ATM Vacuum Pan Deformation [was: Flex-Mirror Notes]

[Aplanatic@aol.com]

Dominic:

>  A vacuum cavity will have flexure 
> caused by constantly changing barometric 
> pressure. 

Do you mean that the mirror's figure would
change with changing barometric pressure?
If so, you are correct unless a method was
employed to keep the pressure difference
constant across the mirror.  This can be 
accomplished in many ways, including:

1) Use a manometer to measure the pressure
difference and compensate by hand (or by
mouth, actually).

2) Use a capacitance sensor to measure the
deflection of the mirror and keep the 
deflection constant using a feedback 
system.

3) Use a barocell to measure the pressure
difference, etc., ....

> It will take a thicker mirror than is 
> practical and the support vessel 
> would have to be also as rigid which in 
> itself becomes overly massive. 

Well, lets run an interesting example:

Mirror diameter = 20" = 508 mm
Focal ratio = f/5

The central deflection of the mirror, Zc,
needed to turn a sphere into a parabola,
to fourth-order, is given by:

Zc = 0.0042 * D / f^3

where D is the mirror diameter and f is
focal ratio.  For our example, 
Zc=17 microns.

The pressure, P, needed to deflect our 
20", f/5 disk is given by:

P = 0.9 * t^3 PSI

where t is the thickness of the disk in 
inches.  So, a one inch thick disk can
be deflected by 0.9 PSI, a reasonable
pressure difference.  Certainly, a 1/2"
thick Aluminum vacuum pan would be
sufficient.  Its central deflection would
be on the order of 5 mils or so.

Notice that the central deflection of 
the glass is about 35 waves.  If 
astigmatism is to be well controlled, the
maximum allowable wedge in the glass should
be less than about 1 part per thousand of
the thickness, or about 1 mil.  I typically
can do 10 times better than this with a
simple wedge-o-meter when making a Schmidt
plate.  Not a problem.

The big problem is getting a round, uniform, 
planar support for the glass.  This is not
so easy, but it can be done with very careful
milling and lapping.

What about residual spherical aberration from
higher-order terms?  The vacuum pan technique
can remove only the fourth-order aberration
from a spherical surface.  As it turns out,
the residual aberration (from sixth and higher
order terms) for our 20" f/5 mirror
is about 2.5 nanometers, or less than 1/20 
wave P-V.  Good enough for me.

In conclusion, a 20" sphere pulled into 
a parabola by the vacuum pan method should
be possible, but maybe a lot of trouble.  I
would try it first with a 10" to get some
idea of the difficulty.  A disk of uniform
thickness is needed, i.e., a section of
a spherical shell is required and it should
be carefully de-wedged.  Most importantly,
the support structure (pan) should be
exceptionally flat, round and uniform.

Dave Rowe