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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: "Vernier acuity" of horizon IC tests
From: Greg Rudzinski
Date: 2009 Jul 4, 16:47 -0700

```Frank,

An unorthodox method that I use for adjusting and determining index
error is to tweak the side error adjustment just enough to split a
star into two images with the sextant set at zero (with a bright star
I even use a weak shade to present a point of light instead of an
asterisk of light). With the two stars side by side I seem to do a
better job of zeroing my index error. A fussy navigator would probably
tweak the side error back but I leave mine off so that I can
periodically recheck index error. Question: What kind of errors get
generated on high altitude observations if side error is a few minutes
out?

Greg

On Jul 4, 2:44�pm,  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
>
> 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
applies.
>
> 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.
>
> -FERwww.HistoricalAtlas.com/lunars
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```
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