Re: [ATM] PLOP Figures

[Mark Holm <mdholm@telerama.com>]

Mark Cowan wrote:

>Hi Mark:
>
>Fine explanation but I think you're mistaking Matt's
>Monte Carlo results (construction accuracy
>sensitivity) for the support deformation, which in a
>typical run at 550nm comes out like:
>
>6-point:  9.17e-6 PV , 1.557e-6 RMS, equiv to 1/60th
>wave PV and 1/350 wave RMS 
>
>9-point:  7.13e-6 PV, 1.14e-6 RMS, equiv to 1/77th
>wave PV and 1/480 wave RMS
>
>  
>
I interpreted the Monte Carlo results as the worst (greatest) RMS 
deformation predicted for each cell design during the Monte Carlo run.  
As such, it is appropriate to evaluate these the same as the nominal RMS 
deformations.

>As you point out these are for the mirror surface and
>must be halved for wavefront, and for this size the
>9-point isn't really worth building, the 6-point will
>perform around 1/30th wave PV on the wavefront.
>
>  
>
After being chided by Jim Burrows and others for some time, I have come 
around to placing the greatest emphasis on RMS results.  I should have 
done so long ago, since the science and math are both sound, and not 
that hard to understand.  (I do have the advantage of a reasonable 
background in math and physics, so it may be easier for me than for some 
others.)  I have a Strehl ratio calculator at my mirror cell web page 
that can help put RMS values into perspective.  One of the nifty things 
about the RMS values is the way they add.  If the wavefront deformations 
from two causes are uncorrelated (probably true for mirror deformations 
in most cases), RMS errors add as the square root of the sum of 
squares.  A result of this is that smaller values quickly become 
insignificant.  For instance, say that you have a really good mirror 
with RMS of 1/70 wave (7 nM) surface on.  Now say you put it on a cell 
that causes  1/300 wave RMS deformation.  The resulting RMS deformation 
is sqrt(1/4900 + 1/90000) = 1/68 wave.  In other words, the RMS value 
barely budges.  Estimated Strehl ratio goes from 0.9745 to 0.9728, not 
enough for anyone to be able to detect.

The same mirror might be about 1/20 wave P-V, and the cell about 1/ 50 
wave P-V.  The sum of these is 1/14 wave.  This makes the cell effect 
look a lot worse, but it isn't an accurate way to do the calculation.  
The RMS way is a lot more likely to be correct.

>The 6-point cell on your website performs very
>closely.
>
>  
>
That was my "sanity check".

>I don't claim to be an expert - didn't realize until I
>searched it out that there is a PLOP user's guide
>online at:
>
>http://www.davidlewistoronto.com/plop/Plop_User.pdf
>
>If you optimize the angle as well it will generate a
>6-point cell of 6.54e-6nm PV, around 1/84th wave PV -
>
>  
>
I haven't tried letting angles vary in a 6-point cell.  Didn't seem to 
be much point in it   Just for curiosity, I'll have to give it a try.  
In any case, don't use the P-V number to decide whether one Plop result 
is better than another.  Use the RMS value.  The P-V number is much more 
likely to mislead you.

Mark Holm
mdholm@telerama.com
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