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    Re: "Vernier acuity" of horizon IC tests
    From: Bill Morris
    Date: 2009 Jul 6, 15:08 -0700

     Frank wrote:
    ?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
    and you responded
    ?I don't understand where such a difference arises, with telescope discarded, 
    between holding the instrument at arm's length and holding it close to the 
    Close to the eye the line between the silvered and unsilvered protions of the 
    horizon mirror is out of focus. At arms length, it is better focussed, as in, 
    say, the foresight of a rifle. A sighting tube, by increasing depth of focus 
    by means of the eye stop, has the same effect.
    Frank also wrote:
    ?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
    and you responded:
    ?It seems logical to me, that if a 7x telescope makes no improvement in the
    eye's ability to align two images of a horizon, that's because either the
    telescope is a very bad one, or, more likely, that the horizon is an unsharp
    one (in which case, magnification will make it no sharper).?
    A x 7 telescope is likely to be a Keplerian rather than a Galilean. Each half 
    of the former ?sees? the whole of the field and Frank is quite correct in 
    saying that there is a wide area of overlap of the two horizon images. Each 
    half of a Galilean ?sees? its own half of the field, but there is still a 
    narrow central area of overlap. Using either type of telescope, we do not 
    align the ends of two lines. Rather, there is a fairly sudden appearance of 
    increased sharpness as the two images merge. This is quite different  from 
    what happens when we align the ends of two lines. 
    If we accept the reality of vernier acuity, and I think we must, we would 
    expect vernier acuity using the naked eye to be at least as good as merging 
    images using a telescope, as Frank has postulated earlier; and this is what 
    an appeal to experiment might show.
    Greg has done an experiment (post 8967), but I feel his numbers in each series 
    are rather small and may not have sufficient statistical power. If no one 
    else does it first, I will repeat the experiment when I have got over a stiff 
    neck from calibrating a series of sextant micrometers.
    Bill Morris
    New Zealand
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