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[OM] depth of field -- threat or menace?

Subject: [OM] depth of field -- threat or menace?
From: William Sommerwerck <williams@xxxxxxxxxx>
Date: Thu, 11 Mar 1999 06:40:31 -0800
"I understand that depth of field is the range of distances that are in focus
for a lens-aperture combination, but don't understand the nature of how focus
varies in this range and the range extending on either side. Is there only one
distance from the lens that is EXACTLY in focus with degrees of being out of
focus on either side? and that at a particular, arbitrary point this degree of
out-of-focus is considered unacceptable? and this is defined as the boundary of
the depth of field? And this limit is rather arbitrary? -- who decides it? Or is
there some characteristic of lenses that starts to put objects badly out of
focus at these well defined points, while between these points the focus remains
very good?"

Imagine a perfect lens -- it has no aberrations of any sort, and it renders a
dimensionless point of light as a dimensionless point on the film. (This is
physically impossible, due to diffraction, but let's ignore it for this
discussion.)

The lens gathers the light from this point and brings it to a focus. There is
only one distance behind the lens at which the light from this point comes to
perfect focus. "Focusing" is the process of positioning the film at this
distance for the part of the image you want to be in sharp focus. (You usually
move the lens rather than the film, but it doesn't matter whether Mohammed goes
to the mountain, or vice-versa.)

Now imagine those rays of light coming to focus behind the lens. They form a
"cone" whose tip is the point of sharpest focus. If an object is closer to the
lens than the object we are focused on, _its_ cones of light will come to focus
_behind_ the film plane. But the film occupies the film plane (!!!), so it
"snips off" the tips of the cones, creating a tiny circle of light, called the
circle of confusion. Similarly, objects farther away than the principal object
come into focus in _front_ of the film plane. The light diverges before hitting
the film, also forming a tiny circle instead of a sharp point.

So... the object you have focused on is in "perfect" focus, while any other
object is out of focus in varying degree, depending on how much closer or
farther it is from the camera than the object focused on. (Whew! Got that?)

Fortunately, the human eye doesn't have infinite resolution. It can't tell the
difference between a very tiny dot and a dimensionless point. Therefore, objects
closer or farther than the object focused on appear acceptably sharp _if_ the
circles of confusion that form their images aren't large enough to be seen as
little disks.

How large the circle of confusion has to be to make an object unacceptably sharp
varies with the degree of final magnification of the image and how far the
viewer is from it. For example, I _think_ most 35mm lenses' DoF scales are
calibrated for an 8x12 print viewed at 1'.

There is also a subjective factor. A critical viewer is less likely to judge a
slightly soft image as "sharp." So a company that expects most of its users to
create large prints might use a smaller circle of confusion when calculating
DoF.


"Also, is depth of field a constant for a particular focal length, aperture
combination regardless of lens design?  Or do different lens of the same focal
length exhibit different depth of field characteristics, and if so is this
feature ever tested in lens tests?"

Depth of field has nothing to do with lens design (other than the fact that bad
lenses have subjectively _greater_ depth of field, because the poor image
quality hides the variation in focusing sharpness). Of course, a lens with a
badly shaped diaphragm would probably produce a more-visible circle of
confusion, thereby reducing the subjective depth of field. But this is never a
factor in the manufacturer's calculations -- nobody goes out and actually
"measures" depth of field.

DoF gets smaller as you get closer to the object, because the image plane
"moves" more rapidly with changes in focusing distance.

The general rule is (and please memorize this, because it's definitely gonna be
on the final):

"For a given focusing distance, equal lens diameters produce equal depths of
field for equal final image magnification."

For example, a 100mm lens set to f/8 will have the same DoF as a 50mm lens set
to f/4.

A little thought will show that this rule means small-format cameras have
greater depth of field than large-format cameras. Don't ask me to explain;
reason it out for yourself.

A year or two ago Pop Photo had an excellent article on depth of field. It's
worth looking up.




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