A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: How flat do sextant mirrors need to be?
From: Gary LaPook
Date: 2009 Jan 30, 17:24 -0800
From: Gary LaPook
Date: 2009 Jan 30, 17:24 -0800
You can check the flatness of the mirror with a Foucault test setup used for telescope mirrors. gl Geoffrey Kolbe wrote: > in  George wrote: > >> Clive, in , and Geoffrey Kolbe, in , 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. >> > > Thankyou for that George, I did indeed forget about that. > > > >> 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. >> > > That I did take into account, by halving the allowable single mirror > defect. That was probably too crude - a reduction of 1 over root 2, rather > than a straight 1/2 is probably more appropriate, given the random way in > which the mirror defects may add or cancel each other out. This hauls back > a good part of the error you pointed out above. > > > >> 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. >> > > Yes George. You are right to make the distinction between the "low > magnification" case, where only a part - which may randomly vary - of the > mirrors are being used at any one time, and the "high magnification" case > where all the mirror surface is contributing to the image. Talking about > "blurring" of the image in the naked eye case, as I did, was not correct. > Though in defence I should say that I was laying out my stall to consider > the case when a telescope is put in the optic train - and the analysis of > how much mirror defect is tolerable before precision is affected is the > same in both cases. > > I should also add that due to the way in which mirror flatness was > specified, the mirror size in the "low magnification" case is not entirely > irrelevant. Where a "saucer shaped" mirror is being considered, a 25mm > mirror that is flat to one wavelength is not as flat as a 50mm diameter > mirror that is flat to one wavelength. Cutting two 25mm mirrors from a 50mm > blank of one wavelength flatness will give two 25mm mirrors that will be > flat to something nearer to a half wavelength. This is the main reason why > large flat mirrors are considerably more expensive than small mirrors of > the same specified flatness. Given their small size, the cost of having > your sextant mirrors polished to tenth wave flatness and front coated, for > example, may be considered a reasonable. Here in the UK, it is possible to > have this done for about �150. > > In conclusion, I think my numbers remain pretty good. Where the usual 3x > Galilean telescope is being used in a standard sextant where the mirror > size is of the order of one inch (25mm), then the mirrors need to be flat > to about one wavelength of light. Where a higher power scope is being used, > the allowable flatness error decreases proportionately. > > > Geoffrey Kolbe > > > > > > > > > --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavListfirstname.lastname@example.org -~----------~----~----~----~------~----~------~--~---