First a brief review of depth of field...
NS 2.0 MSIE 3.0 or later Required
(or skip this and go to the
Depth of field (DOF) is the range of distances
in an image over which the image is said to be "sharp". In actuality, only
one plane of the image can actually be in focus, but all points
lying within the DOF are considered to be "acceptably" sharp. A critical
concept in DOF is the diameter of the circle of confusion (CoC). A point
in the image which is actually in focus will have a typical diameter in
the image plane (diffraction limited spot size) in the 5 to 10 micron range.
Points lying at the limits of the DOF will image with a diameter equal
to the circle of confusion diameter (by definition). For 35mm work this
is typically taken to be around 30 microns and this is based on the appearance of a standard sized print at
a standard viewing distance. While the "standard" is rarely explicitly
defined, it seems to be close to an 8x10 print viewed from about 1 foot.
Here's an attempt at a graphical explanation of what's involved:
In the diagrams above the black lines represent light rays from a subject that is in focus. Light
is focused onto the focal plane (shown in green) to a small spot. The red lines represent a point that's
further from the lens. Light rays from this point come to a focus in front of the focal plane, and by
the time they intersect the focal plane they've diverged to form a larger spot who's size is defined
by how far apart the red lines are when they cross the green focal plane.
The blue lines represent light from a point closer to the lens. These lines cross (focus) at a point
that's behind the focal plane. When they cross the (green) focal plane they form a spot who's size is
defined by how far apart they are when they cross.
It should be evident from the figure that the size of spots formed by the red and blue rays are smaller
in the lower figure (representing a smaller aperture) than in the upper figure (representing a larger
aperture). If the spots are smaller then the circle of confusion value, we can say that the red and blue
rays come from points within the depth of field of the lens.
Thus in the upper figure with the larger aperture the red and blue points may lie outside the DOF, but in the lower
figure they may lie inside. This is why stopping down gives you a greater depth of field/
It's important to note that DOF isn't a lens characteristic like focal length
or aperture. It takes into account some subjective factors like print size and
viewing distance. That's the reason different values for the CoC are
used for different formats. Larger formats need to be enlarged less than smaller
formats, and so a larger CoC can be used. For example to get an 8x10 print from
an 8x10 negative, no enlargement is required, wheras to get the same print from
a 35mm negative, an 8x enlargement is needed. So to get the same sharpness in
a print, the 35mm negative must be 8x as sharp, or in terms of DOF and CoC, the
CoC value used for DOF calculation must be 8x smaller.
From this I think you can see that if you're concerned about an 8x10 print which will be viewed from
a distance of 3 ft, rather than 1ft, you could use a different CoC (one 3x as large in fact), wheras
if you're concerned about a 24x30 print viewed from a distance of 1ft, the CoC value
you need to use is 3x smaller than the "standard" value
DOF is at best a "fuzzy" concept, depending on subjective judgement of what
appears to be sharp. While claculations may give number to 16 decimal places, those
numbers are based on "fuzzy" assumptions. So when a DOF calculation tells you the
far point in focus is at 17.35567423 feet, what that really means is that stuff
that's maybe 16-17ft from the camera shouldn't look too soft. It doesn't mean an
object at 17.35567422 ft from the camera will be razor sharp and stuff that's
17.35567424 ft from the camera will be blurred.
traditional DOF calculations such as this one are based on simple geometric
optics neglecting diffraction effects. Diffraction effects make the smallest
possible focused point (diffraction limited spot size) larger than zero.
In fact at f32, the diffraction limited spot size is around 40 microns.
Clearly using a circle of confusion value of 30 microns (10 microns smaller
than the smallest possible focused spot!) is rather meaningless. The correct
way to estimate DOF would be to use a defocus MTF approach. This isn't
too hard but does involve the use of things like Bessel functions which
most photographers wouldn't be too comfortable with! The simple approximation
is good enough when the diffraction limited spot size is significantly
smaller than the circle of confusion. The diffraction limited spot size
is approximately [1.25 x fstop] microns.
The hyperfocal distance is that distance at
which infinity will lie just inside the depth of field. When a lens is
focused at the hyperfocal distance everything from infinity to 1/2 the
hyperfocal distance will lie within the depth of field (i.e. will be "acceptably"
Note that the notion of "acceptably" sharp
depends on the viewer, so it is a subjective quality of the image. What's
"acceptable" to you may not be "acceptable" to me - and vice versa.
To find the near, far and hyperfocal distance
for a specific lens, enter the focal length (mm), aperture (f/number) and
in focus, far point in focus, depth of focus and hyperfocal distance. The
default unit of measure for distance is feet. This can be overridden by
was written by Michael C Gillett
and thanks are due to him for making the code available for non-commercial
use. The code used here is slightly modified to include digital sensors
The following values are used for the circle
of confusion diameter:
1 micron = 0.001mm. (2) Depth of field calculations only involve focal
length, distance and the value chosen for circle of confusion and do not
include format. Format is only involved insofar as it's a factor in choosing
the circle of confusion value. So, for example, if you're shooting 6x7
but prefer to base your calculations on a circle of confusion value of
50 microns rather than 65 microns, just use the values calculated here
35mm - 30 microns
1.3x DSLR (EOS 1D) - 23 microns
1.5x DSLR (D100) - 20 microns
1.6x DSLR (EOS 10D) 18.75 microns
2x DSLR (E-1) 15 microns
645 - 50 microns
6x6 - 60 microns
6x7 - 65 microns
6x9 - 75 microns
4x5 - 150 microns
5x7 - 200 microns
8x10 - 300 microns
NEW - I've just posted a stand-alone optical calculator which you
can download and run under Windows. It calculates near and far points in focus, hyperfocal
distance, background blur, resolution and spot size.
Please see this page -
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