[ATM] How much cell induced deformation is too much?

[mdholm@telerama.com]

We have Plop, which will predict cell induced deformation, at least under
certain circumstances.  How do we decide when a cell's performance is good
enough?  I'd like to hear various thoughts on the subject.

Some ground rules: 1. RMS only, unless you have a darned good argument to the
contrary.  It took me more time than it should have, but I now realize that RMS
is usually the right way to evaluate these questions.  2. Nanometers only.  It
is to fuzzy talking wavelengths when we all might be referring to different
wavelengths.  Besides, Plop reports in absolute units, not in wavelengths.

I am aware of the rough correspondence between the Raliegh criterion and 1/14
wavlength RMS (is that the Marechal criterion?).  (Can't put the Raliegh
criterion in absolute terms, because it is defined in reference to wavelength.)
 I am aware that the 1/14 wave RMS criterion applies to the wave front, not the
mirror surface.  I am aware that the 1/14 wave value corresponds to a Strehl
ratio of about 0.80, and that cutting the limit in half (1/28 wave) gives a
Strehl of about 0.95.  I assume that, to apply to the mirror surface, it is at
least approximately correct to cut the numbers in half again, because of the
near doubling of path length caused by reflection.  Thus, the values become 1/28
wave and 1/56 wave surface for Strehl = 0.80 and 0.95.

Assuming a wavelength of 500 nM, 1/56 wave equals 9 nM.  I am aware that
uncorrelated RMS values add as square root of sum of squares.  I assume that, if
one wants a Strehl of 0.95 at the final focus, then (neglecting spider
diffraction that I don't know how to factor in) the criterion is 

SQRT(Mirror RMS ^2 + cell induced deformation RMS ^2 + Secondary RMS ^2) <= 9nM

Is this Right?

Is 0.95 Strehl at the final focus realistic for good optics, or is this pie in
the sky?

What are realistic RMS values for good, medium and not so good atm and
commercial mirrors.  I was looking at the mirror test results on the OMI web
site as a way of getting some data on decent commercial mirror quality, but I
realize they give results in waves, and do not specify the wavelength.  Anybody
know if they reference HeNe laser (633nM) or something else?

Anybody got an idea how decent commercial diagonals run?

If the typical decent primary and typical decent secondary already add up to
worse than Strehl 0.95, there isn't much point holding the cell induced
deformation to unrealistic limits.  On the other hand, one wouldn't want to ruin
the performence of a really good set of optics with a bad cell.  I am thinking
that a realistic criterion for maximum cell induced deformation is going to be
somewhere in the range 1 to 5 nM.

I'd like to see reasoned thoughts on the subject.

Mark Holm
mdholm@telerama.com
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