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    Re: "Vernier acuity" of horizon IC tests
    From: Greg Rudzinski
    Date: 2009 Jul 5, 12:57 -0700

    7/5/09 index error data for Tamaya Jupiter at 34�10'N 119�14'W height
    of eye 20ft (horizon distance 5.1 NM)
    
    Sight Tube        4x40 scope       7x35 scope
    1.5' on           0.4' on          1.0' on
    1.6' off          0.5' on          0.6' on
    0.8' on           0.7' on          0.3' on
    0.9' off          0.6' on          1.0' on
    0.6' off          0.3' on          0.7' on
    0.0               0.6' on          0.7' on
    1.4' off          0.4' on          0.6' on
    0.2' off          0.5' on          0.4' on
    1.2' off          0.4' on          0.1' on
    0.8' off          0.2' on          0.1' on
    
    avg. 0.4' off     0.5' on          0.6' on
    SD   1.0'         0.15'            0.28'
    spread 3.1'       0.5'             0.9'
    
    The horizon was a bit fuzzy to the naked eye inspite of very good
    visibility. The sight tube did not provide a confident visual. The
    4x40 scope showed a sharp bright horizon as compared to the 7x35 which
    was less bright and a bit fuzzy.
    
    Conclusion: The 4x40 scope is a narrow winner in the horizon index
    error determination comparison over the 7x35 scope with the sight tube
    performing poorly for this task.
    
    The ability to focus each of the scopes helped with sharpness vs. the
    naked eye. Perhaps I need glasses;-)
    
    On Jul 5, 7:35�am, Greg Rudzinski  wrote:
    > From an intuitive perspective it would seem best to derive index error
    > with the scope or sight tube that will be used to make the observation
    > for the simple sake of optical consistency. Another factor to consider
    > is how the horizon is set onto itself. I like setting the horizon down
    > to itself the same way that a body is set down to maintain micrometer
    > drum slack consistency. Maybe Bill Morris can weigh in on micrometer
    > drum slack. My interest is peaked so I will be off to the beach today
    > to do some data sets (10 each should be enough) using a sight tube,
    > x4, and x7 scope from a height of eye of 25 feet. My prejudice at the
    > moment is to say the highest power scope will produce the tightest
    > data set with averages being the same. Anyone care to wager ;-)
    >
    > On Jul 5, 3:19�am, "George Huxtable"  wrote:
    >
    > > Frank Reed wrote-
    >
    > > "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 name.
    >
    > > 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
    > > "
    >
    > > =====================
    >
    > > That's all very well, but a thin black line across a white screen (or vice
    > > versa) on a computer is a poor model of a horizon. It is useful only to
    > > demonstrate how good the eye is at recognising discontinuities in a thin
    > > straight line (and that isn't in question here).
    >
    > > If Frank wished to simulate real horizon conditions, he would do better to
    > > present on the screen a single interface between two shades of grey (with a
    > > bit of blue in one, if thought fit), with varying degrees of sharpness or
    > > blurring of that interface.
    >
    > > On the other hand, if he considers that the line-on-the-screen provides a
    > > good model, an interesting test would be to look at that line with his 7x
    > > scope, to see how far he can then retreat from the screen and still see that
    > > jiggle. I await any results with some interest.
    >
    > > He continues- "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."
    >
    > > That's a very imprecise claim. 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 eye, as in the following sentence;
    > > perhaps Frank will explain further.
    >
    > > "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."
    >
    > > To me, that's an unconvincing and woolly statement. It ascribes mystical
    > > qualities to this "hyperacuity", which apply to some circumstances of
    > > Frank's choosing, and not to others.
    >
    > > �"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. "
    >
    > > Yes, that's the statement for which I requested some backing evidence; that
    > > the index correction can be measured at least as well without that 7x
    > > telescope, as with it.. That evidence hasn't appeared, yet; only such
    > > assertions.
    >
    > > 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).
    >
    > > George.
    >
    > > contact George Huxtable, at �geo...{at}hux.me.uk
    > > or at +44 1865 820222 (from UK, 01865 820222)
    > > or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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