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Re: ATM Mirror questions...
I am currently making a 16" plate mirror. This is my first mirror. From
what you have said, would it make sense to figure my mirror at a cooler
temperature? My wife and I have a flower business, and I am able to use
a walk-in frige if I so choose. Set it to 50'F put on a sweater and
grind away.
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From: RDuvall@pixworks.com
To: Richard Schwartz
Cc: Robert Duvall; ATM Mailing List
Subject: Re: ATM Mirror questions...
Date: Monday, May 12, 1997 11:59AM
At 9:04 AM 5/12/97, Richard Schwartz wrote:
>> The principle is quite simple. You use the coeff of expansion of the glass
>, the
>> sagitta of the mirror, and the temperature. The thermal coeff is an
>> _experimental_ value, and is very exact, it doesn't matter whether...
>> I am assuming the mirror has _already_ reached equilibrium at the given
>temps.
>
>
>I understand thermal expansion, but I always thought that if all parts of
>the mirror were at the same temperature, the expansion would preserve the
>shape of the mirror. The focal length would change slightly, but if the
>mirror is originally a parabola, it will be a parabola at any temperature.
>
Unfortunately, this is not the case. The parabola is going to change
because the outside of the mirror is thicker than at the center. As
temperature changes, the thickness (and diameter) of the mirror change,
just as in the eyepiece discussion currently going on on the ATM list.
The
diameter chnage is pretty unimportant, but the thickness is. I use the
sagitta, as it represents this difference in thickness. How thick the
mirror is not important, since it is uniform across the diameter of the
mirror and cancels out. If you muliply the sagitta times the thermal
expansion coefficient you get a number that represents how much the
glass
will expand or contract per degree of temperature change. It is quite
small. Multiply this by the temperature difference between what you
tested
at and what you are observing at, and you find how much the curve
changed.
For my 12.5" with
>
>I am more interested in how you compute the error than what the actual
>numbers are. Give me a clue, even a reference to some published paper
>somewhere would be great. I want to learn how to do this calculation!
>
See above discussion.
>I always assume thermal equilibrium. I am working with thin mirrors, so the
>thermal equlibrium is more rapid than with the heavy hunks.
>
That's true,
>> The erors are worse as it temperature changes. I assume you've seen this
>> effect; it's the same principle that causes bad seeing while the mirror
>cools.
>
>Wait a minute... you just said THERMAL EQUILIBRIUM. I thought the bad
>seeing while the mirror cools is caused by currents of hot and cold air
>around the mirror.
Yes, currents of air cause serious problems of course, and these can
cause
errors of _several_ wavelengths I think. But the mirror does change
shape
as it cools. For cooling off calculations, the mirror can be assumed to
be
a simple flat circular plate. The outside diameter of the mirror cools
faster. The glass there starts to contract. Bingo, you now have a turned
down edge. How much depends on the temperature gradient. It is probably
only a few degrees, so it's probably only about 1/8 - 1/4 wave, not too
much to worry about, even for plate.
As the mirror is cooling, this TDE area grows inward toward the center
of
the mirror, but as it arrives at the uniform air temp, it grows less
severe, but the overall figure is now no longer the same parabola as
it's
original design. That's why the focus changed- you can't change focus
without changing the shape of the curve! It also won't resolve as well.
One way out of this is to use a mirror of uniform thickness- the same
curve
on both sides of the glass. I believe some mirrors are being made this
way.
Corrector plates are, and it's a good thing for them.
BTW, you'll notice that the 200" was the first Pyrex mirror. Why do
think
this was? Because the 100" has so much image error at different
temperatures because it was plate glass. The best scientific and
military
mirrors regularly use Cervit and other very low thermal expansion
coefficient materials to eliminate this thermal effect.
I have been debating whether I should post this and our earlier
conversations (condensed) to the ATM group, since others may be
interested.
I see you posted your reply to the group, so perhaps people may want my
earlier posting to you- it at the end of this.
I may also add a writeup on my web pages soon, as I have friends making
20"
scopes with plate and this is a concern of mine. I think one needs to
modify their mirror testing to account for thermal changes, trying to
target your usual observing temp. I have also thought about a 'bizarre'
idea of moving mirror supports to compensate for the effect at different
temps.
Let me know if this helps and is clear. It may need some figures to be
clear and I don't want to attempt that in ascii! That's why I'm thinking
of
a web page.
-----------------------------
Summary of earlier posts:
>I guess the Mt. Wilson 100" telescope is no good; it is made of PLATE glass.
1) It was not figured the same way your glass is likely being figured.
It
was done in a temperture controlled room.
2) They [very likely] calculated in the effect that thermal contraction
would have and adjusted the test accordingly,
3) And yes, it is _not_ 'any good' by Rayleigh criterion and the Airy
disk
_over a wide range of tempeatures_. It will give best results (like ALL
mirrors) at a given temperature. Most mirror/focal lengths of amatures
do
OK over a 10-20 degree temp range. It depends on the focal length,
diameter, and material used (plate, Pyrex, Fused Quartz, or CerVit). If
you
supply me with the f ratio, it would be interesting to see how bad it
[the
100"] can be. I suspect SEVERAL waves.
I have redone my calculation program, since you got me interested in it
again. Give me the diameter and focal length of the mirrors, the temp
you
foucalt tested them at and the observing temp and I can tell you the
error.
Please note I am assuming the mirror has _already_ reached equilibrium
at
the given temps. The erors are worse as temperature changes. I assume
you've seen this effect; it's the same principle that causes bad seeing
while the mirror cools.
My 12.5" f/5.2 pyrex mirror will show 1/4 wave error over a 30 degree
delta
T. So if it is perfect at room temp (70) it will be about 1/4 wave
overcorrected at 40 degrees. A plate glass mirror of exactly the same f
ratio and diameter will be off by 3/4 wave!
Robert Duvall
Software Engineer, Amateur Astronomer (TN),
and General Scientist (according to my son)
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