# Fisheye lens: Wikis

Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.

# Encyclopedia

Updated live from Wikipedia, last check: May 23, 2013 19:11 UTC (40 seconds ago)

 Graphical projection Part of a series on: Parallel projection Orthographic projection Multiviews Plan, or floor plan Section Elevation Auxiliary Axonometric projection Isometric projection Dimetric projection Trimetric projection Oblique projection Perspective projection Views

In photography, a fisheye lens is a wide-angle lens that takes in an extremely wide, hemispherical image. Originally developed for use in meteorology[1] to study cloud formation 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 images, and 15–16 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.

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 forgoing 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

Image taken using a circular fisheye 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°. Most circular fisheye lenses cover a smaller image circle than rectilinear lenses, so the corners of the frame will be completely dark.

### 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°.[2]

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.[3]

### Miniature Fisheye Lenses

Miniature fisheye lenses[4] are designed for small format CCD/CMOS imagers commonly used in consumer and security cameras. 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"). Sunex[5] makes a series of miniature fisheye lenses for popular imager formats.

## Focal length

Sigma currently makes a 4.5mm fisheye lens that captures a 180 degree field of view on a crop body.[6] 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 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 still manufactured by Nikon upon special order[7], 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 kilograms (11 lb) and having a diameter of 236 millimetres (9.3 in). It dwarfs a regular 35 mm SLR camera[8] 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 scientific purposes because of its equidistant (equiangular) projection, in which distance along the radius of the circular image is proportional to zenith angle.

## Other uses

An image shot with a 16mm full-frame fisheye lens, with a 35mm-format digital SLR, before and after remapping to rectilinear perspective with Panorama Tools
• With appropriate software, the curvilinear images produced by a fisheye lens can be remapped to a conventional 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 images.
• 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 whilst also capturing context, for example in skateboarding to focus on the board and still retain an image of the skater.
• The peepholes used in doors generally contain fisheye lenses, so as to give a wide field of view. Security cameras often tend to have such lenses for similar reasons.
• 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 35 mm cameras

### Circular fisheye

• Peleng 8 mm f/3.5
• Canon FD 7.5 mm f/5.6 (note: not EF mount) (not in production)
• Nikkor 8mm f/2.8 lens (not in production)
• 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
• Sunex[9] 185 deg SuperFisheye[10] 5.6mm f/5.6 for DSLRs
• Vemar 12mm f/5.6 Fish-Eye / Ultra-Wideangle—circular image on full-frame 135 cameras if the integral hood is in place, 160 degree view. Usually available as a T2 mount for various cameras, but no longer in production.

### Full-frame fisheye

• AF DX Fisheye-Nikkor 10.5mm f/2.8G ED (full frame on DX sensors, almost circular on FX sensors if integral hood is removed[11] -- the image circle is slightly bigger than the frame and there is some cropping at the top and bottom).[12]
• MC Zenitar 16mm f/2.8 (Models available: MC Zenitar-K - Pentax mount; MC Zenitar-M - M42 screwmount; MC Zenitar-H - Nikon mount)[13]
• Sigma 15 mm f/2.8 EX DG Diagonal Fisheye[14]
• 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
• Canon EF 15mm f/2.8
• Minolta/Sony AF 16mm f/2.8 Fisheye
• Olympus Zuiko Digital ED 8mm f/3.5 Fisheye] for Four Thirds cameras[15]
• Pentax DA 10-17mm f/3.5-4.5 ED(IF) -- full-frame image for APS-C sensors on K-mount cameras
• Samyang 8 mm f/3.5 Fisheye CS for APS-C sensors - also marketed as Bower, Polar, Falcon, Rokinon and the same as the Vivitar 7mm and Opteka 6.5mm lenses. This lens is manual focus and is reported to use stereographic projection[16][17]

## 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 = ftan(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 = fsin(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 as much. Samyang is the only manufacturer ever to be making this kind of fisheye lens. This lens is available under different brandnames. This mapping is easily implemented by software.
• Other mapping functions (for example Tailored Distortion lenses)[18] are also possible for enhancing the off-axis resolution of fisheye lenses.

All types of fisheye lens bend straight lines. Aperture angles of 180° or more are possible only with large amounts of barrel distortion.

## References

1. ^ Hill, R. 1924. A lens for whole sky photographs. Quarterly Journal of the Royal Meteorological Society 50:227-235.
2. ^ The formula is $\text{FOV} = 4 \cdot \arcsin \left(\frac{\text{frame size}}{4\cdot \text{focal length}}\right)$, which comes from inverting the mapping function; Dyxum, Gustavo Orensztajn
3. ^ AF DX Fisheye-NIKKOR 10.5 mm f/2.8G ED specification
4. ^ Miniature fisheye lenses
5. ^ Sunex
6. ^ http://www.sigma-photo.com/lenses/lenses_all_details.asp?id=3336&navigator=6 4.5mm F2.8 EX DC Circular Fisheye HSM
7. ^ "Additional Information on Fisheye-Nikkor 6mm f/2.8 lens". Malaysian Internet Resources. Retrieved 2008-11-11.
8. ^ "Additional Information on Fisheye-Nikkor 6mm f/2.8 lens: Late 70s". Malaysian Internet Resources. Retrieved 2008-11-11.
9. ^ Sunex
10. ^ SuperFisheye
11. ^ [1]
12. ^ AF DX Fisheye-Nikkor 10.5mm f/2.8G ED
13. ^ MC Zenitar
14. ^ Sigma 15 mm f/2.8 EX DG Diagonal Fisheye
15. ^ Olympus Zuiko Digital ED 8mm f/3.5 Fisheye
16. ^ "Samyang 8 mm f/3.5 Aspherical IF MC Fish-eye". lenstip.com. Retrieved 2009-08-14.
17. ^ Samyang 8 mm f/3.5 Fisheye CS
18. ^ Tailored Distortion lenses