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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
"Vernier acuity" of horizon IC tests
From: Frank Reed
Date: 2009 Jul 4, 14:44 -0700
From: Frank Reed
Date: 2009 Jul 4, 14:44 -0700
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. -FER www.HistoricalAtlas.com/lunars --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---