Fisheye lens

Hill/Beck "Sky Lens" (1923, GB 225,398)[10]

In 1924, Robin Hill first described a lens with 180° coverage that had been used for a cloud survey in September 1923[3] The lens, designed by Hill and R. & J. Beck, Ltd., was patented in December 1923.[10] The Hill Sky Lens is now credited as the first fisheye lens.[5]^:146 Hill also described three different mapping functions of a lens designed to capture an entire hemisphere (stereographic, equidistant, and orthographic).[3][11] Distortion is unavoidable in a lens that encompasses an angle of view exceeding 125°, but Hill and Beck claimed in the patent that stereographic or equidistant projection were the preferred mapping functions.[10] The three-element, three-group lens design uses a highly divergent meniscus lens as the first element to bring in light over a wide view followed by a converging lens system to project the view onto a flat photographic plate.[10]

The Hill Sky Lens was fitted to a whole sky camera, typically used in a pair separated by 500 metres (1,600 ft) for stereo imaging, and equipped with a red filter for contrast; in its original form, the lens had a focal length of 0.84 in (21 mm) and cast an image 2.5 in (64 mm) in diameter at f/8.[12] Conrad Beck described the camera system in an article published in 1925.[13] At least one has been reconstructed.[14]

Schulz/AEG Weitwinkelobjektiv (1932, DE 620538)[15]

In 1932, the German firm Allgemeine Elektricitäts-Gesellschaft AG (AEG) filed for a patent on the Weitwinkelobjektiv (wide-angle lens), a 5-element, 4-group development of the Hill Sky Lens.[5]^:148 [15] Compared to the 1923 Hill Sky Lens, the 1932 Weitwinkelobjektiv featured two diverging meniscus elements ahead of the stop and used a cemented achromatic group in the converging section.[15] Miyamoto credits Dr Hans Schulz with the design of the Weitwinkelobjektiv.[11] The basic patented design was produced for cloud recording as a 17 mm f/6.3 lens,[16] and the artist known as Umbo used the AEG lens for artistic purposes, with photographs published in a 1937 issue of Volk und Welt.[17]

The AEG Weitwinkelobjektiv formed the basis of the later Fish-eye-Nikkor 16 mm f/8 lens of 1938, which was used for military and scientific (cloud cover) purposes.[16][18] Nikon, which had a contract to supply optics to the Imperial Japanese Navy, possibly gained access to the AEG design under the Pact of Steel.[18] After the war, the lens was mated to a medium format camera and was produced in slightly modified form (focal length increased slightly to 16.3 mm) as the "Sky-image Recording Camera" in March 1957 for the Japanese government,[19] followed by a commercial release as the Nikon Fisheye Camera (also known as the "Nikon Sky Camera" or "Nikon Cloud Camera") in September 1960, which had a retail price of ¥200,000 (equivalent to ¥1,130,000 in 2019).[20] The revised lens created a circular image 50 mm (2.0 in) in diameter and covered a complete hemispherical field of 180°.[21] Only 30 examples of the Nikon Fisheye Camera were manufactured, and of those, 18 were sold to customers, mainly in the United States; Nikon likely destroyed the remaining stock to avoid tax penalties.[22] A photograph of pole vaulter Bob Gutowski taken by the Fisheye Camera was published in Life in 1957.[23]

Richter/Zeiss Pleon (1938, US 2,247,068)[24]

Also in 1938, Robert Richter of Carl Zeiss AG patented the 6-element, 5-group Pleon lens,[24] which was used for aerial surveillance during World War II. The converging rear group of the Pleon was symmetrical, reminiscent of the 4-element Topogon design, also designed by Richter for Zeiss in 1933. Testing on a captured lens after the war showed the Pleon provided an equidistant projection to cover a field of approximately 130°, and negatives were printed using a special rectifying enlarger to eliminate distortion.[5]^:149 [25] The Pleon had a focal length of approximately 72.5 mm with a maximum aperture of f/8 and used a plano-concave front element 300 mm (12 in) in diameter; the image on the negative was approximately 85 mm (3.3 in) in diameter.[25]

Merté/Zeiss Sphaerogon (1935, DE 672 393[26] and US 2,126,126)[27]

At approximately the same time that Schulz was developing the Weitwinkelobjektiv at AEG, Willy Merté at Zeiss was developing the Sphaerogon, which was also designed to encompass a 180° field of view.[26][27] Unlike the Weitwinkelobjektiv, Merté's Sphaerogon was not limited to medium format cameras; prototype versions of the Sphaerogon were constructed for the Contax I miniature format camera. The first prototype Sphaerogon lenses constructed had a maximum aperture of f/8, but later examples were computed half a stop faster, to f/6.8.[28] Several prototype examples of Sphaerogon lenses were recovered as part of the Zeiss Lens Collection seized by the Army Signal Corps as war reparations in 1945;[29] the collection, which the Zeiss firm had retained as a record of their designs, was later documented by Merté, the former head of optical computation for CZJ, working under Signal Corps officer Edward Kaprelian.[30][31]

The Nikon Fisheye Camera was discontinued in September 1961,[19] and Nikon subsequently introduced the first regular production fisheye lens for miniature cameras in 1962,[11] the Fish-eye-Nikkor 8 mm f/8,[32] which required the reflex mirror on its Nikon F and Nikkormat cameras to be locked up prior to mounting the lens. Prior to the early 1960s, fisheye lenses were used primarily by professional and scientific photographers, but the advent of the fisheye for the 135 format increased its popular use.[33] The Nikkor 8 mm f/8 has a field of view of 180° and uses 9 elements in 5 groups; it is fixed focus and has built-in filters mainly intended for black-and-white photography. Research indicates that fewer than 1,400 lenses were built.[34]

Nikon subsequently released several more milestone circular fisheye lenses in Nikon F mount through the 1960s and 70s:

• 10 mm f/5.6 OP (1968), the first fisheye to feature orthographic projection, which was also the first lens to feature an aspherical element[35]
• 6 mm f/5.6 (1969), the first fisheye to feature a 220° field of view;[7] interestingly, the patent accompanying this lens includes a design for a lens with a 270° field of view.[36] A 6.2 mm f/5.6 SAP fisheye was later produced in limited numbers with an aspherical surface, encompassing a 230° field of view.[37]
• 8 mm f/2.8 (1970), the first circular fisheye with variable focus, automatic aperture, and reflex viewing (mirror lock-up no longer required).[7]

Fish-eye Takumar 11/18mm on a modern Pentax K-1 DSLR

Meanwhile, other Japanese manufacturers were developing the so-called full-frame or diagonal fisheyes, which captured approximately a 180° field of view across the diagonal of the film frame. The first such diagonal fisheye was the Fish-eye Takumar 18 mm f/11, released by Pentax (Asahi Optical) in 1962,[37][38][39] followed by the slightly faster UW Rokkor-PG 18 mm f/9.5 from Minolta in 1966.[40] Both of these were reflex viewing and fixed-focus, and Pentax and Minolta followed up with faster lenses with variable focus in 1967 (Super Fish-eye-Takumar 17 mm f/4)[41] and 1969 (Rokkor-OK 16 mm f/2.8),[42][43] respectively. The 16 mm Rokkor was later adopted by Leica as the Fisheye-Elmarit-R (1974) and then converted to autofocus (1986) for the Alpha system. As of 2018, the same basic optical design is still sold as the Sony SAL16F28.

The focal length is determined by the angular coverage, the specific mapping function used, and the required dimensions of the final image. Focal lengths for popular amateur camera sizes are computed as:

Calculated fisheye focal lengths[lower-alpha 1]

		Stereographic	Equidistant	Equisolid Angle	Orthographic
Inverse Mapping Function[44]		${\displaystyle f={\frac {r}{2\tan(\theta /2)}}}$	${\displaystyle f={\frac {r}{\theta }}}$	${\displaystyle f={\frac {r}{2\sin(\theta /2)}}}$	${\displaystyle f={\frac {r}{\sin(\theta )}}}$
Circular[lower-alpha 2]	APS-C (${\displaystyle r}$ = 8.4 mm)	4.2	5.3	5.9	8.4
	135 (${\displaystyle r}$ = 12 mm)	6.0	7.6	8.5	12.0
	6×6 (${\displaystyle r}$ = 28 mm)	14.0	17.8	19.8	28.0
Full-frame[lower-alpha 3]	APS-C (${\displaystyle r}$ = 15.1 mm)	7.5	9.6	10.6	15.1
	135 (${\displaystyle r}$ = 21.7 mm)	10.8	13.8	15.3	21.7
	6×6 (${\displaystyle r}$ = 39.6 mm)	19.8	25.2	28.0	39.6

Notes

The first types of fisheye lenses to be developed were "circular fisheye"—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°. By design, most circular fisheye lenses cover a smaller image circle than rectilinear lenses, so the corners of the frame will be completely dark.

Sigma currently makes a 4.5mm fisheye lens that captures a 180-degree field of view on a crop body.[45] 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.

Fisheye-Nikkor 6mm f/2.8 mounted on a Nikon F2 in the Nikon Museum.

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,[46] 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), having a diameter of 236 millimetres (9.3 in), a length of 171 millimetres (6.7 in) and an angle of view of 220 degrees. It dwarfs a regular 35 mm SLR camera[47] 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. The lens is extremely rare.[48]

The fish eye lens Laowa 4 mm f/2,8 of the manufacturer Venus Optics

However, there are new developments by the Japanese manufacturer Entaniya for the Micro Four Thirds standard, which offer an angle of view of 250 degrees with lenses that have a focal length of 2.3 millimetres (0.091 in) to 3.6 millimetres (0.14 in), an aperture of f/2.8 to f/4.0, a weight of 1.6 kilograms (3.5 lb), a diameter of 120 millimetres (4.7 in) and a length below 100 millimetres (3.9 in).[49] In 2018 Venus Optics introduced a 210° fisheye lens for the Micro Four Thirds system.[50]

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.

As fisheye lenses gained popularity in general photography, camera companies began manufacturing fisheye lenses that enlarged the image circle to cover the entire rectangular frame, called a "full-frame fisheye".[51]

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 AOV will be 147°, and the vertical AOV will be 94°.[52]

One of the first full-frame fisheye lens to be mass-produced was the Fisheye-Nikkor 16mm f/3.5, made by Nikon in the early 1970s. Digital cameras with APS-C sized sensors require a 10.5 mm lens (or, for Canon APS-C cameras, a 10 mm lens) to get the same effect as a 16 mm lens on a camera with full-frame sensor.[53]

Miniature digital cameras, especially when used as security cameras, often tend to have fisheye lenses to maximize coverage. Miniature fisheye lenses are designed for small-format CCD/CMOS imagers commonly used in consumer and security cameras.[54][55] Popular image sensor format sizes used include ​¹⁄₄", ​¹⁄₃", and ​¹⁄₂". Depending on the active area of the image sensor, the same lens can form a circular image on a larger image sensor (e.g. ​¹⁄₂"), and a full frame on a smaller one (e.g. ​¹⁄₄").

The APS-C image sensor used in Canon cameras is 22.3 mm × 14.9 mm (0.88 in × 0.59 in) or 26.82 mm (1.056 in) on the diagonal, which is slightly smaller than the sensor size used by other popular manufacturers of cameras with APS-C sensors, such as Fuji, Minolta, Nikon, Pentax, and Sony. The other common APS-C sensors range from 23.6 to 23.7 mm (0.93 to 0.93 in) on the long dimension and 15.6 mm (0.61 in) on the shorter side, for a diagonal measurement between 28.2 to 28.4 mm (1.11 to 1.12 in).

• Sigma 4.5 mm f/2.8 for APS-C sensors
• Lensbaby 5.8 mm f/3.5 circular fisheye

• Nikon 10.5 mm f/2.8
• Samyang 8 mm f/3.5. Notable for its stereographic projection
• Samyang 8 mm f/2.8. For various mirrorless cameras. Notable for its stereographic projection
• Sigma 10 mm f/2.8

• Pentax 10–17 mm f/3.5–4.5 / Tokina 10–17 mm f/3.5–4.5 (jointly developed)

A Peleng 8mm circular fisheye lens.

• Peleng 8 mm f/3.5
• Sigma 8 mm f/4.0
• Sigma 8 mm f/3.5 - replaces the Sigma 8 mm f/4.0 EX DG

• Canon EF 15 mm f/2.8 (discontinued)
• Canon Fisheye FD 15 mm f/2.8 (old lens, does not work on EF mount)
• Fuji Photo Film Co. EBC Fujinon Fish Eye 16mm F2.8 (m42 & X-Fujinon mounts)(discontinued)
• Minolta AF 16 mm f/2.8
• Sigma 15 mm f/2.8 EX DG Diagonal Fisheye
• Fisheye-Nikkor AF 16mm f/2.8 D
• Samyang 12 mm f/2.8 ED AS NCS Diagonal Fish-eye
• Zenitar 16 mm f/2.8 Fisheye lens

• Canon EF 8–15 mm f/4L Fisheye USM – lens can be used as both a full-frame fisheye and a circular fisheye on a 35 mm full-frame film or DSLR such as the 5D (Mark I – IV) cameras; it can only be used as a cropped circular or as a full-frame fisheye on EOS DSLRs with APS-C/H size sensors (a zoom lock is included).
• Nikon AF-S Fisheye Nikkor 8–15 mm f/3.5–4.5E ED – designed for Nikon's full-frame FX DSLRs, this lens is a circular fisheye at the short end of the zoom range and becomes a full-frame fisheye at longer focal lengths.
• Tokina AT-X 10–17mm f3.4-4.5 AF DX – a fisheye zoom lens designed for APS-C sensor cameras. It is also sold as a NH version that comes without integrated lens hood, then the fisheye lens is usable on full frame cameras. The lens is also sold under Pentax brand.
• Pentax F 17–28 mm 1:3.5–4.5 Fisheye – lens was born for full-frame film cameras, to take the place of the 16 mm f/2.8 in the AF era. It starts from a 17 mm full-frame fisheye and reaches the end of the excursion as an overdistorted 28 mm. Was intended as a "special effect" lens and never had big sales.[56]
• Pentax DA 3,5-4,5/10-17 ED IF Fisheye is designed for APS-C cameras, but can be used on a full-frame after a small modification of the hood.