There is lots of
confusion out on the web about DOF. Namely, there are two different
types of applets for determining DOF. One, like the one here at
photozone, determines DOF based on sharpness, the other,
at Shuttercity, bases DOF on format.
For some strange reason
people have an allegiance to one or the other and deem the other as
wrong! Yet, it is apparent from discussion boards that these same
people don’t understand what each type of applet means and,
more importantly when to use it. As I see it, the difference lies
between physics and applied photography. In this essay, via a couple
of easy example, I hope to make sense of these applets.
Before I get started I
will give a couple of definitions that everyone agrees with:
DOF (Depth of
Field): The area in front of and behind a focused subject in
which the photographed image appears sharp. In other words, the depth
of sharpness to the front of sharpness to the front and rear of the
subject where image blur in the film plane falls within the limits of
the permissible circle of confusion
Mathematically,
Front DOF
= d • F • a^{2} / (f^{2} + d • F •
a) Rear DOF = d • F • a^{2} / (f^{2} –
d • F • a)
f: focal length
F: F number
d: circle of confusion diameter
a: subject distance (distance from 1st principal point to
subject)
COC (Circle of
Confusion): Images are formed from a composite of dots (not
points, though I’ll call them that for simplicity) having a
certain area, or size. Since the image becomes less sharp as the size
of these dots increases, the dots are called “circles of
confusion.” Thus, one way of indicating the quality of a lens
is by the smallest dot it can form, or its “minimum circle of
confusion.”
The maximum allowable
dot size in an image is called the “permissible circle of
confusion.” In other words, how much can a point be
magnified and still look like a point and not a disk.
Please note COC, thus
DOF, depends on the use of the images and is somewhat subjective.
This is no different that resolution.
Physics
I’ll explain what
I call the physics by use of an example. Let’s say we take a
picture of a point with a 4x5inch camera and crop out a 6x7cm,
6x4.5cm, and a 35mm frame sizes. (If you like, consider all these
formats with the same focal length lens, at the same aperture, and
the same distance to the point). According to the applets that take
into account format size, the DOF changes for each crop. Does this
make sense? Of course not! It is the same point on the same piece of
film. As such, it can’t be magnified any more for each format
and still look like a point and not a disk. Thus, we can conclude
that COC is not a function of format. This leaves DOF
as a property of the lens and focusing distance(review the above
equations). Also note that the sharper the lens, the smaller the
point is that can be produced on the film, the shallower the DOF
(I’ll let you think about this), and the larger a print
can be made and still have the point look like a point.
Photography
“But wait a
minute,” you say, “why do some applets use format instead
of sharpness?” These applets assume that in
photography the subject will be framed the same regardless of format.
In other words, to frame the subject from the same distance the
larger format will need a longer focal length lens, or the smaller
format will need to be moved further away from the subject (or
viceversa). Now consider making an 8x10 print once you do this. Each
point in the larger format will need to be magnified
less than with the smaller format. This is a fancy way of saying you
can make larger prints from larger formats. As a concrete example
let’s consider the Canon dslr’s d30, d60, 10d frame size
verses a 35mm frame size. We all know by now that there is a 1.6x
multiplier factor for angle of view (technically, using the term
“magnification” is wrong) between the digital frame size
of these and a 35mm film size. Ergo, a 100mm lens mounted on a 10D
frames the subject the same as a (100x1.6 =) 160mm lens on a 35mm
body but with 1.6x more DOF for a given aperture. Presuming
the media is equivalent (I don’t want to get into a film vs.
digital debate), the larger format, 35mm, can be made into a larger
print because each point needs to be magnified less. There are
pitfalls to this method. Consider macro photography. Magnification,
e.g. 1:1 or “life size,” has nothing to do with
format. To review this, consider 1:1 or life size. This implies that
the object will be the same size on film as it really is. Moving the
camera or changing lenses for the same angle view negates the 1:1
magnification which only occurs at one distance for a given lens from
the lens to subject. So beware, applets that rely on format will
fail you! Whereas, applets like at photozone will get this right to
first order.
Summary
Hopefully I cleared up
the differences between each type of applet and you can put them to
work for you!
