Re: [ATM] .707*Radius

[Mark Holm <mdholm@telerama.com>]

Jeff Anderson-Lee wrote:
> Also, if you turn off the refocus optimization, PLOP will tell you to 
> place three points at near 0.7R, to let's not bash on Hindle too hard.

For a 200 x 25, f/6 mirror with 39 mm diagonal, I get 0.642r and 5.93 nM 
RMS with refocussing off.  With it on, I get 0.395r, and 2.45nM Rms with 
-0.028mm focus shift.

If I do the Hindle thing, and force it to 0.7071r, I get 6.93 nM RMS 
with Refocus off and 6.84nM with it on. (Focus shift is 0.002mm.)

In the case where I fix the radius and don't let Plop optimize, I 
believe I should evaluate with refocus on, since that is how we use our 
telescopes.

So, I conclude that, even with refocusing turned off, Hindle is off by 
6.5% of the mirror radius (6.5 mm in this example) and it costs an extra 
0.91nM of RMS deformation.  If I make the wild assumption that this is 
the only source of abberation in the system, going from Hindle to Plop's 
non refocussed position would take me from a Strehl of 0.976 to 0.982. 
Surely, no one could notice that difference, but it is in the right 
direction.

Hindle may not have been so far off, but there is no reason to use his 
number when a better choice costs exactly nothing.

Allowing a 2 mm variation in radius and doing a 300 run Monte Carlo run 
gives the following worst case errors.

0.3951r nominal     2.46nM
0.642r  nominal     5.92nM
0.7071r nominal     7.28 nM

Hindle gets the worst of the Monte Carlo analysis too, though it is by a 
  pretty insignificant amount.

This Monte Carlo was set up with all three points varying the same, not 
really a realistic test.  I tried to set it up with separate radii and 
angles for all three points, but I must have screwed up.  Plop really 
didn't like that.  I got a BSD.  I think it is the first one I have ever 
seen from Plop.

In any case, I think one can conclude that the 0.7071 location is likely 
to come out worst on a more realistic Monte Carlo, because it obviously 
is located in a region of higher 1st derivatives.

Now I haven't mentioned the real loser in the 3 point, 200 mm cell 
design sweepstakes.  Texerau, quoting Couder I think, recommends a near 
edge location.  Lets call it 0.95r.  That gives 12.8 nM RMS with 0.028mm 
of focus shift and a Monte Carlo worst case of 13.3nM RMS.  At 12.8 nM 
Strehl drops to 0.916, a significant drop.

Actually, it looks like you could support this mirror with a 40mm 
diameter blob of silicone right at the center and do better than either 
Texerau or Hindle when the mirror is facing straight up.  I did six 
points at 0.1r plus one at 0.0r with refocussing on and got 4.2nm RMS 
with -0.044mm focus shift.  Now I doubt this would be much good as the 
mirror tilted because the torque forces would become high with that 
short moment.
-- 
Mark Holm
mdholm@telerama.com
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