From: "James Lerch" 
To: "Jeff Anderson-Lee" ,
"ATM List"
        
Cc: 
Reply-To: "James Lerch" 


----- Original Message -----
From: "Jeff Anderson-Lee" 


>
> "James Lerch"  wrote:



> > 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.
>
> They are indeed.  Though it might not be an exact bell curve as it looks
> slightly skewed in one direction.

Hi Jeff,

I saw that as well, I assume its because its harder to get a Strehl near 1 than 0.5

> Another interesting graph is the cumulative distribution where you look at
> the fraction of the results that are less than or equal to a given value.
> Were the 1.4% to be your expected error bounds, we might say that there was
> a 90% certainty that the true Strehl ratio was between 0.637 and 0.876.
> That's a fairly wide margin.  Thus it shows that it is worthwhile to try and
> minimize the zone measurement error in order to firm up the Strehl estimate.
> With 320 pixels for the diameter that makes 160 for the radius, or 0.3125%
> (+/- 0.5 pixels) if you restrict yourself to integral zone values.  However
> you may be able to interpolate and get a better estimate.

I think for the moment, I'll just wait and see where Robo lands on the
curve, and then make changes to the code from there.

> How close do you think 1.4% is to your actual expected error values?

Not certain.....  Mike Peck wrote on 7/4 the following:

"In your images the mirror diameter in pixels is usually right around
300 (out of a 320 pixel wide frame). This mirror was 12.5" diameter or
317mm (with a focal ratio around F=4.45), making the image scale about 1
mm/pixel, rounding off a bit. In the general vicinity of the 70 % zone the
repeatability of your zonal measurements might be somewhere around 2
pixels, so call s_y ~= 2 mm."

The part I'm not certain about is, does the above mean +/- 2 pixels or +/-
1 pixel.  When I ran the sim I assumed +/- 2 pixels or +/- 1.33% which I
rounded to +/- 1.4%


>  If
> it's high, you might try running another test using Monte Carlo methods this
> time.

Question, any suggestion on 'how' to select the sub-set to use in the MC
sim? Currently I'm just using a mess of nested For-next loops, which is
pretty simple, but time consuming!)

Another interesting idea I had is based on another bit of Mike's work

http://home.netcom.com/~mpeck1/astro/null%20vs%20zone.png

Which shows my zone radius errors tend to be concentrated near the first 5 or so
zones, maybe I should just 'jiggle' those zones around on one of the next sims...

>  Also, instead of using -1.4%,0,+1.4%, you can choose a random
> variance in the range between -e and +e where e is the expected error range:
>
>     randerr = e*2.0*(rand()-0.5)  ; where rand() is some function that
> returns a value between 0 and 1.0

Copy that!

I also ran some sims on the axis A 7 zone mask, and I think they show some
interesting results as well.

http://lerch.no-ip.com/atm/2ndTry/Kill_Time_7_zone.gif (17KB)

http://lerch.no-ip.com/atm/2ndTry/A_15_StrehlCount.xls (above is included
in columns G & H)

In the image, the smaller graph is the result of only having three error
states for each of the 7 zones (-1/4%, 0 +1.4%).  The Larger graph has Five
error states for each zone (-1.4%, -0.7%, 0, +0.7% + 1.4%)

Thanks again for your time Jeff, at least it seems I'm doing something
productive while I'm killing time :)

James

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