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    "Vernier acuity" of horizon IC tests
    From: Frank Reed
    Date: 2009 Jul 4, 14:44 -0700

    An interesting issue regarding the resolution of the human visual system is 
    the rather strange phenomenon of "hyper-acuity" or "vernier acuity". We are 
    able to detect defects in straight lines which are much smaller than normal 
    resolution. You can test this by drawing a line (un-aliased) in a computer 
    graphics program with a single pixel step in it, e.g. from (x,y)=(10,400) to 
    (990, 401). This is a nearly horizontal line. On a typical computer display, 
    a pixel is about 0.01 inches in diameter. For normal visual resolution tests, 
    this would be visible (with unit magnification, wearing corrective optics) at 
    a distance where 0.01 inches subtends one minute of arc which would be about 
    34 inches from the screen. But in fact, a single pixel "step" in a straight 
    line is perceived at distances five or ten times greater. Detecting a step in 
    a straight line is the critical task in reading a vernier scale, hence the 
    But hey, don't believe me! Go ahead and try it. And if you're concerned about 
    observer bias, you could set up a slideshow that steps through various lines 
    with single-pixel "kinks" in them mixed with perfectly straight lines. Then, 
    before you walk away from your computer, turn around so you can't cheat and 
    randomly select one of the images. Walk as far from your computer 
    For sextant use, vernier acuity may also apply to the standard index error 
    observation, but only under certain circumstances. If you remove the 
    telescope from a sextant and hold it (the sextant) at arm's length pointing 
    at the horizon, the human visual system (eye+visual cortex) is able to detect 
    remarkably small deviations in the visual line of the horizon. In other 
    words, you can get an excellent value for the IC. By contrast, when a 
    telescope is attached or when the instrument is held close to the eye, the 
    horizon on the direct side of the field of view fades away slowly and merges 
    with the reflected view on the other side of the field of view. We align 
    these horizon images by superimposing them. This is not a hyperacuity task, 
    and so the results are limited by normal resolution. In short, you may be 
    able to get an IC looking through a sextant without a telescope that is 
    slightly better than, or at least as good as, the measured IC using the 
    sextant with a 7x telescope. Other typical sextant observations, like placing 
    the Sun on the horizon, or aligning the image of Venus with the Moon in a 
    lunar observation, are not examples of hyperacuity (vernier acuity) so the 
    normal "one minute of arc" (or slightly better) resolution of the eye 
    Note that this one minute of arc resolution is the resolution of what the eye 
    sees AFTER magnification by the telescope. So if you can normally resolve one 
    minute of arc, then through a (good) 7x telescope, you can resolve 0.14 
    minutes of arc in terms of the angle on the sky.
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