From: Dale Eason 
To: James Lerch , atm{at}shore.net
Reply-To: Dale Eason 


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A good algorithm for the MC would be Decide how many samples you want. 
Decide the variance e. 1.4%

for 1 to the number of samples

     Randomly pick a number from 1 to number of zones.
     Randomly pick a number from -e to +e and modify the zone just picked by
that that amount.
     Run the error analysis and save in a bin.

James Lerch  wrote:

----- 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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A good algorithm for the MC would be
Decide how many samples you want.  Decide the variance
e. 1.4%
 
for 1 to the number of samples

  Randomly pick a number from 1 to number of zones.
  Randomly pick a number from -e to +e and modify the
zone just picked
by that that amount.
  Run the error analysis and save in
a bin.James
Lerch <jlerch1{at}tampabay.rr.com>
wrote:
----- Original Message ----- From:
"Jeff Anderson-Lee"
>>
"James Lerch"
wrote:> >
http://lerch.no-ip.com/atm/2ndTry/Kill_Ti me.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 than0.5>
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 1mm/pixel, rounding off a bit. In the general vicinity of
the 70 % zone therepeatability of your zonal measurements might
be somewhere around 2pixels, so call s_y ~= 2
mm."The part I'm not certain about is, does the
above mean +/- 2 pixels or +/- 1pixel. When I ran the sim I
assumed +/- 2 pixels or +/- 1.33% which I roundedto +/-
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
prettysimple, but time consuming!)Another
interesting idea I had is based on another bit of Mike's
 workW" target="new">http://home.netcom.com/~mpeck1/astro/null%20vs%20zone.pngW
hich shows my zone radius errors tend to be concentrated near the first 5
or sozones, maybe I should just 'jiggle' those zones around on
one of the nextsims...> 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 1.0Copy that!I also
ran some sims on the axis A 7 zone mask, and I think they show
someinteresting 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 incolumns G & H)In
the image, the smaller graph is the result of only having three error
statesfor each of the 7 zones (-1/4%, 0
+1.4%). The Larger graph has Five
 errorstates 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
somethingproductive while I'm killing time
:)James
 Do you Yahoo!?
http://pa.yahoo.com/*http://rd.yahoo.com/evt=1207/*http://promo.yahoo.
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