From: "Dwight K. Elvey" 
To: atm{at}shore.net
Reply-To: "Dwight K. Elvey" 


>From: "Bill Mitchell" 
>
>Any ideas how much glass actually gets removed during parabolizing?
>Are we talking microns, nanometers, angstroms?  I don't mean volume,
>just the depth at the center, say for a 20" f/5 just to keep the math
>simple (if possible).
>Thanks and Merry Christmas,
>Bill

Hi Bill
 You can figure out how to do the measurement but
it is simpler for me to just give you the number. It is about 0.000156
inches for this size mirror. Sagitta of your mirror is 0.250 inches.
 I'm not sure how to make the math simple. Maybe
someone else can give you a general equation. If I assume that the edge of
the mirror is untouched and only the center is increased in depth, that
means that the edge has a ROC of 200.25 ( 2F+S ). Using right triangles,
this sphere has the sagitta of 0.24984375" ( s^2 - 2(ROC)s + r^2 = 0 
or  s^2 - 400.5s + 100 = 0 ). I subtract this from the sagitta of the
mirror ( r^2/4f = s ) to get 0.2500000" - 0.24984375" =
0.00015625".

 The tricky part was that you asked how much to remove
from the middle of the mirror. This means that the original sphere needed a
ROC that was 0.25 inches longer that the finished mirror's center. In all
likelhood, with a 20 inch mirror, you'll most likely flatten down the edge
areas a little as well. This is because you most likely won't be doing the
typical mirror on top with a full sized lap, parabolizing stoke. You'll
find it easier to remove about 1/4 from the outer areas and 3/4 from the
center. I'd think this is a reasonable compromise. I've not done a 20 inch
so it is just a suggestion.
Dwight

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