ATM Mirror Bending Experiment

[Aplanatic@aol.com]

As you may know, a group of us are building a large Nasmyth-Cass.  At this 
time we are figuring the spherical secondary (14.5" in diameter, 1.65" thick) 
and testing it against a spherical test plate of the same thickness and 
diameter.  Both the test plate and secondary mirror are made of Pyrex.

Given the recent and continuing discussion of slings, I performed the 
following experiment today:  With the concave reference sphere on the bottom 
and the convex secondary on top, I lifted two opposing sides of the reference 
sphere.  When I had lifted about half the weight of the two mirrors, the 
reference sphere had changed by about 2 fringes in shape, becoming warped by 
my "two-point" mount.  Each fringe corresponds to one wavelength error on the 
wavefront, so I had deformed the wavefront by about two waves by this 
mistreatment.  

>From this I conclude that a mirror of this thickness and diameter will be 
sensitive to sling induced "lifting" if the sling is holding up more than 
about one pound.  (The mirror weights about 20 lbs. and we typically desire 
these effects to be less than 1/10th wave).

I think that the magnitude of bending goes like the span to the fourth power 
divided by the thickness to the third power.  If so, a 25" diameter, 2.125" 
thick mirror will have 4 times the bending amplitude (under the same load) as 
the 14.5" mirror that I tested.  So, I would expect a few ounces of 
sling-induced lifting force to be enough to be noticeable under ideal 
conditions for such a mirror.  

Since Pyrex is not (I think) available in thicknesses greater than 2.125", 
mirrors larger than 25" must be very tricky to sling mount due to the fourth 
power term and also due to the fact that they are heavier, providing a larger 
load.

There certainly is a place, it would seem, for cellular mirror blanks 25" in 
diameter and up.  

Dave Rowe