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

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

Mike,

I have been doing similar simulations, although I'm not trying to follow
Linfoot.  I have been  using an 10" f/5 tested with six zones.  I have a manual
Foucault simulator that works similarly to yours (and Jim Burrrows'), but my
stopping criterion for a nulled zone is when my step size goes below .0005
inches for a moving source tester.  I compare the total intensity across the
mask openings to decide which way to move the stage, reducing the step size by
two when I change direction. I figure this is better than humans can do.  I also
have a simple robo simulator that gets a set of readings from a flip and diff of
the image at a given set of stage settings. I'm not ready to publish results,
but I have found the following things, which you may want to explore:

1. For a perfect optic, Couder always shows a bit of undercorrection.  The
choice of zone center makes a little difference, but not a lot.  Flip and diff
does much better, in general.

2. The Couder results are often highly dependent on the depth of knife cut.
Results are worse for a deeper cut, and go toward perfect for a very, very light
knife cut.  Robo does best with the knife cut in the middle.  I'm experimenting
with a variety of slit widths (.1 mm to .7 mm) and knife cut depths.

3. The shape of the Couder mask makes a significant difference.  When using the
mask like in Nils Olof's page where the zones alternate above and below the
horizontal center line, the results change when you reverse the mask L-R.  The
results are also different for a mask that is symmetrical around the center
line.  It appears that a primary contributor to these smallish errors in
(simulated) Foucault is the portions of the mask openings away from the center
line.  Currently, I'm running the test with individual mask pairs open.  (For
some reason I haven't figured out, my simulation runs off in one direction when
I use the full mask in place.)  I'm curious to find out how using the full mask
changes the results.

4. The most common shape of surface error in the Couder cases is a dip at about
50%, and a rise toward the middle and the edge.  Most often, the P-V error is
about 10 nm on the surface, which is larger than you found.  With some
combinations, this can be coaxed to go a factor of 2 or 3 higher.

5. As you found, too, these results are exactly opposite to what has been
showing up in the Foucault/interferometry comparisons.  It entirely possible
that we are running in to the limits of the simulation.

In summary, my experiments so far show that maskless Foucault with the knife at
50% cut is much more free of bias than a Foucault test with a Couder mask, and
that changing the orientation of the Couder mask can change the bias.  I'm
guessing that the taller the Couder mask openings, the worse the bias.

Another thing I have considered, but not proven, is that actual or test stand
astigmatism may be a contributing factor to errors in Couder readings.  If
there's enough astigmatism, the flip-and-diff circle can go up or down with
respect to the horizontal center line.  This could affect couder mask openings
differentially.

-- Steve
   steve_koehler@securecomputing.com

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