From: "James Lerch" 
To: "ATM List" 
Cc: 
Reply-To: "James Lerch" 


Greetings All,

The mathematically wise among us will probably fall over from laughter, but
I never claimed to be really smart!   To demonstrate this let me
show you my latest adventure in stupid tricks.

Here's where it started, I was considering Vladimir's question on how
errors in my zone radius might effect the resulting surface error.  Not
knowing a simple mathematical way of solving this, I took the "Get a
bigger hammer" method.

Here's what I did, I wrote some code to solve for the Strehl ratio for ALL
possible zone radius errors.  (You math guys probably see the folly in this
already!)  Honestly, it wasn't ALL possible errors, I only considered each
zone being in one of three states:

#1 Estimated Radius - 1.4%
#2 Estimated Radius
#3 Estimated Radius + 1.4%

Since I used the Axis A 15 zone data set to play with, that should have
meant the total possible combinations should have been 3^15 or 14,348,907
possible results.  In actuality it turned out to be 3^14*2 or 9,565,938
results. (Yup, I know you math guys are chuckling now !)

Soooo, 16 hours later, I have a result.  Here's how the result was created. For
each simulation, the resulting Strehl ratio (to 3 significant digits) was found.
For each possible Strehl, I incremented an array element of all possible Strehls
(0-1000).  The resulting array of 'Counts' was put into Excel and charted.
Here's the result:

http://lerch.no-ip.com/atm/2ndTry/Kill_Time.gif (27KB)

I know by now you math guys are really finding this funny, especially since even
I recognize a 'stinking bell curve' when I see one! 

Oh well, at least I can say "I've been there, done that!", and
the results are kind of interesting IMHO.

Also, Here's the raw data if your interested:
http://lerch.no-ip.com/atm/2ndTry/A_15_StrehlCount.xls

Take Care,
James Lerch
http://lerch.no-ip.com/atm (My telescope construction,testing, and coating site)

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