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    Re: October Lunar
    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
    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
    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.
    "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
    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
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