Fisheye lens

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Graphical projection

In photography, a fisheye lens is a wide-angle lens that takes in a broad, panoramic and 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.

Contents

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°. 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 early 1970s. 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]

With the kind of digital technology widely available, the full-frame fisheye effect can be obtained in-camera. Selected images can be digitally changed so as to become full-frame fisheye images without the need for special lenses.

Miniature fisheye lenses

Miniature fisheye lenses are designed for small-format CCD/CMOS imagers commonly used in consumer and security cameras.[4] 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").

Focal length

Sigma currently makes a 4.5mm fisheye lens that captures a 180 degree field of view on a crop body.[5] 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 no longer manufactured by Nikon,[6] 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[7] 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

Fisheye lenses for 35 mm cameras

Circular fisheye

Full-frame fisheye

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:

Fisheye lenses can have many different mapping functions:

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

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. ^ http://www.sigma-photo.com/lenses/lenses_all_details.asp?id=3336&navigator=6 4.5mm F2.8 EX DC Circular Fisheye HSM
  6. ^ "Additional Information on Fisheye-Nikkor 6mm f/2.8 lens". Malaysian Internet Resources. http://www.mir.com.my/rb/photography/companies/nikon/nikkoresources/fisheyes/6mmf28.htm. Retrieved 2008-11-11. 
  7. ^ "Additional Information on Fisheye-Nikkor 6mm f/2.8 lens: Late 70s". Malaysian Internet Resources. http://www.mir.com.my/rb/photography/companies/nikon/nikkoresources/late70nikkor/fisheyes/6mmf28.htm. Retrieved 2008-11-11. 
  8. ^ Sunex
  9. ^ SuperFisheye
  10. ^ [1]
  11. ^ AF DX Fisheye-Nikkor 10.5mm f/2.8G ED
  12. ^ MC Zenitar
  13. ^ Sigma 15 mm f/2.8 EX DG Diagonal Fisheye
  14. ^ Olympus Zuiko Digital ED 8mm f/3.5 Fisheye
  15. ^ "Samyang 8 mm f/3.5 Aspherical IF MC Fish-eye". lenstip.com. http://www.lenstip.com/160.1-Lens_review-Samyang_8_mm_f_3.5_Aspherical_IF_MC_Fish-eye-Introduction.html. Retrieved 2009-08-14. 
  16. ^ Samyang 8 mm f/3.5 Fisheye CS
  17. ^ Tailored Distortion lenses

External links

Alternative photography

Bleach bypass · Cross processing · Fisheye · HDR · Holga · Infrared · Lomography · Multiple exposure · Pinhole · Polaroid art · Redscale · Solarisation · Through the Viewfinder