From: Mark Holm 
To: atm{at}shore.net
Reply-To: Mark Holm 


I am thinking that in my very recent post, I overlooked an important
feature of the question.

The wave front error caused by a diagonal mirror error is affected by the
45 degree angle.

This is not an easy thing for me to visualize.  I have chosen the
physicist's usual route of imagining the simplest possible geometry.

Say I have a perfectly flat diagonal, split neatly into two parallel halves, and
   that the split is in the plane that includes the center of the image plane,
the center of the diagonal and the center of the primary.  Now if I slide
one half of the diagonal perpendicular to the diagonal surface by say 100
nanometers, I will have the same effect as a diagonal with a 100 nanometer
step error on its surface.  If this were a perpendicular folding mirror
instead of a 45 degree diagonal, the 100 nanometer step would cause a 200
nanometer path length difference.  Because it is on a 45 degree angle, the
100 nanometer step causes a  282.8 nanometer path length difference, but
the path is also offset by
141.4 nanometers.

The offset is the troublesome part.  I haven't yet figured out how to allow
for it in the path length calculation.  In calculating the path lengths to
a particular point on the image plane, I need to allow for the fact that
the offset paths are coming from a slightly different place on the primary.
Because
the primary is curved, this will change the path length.  The primary curve
is shallow, so the path length difference due to the offset at the primary
should be considerably less than 141.4 nanometers.  Therefore, the
resulting path length difference should be less than, but probably not too
much less than 282.8
nanometers.

My poor brain isn't up to the calculation just now.  I'll have to let it
wait for a time when I am more alert.  Perhaps someone has already been
down this path and can quote the answer from memory.

If my analysis above isn't too far off the mark, wave front errors
resulting from diagonal mirror errors should be multiplied by slightly less
than the square root of 2 (1.414 etc.) as well as by the usual factor of
two applied to reflections.

Mark Holm
mdholm{at}telerama.com

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