The article you cite is not very good advice if you want great sharpness
for landscape photography: it’s based on the concepts of depth of field
and hyperfocal distance. These concepts are intended to help the
photographer find the required aperture for getting barely acceptable
sharpness across the relevant parts of the picture. What the author
(like many authors) calls “circle of confusion” is actually the maximum
acceptable circle of confusion. In its original sense, the circle of
confusion is the size of the blur spot you would get from a point
source: if it’s larger than the maximum size you can tolerate, then the
image is not acceptably sharp. The key word here is acceptable. If
you are after just-acceptable sharpness, these concepts are good. If you
are after maximal sharpness (likely for the kind of landscapes shown as
examples), they are not.
Assume that there are 3 objects, located at 0.4m, 1.2m, 5.0m.
In such a situation, if you want maximum sharpness, you have to focus at
mid distance between the closest and farthest object, where “mid
distance” is actually the harmonic
mean of the distances:
0.4 m × 5 m
optimal focus distance = 2 × ─────────── = 0.741 m
0.4 m + 5 m
The harmonic mean is easy to estimate by just looking at the distance
scale of your lens: it's exactly halfway between the 0.4 m and the
5 m marks.
Now you can estimate the circle of confusion that you will get at any
subject distance with
N × c │ 1 1 │
───── = │ ──────────────── − ────────────── │
f² │ subject distance focus distance │
where c is the circle of confusion, N the aperture number, and the
vertical bars mean “absolute value”. This formula shows that, at f/11,
both your furthest and closest object will be imaged with a 42 µm
circle of confusion, which is not really that sharp. You have to stop
down to f/16 if you want to stay below the canonical 30 µm limit.
Stopping to f/22 will still increase sharpness, but stopping further
to f/32 will reduce sharpness due to diffraction.
If you want maximal sharpness on both these objects, you will have to
balance the blurring due to defocusing (gets better as you stop down)
with the blurring due to diffraction (gets worse as you stop down).
Rather than going through the math, I suggest you read Selecting the
Sharpest Aperture by Ken
Rockwell. I know the author is controversial, but in this particular
instance the article is very sound.