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    Re: Geometry of SNO-T
    From: Herbert Prinz
    Date: 2004 Oct 14, 01:20 -0400

    Bill wrote:
    > I had posted a question a while back, and have received no response.  Since
    > Alex seems to have a good grasp of this now, I will ask him and others to
    > address it.
    > "If the front-silvered mirror is no longer on the axis of the rotation, will
    > this affect the sextant's performance?"
    It may have a small impact on performance, but it will not directly affect the
    measured altitudes.
    1. It does not directly affect the measured angle, because the mirror remains
    parallel to its previous (or ideal) position. All that matters are the angles of
    the light rays through the instrument and they are still the same. Alexandre
    Eremenko did in fact mention this in passing in an earlier message today.
    2. There is a potential indirect effect in that it becomes more difficult to
    ensure the perpendicularity of the index mirror. This has been discussed. From
    my experience with an Astra with a front silvered mirror which is displaced from
    the pivot by ca. 5 mm, I can say that in actual practice this is not a problem.
    But let's assume for the sake of argument that you have a perpendicularity error
    of 5' that you cannot get rid of. Then the error of any measured angle over 10
    deg would be smaller than 0.1'. Smaller angles suffer more, but they are hardly
    ever used.
    3. If the sextant was originally designed for a centred mirror surface which has
    been later replaced by an off centred one, then the light path that goes through
    the centre of the telescope no longer passes through the centre of the index
    mirror. Consequently, a few square millimetres of mirror surface are lost.
    Earlier today, Cliff Sojourner had asked
    "is there any effect from index of refraction of the glass in"
    "front of the silvered surface?"
    And I answered "Only in so far as the refraction of the glass shifts the
    apparent reflective surface from the back towards the front surface of the
    I should add that this is only true for a glass with perfectly parallel faces.
    (Which we hope we always have.) If, however, the glass is prismatic, in other
    words, the front surface is not perfectly parallel to the mirror surface, then
    the measured altitude will be in error. This error is not constant and can
    therefore not be compensated by index correction. I do not know whether this is
    a real world problem.
    Herbert Prinz

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