ATM Re: Pegasus Answers to Cert Questions

[Bratislav Curcic <epabcc@epa.ericsson.se>]

Despite the colorful language, the (rightfully deserved) reputation of
Pegasus and John Hall, and the fact that his mirrors have proved
themselves as excellent performers again and again in the field, I
still have problem with claims of achieving 1/100 wave peak-valley
repeatability at the wavefront using Foucault test.
If things were so easy, people wouldn't NEED to invent better tests.
And we all know that optical books are full of strange looking setups,
all in search of that elusive perfect test.

One fact stays very clear : in capable hands, Foucault tester will
enable optician to reliably manufacture and verify even large amateur
mirrors (of moderate f/ratio) to 1/10 of wave (on the front). Another
fact is, even marginally good (ubiquitous 1/4 p-p, 0.8 Strehl or 1/14
RMS) LARGE mirror is essentially perfect as atmosphere will almost
never let us enjoy a 20+ inch wide window with 0.1 wave or better
seeing. It would be almost impossible to distinguish between 1/100 wave
miracle 20 incher (I seriously doubt there is more than handfull of
these in existence, if any) and a smooth 1/4 wave one. At least using 
Earth based observations, that is.

Make no mistake, getting a 20" piece of glass within 1/8th of a
wavelength relative to a perfect paraboloid is no piece of cake. It may
take an experienced TN only few weeks of figuring, but let's not forget
years of experience she/he's gained before.

I will also quickly comment here on testing methods that John mentioned :

> (3) A diffraction-limited tolerance, in which every part of the mirror
> must direct its light within the boundary of the diffraction disk. The
> Rayleigh criterion, according to H. R. Suiter in TM 32, is "noticeably
> imperfect" and the diffraction-limited tolerance is "sensibly perfect."

It was Suiter himself who commented not long ago that this so called
"diffraction-limited tolerance" ISN'T perfect. In fact, if we read
carefully Texearau he says that this part of the criteria of
Danjon-Couder is easier to get right for large mirrors than a 1/4 wave
one. If I understood John correctly, his #3 method is in fact inferior
to #2 one (Danjon-Couder), which actually incorporates both Rayleigh
(#1) and "Relative Transverse Aberration" (#3).

Incidently, having "every part of the mirror directing its light within
the boundary of the diffraction disk" will NOT ensure diffraction
limited performance, as it is possible to prove that we can
make such mirror and still have Strehl ratio _below_ 0.8. And this is
widely accepted as "industry standard", if there is one at all.

Bratislav