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Kieran.

Flatness of an optical surface is determined by measuring the maximum
variation of the optical surface in question from a theoretical flat plane
placed on the optical surface.

The flat plane will sit on the high spots of the optical surface and the
maximum distance from the deepest trough on the optical surface to the
theoretical flat plane determines the flatness of the optical surface.

Classically, the optical surface in question will be compared to a known
optical flat in an interferometer using monochromatic light of a known
wavelength. Variations in the flatness of the optical surface in question
show up as interference fringes, which act like the contours on a map. By
counting fringes, you can say how many wavelengths of light by which the
optical surface is in error.

You say your mirror is flat to seven wavelengths, but that will be over the
whole mirror. It may be flat to half a wavelength over most of its surface
and have one bad section. But in any case, how 'bad' this is depends on the
diameter of the mirror, which you do not tell us.

Let us suppose your mirror is 14cm in diameter, but due to the diameter of
the object lens in the telescope on your sextant, you will only be using a
section of the mirror around 2cm in diameter at any given time. The
flatness of that section of mirror will be around one wavelength of light
(around 5x10-7 metres) on average. Your limit on resolution (which equates
directly to the angular error about which you were asking) of this section
of mirror will be roughly equivalent to a perfect mirror about 1cm in
diameter, which is about 1/10th of one minute of arc.

I would say that the flatness of your mirror (or lack of it) will not
contribute significantly to any sextant altitude error.

Standard optical flats can be purchased and are generally flat to 1/10th of
a wavelength of light across their surface.

Geoffrey Kolbe.

At 10:51 AM 11/2/03 +1100, you wrote:
>Gentlemen,
>
>For many years I have used a Zeiss Artificial Horizon in the bush for
>celestial navigation and position fixing. It has a standard three- legged,
>adjustable mount and came supplied with a dark, machine-ground glass
>reflector, for sun observations. Needing to do star observations I had made
>a front-silvered mirror from a piece of float glass. This was obviously not
>machined but as the glass was floated when molten, it should have been
>reasonably accurate due  to the force of gravity on a liquid. To do star
>sights I simply removed the dark glass plate from the frame and inserted the
>front silvered mirror. This arrangement has given great service over the
>years and I am normally not out by more than 2 nautical miles from known
>positions on land (arithmetic calculation errors being the exception).
>
>However, I have often wondered just how flat and accurate is the front
>surfaced, glass mirror. I recently took it to an optical engineering
>workshop here in Sydney who assessed it as being accurate to 7 wavelength's
>of light. They advised that while this was not perfectly level anything
>under 10 wavelengths of light is so accurate that it would not add any
>meaningful error to that already produced by someone holding a hand held
>sextant. It was their belief that even after index error and instrument
>error was accounted for the, minute deficiencies in the sextant would still
>produce greater error than the 7 wavelengths of light in the horizon. Also
>it is clear that the levelling process for the horizon itself i.e. defects
>in the bubble levels that I use and operator error eg in reading the bubbles
>would produce error.
>
>Does anyone on the list have a comment. What is the error in a ground piece
>of glass? The engineering workshop told me they could get it down to
>practically zero wavelengths. What is a 7 wavelength's error? Can this be
>translated into minutes of arc? Can the error in the horizon mirror be
>eliminated through adjustments in the sight reduction process?
>
>Your advice would be appreciated.
>
>Kieran Kelly
>
Dr Geoffrey Kolbe, Border Barrels Ltd., Newcastleton, TD9 0SN, Scotland
Tel. +44 (0)13873 76253  Fax. +44 (0)13873 76214

                         http://www.border-barrels.com

   

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