From: "Richard Schwartz" 
To: "Vladimir Galogaza" 
Cc: "ATM List" 
Reply-To: "Richard Schwartz" 


It should be pretty easy to imagine a SQUARE mirror supported on a knife
edge across its center.   Then you can use beam equations on it to find the
flexure for a given load.   I'll try to do this today, and compare that with
the finite element analysis result when the mirror is circular.  This will
reveal how carefully the glass must be supported to avoid astigmatism.

We are supposed to be engineers with the ability to calculate things, so
let us stop gossipping and let us do our jobs.  Beam formulas are not at
all complicated.   For a cantilevered beam, the deflection is given in the
Handbook of Engineering Fundamentals as y=p*l^3 / 3*E*I.  Oddly enough,
this is the same as in Roark's table 3 situation 1a.  Hello?

What is weird about the Handbook is that the guys who wrote it seem to be
from the century before the last one:  they specify units of P in pounds,
for l in inches, for E in psi, and for I in inches^4.    I guess that means
the formula won't work with any other self-consistent unit system.   I
wonder how my finite element software can do it: they only require that the
units be self-consistent, but they don't tell you what the system must be.

. . . Richard

----- Original Message -----
From: "Vladimir Galogaza" 
To: "ATM shore" 
Sent: Thursday, December 26, 2002 4:57 AM Subject: Re: ATM Astigmatism on
20 inch thin mirror


>
> While reading the list I have noticed very controversial approaches.
>  Depending on context, mirrors are considered to be
"infinitively" stiff
> or "infinitively" soft.
>
> Examples for the "stiff faction" are abundant  when talk  is about
> supporting
> the mirror in grinding , polishing and testing circumstances.
>
> "Soft faction" talks emerge while discussing mirror cells.
>
> Here are two recent examples from this thread:
>
> >. If the mirror is supported WITHOUT FLEXURE, and you
> >are rotating both the mirror and the tool, as you get rid of the TDE the
> astigmatism should clear up.
>
> (This is curiously enough written by "mother of all flexing"
 our Bill.)
>
> While Mutalib wrote:
>
> >Can you guarantee that the terry cloth provides equal support to within
> 1/10
> >ounce in all sectors of your mirror?  I think not.
>
> >Your biggest mistake was probably failing to realize how flexible your
> glass
> >is.   I suspect that if you apply a load by hand to it, you will be able
to
> >SEE the warping in the reflection of distant objects... no tester needed.
> I
> >also suspect that the figure will be distorted in worse ways than
> >astigmatism.   Remember the fairy story of the princess who was
identified
> >as such because she complained about the discomfort of a pea under her
> >mattress?  That mattress is your glass.  It tends to pass the smallest
> lumps
> >underneath to the surface.
>
> Amount of flexing which we are talking about is far beyond our
"feeling"
or
> "instinct" about it (based on everyday experience).
> Forces we are exerting on mirror while grinding and polishing are enormous
> compared to gravity forces
> in the cell  both in intensity and "eccentricity". It is
miracle that we
can
> grind the mirror to Raleigh limits or better at all
> using simple  ATM methods. Therefore in ATM hands this is more sort of art
> than science.
>
> What puzzles me is that our bellowed mirror while in the process of making
> and testing is treated as utterly insensitive
> infinitely stiff princess, happy to sleep on carpets.
> But when finished they are instantly transformed into hypersensitive fairy
> princesses as
> Mutallyb beautifully compared them with in his post.
>
> Regards
> Vladimir.
>
> PS
> To my knowledge first serious ( quantitative and ATM measurable ) hint
that
> usual test stands
> for mirrors indeed induce deformations ( so commonly ignored) is to be
found
> in recent
> James Burrows post on the latest developement of his Hartman webcam test
> method .
>
>
>
>
>
>
>

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