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.

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.

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.

Contents 1 Types of fisheye lenses 1.1 Circular 1.2 Full-frame 2 Focal length 3 Other uses 4 Fisheye lenses for 35mm cameras 4.1 Circular fisheye 4.2 Full-frame fisheye 5 Mapping function 6 See also 7 References 8 External links

Types of fisheye lenses

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. A common type for consumer use is equisolid angle.

Circular

The picture using a circular fish eye lens

The first types of fisheye lenses to be developed were "circular fisheyes" — 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 models for scientific applications.

These have a 180° vertical angle of view, and the horizontal and diagonal angle of view are also 180°.

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.

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°.The formula is $\backslash text\{FOV\}\; =\; 4\; \backslash cdot\; \backslash arcsin\; \backslash left(\backslash frac\{\backslash text\{frame\; size\}\}\{4\backslash cdot\; \backslash text\{focal\; length\}\}\backslash right)$, which comes from inverting the mapping function; Dyxum, Gustavo Orensztajn

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.AF DX Fisheye-NIKKOR 10.5mm f/2.8G ED specification

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.

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.

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.

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

Full-frame fisheye

• 15mm f/2.8 EX DG Diagonal Fisheye
• Sigma 10mm f/2.8 EX DC Fisheye HSM for APS-C sensors.

Mapping function

PeterW zt 1.png Original tunnel to be photographed, with camera looking from inside center to left wall.	PeterW zt 2.png Gmonomical	PeterW zt 3.png Gmonomical, 40° right pan	PeterW zt 5.png Linear scaled (equidistant)
PeterW zt 7.png Orthographic[dubious – discuss]	PeterW zt 6.png Equal area (equisolid angle)	PeterW zt 4.png Stereographic (conform)

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: $r\; =\; f\; *\; \backslash tan(\backslash theta)$. 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): $r\; =\; f\; \backslash cdot\; \backslash theta$, where θ is in radians. Practical for angle measurement e.g., star maps. PanoTools uses this type.
• Orthographic: $r\; =\; f\; *\; sin(\backslash theta)$. Looks like an orb with the surroundings lying on < max. 180° aperture angle.
• Equal area (equisolid angle): $r\; =\; 2\; f\; \backslash sin(\backslash theta\; /\; 2)$. 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): $r\; =\; 2\; f\; \backslash tan(\backslash theta\; /\; 2)$. 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.

See also

• Map projection

References

External links

• Fisheye projection theory
• Fisheye virtual photography
• A large list of fisheye lenses

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