Depth Of Field

In Optics , particularly Film and Photography , the depth of field (DOF) is the distance in front of and beyond the subject that appears to be in Focus .

with very small depth of field.]]
. Decreasing the aperture size (4) reduces the size of the blur circles for points not in the focused plane, so that the blurring is imperceptible, and all points are within the DOF.]]

APPARENT SHARP FOCUS

Precise focus is possible at only one distance; at that distance, a point object will produce a point image. At any other distance, a point object is '' Defocused '', and will produce a circular image. However, when the circle is sufficiently small, it is indistinguishable from a point, and appears to be in focus; it is rendered as “acceptably sharp”. The diameter of the circle increases with distance from the point of focus; 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''. The acceptable circle of confusion is influenced by visual acuity, viewing conditions, and the amount by which the image is enlarged. The increase of the circle diameter with defocus is gradual, so the limits of depth of field are not hard boundaries between sharp and unsharp.

Several other factors, such as subject matter, movement, and the distance of the subject from the camera, also influence when a given defocus becomes noticeable.

For a 35 mm motion picture, the image area on the negative is roughly 22 mm by 16 mm (0.87 in by 0.63 in). The limit of tolerable error is usually set at 0.05 mm (0.002 in) diameter. For 16 mm film , where the image area is smaller, the tolerance is stricter, 0.025 mm (0.001 in). Standard depth-of-field tables are constructed on this basis, although generally 35 mm productions set it at 0.025 mm (0.001 in). Note that the acceptable circle of confusion values for these formats are different because of the relative amount of magnification each format will need in order to be projected on a full-sized movie screen.

(A table for 35 mm still photography would be somewhat different since more of the film is used for each image and the amount of enlargement is usually much less.)

. The depth-of-field scale (top) indicates that a subject which is anywhere between 1 and 2 meters in front of the camera will be rendered acceptably sharp. If the aperture were set to 22 instead, everything from 0.7 meters to infinity would appear to be in focus.]]

The Image Format size also will affect the depth of field. The larger the format size, the longer a lens will need to be to capture the same framing as a smaller format. In motion pictures, for example, a frame with a 12 degree horizontal field of view will require a 50 mm lens on 16 mm film, a 100 mm lens on 35 mm film, and a 250 mm lens on 65 mm film. Conversely, using the same focal length lens with each of these formats will yield a progressively wider image as the film format gets larger: a 50 mm lens has a horizontal field of view of 12 degrees on 16 mm film, 23.6 degrees on 35 mm film, and 55.6 degrees on 65 mm film. What this all means is that because the larger formats require longer lenses than the smaller ones, they will accordingly have a smaller depth of field. Therefore, compensations in exposure, framing, or subject distance need to be made in order to make one format look like it was filmed in another format.

EFFECT OF <VAR>F</VAR>-NUMBER

For a given subject framing, the DOF is controlled by the lens F-number . Increasing the f-number (reducing the Aperture diameter) increases the DOF; however, it also reduces the amount of light transmitted, and increases Diffraction , placing a practical limit on the extent to which the aperture size may be reduced. Motion pictures make only limited use of this 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.

CAMERA MOVEMENTS AND DOF

When the lens axis is perpendicular to the image plane, as is normally the
case, the plane of focus (POF) is parallel to the image plane, and the DOF
extends between parallel planes on either side of the POF. When the lens
axis is not perpendicular to the image plane, the POF is no longer parallel
to the image plane; the ability to Rotate The POF is
known as the Scheimpflug Principle . Rotation of the POF is
accomplished with Camera Movements
(tilt, a rotation of the lens about a horizontal axis, or swing, a rotation
about a vertical axis). Tilt and swing are available on most view cameras, and
are also available with specific lenses on some small- and medium-format
cameras.

When the POF is rotated, the near and far limits of DOF are no longer
parallel; the DOF becomes wedge-shaped, with the apex of the wedge nearest
the camera. With tilt, the height of the DOF increases with distance
from the camera; with swing, the width of the DOF increases with distance.

Rotating the POF with tilt or swing (or both) can be used either to
maximize or minimize the part of an image that is within the DOF.

LIMITED DOF: SELECTIVE FOCUS

Depth of field can be anywhere from a fraction of a millimeter to virtually infinite.
In some cases, such as landscapes, it may be desirable to have the entire image in focus,
and a large DOF is appropriate. In other cases, artistic considerations may dictate that only
a part of the image be in focus, emphasizing the subject while de-emphasizing the background,
perhaps giving only a suggestion of the environment ( Langford 1973 , 81).
For example, a common technique in Melodrama s and Horror Film s is a closeup of a person's face,
with someone just behind that person visible but out of focus. A Portrait or
Closeup still photograph might use a small DOF to isolate the subject
from a distracting background. The use of limited DOF to emphasize one part of an image is known
as ''selective focus'' or ''differential focus''.

Although a small DOF implies that other parts of the image will be unsharp, it does not, by itself,
determine ''how'' unsharp those parts will be. The amount of background (or foreground) blur depends
on the distance from the plane of focus, so if a background is close to the subject, it may be difficult
to blur sufficiently even with a small DOF. In practice, the lens f-number is usually adjusted
until the background or foreground is acceptably blurred, often without direct concern for the DOF.

Sometimes, however, it is desirable to have the entire subject sharp while ensuring that the background
is sufficiently unsharp. When the distance between subject and background is fixed, as is the case with
many scenes, the DOF and the amount of background blur are not independent. Although it is not always
possible to achieve both the desired subject sharpness and the desired background unsharpness, several
techniques can be used to increase the separation of subject and background.

For a given scene and subject magnification, the background blur increases with lens focal length.
If it is not important that background objects be unrecognizable, background de-emphasis can be
increased by using a lens of longer focal length and increasing the subject distance to maintain
the same magnification. This technique requires that sufficient space in front of the subject
be available; moreover, the perspective of the scene changes because of the different camera position,
and this may or may not be acceptable.

The situation is not as simple if it is important that a background object, such as a sign, be unrecognizable.
The magnification of background objects also increases with focal length, so with the technique just described,
there is little change in the recognizability of background objects. However, a lens of longer focal length
may still be of some help; because of the narrower angle of view, a slight change of camera position may suffice
to eliminate the distracting object from the field of view.

Although tilt and swing are normally used to maximize the part of the
image that is within the DOF, they also can be used, in combination with a
small f-number, to give selective focus to a plane that isn't
perpendicular to the lens axis. With this technique, it is possible to
have objects at greatly different distances from the camera in sharp focus
and yet have a very shallow DOF. The effect can be interesting because it
differs from what most viewers are accustomed to seeing.

HYPERFOCAL DISTANCE

The Hyperfocal Distance is the nearest focus distance at which the DOF extends to infinity; focusing the camera at the hyperfocal distance results in the largest possible depth of field for a given f-number. Focusing ''beyond'' the hyperfocal distance does not increase the far DOF (which already extends to infinity), but it does decrease the DOF in front of the subject, decreasing the total DOF. Some photographers refer to this as “wasting DOF”; however, see ''The object field method'' below. Focusing ahead of the hyperfocal distance increases the DOF ahead of the subject, but decreases DOF beyond the subject, including objects near infinity. Of course, this latter approach may be appropriate for images that do not extend to infinity.

THE OBJECT FIELD METHOD

Traditional depth-of-field formulae and tables assume equal circles of
confusion for near and far objects. Some authors, such as
Merklinger (1992) ,
Englander describes a similar approach in his paper
Apparent Depth of Field: Practical Use in Landscape Photography . ( PDF );
Conrad discusses this approach, 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 ( PDF )

have 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, 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.

Moritz Von Rohr also used an object field method, but unlike Merklinger, he
used the conventional criterion of a maximum circle of confusion diameter in
the image plane, leading to unequal front and rear depths of field.

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; as the subject distance decreases, near:far DOF ratio
increases, approaching unity at high magnification. The oft-cited
“rule” that 1/3 of the DOF is in front of the subject and 2/3
is beyond is true only when the subject distance is 1/3 the hyperfocal
distance.

DEPTH OF FIELD FORMULAE

The basis of these formulae is given in the section
Derivation Of The DOF Formulae ;
Derivations of DOF formulae are given in many texts, including
Larmore (1965)
and Ray (2002) .
Complete derivations also are given in Conrad's
Depth of Field in Depth ( PDF )
and van Walree's
Derivation of the DOF equations .

refer to the diagram in that section for illustration of the quantities discussed below.

Hyperfocal Distance

Let

f

be the lens Focal Length ,

N

be the lens F-number , and

c

be the
Circle Of Confusion for a given Image Format . The
hyperfocal distance

H

is given by

:

H \approx rac {f^2} {N c}

Moderate-to-large distances

Let

s

be the distance at which the camera is focused (the
“subject distance”). When

s

is large in comparison with the
lens Focal Length , the distance

D_{\mathrm N}

from the
camera to the near limit of DOF and the distance

D_{\mathrm F}

from the camera to the far limit of DOF are

:

D_{\mathrm N} \approx rac {H s} {H + s}

D_{\mathrm F} \approx rac {H s} {H - s} \mbox{ for } s < H

When the subject distance is the hyperfocal distance,

:

D_{\mathrm F} = \infty

D_{\mathrm N} = rac H 2

The depth of field

D_{\mathrm F} - D_{\mathrm N}

is

:

\mathrm {DOF} \approx rac {2 Hs^2}
{H^2 - s^2} \mbox{ for } s < H

For

s \ge H

, the far limit of DOF is at infinity and the DOF
is infinite; of course, only objects at or beyond the near limit of DOF
will be recorded with acceptable sharpness.

Substituting for

H

and rearranging, DOF can be expressed as

:

\mathrm {DOF} \approx rac {2 N c f^2 s^2} {f^4 - N^2 c^2 s^2}

Thus, for a given Image Format , depth of field is determined
by three factors: the Focal Length of the lens, the f-number of the
lens opening (the Aperture ), and the camera-to-subject distance.

Close-up

When the subject distance

s

approaches the focal length, using
the formulae given above can result in significant errors. For close-up
work, the hyperfocal distance has little applicability, and it usually is
more convenient to express DOF in terms of image magnification. Let

m

be the magnification; when the subject distance is small in
comparison with the hyperfocal distance,

:

\mathrm {DOF} \approx 2 N c \left ( rac {m + 1} {m^2} 
ight ),

so that for a given magnification, DOF is independent of focal length.
Stated otherwise, for the same subject magnification, all focal lengths
give approximately the same DOF. This statement is true only when
the subject distance is small in comparison with the hyperfocal distance,
however.

The discussion thus far has assumed a symmetrical lens for which the
entrance and exit Pupil s coincide with the front and rear
Nodal Planes , and for which the Pupil Magnification
(the ratio of Exit Pupil diameter to that of the
Entrance Pupil )A well-illustrated discussion of pupils and pupil
magnification that assumes minimal knowledge of optics and mathematics is
given in Shipman (1977) . is unity.
Although this assumption usually is reasonable for large-format lenses, it
often is invalid for medium- and small-format lenses.

When

s \ll H

, the DOF for an asymmetrical lens is

:

\mathrm {DOF} \approx rac {2 N c (1 + m/P)}{m^2},

where

P

is the pupil magnification. When the
pupil magnification is unity, this equation reduces to that for a
symmetrical lens.

Except for close-up and macro photography, the effect of lens asymmetry is
minimal. At unity magnification, however, the errors from neglecting the
pupil magnification can be significant. Consider a telephoto lens with

P = 0.5

and a retrofocus wide-angle lens with

P =
2

, at

m = 1.0

. The asymmetrical-lens formula gives

\mathrm {DOF} = 6 N c

and

\mathrm {DOF} = 3 N c

,
respectively. The symmetrical-lens formula gives

\mathrm {DOF} = 4 N
c

in either case. The errors are −33% and 33%, respectively.

Focus and f-number

Not all images require that sharpness extend to infinity; for given near
and far DOF limits

D_{\mathrm N}

and

D_{\mathrm F}

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

:

s = rac {2 D_{\mathrm N} D_{\mathrm F} }
{D_{\mathrm N} +  D_{\mathrm F} }

When the subject distance is large in comparison with the lens focal
length, the required f-number is

:

N \approx rac {f^2} {c}
rac {D_{\mathrm F} -  D_{\mathrm N} } {2 D_{\mathrm N} D_{\mathrm F} }

In practice, these settings usually are determined on the image side of the
lens, using measurements on the bed or rail with a view camera, or using
lens DOF scales on manual-focus lenses for small- and medium-format
cameras. If

v_{\mathrm N}

and

v_{\mathrm F}

are the image distances that correspond to the near and far limits of DOF,
the required f-number is minimized when the image distance

v

is

:

v \approx rac { v_{\mathrm N} + v_{\mathrm F} } {2}
= v_{\mathrm F} + rac { v_{\mathrm N} - v_{\mathrm F} } {2}

In practical terms, focus is set to halfway between the near and far
image distances. The required f-number is

:

N \approx rac { v_{\mathrm N} - v_{\mathrm F} } { 2 c }

The image distances are measured from the camera's image plane to the
lens's image nodal plane, which is not always easy to locate. In most
cases, focus and f-number can be determined with sufficient
accuracy using the approximate formulae above, which require only the
difference between the near and far image distances;
view camera users often refer to the difference

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

as the ''focus spread.''
Most lens DOF scales are based on the same concept.

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

See Also: Focus stacking

Focus Stacking is a Digital Image Processing technique which combines multiple images taken at different focus distances to give a resulting image with a greater depth of field than any of the individual source images. Available programs for multi-shot DOF enhancement include Helicon Focus and CombineZM .

Getting sufficient depth of field can be particularly challenging in macro photography. The images at right illustrate the increase in DOF that can be achieved by combining multiple exposures.

Other digital techniques include Wavefront Coding and Plenoptic Camera s.

DERIVATION OF THE DOF FORMULAE

DOF limits

A symmetrical lens is illustrated at right. The subject at distance

s

is in focus at image distance

v

. Point objects
at distances

D_\mathrm F

and

D_\mathrm N

would be
in focus at image distances

v_\mathrm F

and

v_\mathrm
N

, respectively; at image distance

v

, they are imaged
as blur spots. The depth of field is controlled by the aperture stop
diameter

d

; when the blur spot diameter is equal to the
acceptable Circle Of Confusion

c

, the near and far limits
of DOF are at

D_\mathrm N

and

D_\mathrm F

. From
similar triangles,

:

rac {v_\mathrm N - v} {v_\mathrm N} = rac c d

rac {v- v_\mathrm F} {v_\mathrm F} = rac c d

It usually is more convenient to work with the lens f-number
than the aperture diameter; the f-number

N

is
related to the lens focal length

f

and the aperture diameter

d

by

:

N = rac f d\,;

substituting into the previous equations and rearranging gives
:

v_\mathrm N = rac {fv} {f - Nc}

v_\mathrm F = rac {fv} {f + Nc}

The image distance

v

is related to an object distance

u

by the thin-lens equation

:

rac 1 u + rac 1 v = rac 1 f\,;

substituting into the two previous equations and rearranging gives the
near and far limits of DOF:

:

D_{\mathrm N} = rac {s f^2} {f^2 + N c ( s - f ) }

D_{\mathrm F} = rac {s f^2} {f^2 - N c ( s - f ) }

Hyperfocal distance

Setting the far limit of DOF

D_{\mathrm F}

to infinity and
solving for the focus distance

s

gives

:

s = H = rac {f^2} {N c} + f,

where

H

is the Hyperfocal Distance . Setting the subject
distance to the hyperfocal distance and solving for the near limit of DOF
gives

:

D_{\mathrm N} = rac {f^2 / ( N c ) + f} {2}  = rac {H}{2}

For any practical value of

H

, the focal length is negligible
in comparison, so that

:

H \approx rac {f^2} {N c}

Substituting the approximate expression for hyperfocal distance into the
formulae for the near and far limits of DOF gives

:

D_{\mathrm N} = rac {H s}{H + ( s - f )}

D_{\mathrm F} = rac {H s}{H - ( s - f )}

Combining, the depth of field

D_{\mathrm F} - D_{\mathrm N}

is

:

\mathrm {DOF} = rac {2 H s (s - f )}
{H^2 - ( s - f )^2} \mbox{ for } s < H

Moderate-to-large distances

When the subject distance is large in comparison with the lens Focal Length ,

:

D_{\mathrm N} \approx rac {H s} {H + s}

D_{\mathrm F} \approx rac {H s} {H - s} \mbox{ for } s < H

\mathrm {DOF} \approx rac {2 H s^2}
{H^2 - s^2} \mbox{ for } s < H

For

s \ge H

, the far limit of DOF is at infinity and the DOF
is infinite; of course, only objects at or beyond the near limit of DOF
will be recorded with acceptable sharpness.

Close-up

When the subject distance

s

approaches the lens focal length,
the focal length no longer is negligible, and the approximate formulae
above cannot be used without introducing significant error. At close
distances, the hyperfocal distance has little applicability, and it usually
is more convenient to express DOF in terms of magnification. Substituting

:

s = rac {m + 1} {m} f

and

:

s - f = rac {f} {m}

into the formula for DOF and rearranging gives

:

\mathrm {DOF} = rac
{2 f ( m + 1 ) / m }
{ ( f m ) / ( N c ) - ( N c ) / ( f m ) }

At the Hyperfocal Distance , the terms in the denominator are equal, and
the DOF is infinite. As the subject distance decreases, so does the second
term in the denominator; when

s \ll H

, the second term becomes
small in comparison with the first, and

:

\mathrm {DOF} \approx 2 N c \left ( rac {m + 1} {m^2} 
ight ),

so that for a given magnification, DOF is independent of focal length.
Stated otherwise, for the same subject magnification, all focal lengths for
a given Image Format give approximately the same DOF. This
statement is true only when the subject distance is small in comparison
with the hyperfocal distance, however. Multiplying the numerator and
denominator of the exact formula by

:

rac {N c m} {f}

gives

:

\mathrm {DOF} = rac
{2 N c \left ( m + 1 
ight )}
{m^2 - \left ( rac {N c} {f} 
ight )^2}

Decreasing the focal length

f

increases the second term in the
denominator, decreasing the denominator and increasing the value of the
right-hand side, so that a shorter focal length gives greater DOF. The
effect of focal length is greatest near the hyperfocal distance, and
decreases as subject distance is decreased. However, the near/far
perspective will differ for different focal lengths, so the difference in
DOF may not be readily apparent. When the subject distance is small in
comparison with the hyperfocal distance, the effect of focal length is
negligible, and, as noted above, the DOF essentially is independent of
focal length.

Near:far DOF ratio

From the “exact” equations for near and far limits of DOF, the DOF in front of the subject is

:

s - D_{\mathrm N} = rac {Ncs(s - f)} {f^2 + Nc(s - f)}\,,

and the DOF beyond the subject is

:

D_{\mathrm F} - s = rac {Ncs(s - f)} {f^2 - Nc(s - f)}

The near:far DOF ratio is

:

rac {s - D_{\mathrm N}}  {D_{\mathrm F} - s}
= rac {f^2 - Nc(s - f)} {f^2 + Nc(s - f)}

This ratio is always less than unity; at moderate-to-large subject distances,

f \ll s

, and

:

rac {s - D_{\mathrm N}}  {D_{\mathrm F} - s}
\approx rac {f^2 - Ncs} {f^2 + Ncs} = rac {H - s} {H + s}

When the subject is at the hyperfocal distance or beyond, the far DOF is infinite, and the near:far ratio is zero. It's commonly stated that approximately 1/3 of the DOF is in front of the subject and approximately 2/3 is beyond; however, this is true only when

s \approx H/3

.

At closer subject distances, it's often more convenient to express the DOF ratio in terms of the magnification

:

m = rac f {s - f}

Substitution into the “exact” equation for DOF ratio gives

:

rac {s - D_{\mathrm N}}  {D_{\mathrm F} - s}
= rac {m - Nc/f} {m + Nc/f}

As magnification increases, the near:far ratio approaches a limiting value of unity.

Focus and f-number

Not all images require that sharpness extend to infinity; the equations for
the DOF limits can be combined to eliminate

Nc

and solve for
the subject distance. For given near and far DOF limits

D_{\mathrm N}

and

D_{\mathrm F}

, the
subject distance is

:

s = rac {2 D_{\mathrm N} D_{\mathrm F} }
{D_{\mathrm N} +  D_{\mathrm F} }

The equations for DOF limits also can be combined to eliminate

s

and solve for the required f-number, giving

:

N = rac {f^2} {c}
rac {D_{\mathrm F} -  D_{\mathrm N} }
{D_{\mathrm F} ( D_{\mathrm N} - f ) + D_{\mathrm N} ( D_{\mathrm F} - f ) }

When the subject distance is large in comparison with the lens focal
length, this simplifies to

:

N \approx rac {f^2} {c}
rac {D_{\mathrm F} -  D_{\mathrm N} } {2 D_{\mathrm N} D_{\mathrm F} }

Most discussions of DOF concentrate on the object side of the lens, but the
formulae are simpler and the measurements usually easier to make on the
image side. If

v_{\mathrm N}

and

v_{\mathrm F}

are the image distances that correspond to the near and far limits of DOF,
the required f-number is minimum when the image distance

v

is

:

v = rac {2 v_{\mathrm N} v_{\mathrm F} }
{v_{\mathrm N} +  v_{\mathrm F} }

The required f-number is

:

N = rac {f} {c}
 rac { v_{\mathrm N} - v_{\mathrm F} }
{v_{\mathrm N} +  v_{\mathrm F} }

v \approx rac { v_{\mathrm N} + v_{\mathrm F} } {2}
= v_{\mathrm F} + rac { v_{\mathrm N} - v_{\mathrm F} } {2}

N \approx rac { v_{\mathrm N} - v_{\mathrm F} } { 2 c },

which require only the difference between the near and far image distances;
focus is simply set to halfway between the near and far distances.
View camera users often refer to the difference

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

as the ''focus spread'';
it usually is measured on the bed or focusing rail. On manual-focus
small- and medium-format lenses, the focus and f-number
usually are determined using the lens DOF scales, which
often are based on the two equations above.

For close-up photography, the f-number is more accurately determined using

:

N \approx rac {1} { 1 + m } rac { v_{\mathrm N} - v_{\mathrm F} } { 2 c },

where

m

is the magnification.

Foreground and background blur

If the equation for the far limit of DOF is solved for

c

, and the far distance
replaced by an arbitrary distance

D

, the blur disk diameter

b

at that distance is

:

b = rac {fm_\mathrm s} {N} rac { D - s } { D }

When the background is at the far limit of DOF, the blur disk diameter is equal to the circle
of confusion

c

, and the blur is just imperceptible. The diameter of the background
blur disk increases with the distance to the background. A similar relationship holds for the
foreground; the general expression for a defocused object at distance

D

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