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For many cameras, depth of field (DOF) is the distance between the nearest and the farthest objects that are in acceptably sharp focus in an image. The depth of field can be calculated based on
focal length The focal length of an optical Optics is the branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space ...

, distance to subject, the acceptable
circle of confusion In optics Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (phy ...
size, and aperture. A particular depth of field may be chosen for technical or artistic purposes. Limitations of depth of field can sometimes be overcome with various techniques/equipment.

# Factors affecting depth of field

For cameras that can only focus on one object distance at a time, depth of field is the distance between the nearest and the farthest objects that are in acceptably sharp focus. "Acceptably sharp focus" is defined using a property called the ''
circle of confusion In optics Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (phy ...
''. The depth of field can be determined by
focal length The focal length of an optical Optics is the branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space ...

, distance to subject, the acceptable circle of confusion size, and aperture. The approximate depth of field can be given by: :$\text \approx \frac$ for a given circle of confusion (c), focal length (f),
f-number In optics, the f-number of an optical system such as a camera lens is the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture").Smith, Warren ''Modern Optical Engineering'', 4th Ed., 2007 McGraw-Hill Prof ...
(N), and distance to subject (u). As distance or the size of the acceptable circle of confusion increases, the depth of field increases; however, increasing the size of the aperture or increasing the focal length reduces the depth of field. Depth of field changes linearly with F-number and circle of confusion, but changes in proportional to the square of the focal length and the distance to the subject. As a result, photos taken at extremely close range have a proportionally much smaller depth of field. Sensor size affects DOF in counterintuitive ways. Because the circle of confusion is directly tied to the sensor size, decreasing the size of the sensor while holding focal length and aperture constant will ''decrease'' the depth of field (by the crop factor). The resulting image however will have a different field of view. If the focal length is altered to maintain the field of view, the change in focal length will counter the decrease of DOF from the smaller sensor and ''increase'' the depth of field (also by the crop factor).

## Effect of lens aperture

For a given subject framing and camera position, the DOF is controlled by the lens aperture diameter, which is usually specified as the
f-number In optics, the f-number of an optical system such as a camera lens is the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture").Smith, Warren ''Modern Optical Engineering'', 4th Ed., 2007 McGraw-Hill Prof ...
(the ratio of lens focal length to aperture diameter). Reducing the aperture diameter (increasing the f-number) increases the DOF because only the light travelling at shallower angles passes through the aperture. Because the angles are shallow, the light rays are within the acceptable
circle of confusion In optics Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (phy ...
for a greater distance. For a given size of the subject's image in the focal plane, the same f-number on any focal length lens will give the same depth of field. This is evident from the DOF equation by noting that the ratio ''u/f'' is constant for constant image size. For example, if the focal length is doubled, the subject distance is also doubled to keep the subject image size the same. This observation contrasts with the common notion that "focal length is twice as important to defocus as f/stop", which applies to a constant subject distance, as opposed to constant image size. Motion pictures make only limited use of aperture control; to produce a consistent image quality from shot to shot, cinematographers usually choose a single aperture setting for interiors and another for exteriors, and adjust exposure through the use of camera filters or light levels. Aperture settings are adjusted more frequently in still photography, where variations in depth of field are used to produce a variety of special effects.

## Effect of circle of confusion

Precise focus is only possible at an exact distance from the lens; at that distance, a point object will produce a point image. Otherwise, a point object will produce a blur spot shaped like the
aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of ray (optics), rays that come to a focus (optics), focus ...

, typically and approximately a circle. When this circular spot is sufficiently small, it is visually indistinguishable from a point, and appears to be in focus. The diameter of the largest circle that is indistinguishable from a point is known as the acceptable circle of confusion, or informally, simply as the circle of confusion. Points that produce a blur spot smaller than this acceptable circle of confusion are considered acceptably sharp. The acceptable circle of confusion depends on how the final image will be used. It is generally accepted to be 0.25 mm for an image viewed from 25 cm away. For
35 mm35 mm may refer to: * 135 film, a type of still photography format commonly referred to as 35 mm film * 35 mm movie film, a type of motion picture film stock * Ryan Scott Oliver#35MM, 35MM, a "musical exhibition" by Ryan Scott Oliver that ...
motion pictures, the image area on the film is roughly 22 mm by 16 mm. The limit of tolerable error was traditionally set at 0.05 mm (0.002 in) diameter, while for , where the size is about half as large, the tolerance is stricter, 0.025 mm (0.001 in). More modern practice for 35 mm productions set the circle of confusion limit at 0.025 mm (0.001 in).

## Camera movements

The term "camera movements" refers to swivel (swing and tilt, in modern terminology) and shift adjustments of the lens holder and the film holder. These features have been in use since the 1800s and are still in use today on view cameras, technical cameras, cameras with tilt/shift or perspective control lenses, etc. Swiveling the lens or sensor causes the plane of focus (POF) to swivel, and also causes the field of acceptable focus to swivel with the POF; and depending on the DOF criteria, to also change the shape of the field of acceptable focus. While calculations for DOF of cameras with swivel set to zero have been discussed, formulated, and documented since before the 1940s, documenting calculations for cameras with non-zero swivel seem to have begun in 1990. More so than in the case of the zero swivel camera, there are various methods to form criteria and set up calculations for DOF when swivel is non-zero. There is a gradual reduction of clarity in objects as they move away from the POF, and at some virtual flat or curved surface the reduced clarity becomes unacceptable. Some photographers do calculations or use tables, some use markings on their equipment, some judge by previewing the image. When the POF is rotated, the near and far limits of DOF may be thought of as wedge-shaped, with the apex of the wedge nearest the camera; or they may be thought of as parallel to the POF.

# Object-field calculation methods

Traditional depth-of-field formulas can be hard to use in practice. As an alternative, the same effective calculation can be done without regard to the focal length and f-number.
Moritz von Rohr Moritz von Rohr (4 April 1868 – 20 June 1940) was an optical scientist at in , . A street in Jena is named after him: Moritz-von-Rohr-Straße, near Carl-Zeiss-Promenade and Otto-Schott-Straße. Life Moritz von Rohr was born in near ...
and later Merklinger observe that the effective absolute aperture diameter can be used for similar formula in certain circumstances. Moreover, traditional depth-of-field formulas assume equal acceptable circles of confusion for near and far objects. Merklinger suggested that distant objects often need to be much sharper to be clearly recognizable, whereas closer objects, being larger on the film, do not need to be so sharp. The loss of detail in distant objects may be particularly noticeable with extreme enlargements. Achieving this additional sharpness in distant objects usually requires focusing beyond the
hyperfocal distance In optics and photography Photography is the art, application, and practice of creating durable images by recording light, either electronically by means of an image sensor, or chemically by means of a light-sensitive material such as photograp ...
, sometimes almost at infinity. For example, if photographing a cityscape with a traffic bollard in the foreground, this approach, termed the ''object field method'' by Merklinger, would recommend focusing very close to infinity, and stopping down to make the bollard sharp enough. With this approach, foreground objects cannot always be made perfectly sharp, but the loss of sharpness in near objects may be acceptable if recognizability of distant objects is paramount. Other authors such as
Ansel Adams Ansel Easton Adams (February 20, 1902 – April 22, 1984) was an American landscape photographer and environmentalist known for his black-and-white images of the . He helped found , an association of photographers advocating "pure" photography ...

have taken the opposite position, maintaining that slight unsharpness in foreground objects is usually more disturbing than slight unsharpness in distant parts of a scene.

# Overcoming DOF limitations

Some methods and equipment allow altering the apparent DOF, and some even allow the DOF to be determined after the image is made. For example,
focus stacking 250px, Focus stacking (for extended depth of field) in Bright field microscopy, bright field light microscopy. This example is of a diatom microfossil in diatomaceous earth. Top left are the three source images captured at three different focus di ...

combines multiple images focused on different planes, resulting in an image with a greater (or less, if so desired) apparent depth of field than any of the individual source images. Similarly, in order to reconstruct the 3-dimensional shape of an object, a
depth map In 3D computer graphics and computer vision Computer vision is an Interdisciplinarity, interdisciplinary scientific field that deals with how computers can gain high-level understanding from digital images or videos. From the perspective of engi ...
can be generated from multiple photographs with different depths of field. Xiong and Shafer concluded, in part, "...the improvements on precisions of focus ranging and defocus ranging can lead to efficient shape recovery methods." Another approach is focus sweep. The focal plane is swept across the entire relevant range during a single exposure. This creates a blurred image, but with a convolution kernel that is nearly independent of object depth, so that the blur is almost entirely removed after computational deconvolution. This has the added benefit of dramatically reducing motion blur. Other technologies use a combination of lens design and post-processing:
Wavefront codingIn optics Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), ...
is a method by which controlled aberrations are added to the optical system so that the focus and depth of field can be improved later in the process. The lens design can be changed even more: in colour
apodization Apodization is an optical filtering technique. Its literal translation from Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in S ...
the lens is modified such that each colour channel has a different lens aperture. For example, the red channel may be ''f''/2.4, green may be ''f''/2.4, whilst the blue channel may be ''f''/5.6. Therefore, the blue channel will have a greater depth of field than the other colours. The image processing identifies blurred regions in the red and green channels and in these regions copies the sharper edge data from the blue channel. The result is an image that combines the best features from the different ''f''-numbers. At the extreme, a
plenoptic camera A light field camera, also known as plenoptic camera, captures information about the light field emanating from a scene; that is, the intensity of light in a scene, and also the direction that the light rays are traveling in space. This contrasts ...
captures 4D light field information about a scene, so the focus and depth of field can be altered after the photo is taken.

# Diffraction and DOF

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causes images to lose sharpness at high F-numbers, and hence limits the potential depth of field. In general photography this is rarely an issue; because large f-numbers typically require long exposure times,
motion blur Motion blur is the apparent streaking of moving objects in a photograph A photograph (also known as a photo) is an image An SAR radar image acquired by the SIR-C/X-SAR radar on board the Space Shuttle Endeavour shows the Teide vol ...
may cause greater loss of sharpness than the loss from diffraction. However, diffraction is a greater issue in close-up photography, and the tradeoff between DOF and overall sharpness can become quite noticeable as photographers are trying to maximise depth of field with very small apertures. Hansma and Peterson have discussed determining the combined effects of defocus and diffraction using a root-square combination of the individual blur spots. Hansma's approach determines the f-number that will give the maximum possible sharpness; Peterson's approach determines the minimum f-number that will give the desired sharpness in the final image, and yields a maximum depth of field for which the desired sharpness can be achieved. In combination, the two methods can be regarded as giving a maximum and minimum f-number for a given situation, with the photographer free to choose any value within the range, as conditions (e.g., potential motion blur) permit. Gibson gives a similar discussion, additionally considering blurring effects of camera lens aberrations, enlarging lens diffraction and aberrations, the negative emulsion, and the printing paper. Couzin gave a formula essentially the same as Hansma's for optimal ''f''-number, but did not discuss its derivation. Hopkins, Stokseth, and Williams and Becklund have discussed the combined effects using the
modulation transfer function The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or image projector, projector specifies how different spatial frequencies are handled by the system. It is used by optical engineers to describe how ...
.

# DOF scales

Many lenses include scales that indicate the DOF for a given focus distance and f-number; the 35 mm lens in the image is typical. That lens includes distance scales in feet and meters; when a marked distance is set opposite the large white index mark, the focus is set to that distance. The DOF scale below the distance scales includes markings on either side of the index that correspond to f-numbers. When the lens is set to a given f-number, the DOF extends between the distances that align with the f-number markings. Photographers can use the lens scales to work backwards from the desired depth of field to find the necessary focus distance and aperture. For the 35 mm lens shown, if it were desired for the DOF to extend from 1 m to 2 m, focus would be set so that index mark was centered between the marks for those distances, and the aperture would be set to f/11. On a view camera, the focus and f-number can be obtained by measuring the depth of field and performing simple calculations. Some view cameras include DOF calculators that indicate focus and f-number without the need for any calculations by the photographer.

# Near:far distribution

The DOF beyond the subject is always greater than the DOF in front of the subject. When the subject is at the hyperfocal distance or beyond, the far DOF is infinite, so the ratio is 1:∞; as the subject distance decreases, near:far DOF ratio increases, approaching unity at high magnification. For large apertures at typical portrait distances, the ratio is still close to 1:1.

# DOF formulae

This section covers some additional formula for evaluating depth of field; however they are all subject to significant simplifying assumptions: for example, they assume the
paraxial approximation In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and Ray tracing (physics), ray tracing of light through an optical system (such as a lens (optics), lens). A paraxial ray is a Ray (optics), r ...
of
Gaussian optics Gaussian optics is a technique in geometrical optics Geometrical optics, or ray optics, is a model of optics Optics is the branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of na ...
. They are suitable for practical photography, lens designers would use significantly more complex ones.

## Focus and f-number from DOF limits

For given near and far DOF limits $D_$ and $D_$, the required f-number is smallest when focus is set to :$s = \frac,$ the
harmonic mean In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. Sometimes it is appropriate for situations when the average rate (mathematics), rate is desired. The harmonic mean can be express ...
of the near and far distances. In practice, this is equivalent to the
arithmetic mean In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and t ...
for shallow depths of field.https://www.largeformatphotography.info/articles/DoFinDepth.pdf Sometimes, view camera users refer to the difference $v_ - v_$ as the ''focus spread''.

## Foreground and background blur

If a subject is at distance $s$ and the foreground or background is at distance $D$, let the distance between the subject and the foreground or background be indicated by :$x_ = , D - s, .$ The blur disk diameter $b$ of a detail at distance $x_\mathrm$ from the subject can be expressed as a function of the subject magnification $m_\mathrm$, focal length $f$, f-number $N$, or alternatively the
aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of ray (optics), rays that come to a focus (optics), focus ...

$d$, according to :$b = \frac \frac = dm_\mathrm \frac.$ The minus sign applies to a foreground object, and the plus sign applies to a background object. The blur increases with the distance from the subject; when $b$ is less than the circle of confusion, the detail is within the depth of field.

# References

## Sources

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Large Format page
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*Hummel, Rob (editor). 2001. ''American Cinematographer Manual''. 8th ed. Hollywood: ASC Press.