# Depth Of Field In Photography

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Distance between the nearest and the furthest objects that are in focus in an image

A macro photo illustrating the effect of depth of field on a tilted object.

This photograph was taken with an aperture of f/22 creating a by and large in-focus backrground.

The aforementioned photo just with an aperture of f/1.8. Notice how much more blurred out the background is in this photo.

The
depth of field
(DOF) is the distance between the nearest and the furthest objects that are in acceptably abrupt focus in an image captured with a photographic camera.

## Factors affecting depth of field

Effect of aperture on blur and DOF. The points in focus (two) projection points onto the image plane (5), just points at different distances (ane
and
3) project blurred images, or circles of confusion. Decreasing the discontinuity size (iv) reduces the size of the mistiness spots for points non in the focused plane, and so that the blurring is ephemeral, and all points are within the DOF.

For cameras that tin merely focus on 1 object distance at a fourth dimension, depth of field is the distance between the nearest and the farthest objects that are in passably precipitous focus.[1]
“Acceptably sharp focus” is defined using a property called the “circle of confusion”.

The depth of field can exist determined by focal length, distance to subject, the acceptable circumvolve of defoliation size, and aperture.[two]
Limitations of depth of field can sometimes be overcome with various techniques and equipment. The approximate depth of field can be given by:

${\displaystyle {\text{DOF}}\approx {\frac {2u^{2}Nc}{f^{2}}}}$

DOF

two

u

two

N
c

f

2

{\displaystyle {\text{DOF}}\approx {\frac {2u^{2}Nc}{f^{two}}}}

for a given circle of defoliation (c), focal length (f), f-number (N), and distance to subject (u).[3]
[4]

Every bit altitude or the size of the adequate 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 circumvolve of confusion, but changes in proportional to the square of the focal length and the altitude to the bailiwick. Equally a result, photos taken at extremely close range accept 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 property focal length and aperture constant will
decrease
the depth of field (by the crop factor). The resulting image still will have a dissimilar field of view. If the focal length is altered to maintain the field of view, the alter in focal length will counter the subtract of DOF from the smaller sensor and
increment
the depth of field (also by the ingather factor).[5]
[6]
[7]
[8]

### Effect of lens discontinuity

For a given subject framing and camera position, the DOF is controlled by the lens aperture diameter, which is unremarkably specified as the f-number (the ratio of lens focal length to aperture diameter). Reducing the aperture diameter (increasing the
f-number) increases the DOF considering only the low-cal travelling at shallower angles passes through the discontinuity. Because the angles are shallow, the low-cal rays are within the acceptable circle of confusion for a greater distance.[nine]

For a given size of the field of study’s image in the focal airplane, the aforementioned f-number on any focal length lens volition give the same depth of field.[x]
This is evident from the DOF equation past noting that the ratio
u/f
is abiding for constant image size. For example, if the focal length is doubled, the subject altitude is also doubled to continue the discipline image size the same. This observation contrasts with the mutual notion that “focal length is twice as important to defocus as f/terminate”,[xi]
which applies to a constant discipline distance, equally opposed to constant prototype size.

Move pictures brand but express utilize of discontinuity 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.

Aperture = f/1.4. DOF=0.8 cm

Aperture = f/4.0. DOF=2.2 cm

Aperture = f/22. DOF=12.4 cm

Depth of field for different values of discontinuity using 50 mm objective lens and full-frame DSLR camera. Focus point is on the first blocks column.[12]

### Result of circle of defoliation

Precise focus is only possible at an exact distance from the lens;[a]
at that distance, a point object will produce a point epitome. Otherwise, a point object will produce a blur spot shaped like the aperture, typically and approximately a circumvolve. When this circular spot is sufficiently small, it is visually indistinguishable from a indicate, and appears to be in focus. The diameter of the largest circle that is indistinguishable from a point is known as the adequate circle of confusion, or informally, merely as the circumvolve of confusion. Points that produce a mistiness spot smaller than this acceptable circle of defoliation are considered acceptably sharp.

The acceptable circumvolve of defoliation depends on how the final epitome volition be used. It is mostly accustomed to be 0.25 mm for an image viewed from 25 cm away.[thirteen]

For 35 mm motion pictures, the image area on the picture show is roughly 22 mm by sixteen mm. The limit of tolerable fault was traditionally set up at 0.05 mm (0.002 in) diameter, while for 16 mm film, where the size is almost half as large, the tolerance is stricter, 0.025 mm (0.001 in).[14]
More modern do for 35 mm productions gear up the circle of confusion limit at 0.025 mm (0.001 in).[fifteen]

### Camera movements

The term “photographic camera movements” refers to swivel (swing and tilt, in modernistic terminology) and shift adjustments of the lens holder and the film holder. These features have been in utilise since the 1800s and are still in apply today on view cameras, technical cameras, cameras with tilt/shift or perspective control lenses, etc. Swiveling the lens or sensor causes the airplane of focus (POF) to swivel, and also causes the field of acceptable focus to hinge with the POF; and depending on the DOF criteria, to also change the shape of the field of adequate focus. While calculations for DOF of cameras with swivel prepare to zero have been discussed, formulated, and documented since before the 1940s, documenting calculations for cameras with non-zilch hinge seem to have begun in 1990.

More so than in the case of the zippo hinge camera, there are diverse methods to form criteria and fix calculations for DOF when swivel is not-null. There is a gradual reduction of clarity in objects as they motion away from the POF, and at some virtual flat or curved surface the reduced clarity becomes unacceptable. Some photographers do calculations or employ tables, some use markings on their equipment, some guess by previewing the image.

When the POF is rotated, the nigh and far limits of DOF may be thought of as wedge-shaped, with the apex of the wedge nearest the photographic camera; or they may exist thought of every bit parallel to the POF.[16]
[17]

Traditional depth-of-field formulas can be hard to use in practice. As an alternative, the same effective calculation tin be done without regard to the focal length and f-number.[b]
Moritz von Rohr and later Merklinger observe that the effective absolute discontinuity diameter can be used for similar formula in certain circumstances.[xviii]

Moreover, traditional depth-of-field formulas assume equal acceptable circles of defoliation for nigh and far objects. Merklinger[c]
suggested that distant objects often demand to exist much sharper to exist clearly recognizable, whereas closer objects, beingness larger on the film, do not need to be so sharp.[18]
The loss of particular in afar objects may be particularly noticeable with extreme enlargements. Achieving this boosted sharpness in distant objects commonly requires focusing beyond the hyperfocal distance, sometimes almost at infinity. For instance, if photographing a cityscape with a traffic bollard in the foreground, this approach, termed the
object field method
past Merklinger, would recommend focusing very close to infinity, and stopping downwardly to make the bollard abrupt enough. With this approach, foreground objects cannot always exist fabricated perfectly sharp, only the loss of sharpness in near objects may be acceptable if recognizability of distant objects is paramount.

Other authors such as Ansel 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.[19]

## Overcoming DOF limitations

Some methods and equipment let altering the apparent DOF, and some fifty-fifty let the DOF to be determined afterwards the paradigm is made. For instance, 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 to reconstruct the 3-dimensional shape of an object, a depth map can be generated from multiple photographs with different depths of field. Xiong and Shafer ended, in function, “…the improvements on precisions of focus ranging and defocus ranging can lead to efficient shape recovery methods.”[20]

Another arroyo is focus sweep. The focal plane is swept beyond the entire relevant range during a unmarried exposure. This creates a blurred epitome, simply with a convolution kernel that is near contained of object depth, so that the blur is well-nigh entirely removed afterwards computational deconvolution. This has the added benefit of dramatically reducing motion blur.[21]

Other technologies employ a combination of lens pattern and post-processing: Wavefront coding is a method past which controlled aberrations are added to the optical system and so that the focus and depth of field tin be improved afterwards in the process.[22]

The lens blueprint can be inverse even more: in color apodization the lens is modified such that each colour channel has a different lens aperture. For example, the cherry-red channel may exist
f/2.4, light-green may be
f/ii.4, whilst the blue aqueduct may be
f/5.6. Therefore, the blue channel volition take 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 all-time features from the different
f-numbers.[23]

At the extreme, a plenoptic camera captures 4D low-cal field information virtually a scene, so the focus and depth of field can be altered afterward the photograph is taken.

## Diffraction and DOF

Diffraction causes images to lose sharpness at loftier F-numbers, and hence limits the potential depth of field.[24]
In general photography this is rarely an issue; considering large
f-numbers typically require long exposure times, motility mistiness may cause greater loss of sharpness than the loss from diffraction. However, diffraction is a greater effect 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.[25]
[26]

Hansma and Peterson take discussed determining the combined effects of defocus and diffraction using a root-square combination of the individual blur spots.[27]
[28]
Hansma’due south approach determines the
f-number that will give the maximum possible sharpness; Peterson’s approach determines the minimum
f-number that volition give the desired sharpness in the concluding image, and yields a maximum depth of field for which the desired sharpness can be accomplished.[d]
In combination, the two methods can be regarded as giving a maximum and minimum
f-number for a given state of affairs, with the lensman complimentary to choose whatsoever value within the range, as conditions (e.thou., potential motion mistiness) permit. Gibson gives a like give-and-take, additionally considering blurring effects of camera lens aberrations, enlarging lens diffraction and aberrations, the negative emulsion, and the printing paper.[24]
[eastward]
Couzin gave a formula essentially the aforementioned as Hansma’s for optimal
f-number, simply did not discuss its derivation.[29]

Hopkins,[30]
Stokseth,[31]
and Williams and Becklund[32]
take discussed the combined effects using the modulation transfer function.[33]
[34]

## DOF scales

Detail from a lens fix to
f/11. The bespeak half-way between the ane m and two m marks, the DOF limits at
f/eleven, represents the focus distance of approximately ane.33 m (the reciprocal of the mean of the reciprocals of 1 and ii beingness four/3).

DOF scale on Tessina focusing dial

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 anxiety and meters; when a marked altitude is prepare opposite the large white index marking, the focus is set to that distance. The DOF scale beneath 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 betwixt the distances that align with the
f-number markings.

Photographers tin can utilize the lens scales to work backwards from the desired depth of field to detect the necessary focus distance and aperture.[35]
For the 35 mm lens shown, if it were desired for the DOF to extend from 1 chiliad to 2 m, focus would be set so that index marking was centered between the marks for those distances, and the discontinuity would be prepare to
f/eleven.[f]

On a view camera, the focus and
f-number can be obtained by measuring the depth of field and performing uncomplicated calculations. Some view cameras include DOF calculators that betoken focus and
f-number without the need for any calculations by the photographer.[36]
[37]

## Hyperfocal distance

Zeiss Ikon Contessa with red marks for hyperfocal distance 20 ft at
f/eight

Minox Lx camera with hyperfocal blood-red dot

Nikon 28mm f/2.eight lens with markings for the depth of field. The lens is fix at the hyperfocal distance for f/22. The orangish mark corresponding to f/22 is at the infinity mark (

${\displaystyle \infty }$

{\displaystyle \infty }

). Focus is acceptable from nether 0.7 thousand to infinity.

Minolta 100-300 zoom lens. The depth-of-field, and thus hyperfocal distance, changes with the focal length as well as the f/stop. This lens is ready to the hyperfocal distance for f/32 at a focal length of 100mm.

In eyes and photography, hyperfocal distance is a distance beyond which all objects can be brought into an “acceptable” focus. As the hyperfocal altitude is the focus distance giving the maximum depth of field, it is the most desirable altitude to ready the focus of a fixed-focus camera.[38]
The hyperfocal distance is entirely dependent upon what level of sharpness is considered to be acceptable.

The hyperfocal distance has a holding called “sequent depths of field”, where a lens focused at an object whose altitude is at the hyperfocal distance
H
volition hold a depth of field from
H/2 to infinity, if the lens is focused to
H/2, the depth of field will extend from
H/three to
H; if the lens is then focused to
H/iii, the depth of field volition extend from
H/4 to
H/2, etc.

Thomas Sutton and George Dawson get-go wrote virtually hyperfocal distance (or “focal range”) in 1867.[39]
Louis Derr in 1906 may have been the first to derive a formula for hyperfocal distance. Rudolf Kingslake wrote in 1951 nearly the 2 methods of measuring hyperfocal altitude.

Some cameras accept their hyperfocal altitude marked on the focus dial. For example, on the Minox Lx focusing dial there is a red dot between 2 m and infinity; when the lens is set at the red dot, that is, focused at the hyperfocal distance, the depth of field stretches from 2 chiliad to infinity. Some lenses have markings indicating the hyperfocal range for specific f-stops.

## Most:far distribution

The DOF beyond the field of study is always greater than the DOF in forepart of the field of study. When the subject area is at the hyperfocal distance or across, the far DOF is space, so the ratio is one:∞; equally the subject field altitude decreases, nearly:far DOF ratio increases, approaching unity at high magnification. For large apertures at typical portrait distances, the ratio is even so shut to 1:1.

## DOF formulae

This section covers some additional formula for evaluating depth of field; nonetheless they are all field of study to significant simplifying assumptions: for example, they assume the paraxial approximation of Gaussian optics. They are suitable for applied photography, lens designers would apply significantly more complex ones.

### Focus and f-number from DOF limits

For given near and far DOF limits

${\displaystyle D_{\mathrm {N} }}$

D

N

{\displaystyle D_{\mathrm {N} }}

and

${\displaystyle D_{\mathrm {F} }}$

D

F

{\displaystyle D_{\mathrm {F} }}

, the required
f-number is smallest when focus is set to

${\displaystyle s={\frac {2D_{\mathrm {N} }D_{\mathrm {F} }}{D_{\mathrm {N} }+D_{\mathrm {F} }}},}$

south
=

two

D

N

D

F

D

N

+

D

F

,

{\displaystyle due south={\frac {2D_{\mathrm {N} }D_{\mathrm {F} }}{D_{\mathrm {N} }+D_{\mathrm {F} }}},}

the harmonic mean of the nigh and far distances. In practice, this is equivalent to the arithmetic mean for shallow depths of field.[40]
Sometimes, view camera users refer to the deviation

${\displaystyle v_{\mathrm {N} }-v_{\mathrm {F} }}$

v

N

v

F

{\displaystyle v_{\mathrm {N} }-v_{\mathrm {F} }}

as the

### Foreground and background blur

If a subject field is at distance

${\displaystyle s}$

s

{\displaystyle s}

and the foreground or groundwork is at distance

${\displaystyle D}$

D

{\displaystyle D}

, let the distance betwixt the bailiwick and the foreground or background be indicated past

${\displaystyle x_{\mathrm {d} }=|D-s|.}$

10

d

=

|

D

s

|

.

{\displaystyle x_{\mathrm {d} }=|D-southward|.}

The blur disk diameter

${\displaystyle b}$

b

{\displaystyle b}

of a detail at altitude

${\displaystyle x_{\mathrm {d} }}$

x

d

{\displaystyle x_{\mathrm {d} }}

from the subject tin can be expressed every bit a function of the field of study magnification

${\displaystyle m_{\mathrm {s} }}$

1000

south

{\displaystyle m_{\mathrm {s} }}

, focal length

${\displaystyle f}$

f

{\displaystyle f}

,
f-number

${\displaystyle N}$

N

{\displaystyle N}

, or alternatively the aperture

${\displaystyle d}$

d

{\displaystyle d}

, according to

${\displaystyle b={\frac {fm_{\mathrm {s} }}{N}}{\frac {x_{\mathrm {d} }}{s\pm x_{\mathrm {d} }}}=dm_{\mathrm {s} }{\frac {x_{\mathrm {d} }}{D}}.}$

b
=

f

grand

south

N

10

d

s
±

x

d

=
d

m

s

x

d

D

.

{\displaystyle b={\frac {fm_{\mathrm {s} }}{N}}{\frac {x_{\mathrm {d} }}{due south\pm x_{\mathrm {d} }}}=dm_{\mathrm {s} }{\frac {x_{\mathrm {d} }}{D}}.}

The minus sign applies to a foreground object, and the plus sign applies to a background object.

The blur increases with the altitude from the subject; when

${\displaystyle b}$

b

{\displaystyle b}

is less than the circumvolve of confusion, the item is within the depth of field.

• Angle of view
• Bokeh
• Photographic camera bending
• Depth of focus
• Frazier lens (very deep DOF)
• Light-field camera
• Miniature faking
• Numerical aperture
• Perspective distortion

## Notes

1. ^

strictly, at an exact distance from a plane

2. ^

however that the f-number is derived from the focal length

3. ^

Englander describes a similar approach in his newspaper Apparent Depth of Field: Applied Utilise in Landscape Photography; Conrad discusses this arroyo, under Different Circles of Confusion for Near and Far Limits of Depth of Field, and The Object Field Method, in Depth of Field in Depth

4. ^

Peterson does not give a closed-form expression for the minimum
f-number, though such an expression obtains from simple algebraic manipulation of his Equation 3

5. ^

The analytical section at the end of Gibson (1975) was originally published equally “Magnification and Depth of Detail in Photomacrography” in the
Journal of the Photographic Society of America, Vol. 26, No. 6, June 1960

6. ^

The focus distance to have the DOF extend between given about and far object distances is the harmonic mean of the
object conjugates. Most helicoid-focused lenses are marked with prototype airplane-to-bailiwick distances,[
citation needed
]

and so the focus determined from the lens distance scale is not exactly the harmonic hateful of the marked near and far distances.

## References

### Citations

1. ^

Salvaggio & Stroebel 2009, pp. 110-.

2. ^

Barbara London; Jim Stone; John Upton (2005).
Photography
(8th ed.). Pearson. p. 58. ISBN978-0-13-448202-6.

3. ^

Elizabeth Allen; Sophie Triantaphillidou (2011).
The Transmission of Photography. Taylor & Francis. pp. 111–. ISBN978-0-240-52037-vii.

4. ^

“Depth of field”.
graphics.stanford.edu.

5. ^

Nasse, H.H. (March 2010). “Depth of Field and Bokeh (Zeiss Whitepaper)”
(PDF).
lenspire.zeiss.com.

6. ^

“Digital Camera Sensor Sizes: How it Influences Your Photography”.
www.cambridgeincolour.com.

7. ^

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Photography Life.

8. ^

Vinson, Jason (22 January 2016). “The Smaller the Sensor Size, the Shallower Your Depth of Field”.
Fstoppers.

9. ^

“Why Does a Small Aperture Increment Depth of Field?”.

10. ^

“DOF2, Jan xiii, 2009 by Michael Reichmann, Luminous Landscape”.

11. ^

“Ken Rockwell”.

12. ^

“photoskop: Interactive Photography Lessons”. Apr 25, 2015.

13. ^

Savazzi 2011, p. 109.

14. ^

Film and Its Techniques. University of California Press. 1966. p. 56. Retrieved
24 February
2016
.

15. ^

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Digital Filmmaking: The Changing Art and Arts and crafts of Making Motion Pictures. CRC Printing. p. 96. ISBN9781136053542
. Retrieved
24 February
2016
.

16. ^

Merklinger 2010, pp. 49–56.
sfn error: no target: CITEREFMerklinger2010 (help)

17. ^

Tillmanns 1997, p. 71.
18. ^

a

b

Merklinger 1992.

19. ^

20. ^

Xiong, Yalin, and Steven A. Shafer. “Depth from focusing and defocusing.” Computer Vision and Pattern Recognition, 1993. Proceedings CVPR’93., 1993 IEEE Computer Gild Conference on. IEEE, 1993.

21. ^

Bando et al. “Near-Invariant Blur for Depth and 2D Movement via Fourth dimension-Varying Light Field Assay.” ACM Transactions on Graphics, Vol. 32, No. 2, Article 13, 2013.

22. ^

Mary, D.; Roche, M.; Theys, C.; Aime, C. (2013). “Introduction to Wavefront Coding for Incoherent Imaging”.
EAS Publications Series.
59: 77–92. doi:x.1051/eas/1359005. ISSN 1633-4760.

23. ^

Kay 2011.
24. ^

a

b

Gibson 1975, p. 64.

25. ^

Gibson 1975, p. 53.

26. ^

Lefkowitz 1979, p. 84.

27. ^

Hansma 1996.

28. ^

Peterson 1996.
sfn fault: no target: CITEREFPeterson1996 (help)

29. ^

Couzin 1982.
sfn error: no target: CITEREFCouzin1982 (help)

30. ^

Hopkins 1955.
sfn error: no target: CITEREFHopkins1955 (help)

31. ^

Stokseth 1969.
sfn mistake: no target: CITEREFStokseth1969 (help)

32. ^

Williams & Becklund 1989.
sfn fault: no target: CITEREFWilliamsBecklund1989 (aid)

33. ^

“Depth of Field in Depth”, Jeff Conrad

34. ^

“Photographic Lenses Tutorial”, David 1000. Jacobson, 26 Oct 1996

35. ^

Ray 1994, p. 315.

36. ^

Tillmanns 1997, p. 67-68.

37. ^

Ray 1994, p. 230-231.

38. ^

Kingslake, Rudolf (1951).
Lenses in Photography: The Practical Guide to Optics for Photographers. Garden Metropolis, NY: Garden City Press.

39. ^

Sutton, Thomas; Dawson, George (1867).
A Lexicon of Photography. London: Sampson Low, Son & Marston.

40. ^

https://world wide web.largeformatphotography.info/manufactures/DoFinDepth.pdf[
bare URL PDF
]

41. ^

Hansma 1996, p. 55.

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[
self-published source?
]