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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  george@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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