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    Stacked-mirror sextant
    From: Peter Monta
    Date: 2018 May 30, 23:09 -0700
    I was thinking about compact fixed-angle sextants like the Bris, and am wondering whether the following scheme makes sense.  Imagine two glass plates around 25 mm square and 2mm thick, polished and aluminized along one of the edges to form mirrors with aperture 2 x 25 mm.  Now bond the plates together, with the two large faces stacked one on top of the other but twisted, something like the main mirror of Hipparcos.  The two edge-mirrors fuse two fields separated by twice the mirror angle, and downstream optics can form an image.

    So far so good.  This is already a sextant; one could place it in the position normally occupied by the index mirror, and add a folding mirror in the position of the horizon mirror.  In this case, though, the second mirror is just there for folding and to supply a second reflection.

    The stack of mirrors can now be extended by adding more plates on top, in a pattern something like a spiral staircase.  Select the mirror angles so that two adjacent mirrors give a good selection of angles over the desired range (0 to 90 degrees say, or 0 to 120).  A stack of eleven mirrors gives ten angles and would be a chunk of glass 22 mm tall and about 50 mm in diameter (because the stack of mirrors is twisted).  If the desired half-angles are a,b,c,d, then the mirror azimuths are 0,a,a+b,a+b+c,a+b+c+d.  (This may end up wrapping around the complete circle several times.)

    Now ten angles are not enough.  The number can be increased, though, by using the same trick on the second, folding mirror, replacing the simple planar mirror with a segmented stack also.  Here the angles can be smaller, since they just touch up the angle from the first mirror-pair.  And finally, two additional mirror stacks, giving a third and fourth reflection, raise the number of angles to 10^4, good enough for a roughly arcminute palette of angles.  All the accuracy is in the glass blocks, and the frame of the sextant holding everything in position has no effect on accuracy (to first order).  There must be some provision to slide the mirror stacks axially to select the desired mirror-pairs along the eye path, and mechanical detents would make this easy.  With modern coatings, four reflections would not be a problem.

    The shades could, I think, go between the first and second mirror stacks.  One thing I don't like about the Bris is the inherent tradeoff with the shade, which must participate in both paths.  In this case a shade could be made in the shape of a strip which would be moved into the right spot, affecting only the skyward path.

    Disclaimer: I haven't prototyped this yet and there could be some blunder that makes the whole scheme bonkers.  But I thought I would throw it out there.  Some of the mechanical rotary tables use similar cascades of basic angles, but for pure rotation, not so much any optical use.

    Cheers,
    Peter

       
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