Re: plop auto cell 36 and 54 points bugfix [was: Re: [ATM], mirrorcell design]

[Mark Holm <mdholm@telerama.com>]

Ken Hunter wrote:

>Remember that we are talking of glass expansion and
>bending in the sub nano-meter range 
>

Actually, it isn't sub nanometer.  If it were, meter class mirrors could 
be mounted on the heads of three carriage bolts and we could get on with 
observing.

A wavelength of light is roughly 500 nanometers.  That makes the famous 
Raleigh criterion 125 nanometers at the wavefront and 62.5 nanometers at 
the mirror surface.  Since most atms and amateur astronomers agree that 
the Raleigh criterion is too loose for fine imaging by a factor of about 
2, we cut it down to 31 nanometers.  These numbers use the much maligned 
P-V scheme of expressing errors.

In RMS terms, the Raleigh criterion comes out at roughly 1/14 wavelength 
at the wave front 
(http://home.earthlink.net/~burrjaw/atm/atm_math.lwp/atm_math.htm),  or 
1/28 at the mirror.  If we apply the same factor of 2 argument, that 
gets us to 1/58 wavelength or about 9 nM.  So, atms, making good mirrors 
for high quality observing want to hold surface errors to less than 
about 31 nM P-V, or, using the better criterion of RMS, about 9 nM.  
(And these levels are regularly met by careful atm's)  Mirror surface 
errors are additive, though the addition rules may not always be 
straightforward.  If you make a mirror with 5 - 8 nM RMS, not at all a 
bad mirror, you don't want the rest of the system to push you above 9 nM 
RMS, if possible.  Luckily, uncorrelated RMS error adds by square root 
of sum of squares, so there is a realistic chance of achieving that, or 
at least not much worse.  Deformations due to lack of perfect support 
will need to be held under about 5 nM.  Sqrt (5^2 + 5^2) = 7.07  If your 
diagonal is as good as your primary, then you have Sqrt(5^2 + 5^2 + 5^2) 
= 8.66

The numbers, from Plop, coupled with a long history of both atm and 
professional experience, show that  support induced deformation becomes 
a real, observable effect, significantly degrading images, for mirrors 
in the size range that atm's commonly make.  The trend to thinner 
mirrors brings the need for more sophisticated support down to even 
smaller mirrors.

A 10 inch diameter, 7/8 inch thick mirror mounted on a Plop optimized 3 
point support will have about 29 nM P-V and 7 nM RMS surface deformation 
due to sagging under it's own weight.  The same mirror mounted on a Plop 
optimized 6 point support will have 6.8 nm P-V and 1.6 nM RMS 
deformation.  So, for high quality observing, a 3-point support for this 
mirror isn't really good enough.  6-points is plenty good enough, and 
you could cut to 5 or maybe even 4.

Richard Schwartz (anybody going to challenge Richard's skepticism?) and 
Luc Arnold, did analyses similar to Plop's using other software (in 
Richard's case, I know it was one of the big name, commercial FEA 
programs).  Their results were in reasonably good agreement with Plop.  
You can be pretty darned certain that if Richard's results had not 
supported Plop's validity, we would have heard about it.  David Lewis, 
Plop's author, is a PhD engineer and professor of EE at a reputable 
university in Toronto.  Not the sort of person to foist half baked 
software, or half baked conclusions off on unsuspecting atms.  Plop is 
an extension of Plate written by Toshimi Taki, a trained engineer 
working in the aerospace industry in Japan.  David and Richard have both 
contributed to this list, sometimes specifically commenting on the 
interpretation of Plop results.  Jeff Anderson Lee, Tom Krajci, myself 
and others who regularly read and contribute to the list have a 
reasonably solid handle on the use of Plop, and it's realistic 
interpretation.  Jeff and Tom have each used it to explore some of the 
more arcane questions such as effects of construction tolerances and 
support pad size.

Overall, I think the use of Plop and it's results as presented on this 
list has been realistic and responsible..  We are not tilting at 
windmills, or gilding lilies.

The truth of the matter is that, although we use relatively crude 
methods to make our mirrors, the precision we achieve, and realistically 
require, is pretty amazing.   A key to this success is that glass is a 
pretty magical material.  We tend to think of it as ordinary and 
unremarkable, but that really isn't true.  It is cool stuff and what we 
achieve with it is cool precision.  Even the pros have to work pretty 
hard to do better than what an atm can do in his basement.  (The pros 
can today, with literally centuries of experience behind them and a fair 
amount of high tech, do significantly better than most atm's, but they 
do have to work at it.  A lot of the really high quality professional 
mirrors in amateur telescopes are made by opticians who apply 
essentially the same methods as atm's.  They have refined and perfected 
these methods, but they are not fundamentally different from what atm's 
use.)

Mark Holm
mdholm@telerama.com

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