Re: [ATM] Worms in interferometry data

["Stephen Koehler" <s.c.koehler@gmail.com>]

> The above is a real foucault image (left) and one
> simulated from high resolution interferometry analysis
> (right).

I would like to make some comments on Dale's result, since I made an
unsuccessful attempt to do the same, which I posted on the ATM list.
Dale didn't give many details of what he did, so I will fill in a few.

Dale is using a Bath interferometer at COC and capturing
interferograms with many lines (about 150).  These are suitable for
the Fourier technique of analysis, which Dale's program OpenFringe
implements.  In my attempt to see the "worm tracks", I worked from a
single interferogram from Dale, hoping to use filtering techniques to
get rid of enough noise to see the tracks.  This failed.  Even with
noise reduction, the worm tracks were not visible.

Dale was able to eke out more detail by using averaging to reduce the
noise.  He took three interferograms at each of four rotations of the
mirror, analyzed each, then averaged the sets of three, and finally
counter-rotated the sets for a final average.  I believe the simulated
Foucault I created was based on an average of twelve interferograms.
Clearly, this technique reduced the noise enough to see the faint worm
tracks in interferometry.  If you stare at the pair of images Dale
posted, you can see many, many features in common.

Averaging reduces a few different kinds of noise.  First, a Fourier
analysis leaves some rippling, called fringe print-through.  Dale
takes the three interferograms in a set at three different fringe
angles to counter this.  Second, the interferograms show various
artifacts from dust on the interferometer optics.  By rotating the
mirror, these artifacts show up in different places in the
interferogram (with respect to the mirror), so averaging can reduce
the effects.  Finally, there is an overall graininess from laser
speckle on the interferograms.  Averaging also helps reduce this.

Finally, I think it's pretty interesting that this amount of detail
can be extracted from a Fourier analysis.  The fringes in these
interferograms are only about four to six pixels wide from fringe
center to fringe center.  The surface detail is represented as subtle
"wiggles" in these lines.  If Dale is measuring features that are 5nm
deep (surface), then they are 10nm/650nm of a wave deep on the
wavefront, which is 1/65 wave.  That means that the analysis is able
to detect wiggles in the fringe lines of 5/65 (or 1/13) of a pixel in
magnitude.

-- 
Steve Koehler
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