Thedepth of field (DOF) is the distance between the nearest and the farthest objects that are in acceptably sharpfocus in an image captured with acamera. See also the closely relateddepth of focus.
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 in the image.[1] "Acceptably sharp focus" is defined using a property called the "circle of confusion".
The depth of field can be determined byfocal length, distance to subject (object to be imaged), the acceptable circle of confusion size, and aperture.[2] The approximate depth of field can be given by:
for a given maximum acceptable circle of confusion diameterc, focal lengthf,f-numberN, and distance to subjectu.[3][4]
As distance or the size of the acceptable circle of confusion increases, the depth of field increases; however, increasing the size of the aperture (i.e., reducingf-number) or increasing the focal length reduces the depth of field. Depth of field changes linearly withf-number and circle of confusion, but changes in proportion to the square of the distance to the subject and inversely in proportion to the square of the focal length. As a result, photos taken at extremely close range (i.e., so smallu) have a proportionally much smaller depth of field.
Rearranging theDOF equation shows that it is the ratio between distance and focal length that affectsDOF;
Note that is thetransverse magnification which is the ratio of the lateral image size to the lateral subject size.[5]
Image sensor size affectsDOF 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 willdecrease the depth of field (by the crop factor). The resulting image will also have a different field of view. If, however, the focal length is altered to maintain the original field of view, while holding the aperture constant, theDOF will remain constant.[6][7][8][9]
For a given subject framing and camera position, theDOF is controlled by the lens aperture diameter, which is usually specified as thef-number (the ratio of lens focal length to aperture diameter). Reducing the aperture diameter (increasing thef-number) increases theDOF because only the light travelling at shallower angles passes through the aperture so only cones of rays with shallower angles reach the image plane. In other words, thecircles of confusion are reduced or increasing theDOF.[10]
For a given size of the subject's image in the focal plane, the samef-number on any focal length lens will give the same depth of field.[11] This is evident from the aboveDOF equation by noting that the ratiou/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",[12] which applies to a constant subject distance, as opposed to constant image size.
Motion pictures make limited use of aperture control; to produce a consistent image quality from shot to shot, cinematographers usually choose a single aperture setting for interiors (e.g., scenes inside a building) and another for exteriors (e.g., scenes in an area outside a building), 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.
Precise focus is only possible at an exact distance from a lens;[a] at that distance, a point object will produce a small spot image. Otherwise, a point object will produce a larger or blur spot image that is 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 theacceptable circle of confusion, or informally, simply as the circle of confusion.
The acceptable circle of confusion depends on how the final image will be used. The circle of confusion as 0.25 mm for an image viewed from 25 cm away is generally accepted.[14]
For35 mm 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 (0.0020 in) diameter, while for16 mm film, where the size is about half as large, the tolerance is stricter, 0.025 mm (0.00098 in).[15] More modern practice for 35 mm productions set the circle of confusion limit at 0.025 mm (0.00098 in).[16]
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 thePOF; and depending on theDOF criteria, to also change the shape of the field of acceptable focus. While calculations forDOF 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 forDOF when swivel is non-zero. There is a gradual reduction of clarity in objects as they move away from thePOF, 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 thePOF is rotated, the near and far limits ofDOF 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 thePOF.[17][18]
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 andf-number.[b]Moritz von Rohr and later Merklinger observe that the effective absolute aperture diameter can be used for similar formula in certain circumstances.[19]
Moreover, traditional depth-of-field formulas assume equal acceptable circles of confusion for near and far objects. Merklinger[c] 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.[19] 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 thehyperfocal distance, sometimes almost at infinity. For example, if photographing a cityscape with atraffic bollard in the foreground, this approach, termed theobject 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 asAnsel Adams 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.[20]
Some methods and equipment allow altering the apparentDOF, and some even allow theDOF to be determined after the image is made. These are based or supported by computational imaging processes. For example,focus stacking 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 toreconstruct the 3-dimensional shape of an object, adepth map 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."[21]
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.[22]
Light Scanning Photomacrography (LSP) is another technique used to overcome depth of field limitations in macro and micro photography. This method allows for high-magnification imaging with exceptional depth of field. LSP involves scanning a thin light plane across the subject that is mounted on a moving stage perpendicular to the light plane. This ensures the entire subject remains in sharp focus from the nearest to the farthest details, providing comprehensive depth of field in a single image. Initially developed in the 1960s and further refined in the 1980s and 1990s, LSP was particularly valuable in scientific and biomedical photography before digital focus stacking became prevalent.[23][24]
Other technologies use a combination of lens design and post-processing:Wavefront coding 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.[25]
The lens design can be changed even more: in colourapodization the lens is modified such that each colour channel has a different lens aperture. For example, the red channel may bef/2.4, green may bef/2.4, whilst the blue channel may bef/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 differentf-numbers.[26]
At the extreme, aplenoptic camera captures4D light field information about a scene, so the focus and depth of field can be altered after the photo is taken.
Diffraction causes images to lose sharpness at highf-numbers (i.e., narrow aperture stop opening sizes), and hence limits the potential depth of field.[27] (This effect is not considered in the above formula giving approximateDOF values.) In general photography this is rarely an issue; because largef-numbers typically require long exposure times to acquire acceptable image brightness,motion blur may cause greater loss of sharpness than the loss from diffraction. However, diffraction is a greater issue in close-up photography, and the overall image sharpness can be degraded as photographers are trying to maximize depth of field with very small apertures.[28][29]
Hansma and Peterson have discussed determining the combined effects of defocus and diffraction using a root-square combination of the individual blur spots.[30][31] Hansma's approach determines thef-number that will give the maximum possible sharpness; Peterson's approach determines the minimumf-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.[d] In combination, the two methods can be regarded as giving a maximum and minimumf-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.[27][e] Couzin gave a formula essentially the same as Hansma's for optimalf-number, but did not discuss its derivation.[32]
Hopkins,[33] Stokseth,[34] and Williams and Becklund[35] have discussed the combined effects using themodulation transfer function.[36][37]
Many lenses include scales that indicate theDOF for a given focus distance andf-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. TheDOF scale below the distance scales includes markings on either side of the index that correspond tof-numbers. When the lens is set to a givenf-number, theDOF extends between the distances that align with thef-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.[38] For the 35 mm lens shown, if it were desired for theDOF 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 tof/11.[f]
On a view camera, the focus andf-number can be obtained by measuring the depth of field and performing simple calculations. Some view cameras includeDOF calculators that indicate focus andf-number without the need for any calculations by the photographer.[39][40]
Inoptics andphotography,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 afixed-focus camera.[41] The hyperfocal distance is entirely dependent upon what level of sharpness is considered to be acceptable.
The hyperfocal distance has a property called "consecutive depths of field", where a lens focused at an object whose distance from the lens is at the hyperfocal distanceH will hold a depth of field fromH/2 to infinity, if the lens is focused toH/2, the depth of field will be fromH/3 toH; if the lens is then focused toH/3, the depth of field will be fromH/4 toH/2, etc.
Thomas Sutton and George Dawson first wrote about hyperfocal distance (or "focal range") in 1867.[42] Louis Derr in 1906 may have been the first to derive a formula for hyperfocal distance.Rudolf Kingslake wrote in 1951 about the two methods of measuring hyperfocal distance.
Some cameras have their hyperfocal distance marked on the focus dial. For example, on theMinox LX focusing dial there is a red dot between2 m and infinity; when the lens is set at the red dot, that is, focused at the hyperfocal distance, the depth of field stretches from2 m to infinity. Some lenses have markings indicating the hyperfocal range for specificf-stops, also called adepth-of-field scale.[43]
TheDOF beyond the subject is always greater than theDOF in front of the subject. When the subject is at the hyperfocal distance or beyond, the farDOF is infinite, so the ratio is 1:∞; as the subject distance decreases, near:farDOF ratio increases, approaching unity at high magnification. For large apertures at typical portrait distances, the ratio is still close to 1:1.
This section covers some additional formula for evaluating depth of field; however they are all subject to significant simplifying assumptions: for example, they assume theparaxial approximation ofGaussian optics. They are suitable for practical photography, lens designers would use significantly more complex ones.
For given near and farDOF limitsDN andDF, the requiredf-number is smallest when focus is set to
theharmonic mean of the near and far distances. In practice, this is equivalent to thearithmetic mean for shallow depths of field.[44] Sometimes, view camera users refer to the differencevN −vF as thefocus spread.[45]
If a subject is at distances and the foreground or background is at distanceD, let the distance between the subject and the foreground or background be indicated by
The blur disk diameterb of a detail at distancexd from the subject can be expressed as a function of the subject magnificationms, focal lengthf,f-numberN, or alternatively theapertured, according to
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; whenb is less than the circle of confusion, the detail is within the depth of field.
Adams, Ansel. 1980.The Camera.
