NavList:

Alex, you wrote:

"As I understand, a marksman does not really see the central circle
on the target s/he intends to hit. She only sees the larger circle,
but with some training she is able to aim at its center
with better accuracy than her eye resolution.
Something similar probably happens when an experienced observer
determines the touch of two discs as you described."

 

Makes sense. The ability to "interpolate" the center of a visible circle is probably a couple of times better in angular resolution than the usual "separate these two dots" test.

And:

"According to my mother (an ophtalmologist), the density
of those cone packing does not vary much among people,
and 1' is the theoretical limit derived from this density."

 

That sounds about right to me. The optical system itself should have a diffraction limit of half a minute or even a third of a minute (blue light, pupil fully dilated would be the best case) but in practical experiments, it seems to be closer to 1 to 1.5 minutes. The density of the detector array is too low. Perhaps we should wait for the new model to come out...

 

And:
"However there are well documented cases of much higher resolution.
(One person tested in XIX century had resolution of 1",
but this seems to be the world record. Several people were described
who could see the phases of Venus with naked eye)."

 

I've heard of some of these stories before, but I'm somewhat skeptical. With so many more people alive today, it's always more likely that the extremes of the human condition are alive today than in centuries past. Still, I'm not suprised that there is at least some ability for the cone cells in the fovea to be smaller or more tightly packed.

 

And you wrote:

"By the way the well-known double star (Mizar, zeta of Big Diper)
was used to test the vision of ancient Arab warriors.
The distance is 12', so this was not a very rigorous test"

 

I heard this when I was about twelve years old after I had seen this pair separately for as long as I knew the stars of the Big Dipper. It struck me as strange back then, and I have a feeling that this may be nothing more than legend. Or possibly they needed a lot of warriors! I found a web site tonight (following Jared's suggestion that it's gotta be out there somewhere) that had made an interesting error possibly influenced by the Mizar and Alcor story. The author had calculated the diffraction limited resolution of the human eye and had come up with 7 minutes of arc. He then told the story of Mizar and Alcor and indicated that this demonstrated how good a test it is of one's vision since their separation is less than twice the diffraction limit. Of course, he had dropped a factor of ten. It's easy to re-work his numbers and show that his calculation should have yielded 0.7 minutes of arc. His familiarity with the Mizar and Alcor story may have prevented him from catching this error.

 

When I think about resolution and describe it to people, I sometimes ask them what they can see when they look at the Full Moon. How many features are visible across its face? If you draw the Moon, what's the smallest thing you can see? If the eye's resolution were in fact as bad as 7 minutes, there would be about four "pixels" across the Moon. It's obviously much better than that --somewhere around a minute of arc. A little more? A little less? Hard to say.

 

But I recommend the experiment: stick in your contacts or put on your eyeglasses if necessary and draw a "unit magnification" map of the Full Moon. It's a fun way to learn the lunar landscape and an interesting test of the eye's resolution.