All images on this website are © copyright 2004 Gary &
Anna Ayton. Contact me if you want prints from the originals.
see depth of field examples using the C8080
DEPTH OF FIELD IS NOT PURELY A
FUNCTION OF LENS FOCAL LENGTH AND F/RATIO BUT IS VERY DEPENDENT ON HOW MUCH THE
RESULTING IMAGE WILL BE ENLARGED AND THUS IS DEPENDENT ON ALSO ON FILM SIZE OR
SENSOR SIZE.
DEPTH OF FIELD HAS NOTHING TO DO WITH
DEGREE OF BACKGROUND BLURRING OTHER THAN SOMETIMES IT WILL EXTEND TO INCLUDE THE
BACKGROUND.
WARNING: traditional DOF calculations such as those below and lens markings
only apply to 4-8x enlargements which is OK for film, but for small digital
sensors when we are often looking to make enlargements of A4 and larger, these
DOF calculations will give increasingly soft images as enlargement size
increases, and nothing impacts more on an image than lack of sharpness when you
want it.
There is a lot of mis-information and misunderstanding on the internet when
it comes to depth of field, hopefully, I won't be contributing to it. Firstly,
many people state that DOF is purely a function of the lens - its native focal
length (not its 35mm equivalent focal length), camera to subject distance and
aperture and if that lens is used on a full frame camera you will have the same
DOF as when it is used on a cropped sensor. This would be true if you used the
same subject distance, native focal length and aperture AND you printed an
enlargement with the SAME amount of magnification AND viewed it from the same
distance - ie. the cropped sensor print would have a cropped print size, so the
prints would look pretty much identical other than the cropped sensor print
being smaller with the outer parts of the image missing.
In reality, when one uses a cropped sensor, one usually would print to the
same size as if it were not cropped and thus the magnification of the print
becomes greater and when viewed at the same distance, the amount of acceptable
depth of field becomes shallower.
It is complicated further by what people mean - many people concentrate on
the degree and quality of background blurring so that the subject is then
emphasised and has more impact, but this is actually due to a mix of different
factors:
- depth of field
- how sharp the region proximal and distant to the focus plane is
rendered in a final print or image that is viewed from a given distance.
- dependent on magnification (subject distance and focal length), aperture, circle of
confusion size & intended degree of enlargement and viewing
distance.
- degree of background blurring (convolution)
- for the same subject magnification (ie. change subject distance when
change focal length) with same subject to background distance, degree of
background burring is inversely proportional to aperture alone.
- quality (aesthetics) of background blurring (bokeh)
- this is primarily dependent on the shape of the aperture with a
circular aperture usually giving the best bokeh, but additional factors
include potential clipping of the cone of light by the mirror
compartment at wide apertures, vignetting & lens aberrations
affecting out of focus areas which may be corrected for in-focus areas.
Mirror lenses in particular give donut-shaped out-of-focus highlights of
double contours which generally are not aesthetic.
- see http://www.vanwalree.com:80/optics/bokeh.html
Depth of field:
- traditional depth of field (DOF) is the distance ranges from the camera within which a
subject will appear acceptably sharp when enlarged to a 8"x10"
print and viewed from 15" and thus a dot produces a dot no larger than
250micron on the print.
- this 250 micron dot when represented on the film or sensor (=
250micron/magnification to print) is the circle of confusion (COC) for
that film or sensor
- COC values: 35mm film = 29.5micron; Olympus C8080 digital = 8
micron;
- note that at small apertures, the diffraction limit may be larger than
the COC and thus the estimated COC no longer applies. The diffraction
limited spot size is 6 microns at f4.5, 8.45 microns at f6.3 and 10.7
microns at f/8.
- NB. the COC may not really be a circle but the shape of the lens
diaphragm and this impacts on bokeh - the nature of out of focus
areas in the image.
- for a given lens and focus position, there is really only one plane which
will be in focus (in most lenses apart from special flat-field macro lenses,
this plane is usually a curve with all points equidistant to the camera).
Everything else closer or further away than this plane will be out of focus,
but the amount of out of focus will determine whether we will perceive it as
being acceptably sharp or not, hence the depth of field concept.
- some rules of thumb:
- for the same subject image magnification, DOF is dependent on f ratio
and NOT on focal length as you must alter subject distance when you
change focal length.
- different sensor sizes of the same number of pixels will give
equivalent DOF if:
- f/ratio is multiplied by the ratio of the pixel sizes, and,
- focal length used is multiplied by the ratio of the pixel sizes to
give the same effective focal length, and,
- camera to subject distance is kept constant
- obviously, for the same exposure, either shutter speed must be
changed, or if kept constant, the ISO must be multiplied by the
square of the ratio of the pixel sizes, which according to Clark
should give equivalent S/N ratios.
- in other words, a larger sensor CAN give the same DOF as a smaller
sensor at the same shutter speed and image noise by increasing ISO
to allow the f/ratio to be increased.
- the zone of acceptable sharpness is equal closer and more distant to
the focused subject NOT 1/3 : 2/3 as usually stated.
- stopping down the lens 1 stop gives 40% more DOF, while opening it up
1 stop gives 30% less DOF.
- stopping down the lens 2 stops gives twice the DOF, while opening it
up 2 stops gives 50% less DOF.
- stopping down the lens 7 stops gives 10x the DOF
- DOF scales linearly with focus distance for a given focal length, thus
DOF at 10m will be twice that when focused at 5m.
- if you want everything 5mm and larger to be resolved, then you must
use an effective lens diameter of 5mm (ie. f/10 on a 50mm lens) or
smaller AND focus no closer than half the distance to the most distant
object you wish to be sharp.
- when photographing people more than 3m away with a focal length <
50mm (in 35mm terms), then:
- for best resolution of distant subjects such as landscapes,
acceptable results may be possible by focusing on infinity as long
as effective lens diameter is less than 5-6mm (eg. f/10 or more on
50mm lens).
- if resolution of distant objects is not so important, consider
focusing at the hyperfocal length as long as it is less than 6m.
- if you want the subjects eyes to be the key and the rest of the
scene is not important, focus on the eyes.
- everything sharp:
- sometimes, we want everything to be as sharp as possible including
distant objects, in which
case we should set the focus position of the lens on the hyperfocal
distance for that focal length/aperture combination, and then
everything from half the hyperfocal distance to infinity will be
acceptably sharp. In fact, I suspect the designers of the Olympus 8080
do this by default when auto-focus fails - the only problem is that your
subject may be closer than the DOF allows and thus appear blurry.
- on the other hand, Merklinger
suggests that:
- if you want anything at infinity to be sharp, then it is be best
to focus on infinity assuming you have a good lens and technique, as
to do so means you would lose a factor of two in the subject
resolution at near limit of depth of field, but gain a factor of six
in the subject resolution for distant subjects. (ref: page 32 of his
pdf)
- the closest hyperfocal distance is usually achieved by using a small
aperture and wide angle lens with a small sensor or film, examples:
-
|
f/5.6 |
f/8 |
f/16 |
| 35mm with 28mm lens |
4.7m |
3.3m |
1.6m |
| 35mm with 50mm lens |
14.9m |
10.6m |
5.2m |
| 35mm with 90mm lens |
48m |
34m |
17m |
| Oly8080 with 28mm |
1.1m |
0.8m |
n/a |
| Oly8080 with 55mm |
4.4m |
3.1m |
n/a |
| Oly8080 with 90mm |
14m |
9.8m |
n/a |
|
|
|
|
- blur the background (convolution):
- at other times we wish to render the foreground and background out of
focus and blurred so that the viewer will be drawn to the subject rather
than distracted by the background. In this situation, we need to
minimise the depth of field to just enough to cover the depth of the
subject.
- this is one of the reasons a portrait lens is a medium telephoto with
wide aperture
- however, depth of field is NOT directly related to degree of background blur. Depth of field equations tell you over what range of distances objects will appear to be acceptably sharp (or at least not
unacceptably unsharp). It tells you nothing about how much blur there will be of objects well outside the depth of field. That's governed by different physical parameters and determined using totally
different equations:
- background blur of infinity point source = focal length x image
magnification / f-stop
- in addition, modern lenses are often over-corrected for spherical
aberration to produce a more pleasing blurred background (bokeh) at the
expense of quality of foreground blurring.
- Merklinger uses the concept of disk-of-confusion to help
determine what will be in focus (see page 32 of his pdf):
- the disk-of-confusion is the hypothetical diameter of the cone of
light from the film projected onto an object
- disk-of-confusion at distance of the object =
- (focus distance - lens to object distance) x focal length /
(focus distance x f ratio)
- THUS, at the same subject and background distance, a 100mm
lens should have about the same degree of background blurring at
f/2.8 as a 50mm lens would have at f/1.4 but of course, the
subject will be twice as large as well.
- IF you adjust your subject magnification to be constant by
moving in closer or further from subject depending on lens focal
length, but keep distance of subject to background constant and
aperture constant, then theoretically, the degree of blurring
remains constant irrespective of lens focal length, but the
width of the background will get smaller in proportion to the
effective focal length (ie. perspective changes).
- the longer the focal length, the bigger and more expensive
it is to make a lens of the same aperture, this is why a
85mm f/1.2 or f/1.4 lens is often the sweet spot in portrait
lenses
- if you wish to make letters on a sign in the background
unreadable:
- the disk of confusion of the sign must be equal to or larger
than the letter height
- NB. it will be readable if disk-of-confusion is less than
1/5th of letter height
- NB. between 1/5th of letter height and letter height,
readability will depend on style of letter, shape of lens
diaphragm (bokeh effect), orientation of diaphragm shape to
letter, contrast of letter, and characteristics of lens itself.
- unfortunately we may run into the problem that at the f ratio
needed to blur the background letters will result in
insufficient depth of field for our primary subject. Changing
focal length will not help this, as to keep the same subject
size, we need to alter our camera-subject distance and thus
while the actual relative size of the letters in the background
may change due to the change in perspective, the degree of
readability is only dependent on f ratio.
- DOF is inversely proportional to size of sensor or film if both f/ratio
and effective focal length in 35mm terms are constant
- DOF and focal length at same subject distance and f/ratio:
- DOF is narrower as you increase the focal length of your lens and keep
the subject distance and f-stop the same because you are increasing the
subject's magnification.
- total DOF is dependent on image magnification than on focal length for
relatively close subjects such as macro & portrait subjects:
- DOF is proportional to coc x effective f-stop / magnification2
- THUS for the same f-stop and film/sensor size, if you keep the subject
the same magnification (ie. the same size in the viewfinder by adjusting
the distance to the subject), the total DOF actually remains
approximately constant with changing focal length.
- thus when choosing a focal length to use for a subject where you
can adjust camera position to maintain a constant magnification, the
total DOF will be constant but the following will change:
- the shorter focal length lens will have less front depth of field
and more rear depth of field at the same effective f-stop but the
same total DOF.
- the perspective changes as the background becomes more magnified
as you increase the focal length.
- distant background points will be rendered more blurry in
proportion to the focal length chosen as their image circles = focal
length x magnification / f-stop, this is part of the reason why
longer focal length lenses at wide apertures are used for portraits
to ensure distracting backgrounds are adequately blurred - in
addition the quality of this blurring becomes important "bokeh"
and this is dependent on the lens design, in particular, the
construction of the iris, hence the new Olympus lenses have circular
irises to give better bokeh.
- for action photos with a moving subject coming towards you, a
longer focal length at the same image magnification actually makes
focusing easier as the lens will not need to move through as much of
its focus range and thus auto-focus should be quicker.
- see http://www.luminous-landscape.com/tutorials/dof2.shtml
- and http://www.photo.net/photo/optics/lensTutorial
- DOF equation:
-
The near and far distance values of depth of field can be
calculated as
d = s/[1 ± ac(s-f)/f²]
with plus in the denominator used for the near, and minus
— for the far value. The notation is:
- s — the subject distance (measured from the lens entrance
pupil)
- f — lens focal length
- a — aperture (or F-stop), like e.g., 2.8
- c — the diameter of the acceptable circle of confusion.
Negative results for the far limit (i.e., with a '-' in
the denominator) mean that it reaches the infinity.
The value of c is often set to the 1/1440 of the
diagonal of the film frame or light sensor: 0.03 mm for 35 mm cameras,
0.0061 mm for the C-3000/3030Z, and 0.0077 mm for the E-10.
- for a really in depth look at DOF equations see http://www.vanwalree.com/optics/dofderivation.html
- total DOF = 2 x f-stop x coc x (1 + image magnification/pupil
magnification) / [image magnification2 - (coc2
x f-stop2/focal length2)]
- and if coc x f-stop / focal length is much smaller than image
magnification as occurs when subject distance is much smaller than
the hyperfocal distance, then the denominator can be simplified to
just the square of image magnification.
- hyperfocal distance equation:
-
Have a look at the formula above again. The far DOF limit
(with a '-' sign used) becomes infinity for a single value of the
subject distance, s, which is
sh = (f²/ac) + f
(many sources skip the final f, as it is usually
much smaller than f²/ac). This is the so-called hyperfocal
distance, and, as you can see, for any given focal length f it
depends on the used aperture, a.
Also note, that when we use s=sh
in the previous formula to compute the near DOF limit, the result
will be sh/2.
-
The N-times-F rule for digital cameras:
- as an approximation, the DOF of a digital camera with 35mm film focal
length multiplier of N will be the same as that for the equivalent lens on a
35mm camera stopped down to an aperture of N times the f/ratio of the
digital camera.
- thus the Olympus C8080 sensor has a 35mm focal length multiplier of 3.6 (a
7.1mm focal length lens is equivalent to a 28mm lens on a 35mm camera), and
thus at 7.1mm lens at f/4 it has the same depth of field as a 28mm lens at
f/14.
- ie:
- a camera with a CCD 1/N the size of a 35mm frame has the same depth of field at Fx as the 35mm camera a F N*x, where x is
the F-number.
- to make an example, the 5050 has a CCD with a crop factor of approx. 5. At F1.8 the 5050 will have the same DOF as a full-frame camera at
F9 (= 1.8 * 5). The D70 with its 1.5 crop factor will have the same DOF at F6 as a full frame camera at F9. Of course all this at the
same 35mm equivalent focal length.
A comparison of calculated depth of fields:
- DOF range at largest lens aperture when focused at 3m (courtesy of
Jens Birch):
-
| Camera / EFL |
28mm |
35mm |
50mm |
80mm |
max. telephoto |
| Nikon D70 with Nikon 18-70/F3.5 - 4.5 |
f/3.5 6.4m |
f/3.6 3.8m |
f/4.0 1.6m |
f/4.0 0.6 m |
112mm f/4.5 0.32m |
| Nikon D70 with Sigma 18-50/F3.5 - 5.6 |
f/3.5 6.4 m |
f/3.8 4.0 m |
f/4.5 1.8 m |
f/5.6 0.8 m |
80mm f/5.6 0.8 m |
| Olympus C5050 |
n/a |
f/1.8 6.8m |
f/2.0 2.5m |
f/2.2 1.0m |
105mm f/2.8 0.7m |
| Olympus C5060 |
f/2.8 infinite |
f/2.9 infinite |
f/3.2 5.1m |
f/3.6 1.6m |
114mm f/4.6 0.9m |
| Olympus C8080 |
f/2.4 infinite |
f/2.5 10m |
f/2.8 3.1m |
f/3.2 1.2m |
140mm f/3.5 0.9m |
| Olympus E-1 with Digital Zuiko 14-54/F2.8 - 3.5 |
f/2.8 6.7m |
f/2.9 3.1m |
f/3.2 1.4m |
f/3.4 0.6m |
108mm f/3.5 0.3m |
| Olympus E-300 with Digital Zuiko 14-45/F3.5 - 5.6 |
f/3.5 12.9m |
f/3.6 4.5m |
f/4.0 1.9m |
f/4.5 0.76m |
90mm f/5.6 0.75m |
- if you need large DOF and you have low light levels (eg. indoors or macro)
then consider the Olympus C5050:
- if you can shoot f/1.8 at ISO64 on the Olympus C5050, to get the same
DOF at the same effective focal length on a Nikon D70, you would need to
shoot at f/6 at ISO 880 which would be more noisey.
- but if you need to shoot action photos, don't bother with the C5050.
- if you need small DOF at telephoto (eg. portraits) at low light levels
then consider the Olympus E series with the 14-54 lens:
- at 108mm, DOF of the E-1 at f/3.5 is comparable to the D70 at f/4.5
but you can use lower ISO with the E1 as it is f/3.5.
-
Depth of field in view camera scenarios:
- N = D/(2c)
Where 'N' is the admissable aperture, 'D' is the focus spread between focus at the furthest point to be recorded sharply and focus at the nearest point to be recorded sharply and 'c' is the circle of confusion for the print size and viewing distance that you require.
- circle of confusion for an 11x14 print at minimum viewing distance:
- 4x5 film = 0.066
- 5x7 film = 0.1
- 8x10 film = 0.133
- NB. coc used for calculating DOF marks on lenses for 35mm is for
5"x7" print while medium format it is 8"x10" print.
- Finely check the focus at the furthest element in the scene which you want to render as sharp. Mark this point on the focus track. Now, focus on the nearest point in the scene which you want to render as sharp. Mark it also and subtract determine how many millimetres separate the two points (let's say the focus spread is 4 mm) Focus the camera at a point half way between those two points - that is 2 mm away from
other end point.
- 'D' in the equation becomes 4 and for a 4x5 the C. of C is 0.066.
- The admissable aperture becomes 4/(2 x 0.066) which is 30.3 and so a working aperture of f32 will render the range in the scene acceptable sharp in an 11 x 14 print.
Image resolution:
- image resolution is dependent upon:
- film or sensor resolution
- optical resolution - aperture size vs optical aberrations of the lens
vs wavelength of light
- resolving power of a telescope:
-
Dawe's limit of telescope resolving power in arc seconds
= 116 / telescope lens diameter in mm
- actually, in arc seconds = 2270000 x wavelength of light / telescope
lens diameter in mm
- optical diffraction effects at small apertures
- focus accuracy
- lens flare
- atmospheric aberrations of light ("seeing")
- in general, the following is what limits image resolution assuming same
contrast/detail subject, good photographic technique, minimal flare, high
quality lens, etc:
- large format film: ability to keep the film flat to ensure accurate
focus
- medium format film: lens optical resolution
- 35mm film or digital sensor: film or image resolution
- consumer size digital sensor: sensor resolution, or at small f-stops,
diffraction limits (hence cannot usually use smaller than f/8)
Image magnification:
- a bit of physics - let So = front principal point to subject distance, Si
= rear principal point to image (eg. film) distance and f = focal length
- 1/f = 1/So + 1/Si and as magnification (M) = Si/So, then M = f/(So-f) = (Si-f)/f
-