[ATM] RE: [atm_free] The zonal Foucault test is free of inherentcorrection bias - some supporting graphs

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

Mike and Group(s),

I have gotten to a point in my simulation experiments where I can show some
results.  The quick summary is that I am not finding any significant bias in
Foucault measurements.  As Mike did, I am posting graphics to the upload area of
atmlist.net.

For any of you who might be following how my simulation has been changing, I
made the following changes:

  - I increased the size of my working arrays to 400x400, which gets me 
    farther away from possible fft aliasing effects.

  - I improved the running speed by finding the position of null using a
    linear interpolation.  In other words, I run two simulations at an
    estimated null position, then use the relative brightness differences
    of the zones to improve the estimate.  Usually, it only takes two or
    three iterations to get the brightness difference very close.

For the first set of simulations, I started with a perfect optic, and tried
various source slit widths (.7 mm, .3 mm, and .1 mm).  I simulated five depths
of knife cut in the range of +/- .4 * slit width.  The simulated optic is a 10"
f/5 with no test stand astigmatism.  

For each of the five knife depths, I show a sample Foucault image at the 70%
zone and a graph comparing what a six-zone Foucault test using Couder mask would
see (blue), compared to what a maskless Foucault test at the same stage
positions would see (red).

The results are in:

<http://www.atmlist.net/contrib/steve_koehler-at-securecomputing-dot-com/foucaul
t/compare_1_400.png>

<http://www.atmlist.net/contrib/steve_koehler-at-securecomputing-dot-com/foucaul
t/compare_3_400.png>

<http://www.atmlist.net/contrib/steve_koehler-at-securecomputing-dot-com/foucaul
t/compare_7_400.png>

Finally, in an a attempt to explore whether test stand astigmatism affects the
results, I performed a run at .3 mm slit width of a simulation of my 18" f/4.5
using nine zones.  For the wavefront input I started with an average of results
from 15 interferograms, purposely leaving in test stand astigmatism, as seen by
the interferometer.  That result is in:

<http://www.atmlist.net/contrib/steve_koehler-at-securecomputing-dot-com/foucaul
t/compare_3_400_koehler.png>

At this point, I'm very skeptical that there is systematic error to be found in
Foucault simulations using these techniques, unless the problems start showing
up at larger slit widths than I can practically simulate.  Please note that I
was not trying to simulate how a human might misread a knife test--my
simulations assume a perfect shadow reader.

I'm not sure what to do next.  I have seen some very significant examples of
Foucault not agreeing with interferometry.  At least one of them must be wrong,
in those cases.  There's one interesting case that Dale Eason is working with.
We will also have some important data points when Scott Milligan's mirror makes
the rounds.

-- Steve Koehler
   steve_koehler@securecomputing.com


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