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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
    I wrote earlier
    > Imaging resolution in any
    > 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":-)."
     
    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.
     
    -FER
    42.0N 87.7W, or 41.4N 72.1W.
    www.HistoricalAtlas.com/lunars
     
    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!
       
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