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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.

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 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

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 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.

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, 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 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 because the lens is heavier than the camera.

An 8 mm 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.
• Many scenes of the film A Clockwork Orange were filmed with a fisheye lens.
• The first music video to be shot completely with fisheye lens was for the Beastie Boys song "Shake Your Rump" in 1989.
• Miniature fisheye lenses are used in automotive rear-view cameras and security cameras.
• Fully immersive 360 degree panorama can be created from 2 or 3 shots taken with a full circular SuperFisheye lens.

Fisheye lenses for 35 mm cameras

Circular fisheye

• Sigma 8 mm f/3.5 EX DG (replaces the Sigma 8 mm f/4 EX DG.
• Sigma 4.5 mm f/2.8 EX DC Circular Fisheye HSM for APS-C sensors.
• Canon FD 7.5 mm f/5.6; note that this is not a EF mount, and is not in production.
• Peleng 8 mm
• Sunex circular 185 degree SuperFisheye 5.6mm

Full-frame fisheye

• 15 mm f/2.8 EX DG Diagonal Fisheye
• Sigma 10 mm 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

Mapping function

• Original tunnel to be photographed, with camera looking from inside center to left wall.
• Gnomonical
• Gnomonical, 40° right pan
• Linear scaled (equidistant)
• Orthographic
• Equal area (equisolid angle)
• 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: ${\displaystyle r=f\tan(\theta )}$. 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): ${\displaystyle r=f\cdot \theta }$, where θ is in radians. Practical for angle measurement e.g., star maps. PanoTools uses this type.
• Orthographic: ${\displaystyle r=f\sin(\theta )}$. Looks like an orb with the surroundings lying on < max. 180° aperture angle.
• Equal area (equisolid angle): ${\displaystyle r=2f\sin(\theta /2)}$. 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): ${\displaystyle r=2f\tan(\theta /2)}$. This mapping would be ideal for photographers because it doesn't compress marginal objects as much. Although no lens has yet been developed for this type except for unique applications (for example Tailored Distortion lenses), 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

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

External links

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

• Photographic lenses