25 inches mirror on 6 points

Robert Houdart, a member of the BigDob community (http://tech.groups.yahoo.com/group/bigdob/) asked me to cross check a benchmark he run with PLOP and a MirrorMesh3D (http://www.cruxis.com/scope/scope1100_mirrormesh3d.htm).
I run benchmark 1 in his webpage. It is the case of a 25" 2" thick F/5 mirror supported by 6 points. Here are my raw numbers (before removing defocus): PTV 415 nm, rms 125 nm. Plop says 420 nm and 127 nm respectively, MirrorMesh3D 432 nm and 138 nm.
The pictures show the deformed shape after defocus has been (roughly) removed. I write "roughly" because I did not find the best fitting parabola accurately, but only in the post processing by trial and errors (it is not that difficult).
Picture 1 shows the top view. Picture 2 the view from bottom. Note that support points produce large local deformations that are smoothed on the top side of the mirror.

Astigmatism

The picture of the previous post shows the crude deformation of the mirror. However not all that deformation is abberation. In fact the mirror is tilted and its radius of curvature modified. To evaluate the real abbertions tilt, piston and defocus must be removed (defocus only means that the best focus position must be adjusted).
The picture in this post was obtained by manually tilting and defocusing the surface (you may see the expression for the plotted surface in the picture). Although they are not exactly the best fitting parabola, they are close. Once they are removed what remains is mostly astigmatism: the sides of the mirror are lifted and the vertical diameter pushed back (this is due to the sling which compresses the mirror in the horizontal diameter, which is strictly unnecessary). The amount of astigmatism is thus rougly 60-70 nm PTV (about 1/4 wave on wavefront).

Sling support for a 30" mirror

Here is the result of a finite element static three-dimensional analysis for a 30" diameter mirror. The mirror is 2" thick and supported by a sling. It is assumed that the sling applies uniform pressure across the edge. This means that the centre of sling forces is not exactly on the plane of the centre of gravity, but slightly forward. One could reduce deformations by accurately centering the sling. This analysis is representative of what might happen if the sling is not exacly centered. In a certain sense it shows what is likely to happen. No other defects are there. The deformed hape is magnified 1 million times. The material is Pyrex 7740.
The deformed shape is ugly: the mirror centre goes back 40 nm, while the whole lower edge moves forward 140 nm. The total surface error is thus 1/3 wave. 0.66 wave on wavefront. This is much worse than for a 16 inch diameter, same thickness mirror described in a past post. Of course the above numbers include tilt and defocus. The real abberations are somewhat less.