FW: Alternative mirror technologies, WAS ATM Liquid-mirror tel escopes

[Sean Scott <sscott@prxm.com>]

<snip>
> I've got a question.  I've seen occasional references to mylar
> film mirrors...pulled into a parabola with a vacuum.  What
> makes it take on a parabolic shape?

That's the problem: it doesn't.  But I don't have ready access to a   
finite
element program (or expertise with the math) to calculate just what shape
it does take.
<snip>
The shape taken by a mylar sheet acted on by a vacuum should be a   
catenary of revolution. A catenary curve is what's created when you hold   
a perfectly homogenous and perfectly flexible string by the ends,   
assuming the string is not elastic. In the case of the mylar mirror the   
gravity and the vacuum supply an equal force along the entire length.   
(Remember that because of the effects of gravity, a string held   
horizontally can never be straight - the mass in the center represents a   
force component that can't be eliminated.)

The equation is y = a*cosh(x/a). I'd say the three obstacles to be   
overcome if you want to create a mirror using a vacuum and a thin film   
would be:
1. When you tilt the mirror, gravity would add an off-balanced effect to   
the force created by the vacuum and alter the curve. Your point of focus   
will change, and probably the focal length, too. You could fix this with   
a sideriostat typoe arrangement so the mirror would always be horizontal.
2. Creating a sheet of mylar that's 'infinitely flexible'. If you assume   
the mylar is flat to begin with, then you pull (or push) down in the   
middle of the round sheet, the edges are going to 'bunch up' and crease,   
causing the surface to be unsuitable optically. Mold the mylar to shape   
would possibly resolve this problem.
3. Maintaining the vacuum accurately. The mylar will diffuse air through   
it eventually (though those mylar baloons stay inflated a lot longer than   
rubber ones, they aren't inflated to the same pressure) so you'd need to   
be making periodic changes to the vacuum pressure. Those changes would   
have to be small enough to not disturb the surface (adding too large a   
force at once would cause the figure of the surface to 'shake'. Changes   
to the vacuum would also alter focal length and the focus point.   
Alternately, make the change while there's no science going on.

Maybe by varying the thickness along the radius of the mylar you could   
cause the curve to more closely fit a parabola. (Remember that the above   
equation is for a perfectly homogenous, perfectly flexible material) Or,   
design a corrector lens to fix the image. Or perhaps you could add   
another element to the equation by creating an electrical field to cause   
some of the deformations. But then we'd be getting complicated...

Sean Scott
sscott@prxm.com