From: "James Lerch" 
To: "Mark Suchting" , "Jeff
Anderson-Lee"
        ,
   "Michael Peck" 
Cc: "ATM List" , 
Reply-To: "James Lerch" 


----- Original Message -----
From: "Mark Suchting" 

> Royce seems to report overcorrected figure and the Robo undercorrected ( ?)
> so the total difference is still 40 nm RMS or so even allowing for halving
> of the Royce RMS to give a surface RMS.
>
> ~Mark

Well,,,,,,,,,, 

First let me tally up a list of all the results from Robo as seen by FigXP
and Sixtests.  The first set of data is all reference a parabola (b= -1),
using each
axes' 15 zone Robo data (no 7 zone data included!)

#1 FigXP (paraxial roc +/- the entered measure roc of 2828.93mm)

                 Best Fit
Axis       Paraxial ROC    Surface RMS
-----       -----------       --------------
A            +0.079mm            22.8nm
B            +0.002mm            22.4nm
C            +0.118mm            23.8nm

#2 SixTests (paraxial roc +/- the entered measure roc of 2828.93mm)

                 Best Fit
Axis       Paraxial ROC    Surface RMS
-----       -----------       --------------
A            -0.268mm             21.2nm
B            -0.381mm             21.3nm
C            -0.289mm             21.7nm

OK, now lets try and answer the Over/Under correction question.  I think this is
the correct procedure (at least its what I do).  In FigXP I hit the 'Find
best fit Conic Constant button, on Sixtests I click "Conic".  If
the result is between 0 and -1 I call it undercorrected, Less than -1 I
call it overcorrected.
Here's the results

#1 FigXP (paraxial roc +/- the entered measure roc of 2828.93mm)

                 Best Fit
Axis       Paraxial ROC    Surface RMS     b
-----       -----------       --------------     --
A           +0.050mm         22.6nm           -1.012
B           +0.042mm         21.7nm           -0.981
C           +0.067mm         23.1nm           -1.022

#2 Sixtests (paraxial roc +/- the entered measure roc of 2828.93mm)

                 Best Fit
Axis       Paraxial ROC    Surface RMS     b
-----       -----------       --------------     --
A             -0.277mm              21.1nm      -1.004
B             -0.319mm              20.2nm      -0.972
C             -0.319mm              21.4nm      -1.013

From these results, I'd say axes A & C are 'overcorrected' and B is
'undercorrected'.

Its interesting that both FigXP and Sixtests come up with near the same b
value for each axis.  I also wonder if this result might be trying to tell
us something about primary astigmatism (I know, KE testing can't do that,
but....)

Another interesting observation from this data is the 'best fit offset from
paraxial ROC".

The first interesting thing is the signage difference between FigXP &
Sixtests, in this case I will to defer to Sixtests as being the most
accurate, and go double check the code for FigXP to see if I just found a
Bug.

The second interesting thing is with the b = -1 data set, both FigXP &
Sixtests offset from paraxial ROC put Axes A & C close to each other,
and B as being
'different'.  Again I wonder if this is trying to tell us something about
primary astigmatism.  (I know, KE testing can't do that) however suppose
for a moment that it might in this case, based on the following
suppositions:

#1 The intereferometry shows limited amount of astigmatism near the center of
the mirror

#2 The 1st zone on the Robo tests has a zone radius of only 29.7mm (this radius
also has the highest StdDev error, so I might be making a fool of myself
with this supposition.)

#3 Supposing now that the center 30mm of the optic has 0 astigmatism, and Robo
found this radius and its longitudinal reading, and Robo measured the
remaining longitudinal readings for each zone radius correctly for each
axis, then "MAYBE"
we can measure primary astigmatism "in this case?"   (I'm not sure HOW)

At this point, we might suppose that Robo and the Interferometer agree that
the mirror has astigmatism.  We might even be able to prove that Robo saw
this astigmatism because Mr. Royce said the 0-degree interferometry had
Axis A 'Up'. IF we can correlate the 3D plot to the 3 Robo Axes, we might
be able to show that axes A&C should be close, and axis B 'different'. 
However, I don't know how to do this.......

OK, lets forget about all this astigmatism supposition, and lets look at
the difference between Robo and the intereferometry in terms of total
correction.

On the Intereferometry report, testdata.jpg,
http://lerch.no-ip.com/atm/2ndtry/lerchtest01.zip

In the bottom right corner I see a profile along the 0 degree axis.  If I
saw this profile on FigXP I'd say the mirror is strongly overcorrected.  To
find out
'how much' I'd do two things,

A) I'd click "Find best fit conic constant" and I'd say "The
mirror's overcorrected and has a b of "X", when it should have a
b of  -1"

B) I'd look at the longitudinal KE readings and say "Between zone 1
and zone 15 you have "X" amount of KE longitudinal travel, and
ideally you should only have 4.14mm (0.163") of KE travel."

Here's the question for the list, can we do something similar for this
intereferometry?

 If so, then we should be able to work backwards from the interferometry's
surface profile, and figure out what Robo should have seen in the following cases:

A) Given that Robo found the zone radius correctly and erred in the longitudinal
KE readings, we should be able to calculate the amount of error and see if
its in the "realm of possibilities"

B) Given that Robo found the longitudinal KE readings correctly and erred on the
zone radius, we should be able to calculate what the zone radiuses should
have been, and again see if this is in the "realm of
possibilities"


That's all the crazy suppositions I can come up with at the moment. 
Currently UPS says the Optic is on its return trip, and I should have it
back in a few days.

Once its back, here's the plan.

#1 Charlie has the OTA ready, so its time to image some star tests, and see
what
we see!
#2 Ronchi Test, looking for astigmatism and what not
#3 Mr. Burrow's 1d Hartmann


Finally, I'm going to end this post with a "Moment of Zen"
http://lerch.no-ip.com/atm/2ndTry/Freaky.gif (560KB)

Above created from the "Synthetic Interferogram" and FigXP.

James

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