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

[Vladimir Sacek <vladis.2@juno.com>]

John, you may be tired of reading books, but it's all different story
when it comes to writing :) Let me address the core of our disagreement:

> I say it IS worthwhile to strive for a superb surface and figure on a
large mirror, and to mount it as well as you can. It is possible to buy
or make a large mirror with a Strehl in the high 90's. It is very
desirable to own one of these mirrors. Because you can see the
difference. We should address those problems you mentioned and minimize
them, as you said. But I think that we can !
 achieve a final wavefront error much better than 80%, and I'm sure we
are achieving well over 90%. <

There is no reason not to strive for a superb mirror and cell. My point
was that after the error has been reduced to a certain (very low ) level,
there is no practical gains from investing into further error reduction. 

Seems that your final error figure for a large telescope is something you
wish for, rather than something you arrive to by the means of any sort of
analytical consideration. It is easy to get an idea what is an expected
level for the total error in a larger telescope.
The simplest way is to use square root of the sum of all the errors
squared. Although not quite exact, it is good for the illustration. The
following are some of the common error sources, with errors quantified in
rather optimistic manner for ~20" f/4.5 amateur reflector.

Primary 1/25 wave RMS wavefront, flat 1/25 wave RMS, pinching 1/30 wave
RMS, thermal 1/20 wave RMS, miscollimation 1/20 wave RMS and 1/13 wave
RMS seeing.
Cumulative error from these sources comes to ~1/8 wave RMS ( 1/2.4 wave
spherical aberration level), resulting in 0.55 Strehl. Add a couple of
degradation factors: for 17% c.obstruction (0.94), cell induced error
(0.97 for both, primary and flat) and scattering on the coatings (0.98,
although can be significantly more for older or improperly applied
coatings), and we arrive at the final Strehl of ~0.50. 

It is almost as bad as 1/2 wave of spherical aberration. But the star
test still can appear near-perfect, except for the roughening caused by
the seeing. The reason is that all of the error contributions are quite
small, hard or impossible to detect. For instance, the 
1/25 wave RMS error at the primary comprises spherical aberration,
astigmatism, zones, TE and random wavefront irregularities. Share of the
spherical aberration may be as little as 1/35 wave RMS (~1/10 wave p-v)
or less: very hard to detect isolated, and nearly impossible mixed with
other errors, especially with this aperture size, requiring very high
test magnfication under relatively large seing error. And nothing much
will change if the primary is 1/50 wave RMS. Primary needs to be closer
to 0.80 (actual) Strehl, to begin to make a difference to the worse. And
if it is ~0.50 Strehl (not as rare a bird as you might think), it would
definitely make noticeable difference.

A 0.50 Strehl total error doesn't mean your 22" would produce bad images.
In theory, it would be as good contrast/resolution-wise as 13"-14"
perfect aperture, enhanced by extra light-gathering power. That would be
quite powerful instrument. 

Thanks for the invitation. It is tempting, for selfish reasons. Seems
that your telescope has power to make people happy, and that's about as
good as a little golden fish fulfilling all the wishes. You don't want me
to come; I might as well want to keep it for myself...

Vlad
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