wim wiskerke said:
Some years ago there was an interesting discussion about this in the
science section of a dutch newspaper. People (even 40 and 50 year
olds) reported being able to discern the stays of a tall communication
tower from a distance of many miles. This contradicted and far exceded
the long accepted 1 arc-minute limit of the resolution of the eye.
0.25 arc-minute seemed possible in certain high contrast situations.
That is a different effect though, and it doesn't just apply to human
eyesight. Some years ago in the early days of CCDs, we were working on
a low resolution (a massive 4Kilopixels!) camera that was pointing out
of the lab window when someone cycled by. All of us could clearly see
the wire spokes on the bicycle wheels which were only 2-3mm thick. When
we worked it out, the wire spokes represented less than a tenth of a
pixel in thickness! Very similar to your anecdote of observers seeing
wire stays in communication towers.
However there is nothing here that disputes the resolution measurements
- well there was a little in my example, which in turn lead to the
development of an image resolution enhancement technique we called
microscan, but that is outside the scope of this thread.
A large part of this effect is the same as being able to see stars in
the night sky. You can't resolve any of them, but you can certainly see
them. The closest star is 4.3 light years away, which is almost
2.5x10^13 miles. Even if that was the same size as our sun, of 8.7x10^5
miles in diameter, it would only subtend 35nanoradians! That is about
50,000x the resolution of the human eye, but you don't have any problem
seeing stars that are hundreds and thousands of light years away, so
even smaller. The issue is one of detection, not resolution. You can
detect the star at sub-resolution dimensions because the contrast of the
star against the blackness of space is so high. And you can detect the
pylon wires because they are high contrast against the sky background,
albeit much less than the star.
A second effect is also significant in this process though - visual
connectivity, which is also responsible for the "Vernier effect", used
in precision instruments. This is a purely mental process that is going
on in your eye/brain, well past the photoreceptors. You are just
extremely good at connecting points together to discriminate lines.
Typically the vernier effect allows you to discern a displacement in a
line which is less than one fifth of the visual resolution limit. Even
when the contrast from the cables and stays was just marginal to be
detected by the photoreceptors in your eye, your brain can still link
the parts that it does detect to create the illusion of a solid straight
line.
Finally, persistence of vision means that the eye can retain images even
after they have been removed. Again, when the contrast is just on the
limit of detection threshold, the eye 'holds' the parts which are
detected when the random fluctuations in contrast exceeds the detection
threshold once it fluctuates below the detection threshold.
All of these effects combine to permit you to be able to see cables,
wires, stays and similar structures even when their thickness is well
below the traditional resolution limit of the eye.
This suggests that in some prints, not only small detail can be seen
at 1200x1200 dots per inch, but even the dots itself. In
transparencies this certainly will be the case.
You certainly won't resolve the dots themselves, but you can discern
discontinuities in dot placement at 1200dpi or more if they are printing
a perfectly vertical edge or a line that is only one dot thick, such as
the stroke of a font. This is one of the issues that has driven laser
printers to higher resolutions just to produce better quality text.
You will have noticed that dpi or ppi is not the way to describe the
resolution of the eye.
Exactly. Resolution requires the differentiation of two objects as
distinct from one - and that requires cycles. All you can do is
determine the *minimum* number of pixels or dots necessary to represent
those cycles.
