In photographic optics, the Zeiss formula is a supposed formula for computing a circle of confusion (CoC) criterion for depth of field (DoF) calculations. The formula is , where is the diagonal measure of a camera format, film, sensor, or print, and the maximum acceptable diameter of the circle of confusion.
The Zeiss formula is apocryphal, in the sense that it has grown to be a well-known named concept by propagation through the internet, even though it has no official origin, little connection to Carl Zeiss Company, and no recognition or usage in the photographic industry outside the web community.
The number 1/1730 derives from a circle of confusion diameter of 0.025 mm on a full-frame 35 mm film format, with diagonal size about 43.25 mm (43.25/0.025 is 1730). The CoC size of 0.025 mm for this format appears in Jacobson's Photographic Lenses Tutorial, [1] and the 1730 in his 1996 Photographic Lenses FAQ. [2] Jacobson derived the 0.025 mm CoC number from analysis of the Zeiss Triotar lens DoF markings on the Rollei B35 (see photo). The manual for the Rollei B35 also states 0.025 mm CoC for its tabulated DoF distances, though it also includes an example DoF reading that implies a larger CoC. [3]
By 2001, the term "Zeiss formula" had appeared, in the manual for the on-line DoF calculator f/calc. [4]
On the other hand, Zeiss gives the values d/1000 as the traditional standard and d/1500 as the modern standard. [5]
The depth of field (DOF) is the distance between the nearest and the farthest objects that are in acceptably sharp focus in an image captured with a camera. See also the closely related depth of focus.
In optics, a circle of confusion (CoC) is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source. It is also known as disk of confusion, circle of indistinctness, blur circle, or blur spot.
In photography, angle of view (AOV) describes the angular extent of a given scene that is imaged by a camera. It is used interchangeably with the more general term field of view.
Carl Zeiss AG, branded as ZEISS, is a German manufacturer of optical systems and optoelectronics, founded in Jena, Germany in 1846 by optician Carl Zeiss. Together with Ernst Abbe and Otto Schott he laid the foundation for today's multinational company. The current company emerged from a reunification of Carl Zeiss companies in East and West Germany with a consolidation phase in the 1990s. ZEISS is active in four business segments with approximately equal revenue in almost 50 countries, has 30 production sites and around 25 development sites worldwide.
Subminiature photography is photographic technologies and techniques working with film material smaller in size than 35mm film, such as 16mm, 9.5mm, 17mm, or 17.5mm films. It is distinct from photomicrography, photographing microscopic subjects with a camera which is not particularly small.
A fisheye lens is an ultra wide-angle lens that produces strong visual distortion intended to create a wide panoramic or hemispherical image. Fisheye lenses achieve extremely wide angles of view, well beyond any rectilinear lens. Instead of producing images with straight lines of perspective, fisheye lenses use a special mapping, which gives images a characteristic convex non-rectilinear appearance.
Mamiya Digital Imaging Co., Ltd. is a Japanese company that manufactures high-end cameras and other related photographic and optical equipment. With headquarters in Tokyo, it has two manufacturing plants and a workforce of over 200 people. The company was founded in May 1940 by camera designer Seiichi Mamiya and financial backer Tsunejiro Sugawara.
In optics and photography, hyperfocal distance is a distance from a lens beyond which all objects can be brought into an "acceptable" focus. As the hyperfocal distance is the focus distance giving the maximum depth of field, it is the most desirable distance to set the focus of a fixed-focus camera. The hyperfocal distance is entirely dependent upon what level of sharpness is considered to be acceptable.
Cosina Co., Ltd. is a manufacturer of high-end optical glass, optical precision equipment, cameras, video and electronic related equipment, based in Nakano, Nagano Prefecture, Japan.
Rollei was a German manufacturer of optical instruments founded in 1920 by Paul Franke and Reinhold Heidecke in Braunschweig, Lower Saxony, and maker of the Rolleiflex and Rolleicord series of cameras. Later products included specialty and nostalgic type films for the photo hobbyist market.
Jos. Schneider Optische Werke GmbH is a manufacturer of industrial and photographic optics. The company was founded on 18 January 1913 by Joseph Schneider as Optische Anstalt Jos. Schneider & Co. at Bad Kreuznach in Germany. The company changed its name to Jos. Schneider & Co., Optische Werke, Kreuznach in 1922, and to the current Jos. Schneider Optische Werke GmbH in 1998.
Depth of focus is a lens optics concept that measures the tolerance of placement of the image plane in relation to the lens. In a camera, depth of focus indicates the tolerance of the film's displacement within the camera and is therefore sometimes referred to as "lens-to-film tolerance".
In digital photography, the crop factor, format factor, or focal length multiplier of an image sensor format is the ratio of the dimensions of a camera's imaging area compared to a reference format; most often, this term is applied to digital cameras, relative to 35 mm film format as a reference. In the case of digital cameras, the imaging device would be a digital image sensor. The most commonly used definition of crop factor is the ratio of a 35 mm frame's diagonal (43.3 mm) to the diagonal of the image sensor in question; that is, . Given the same 3:2 aspect ratio as 35mm's 36 mm × 24 mm area, this is equivalent to the ratio of heights or ratio of widths; the ratio of sensor areas is the square of the crop factor.
The double Gauss lens is a compound lens used mostly in camera lenses that reduces optical aberrations over a large focal plane.
The Rollei 35 is a 35mm miniature viewfinder camera built by Rollei. The original Rollei 35, when introduced at photokina in 1966, was the smallest existing 135 film camera. The Rollei 35 series remains one of the smallest 35 mm cameras after the Minox 35 and Minolta TC-1. In 30 years, about 2 million Rollei 35 series cameras were manufactured. The Rollei 35 was manufactured by DHW Fototechnik up to 2015, the successor of Franke & Heidecke as small-batch production. The last version is the Rollei 35 Classic, an updated Rollei 35 SE.
The Zeiss Sonnar is a photographic lens originally designed by Dr. Ludwig Bertele in 1929 and patented by Zeiss Ikon. It was notable for its relatively light weight, simple design and fast aperture.
Lens speed is the maximum aperture diameter, or minimum f-number, of a photographic lens. A lens with a larger than average maximum aperture is called a "fast lens" because it can achieve the same exposure as an average lens with a faster shutter speed. Conversely, a smaller maximum aperture is "slow" because it delivers less light intensity and requires a slower (longer) shutter speed.
The design of photographic lenses for use in still or cine cameras is intended to produce a lens that yields the most acceptable rendition of the subject being photographed within a range of constraints that include cost, weight and materials. For many other optical devices such as telescopes, microscopes and theodolites where the visual image is observed but often not recorded the design can often be significantly simpler than is the case in a camera where every image is captured on film or image sensor and can be subject to detailed scrutiny at a later stage. Photographic lenses also include those used in enlargers and projectors.
The Quick Bayonet Mount (QBM) is the bayonet mount system for the range of interchangeable lenses fitted to 135 film cameras built by Rollei in Germany and Singapore from 1970 through 1990, including the Rolleiflex SL35, Rolleiflex SL2000F, and Voigtländer VSL series. Lens brands sold with QBM included Carl Zeiss, Rolleinar, Schneider, and Voigtländer. QBM has a flange focal distance of 44.5 mm.
The Vito and Vitomatic, Vitoret, and Vito Automatic were several related lines of 35 mm compact viewfinder and rangefinder cameras made by Voigtländer from the 1940s through the early 1970s, equipped with leaf shutters, similar in concept to and marketed against the competing Kodak Retina cameras manufactured by Kodak. All of these cameras were fixed-lens models; the models in the Vito line identified with Roman numerals were equipped with folding mechanisms and collapsible lenses for portability, while the others were rigid, non-folding cameras.
Although there is no one diameter that marks the boundary between fuzzy and clear, .03 mm is generally used in 35mm work as the diameter of the acceptable circle of confusion. (I arrived at this by observing the depth of field scales or charts on/with a number of lenses from Nikon, Pentax, Sigma, and Zeiss. All but the Zeiss lens came out around .03mm. The Zeiss lens appeared to be based on .025 mm.)
There is no one circle 'small enough' for all circumstances, but rather it depends on how much the image will be enlarged, the quality of the rest of the system, and even the subject. Nevertheless, for 35mm work c=.03mm is generally agreed on as the diameter of the acceptable circle of confusion. Another rule of thumb is c=1/1730 of the diagonal of the frame, which comes to .025mm for 35mm film. (Zeiss and Sinar are known to be consistent with this rule.)
ƒ/Calc calculates the CoC using the Zeiss formula: d/1730, where d is the diagonal measure of the imaging area, in millimeters.
A certain amount of blur is supposed to be tolerable. According to international standards the degree of blur tolerable is defined as 1/1000 of the camera format diagonal, as the normally satisfactory value. With 35mm format and its 43 mm diagonal only 1/1500 is deemed tolerable, resulting in 43 mm/1500 ≈ 0.030 mm.