[ATM] data and musings on thin mirror

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

ATM and atm_free,

I have generated a few graphics that display some interesting results
from Dale's interferometry of one of David Davis' thin mirrors (the
coated one).  In short, I was able to separate out test stand effects
from mirror aberrations for one set of data.  Using this, I can show
the wild test stand effects for the second set of data.

First, some background.  Dale took 16 sets of interferograms at 22.5
degree increments with the mirror tilted back 35 degrees in his
18-point cell.  It was very hard to see any rotation in the results,
because of the wild test stand aberrations.  Dale then took 9 sets of
data (one half rotation at 22.5 degree increments) with the mirror
held vertically on 90 degree pegs.  Fortunately, the test stand
effects were pretty consistent, which has allowed me to derive the
test stand and mirror aberrations.

The first graphic shows the raw surface maps for the 9 sets of
interferograms.  I removed piston, tilt, defocus, coma, and SA
(because it swamps everyting else).  The index mark shows how the
features rotate with the mirror.  The annotation is P-V error.  Note
how the astigmatism grows stronger and weaker as the mirror rotates. 
This is because at certain angles, test stand and mirror astigmatism
cancel.

http://www.visi.com/~mkoehler/eason_davis_misc/davis.png

With data this good, I could use my algorithm to separate test stand
aberrations from mirror aberrations, which works on pairs of zernike
data at arbitrary rotations.  The next graphic shows the test stand
aberrations derived from each possible pair (0:180 is not allowed). 
In these images, blue is higher than green.  In general, there is a
raised area at the top of the mirror (due to flop on the test stand)
and a raised area near one or both of the lower pegs.  There is fairly
good consistency in P-V error.  The final frame shows an average
derived from the 36 individual calculations.  So, the test stand
imparted about 1 1/4 waves P-V of error.

http://www.visi.com/~mkoehler/eason_davis_misc/davis_stand.png

The next graphic shows the nine surface maps with test stand (and SA)
removed.  Now, the astigmatism stays constant and rotates with the
mirror.  Finally, we have success in estimating mirror primary
astigmatism.

http://www.visi.com/~mkoehler/eason_davis_misc/davis_stand_removed.png

The next graphic gives a summary of test stand (left) and mirror
(center) aberrations.  The mirror is an average of all nine
orientations rotated to line up.  Yikes!  There are 6.8 waves P-V of
error when spherical aberration is included.  The right frame shows
mirror aberrations with SA removed.  On this mirror, primary
astigmatism is large, but SA is larger.

http://www.visi.com/~mkoehler/eason_davis_misc/davis_summary.png

Now that we have believable reading of the mirror aberrations
including astigmatism, this can be used to try to understand what went
wrong when the mirror rested in Dale's mirror cell.  I accomplished
this by subtracting off the mirror aberrations (rotated appropriately)
from the 16 surface maps from the cell data.
The following graphic shows the result.  It attempts to show the test
stand aberrations imparted by Dale's mirror cell for 16 separate
placements of the mirror.
P-V error ranges all over the map from 1.5 to 6!  In about 1/2 of the
frames, the cell-induced aberrations are relatively small (less than 2
waves).  In the other half, there is an odd 45 degree astigmatism that
looks very much like it is caused by the mirror hanging up on one of
the other of the pegs.

http://www.visi.com/~mkoehler/eason_davis_misc/davis_stand_cell.png

One interesting point to take away from this is that at its best,
Dale's cell angled at 35 degrees from vertical imparted at least 1.5
waves P-V of error, which is huge.  It seems likely that the large
error is due to some aspect of the edge support pegs, not the back
support.  The lesson here is that very thin mirrors are tricky to
support properly.

--
Steve Koehler
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