonly known as the Monarch butterfly. ... A vineyard A vineyard is a place where grapes are grown for making wine, raisins, or table grapes. ... Skateboarders Skateboarding is the act of riding on and performing tricks with a skateboard. ... The Beastie Boys are a hip hop musical group from New York City consisting of Michael Mike D Diamond, Adam MCA Yauch, Adam Ad-Rock Horovitz. ... Shake Your Rump is the 2nd track on Pauls Boutique by American hip hop group the Beastie Boys, released on July 25, 1989. ...

## Fisheye lenses for 35mm cameras

### Circular fisheye

• Sigma 8mm f/3.5 EX DG (replaces the Sigma 8mm f/4 EX DG.
• Sigma 4.5mm f/2.8 EX DC Circular Fisheye HSM for APS-C sensors.
• Canon FD 7.5mm f/5.6; note that this is not a EF mount, and is not in production.
• Peleng 8mm

Advanced Photo System type-C (APC-C) is a type of sensor used in digital Single Lens Reflex cameras, also called dSLRs. ...

### Full-frame fisheye

• 15mm f/2.8 EX DG Diagonal Fisheye
• Sigma 10mm f/2.8 EX DC Fisheye HSM for APS-C sensors.
• Zoom Tokina 10-17mm f/3.5-4.5 fisheye lens for APS-C sensors

Advanced Photo System type-C (APC-C) is a type of sensor used in digital Single Lens Reflex cameras, also called dSLRs. ...

## 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'.

Normal (non-fisheye) lens:

• Gnomonical or perspective: r = f * tan(θ). Works like the pinhole camera. Straight lines remain straight (distortion free). "θ" 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 lenses can have many different mapping functions:

• Linear scaled (equidistant): $r = f cdot theta$, where θ is in radians. Practical for angle measurement e.g., star maps. PanoTools uses this type.
• Orthographic: r = f * sin(θ). Looks like an orb with the surroundings lying on < max. 180° aperture angle.
• Equal area (equisolid angle): r = 2fsin(θ / 2). 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.
• Stereographic (conform): r = 2ftan(θ / 2). This mapping would be ideal for photographers because it doesn't compress marginal objects. Although no lens has yet been developed for this type, this mapping is easily implemented by software.

All types of fisheye lens bend straight lines. Aperture angles of 180° or more are possible only with large amounts of barrel distortion. For the musical group, see Radian (band). ... Panorama Tools is a collection of free software programs for creating panoramas from multiple images. ... Barrel Simulation Barrel distortion is a divergence from the rectilinear projection in geometric optics where image magnification decreases with increasing distance from the optical axis. ...

The Mercator projection shows courses of constant bearing as straight lines. ...

## References

1. ^ The formula is $text{FOV} = 4 cdot arcsin left(frac{text{frame size}}{4cdot text{focal length}}right)$, which comes from inverting the mapping function; Dyxum, Gustavo Orensztajn
2. ^ AF DX Fisheye-NIKKOR 10.5mm f/2.8G ED specification

In mathematics, an inverse function is in simple terms a function which does the reverse of a given function. ...

Results from FactBites:

 Fisheye Photos and Theory (869 words) A 15mm fisheye is described as a distorting lens, while a 15mm wideangle is "corrected". The fisheye is not a distorted perspective, it is actually the natural perspective for an extreme wide angle. None of the three full circle lens combinations I have used indicate what their mapping is, in fact I suspect that "semi fisheye" means that the makers are not altogether sure themselves.
 Circular Fisheye Camera (973 words) Fisheye photo of bridge and downtown Saskatoon: Parallel view, Cross view, Closeup (2d). This lens is a full frame fisheye which means that it is 180 degrees angle of view only on the diagonals. By checking infinity focus at the top, bottom, left and right of the image I could tell that the lens is slightly tilted relative to the film plane but only by the with of the 2.2 markings on the lens.
More results at FactBites »

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