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    Re: How flat do sextant mirrors need to be?
    From: George Huxtable
    Date: 2009 Jan 28, 18:51 -0000

    Clive, in [7074], and Geoffrey Kolbe, in [7187], have tackled Bill's
    question, about how flat a sextant mirror needs to be. I suggest there are
    errors in both those analyses, and ask them to reassess.
    
    First, neither of those contributors appears to have allowed for the fact
    that tilt of a mirror surface produces a doubled tilt in the image.
    
    Second, as there are two mirrors involved, the defects of which will
    probably add together in some way, that reduces further the defect that's
    may be tolerable  in each one.
    
    Geoffrey tells us that he first considered an unmagnified naked-eye image
    with just a peep tube, and attempts to assess the fuzziness caused by
    surface defect in a 25mm mirror. But he has forgotten that the eye pupil
    will only have an aperture of 5mm or so, so only a pencil of light of that
    width is relevant; the rest won't enter the eye and contribute to fuzz. The
    mirror size is irrelevant, in that case.
    
    However, even for the naked eye, there's a more important factor than
    fuzziness, which is this- You may have checked for index error with the
    image centralised  in the mirrors. Then, when you make an actual
    observation, you might well be looking at the star, reflected in another
    part of the mirror, away from the centre. You don't want that image to shift
    about, relative to the direct view, affected by lack of flatness of either
    mirror. That sets a limit on the curvature that can be tolerated in the
    mirror.
    
    Once a telescope has been added, then a larger area of the mirrors, perhaps
    30mm diameter or more, becomes relevant, the size of the objective. Any
    curvature in the mirrors over that aperture will contribute to fuzziness of
    the image in the 'scope. The sensitivity to image displacement remains as it
    was with the naked eye, with one big proviso, which is that when using
    magnification, you will be expecting a correspondingly higher precision, so
    will be prepared to tolerate correspondingly less displacement error.
    
    George.
    
    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message -----
    From: "Geoffrey Kolbe" 
    To: 
    Sent: Wednesday, January 28, 2009 3:02 PM
    Subject: [NavList 7187] Re: How flat do sextant mirrors need to be?
    
    
    |
    | Ok Bill, as no-one else is prepared to give you a definite number, I will
    | wave my arms about.
    |
    | Suppose you have index and horizon mirrors 25mm square. Suppose you are
    | just using a 'peep tube' with no telescope. The resolution of the human
    eye
    | is about one MOA, so what mirror flatness is required to give this
    resolution?
    |
    | To rotate a 25mm mirror by one MOA, one edge of the mirror needs to be
    | moved 25/3400mm (approximately) while the opposing edge stays where it is.
    | This is about 6 microns or 12 wavelengths of light.
    |
    | From this, we can see that if the mirror is slightly saucer shaped, so
    | that the middle is about 6 wavelengths lower than the edges, our 25mm
    | mirror will cause sufficient blurring of the image to be just noticeable
    by
    | the naked eye. To ensure that two mirrors in the optic train give blurring
    | of the image below the one MOA level, the mirrors should each be flat to
    | better than 3 wavelengths of light.
    |
    | How flat the mirror needs to be then depends on the power of the telescope
    | being used. With a 3 power scope, you need the mirror to be flat to one
    | wavelength of light. When using a 25 power scope - such as the one I made
    | for my Husun - you can see that I had to have the mirror polished to
    better
    | than an eighth of a wavelength of flatness.
    |
    | Geoffrey Kolbe
    |
    | At 06:20 27/01/2009, you wrote:
    | >
    | >
    | >I recently checked some old sextant mirrors against a tenth wave
    | >optical flat prior to resilvering them and found that the greatest
    | >deviation was a half wavelength. 3 mm modern mirror float glass
    | >compared favourably, suggesting a cheap solution to replacing
    | >deteriorated mirrors in old instruments.
    | >
    | >I have posted some images in my blog on my website www.sextantbooks.com
    | >
    | >Can one of our erudite members suggest how flat the mirrors need to be on
    | >theoretical grounds? I have vague memories that people aimed for a
    quarter
    | >wave when making the flats of amateur Newtonian telescopes, but this may
    | >well be irrelevant.
    | >
    | >Bill Morris
    | >
    | >
    | >
    | >
    | >
    |
    | |
    |
    |
    
    
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