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    Re: "Vernier acuity" of horizon IC tests
    From: Douglas Denny
    Date: 2009 Jul 6, 13:42 -0700

    Dear Mr. Rudzinski,
    
    No confusion. I am interested in the standard deviation figures only, which 
    are a measure of the spread of the results,  which is depndent on, and a 
    function of, the resolving power of the eye, and hence what I am interested 
    in.
    The index error itself is not the valued quantity of interest - the sigma of the results is.
    
    The sight tube gives a sigma of:-  1.0'
    The 4 x 40       "       "     :-  0.15'
    The 7 x 35       "       "     :-  0.28'
    
    Using the usual criteria of twice sigma for obtaining 68% of all expected 
    readings which will fall into that spread;
    and four times sigma for an expected range of 95% of all readings we have:-
    
    sight tube      twice sigma:  2.0'
    4 x 40 scope         "     :  0.3'
    7 x 35 scope         "     :  0.56'
    
    sight tube       four times sigma :  4.0'
    4 x 40 scope           "          :  0.6'
    7 x 35                 "          :  1.12'
    
    These are very interesting. They illustrate a number of points.
    
    Firstly that someone can go out with their sextant, take a  number of sights, 
    and with a fairly small sample obtain very consistent results.
    
    Secondly, the sight tube only (eye only) gives a spread (measured by sigma) of 
    around one minute of arc. This is exactly the same as standard "letter 
    acuity" as measured by your optometrist with his chart and is the expected 
    recognised average minimum acuity expected for a large sample population.
    
    Thirdly, sigma with telescopes used is indeed improved, and better than simple 
    "letter acuity" of one minute of arc (the increase in resolution of course 
    might be expected with the greater resolving power of a telescope) and comes 
    down to that of around the graticule resolution of the eye (black/white 
    bars).. but is not _tremendously_  improved compared to the much greater 
    theoretical resolving power that a magnified image gives with the telescope 
    ... which in turn suggests the eye is still the limiting factor in the 
    resolution achieved.
    This is to me, very interesting indeed.
    
    
    Fourthly, increasing the magnification from four to seven did not materially 
    affect the resolution very greatly, and in fact degraded it.
    Gordon found anomalous effects with telescopes too.
    This is very interesting. Gordon suggests the optical qualities of the 
    telscope are very important; and your own results suggest, as Gordon found, 
    telescopes
    definitely can improve the quality of sight taking with a sextant, but the 
    results cannot be predicted with particular telescope magnification/aperture 
    combinations.
    
    There is scope (pardon pun-can't resit it) for practical research here for 
    people on this forum to go out with their sextants with different telescopes 
    and sextants and obtain a list of results like yours, then using this forum 
    as a central exchange, collecting and analysing the results which might give 
    an interesting insight into the qualities of the different telescopes and 
    their aid to resolving power with practical sextant use.  It would be an 
    intersting and useful extension of the work Gordon started in the 1960s.  He 
    was acutely aware his results were dependent on only 500 observations; but 
    the power of the internet now brings the possibility of many people around 
    the world with their sextants adding to this simple basic research data 
    started by Gordon.  It would be a fitting tribute to Gordon's work. 
    
    If it were done, all must do the same thing though to try to keep parameters 
    constant - so simple index error check using a horizon would do admirably, 
    with as many sights taken as possible; and with a note of details such as 
    conditions of horizon; sextant, telescope, height above sea level, refraction 
    (glasses prescription) of the individual, if any eye condition present 
    (cataract for example) and suchlike.
    
    This would be expected to give results better than simple letter acuity,  as a 
    straight line is involved and theoretically can get down to the ultimate 
    resolving power of the eye approaching ten seconds of arc at best.  Degrading 
    parameters in the sextant/telescope conmbination are likely to mean this is 
    not achieved of course, but it would be fascinating to get some real hard 
    analytical data on this.
    
    Douglas Denny.
    Chichester. England.
    
    
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