Fisheye lens

In photography, a fisheye lens is a special lens that can image a complete field of view with the necessary distortion. In contrast to conventional non-fisheye lenses, which proportionally image an object plane perpendicular to the optical axis (gnomonic projection mode, see below: imaging functions), fisheye lenses image a hemisphere or more, with significant but not excessive distortion, on the image plane. Straight lines that do not pass through the center of the image are imaged curved; the image is strongly barrel-shaped (see distortion). It usually reproduces surface ratios or radial distances more faithfully than an ordinary, gnomonic-projecting wide-angle lens and has a very large angle of view (usually 180° in the image diagonal, in extreme cases even up to 220°, in designs even 270° and 310°). Image angles of 180° or more are not achievable with the conventional projection method. Despite the exceptionally large image angles, the brightness drop towards the edge of the image is easier to correct than with wide-angle lenses, because the image scale does not increase so much towards the edge of the image and the light does not have to illuminate such large areas.

The world's first mass-produced fisheye lens was introduced by Nikon in 1962 (Fisheye-Nikkor 1:8, f = 8 mm). The lens protruded far into the camera body, so that the mirror had to be folded up and locked in place, and an external viewfinder had to be attached to the flash shoe.

In the meantime there are a lot of manufacturers producing fisheye lenses. For single-lens reflex cameras, they are usually designed as retrofocus lenses, so that the mirror has enough space between the shutter and the rear lens.

Modern mirrorless camera systems with considerably shorter flange focal lengths allow less effort for retrofocus constructions due to the small distance between optics and sensor. This reduces weight and price or allows larger image angles or higher light intensities with the same effort.

Miniature fisheye lenses for very small sensors, as used in surveillance cameras or action camcorders, are even cheaper, so that even larger image angles up to 280° are offered, and do not cost more than a 180° retrofocus fisheye lens for 35 mm format. Meanwhile, there are also enlarged variants of miniature fisheyes with image angles up to 250° for mirrorless system cameras.

Types

Fisheye lenses are distinguished on the one hand according to their projection type (see imaging functions below) and on the other hand according to their image circle diameter in relation to the recording format.

Circular

Fisheye lenses whose image circle diameter is (at most) as large as the shorter edge of the recording format of the camera are called circular fisheye (also "circular image fisheye" or "round image fisheye") because they design a circular image within the rectangular recording format. The image circle of the lens is used 100%. In plate 1 the maximum possible sensor utilization is given; it turns out to be smaller due to a practically slightly smaller image circle. In order not to cut the image circle, circular fisheyes do not have a lens hood. Circular fisheyes are the first choice when as much of the surroundings (usually a hemisphere) as possible is to be captured. The first fisheye lenses developed were circular fisheyes. Lacking a full frame fisheye, cropping a rectangular area further reduces sensor or film utilization to a maximum of 31% (3:2) or 36% (4:3) and would be conceivably awkward.

Full format

Fisheye lenses whose image circle diameter is (at least) as large as the diagonal of the camera's shooting format are called "full-format fisheye" (also "diagonal fisheye" because of the double meaning of the term "full-format" for sensor utilization or sensor size). They achieve their largest angle of view (usually 180°) only across the image diagonal; their horizontal and vertical angles of view are correspondingly smaller, and parts of the lens' field of view are not used. The sensor, on the other hand, is utilized to 100 %. The lens hood turns out to be very small, limiting the field of view to an approximately rectangular area that extends only slightly beyond the intended shooting format. As fisheyes became popular in general photography, camera manufacturers began to develop full-frame fisheyes. The rectangular format is most comfortable for direct reproduction of the original images (without conversion).

Trimmed circle

If the camera does not have the sensor format for which the fisheye lens is intended, the angle of view and format utilization change. With certain combinations, a usable field of view in the form of a cropped circle can be achieved as an intermediate format of circular and full frame. This results in good sensor utilization and usually less loss in rectangular cropping of images converted to another projection type.

Either a circular fisheye for 35mm format is used on an APS-C or DX camera, or a full-frame fisheye for DX format is used on a full-frame 35mm camera. In the second case, the lens hood crops the image and must be removed. If it is not removable, it can be shortened with a tool (shaving the lens). Some fisheye zoom lenses can also achieve a cropped circle.

Ideally, the image field is a circle cropped on two sides. The image circle diameter is then (at most) as large as the longer side of the recording format. The angle of view becomes maximum, e.g. with landscape format, at the round image edges both diagonally and horizontally; only vertically is it smaller. In practice, there is also the three-sided cropped circle when the sensor area is not centered on the image circle (e.g. area-true Sigma 8 mm fisheye [older model with aperture F/4] and camera with APS-C sensor), or the four-sided cropped circle when the imaging function creates a larger image circle (e.g. angle-linear Canon 8-15 mm fisheye at 8 mm and camera with APS-C sensor).

When converting to stereographic projection, a full-frame image with 180° diagonal angle of view can be obtained after rectangular cropping (Starting from a full-frame image, the stereographic projection would be pincushion-shaped. Rectangular cropping would remove the pincushion peaks and thus reduce the diagonal angle of view). It may be that image angles of 180° are no longer possible with the original format, but only with a wider format (e.g. 16 : 9) of the converted image.

Focal length

Full-frame fisheyes have focal lengths of about 16 mm for the 35 mm format and are thus in the range of strong wide-angle lenses. For the common APS-C or DX format of digital SLR cameras with a cropfactor of 1.5...1.6, the focal length is about 8 to 10 mm, depending on the projection type.

Circular fisheyes have the shorter focal lengths. The focal length is about 8 mm for 35 mm format and about 4.5 mm for APS-C or DX format.

Zoom fisheyes include the circular and full-frame fisheye with their focal length range when designed for that purpose and used for the intended shooting format. Or they close the gap between a full-frame fisheye and a wide-angle or general-purpose zoom lens while retaining barrel distortion throughout the zoom range.

Fisheyes for other formats (e.g. medium format - crop factor approx. 0.5 or FourThirds - crop factor 2) have correspondingly different focal lengths proportional to the format size.