[ATM] updated mirror C comparison

["Koehler, Steve" <Steve_Koehler@securecomputing.com>]

I updated my modal comparison of mirror C data by adding the missing Scott R.
data and adding in Dale Eason's Robo-Foucault and Interferometric results.  The
updated figure is in

http://www.atmlist.net/contrib/steve_koehler-at-securecomputing-dot-com/roundrob
in/c_modal_5_updated.png

The Robo-Foucault line is not a modal fit, but a standard integration like what
SixTests does.  The interferogram line used the first seven symmetric Zernike
terms.  (This is a way to get an average diametrical profile from the 2D
interferometric results.)

I also included another graph to show why I chose seven terms for the
interferometry line.

http://www.atmlist.net/contrib/steve_koehler-at-securecomputing-dot-com/roundrob
in/orders.png

This graph shows what happens to the computed surface when using between 3 and 9
symmetric Zernike terms.  3 terms is clearly too few.  From 4 to 7 terms seem to
settle into a reasonable pattern.  Starting at 8 terms, the surface all of a
sudden gets many more wiggles back and forth.  This is strong evidence that the
data has been over-fit, and the Zernike results are showing artifacts that are
not real.

I didn't draw any conclusions in my last post, so I will take the time to do so
now.  First, the Robo and Igram lines are arguably the most believable, and
probably show more correct detail than any of the 5-zone Foucault results.  This
is because of larger volume of data that went into these results.  (Dale's
Robo-Foucault typically uses 100 zones from the center to the edge.)  Between
these two, I think Robo captures what is happening at the center of the mirror
the best.  The Igram results are limited a bit by being filtered through a
Zernike fit, which often does poorly right in the center and at the edge.

I think there's a remarkable consistency between all the results, even though
there was a large discrepancy in tester experience.  All results clearly show a
high spot just outside the center of zone 1, and a low spot centered
approximately on zone 3.  It's a little less clear what is happening toward the
edge.  All show that the surface rises beyond zone 3, but how far and where the
rise begins is not consistent.

-- Steve Koehler
   steve_koehler@securecomputing.com


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