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Re: Sextant accuracy (was : Plumb-line horizon vs. geocentric horizon)
From: Frank Reed CT
Date: 2005 Feb 23, 03:02 EST
From: Frank Reed CT
Date: 2005 Feb 23, 03:02 EST
I wrote earlier
> Imaging resolution in any
> optrical [sic] system is ultimately limited by diffraction
> optrical [sic] system is ultimately limited by diffraction
And Alex you replied:
"Yes. I think some misunderstanding comes from your implicit assumption that the eye is an "optical system":-)."
"Yes. I think some misunderstanding comes from your implicit assumption that the eye is an "optical system":-)."
Don't worry. I've made no such assumption. The human vision
system is not only an "optical" system. It is also a detector array, a
transmission network, and a great big chunk of the human brain's processing
power. It also makes a great cup of coffee. <g>
And yet, the eye is STILL an optical system first. The input to all that
detection, transmission, and processing power is still just light passing
through an aperture. The resolution limit imposed by diffraction is very strong.
Yes, you can tease out *some* details at levels a little below the resolution
limit but there's precious little to work with. I mentioned this hyperacuity and
"vernier acuity" in a few posts. It's a very specific capability of the vision
system to go beyond the limits of standard "imaging resolution" in certain
special discrimination tasks.
Try this hyperacuity experiment (I did it earlier): get out your favorite
drawing software and make two simple white-on-black drawings-- 1: make a simple
image resolution drawing. It could be a "Snellen" E like in eyecharts or it
could be a smiley face or some other simple pattern. Make it five pixels
tall with detail at the one pixel level. 2: make a straight horizontal or
vertical line perhaps five pixels thick stretching across maybe a hundred pixels
of the drawing. In this straight line, make a one pixel "step" at the middle so
the line has a "kink" in it (a line five pixels wide drawn from x,y coordinates
100,100 to 200,101 would do nicely). Now display those two simple drawings on
your monitor and step back. At what distance from your display do the features
in the first small pattern merge into one common blur? If your eyes are good or
you're wearing eyeglasses or contacts that correct them to "good", then you
should find that this happens when the features have an angular size of just
about 1 minute of arc or perhaps a little less. And this is just about what you
would expect from the limitations of diffraction as well as the limitations of
the detector array (the cones in the fovea). But if you look at that line
with the step in it, you should find that it looks distinctly non-straight
at four or five times greater distance. Somehow the visual system is
detecting something in the image that is much smaller than the eye's imaging
resolution, and the experts apparently don't know how this works though it is
assumed that it's happening well behind the eyes themselves, persumably having
something to do with the brain's pattern-matching capabilities [I find that when
I see this effect, I can't localize where the step is in the line --I can tell
that it's not straight "somehow"]. This hyperacuity only happens in
these very specialized tasks, like a kink in a long straight line. And the
interesting thing for us is that some of these tasks should be very
relevant for sextant use. A step in the horizon should be discernible at much
finer resolution than the diffraction limit (but it ought to be a sharp step so
a telescope may actually make things worse by providing a smooth transition
across the field of view --thinking aloud here).
And you wrote:
"Several participants of this discussion mentioned a conjecture that the
eye resolution higher than optical limit might be due to the eye micro
MOTION."
One could
also conjecture that the eyes work together as an interferometry pair which
would imply a much finer diffraction-limited resolution. But they don't. So it
doesn't really matter, if ya see what I mean...
And:
"Let me also define what I mean by resolution: It is the ability to decide
whether the images of two points coincide. You don't necessarily have to SEE
them as separate points when they dont coincide for this."
That's one
very specific definition of resolution and it may qualify as a hyperacuity
task, but it's certainly not the general definition of resolution (just so we
don't get tangled up in definition-land).
And you concluded:
"In the case of measuring star distances with a sextant, I can see two
stars as one dot, but still understand that this dot is somehow "imperfect".
This really happens when the distance is about 0.5' (with my scope). But still I
somehow can measure to 0.1' in many cases."
What's the magnification of your scope again? If it's 7x, then on the
retina, 0.5 minutes of separation is magnified to 3.5 minutes and 0.1 minutes is
magnified to 0.7 minutes. So if that's what you're seeing, there's no surprise
here. This is just what you should expect from normal, correctly
focused imaging resolution. With a quality sextant and a good 7x telescope,
you should expect to get 0.1' accuracy repeatably. But can you do this when you
un-mount the scope?? If you can reach that accuracy with your unaided eye, then
this would qualify as a hyperacuity task. It's worth testing.
PS: I got a kick out this sentence from the "webvision" web site at
utah-edu that I linked earlier: "It does appear possible then, that a
multiheaded midget or diffuse cone bipolar with a small dendritic tree, could
contact all the same spectral type of cones in the primate fovea."
It all makes sense... once you learn the lingo!