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

["Nils Olof Carlin" <nilsolof.carlin@telia.com>]

Mark,


> 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.

Agreed!

For small deviations, strehl ratio (see Suiter p. 238) is appr=1-(2*pi*d)^2
where d is the (total) RMS wavefront deviation. Thus the lowering of the
strehl ratio is proportional to the mean square deviation (not the root of
it!!!) - ensuring that the worst error tends to dominate the total. Also,
the various sources add (or subtract, rather, here) more or less
independently, and e.g. the cell contribution will lower the diffraction
peak by a certain percent of the ideal (assuming an independence that I
think makes sense) regardless of how much other aberrations contribute.

So, if we would let the cell lower by say 1% (to 0.99 for a perfect mirror,
or from 0.95 to 0.94 for a more realistic one), how much RMS wavefront
error - assuming a reference wavelength of 550 nm, near the peak of photopic
vision? I get some 8.7 nm, or a little more than 4 nm on the surface. This,
4 nm RMS, I think could be a practical upper design limit for PLOP, allowing
some realistic margin for less than perfect implementation. But then again,
this is quite arbitrary.

>
> 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?

Seems quite realistic to me.
>
> What are realistic RMS values for good, medium and not so good atm and
> commercial mirrors.


I suspect MMMMs (mass market mirror makers) publish some kind of design
goals rather than actual measurements. But there are craftsmen that make and
test their individual mirrors and give guaranteed specs of different kinds.

I'd like to think of worse than 20 nm surface RMS as unacceptable (below the
Marechal limit, really rather lenient), and 10 nm as a limit between
acceptable and good. But that's one of many possible opinions, and we're
after all talking of measuring some VERY small quantities!

Nils Olof


_______________________________________________
ATM mailing list http://www.atmlist.net/