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Re: October Lunar
From: Frank Reed
Date: 2008 Oct 16, 01:35 -0400
From: Frank Reed
Date: 2008 Oct 16, 01:35 -0400
George H, you wrote: "Well, it's still only a small angle of 1', that discrepancy, just as I wrote. Indeed, such an angle may well be plainly visible in a 7x scope, but the aim is not just to see it, but to measure it, systematically. And it's near, but not (I agree) at, the limits of such measurement." Well, hey, under the right circumstances, even an angle of five degrees can be called a "small angle". But an angle of 1' is a PLAINLY VISIBLE and readily measurable small angle when you're looking through a 7x telescope. Your previous point about it being near the limits of observation was simply incorrect. At unit magnification, one minute of arc is basically the normal limit of resolution, but at 7x magnification, a minute of arc (on the sky) is seven times larger than the limit of resolution. I wrote: "Yes, and because the plains and mountain ranges on the Moon vary the outline (at average sextant scope resolutions) by anywhere from one to two seconds of arc, that is the absolute limit on any historical lunars (a modern computation could include limb effects)." And you replied: "Errors of a second or two are quite irrelevant to the present discussion; a red-herring." George, you are the one who brought up the uneven limb of the Moon. I was merely pointing out the scale of the errors involved. If the uneven limb of the Moon is a 'red herring' then it's your 'red herring'. But maybe you meant something else when you spoke of the uneven limb... Regarding my comment that irradiation was irrelevant to this Moon-Venus lunar, you wrote: "That's an assertion; can Frank back it up?" Observational situations that lead to the perceptual phenomenon of irradiation are those where there is a great contrast in brightness between the two objects and/or the background. The lunar distance observation under consideration was a case where the crescent Moon was being aligned with Venus in early twilight --this is definitely not a case where irradiation would be an issue. Have you yourself tried a lunar under such conditions? I think if you had, you would be unlikely to attribute this error to irradiation. And you asked: "And is irradiation irrelevant when assessing index-error using the Sun, the measurement that may be at the root of the problem we're discussing?" Yes. It could be a real issue if I.E. is assessed using the Sun IF insufficient shades are available on the instrument. As I said previously, getting the IC correct is the single most important thing that one can do to improve the systematic accuracy of these observations. And: "Irradiation is a real effect. It's been dropped from upper-limb predictions, in the Almanac, not because it's negligible, or unreal, but because it's so variable between different observers." Irradiation is a "perceptual illusion". This doesn't mean it's imaginary --it means it's a phenomenon of human visual perception that depends on the individual. It can be essentially eliminated by using shades properly. Simply, the Sun's (or other object's) image should be adjusted with shades (or by moving the telescope in or out relative to the sextant frame) until the image of the Sun appears to have "moderate" contrast relative to the background. By moderate, I mean contrast such that the object is clearly visible, but no more. With some sextants, it can be very hard to achieve this level of contrast because the shades on the sextant do not provide enough options. Fortunately, most mid-range or better sextants have a good variety of shades, and they are also built so that the telescope can moved in/out relative to the frame. I wrote previously: "The "limits" of what we can perceive are well-known. The resolution of the human visual system is about one minute of arc for standard optical resolution tests at unit magnification (with corrective lenses or adjusted focus as necessary --in other words, when wearing eyeglasses or contacts--and assuming no exotic uncorrected eye defects)." And George, you replied: "That's a gross over-simplification: that everyone's eye is the same." No, it is not a "gross over-simplification". It is well-known science. Of course, no one would confuse my one paragraph summary with a detailed treatise on human visual acuity, so naturally there are a few details left out. The biggest detail left out is that visual acuity is somewhat higher under bright daylight conditions. Under those circumstances, visual acuity is frequently doubled. It is also lower under dark lighting conditions because more of the cornea becomes involved in focusing light as the pupil dilates (and the human cornea is a rather poor optical surface even for people with excellent vision). Again this applies to optically corrected vision --what you see when you wear your glasses or other corrective optics. It also applies to vision through a telescope for most people since focusing the telescope can compensate for the most common visual defects. That is, the resolution of angles through a telescope is one minute of arc divided by the magnification; through a 60x spotting scope, most people can distinguish angular separations of 1 second of arc. In bright lighting, the resolution can be as much as twice that. Of course, those with significant astigmatism must wear their prescription lenses even when looking through a telescope since focusing the scope cannot correct for the cylindrical distortions of astigmatism (and even for astigmatism, with respect to ordinary sextant observations, there is an option involving special focusing). You added: "There's a wide spectrum of visual perception. I would put, at one end of the scale, the astronomer Hevelius, from Danzig, in the late 1600s, who amazed his contemporaries by the precision of his star catalogue, obtained without use of the new-fangled telescopes, or Copernicus' mother, who, shown Venus through such a telescope, asked why it was upside-down." Stories from the 16th and 17th centuries are certainly fun, but they hardly qualify as data points. We all have eyes. We can ALL conduct our own vision tests. And in addition, we can turn to over a century of detailed data on the optical resolutions of different people with visual problems. The majority of people have vision which, when corrected with simple eyeglasses, corresponds to about 20/20 or one minute of arc resolution, for standard resolution tasks, under mid-level lighting conditions. "Out of contention, at the other end of the scale, is my own eyesight, raddled by age and retinal lasering." Have you tried measuring your own angular resolution recently? Perhaps through a low-power telescope so that you can adjust focus? And you wrote: "All we can say about the eyesight of the observer in question is that it's good enough for a watchkeeper's certificate (which must mean reasonably good)." That's 'all we can say'? Nah. Unless there is something UNUSUAL about the observer's vision, such as a serious 'higher order' optical defect or profound color blindness, the majority of people have visual acuity of one minute of arc or slightly better (and a bit better than that in bright sunlight, a bit worse in low light) when corrected using ordinary eyeglasses or contacts. While we're on the subject, there are a couple of other points worth mentioning. Bill and I discussed an interesting vision issue a couple of years ago that runs counter to some common assumptions about twilight sextant sights. Many observers work hard to get their eyes throughly dark-adapted so that they can find the stars quickly during twilight and also see the horizon. And those are good reasons for doing this. Unfortunately, a dark-adapted eye, with the pupil wide open, uses a larger portion of the cornea as an optical element and leads to serious optical distortion for most people. That's what makes the stars look "spikey". This also reduces the resolution of the eye. So it may make sense for some observations to go completely in the opposite direction. Expose your eyes to bright light for accuracy. Another 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. 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 better than 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" resolution of the eye applies. George, I will address your last comments in a separate message, maybe tomorrow. -FER --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---