Mirror Deformation
Clay Spence (72713.2540@compuserve.com)
30 Jul 95 22:11:46 EDT
Well, upon checking the Sky and Telescope Gleanings article (September '94,
"Mirror support: 3 or 9 Points" by Toshimi Taki, Sinnott edited), I see that
I was slightly right and mostly wrong. Toshimi did not compute the best-fit
paraboloid, but it doesn't seem to matter much. In all his computations
they give the maximum and minimum of the deformation. Supporting at the rim
gives a very large deformation, and they note (in a figure caption) that
some of that could be canceled by focusing. However, the deformation at the
rim varies from 0 (at the supports) to -.15 wavelength (2.16 x 10^-5 inch).
Since it's asymmetric, focusing will do nothing to cancel it. (This was for
an 8 inch pyrex mirror, 0.8 inches thick.) The best of those support radii
he computed was 61%. 71% was worse than this, but not by a lot. A
nine-point support had ten times less peak-to-valley deformation.
If I figured his equations correctly in my head, the peak-to-valley
deformation goes as the foruth-power of the mirror's diameter and as one
over the square of the thickness. So for an 8 inch mirror with a thickness
of 4/3 inch, the deformation will be 0.36 of the figureshe quoted.
Clay Spence
cspence@sarnoff.com