[ATM] Foucault Simulation analysis of non-symmetric aberrations

[Dale Eason <atmpob@yahoo.com>]

This is primarily a question for Jim Burrows but
others who have experience in this area are welcome to
reply.  I have been trying some experiments using
simulated Foucault images generated using algorithms
developed my Jim Burrows and published in his Diffract
source.  My tools have been based on the R work of
Steve Koehler and his was based on information from
Jim Burrows and others like Mike Peck, and Andy Rowe.

What I have been investigating is how blind is the
Foucault test to non-figures of revolution error.  I
have been doing this by using Steve Koehler’s R code
to generate Foucault images using the first 25 Zernike
terms for the surface definition.  I use the Zernike
terms to add astigmatism , trefoil, and quatrefoil
aberrations.  I step the knife out from ROC  and take
simulated images along the way.  I then analyze these
images using the algorithm described by Mike Peck and
also used by me in my Robo Foucault tester to find the
Null on the mirror at each knife position.  I feed
these simulated readings into Sixtests to get surface
errors in PV, RMS and Strehl numbers.  I compare these
numbers with those generated by Steve’s R code from
the Zernike terms.

To validate this technique I first used only
symmetrical Zernike terms (those that produced only
spherical aberrations.)  The R numbers and the
simulated Sixtests results agree very closely.  Next I
added  astigmatism,  I know that it will not show up
in the data analysis as an error.  I added enough
astigmatism so that I could see the Ying/Yang pattern
in the simulated image.  It took about 1 wave pv on
the wavefront  of astigmatism before I could see it. 
The Sixtests results did not show any problem in the
Strehl or RMS as expected,  the ROC shifted by less
than .1 mm.  Next I added other non-symmetric terms of
aberration such that they would be across the
horizontal direction of the mirror.

What I found was that it was completely blind to all
forms of non-symmetric aberration. It was blind to
even several waves of error.   My question then is:

Does this really simulate what actually happens or is
there a flaw in the simulation math?  Steve is using
Jim’s math and algorithms from his Diffract code. 
Could there be a simplification in that code that does
not apply to this situation.

I believe this simulation is valid because it agrees
with results I and James Lerch have had measuring
mirrors with both Foucault and Interferometery. But I
am surprised by the degree of the blindness of the
Simulated Foucault test.  It sees no non-symmetric
errors in the mirror what so ever.


Dale Eason



		
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