[ATM] Re: Satisfying "Mililes-Lacroix" is neither necessary norsufficient for "diffaction-limited" performance

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

Mike,

>The next question I have is, does satisfying "M-L" do anything more than

force you to work a little harder? Maybe you would do just as well by 
setting your standards for measured RMS wavefront error higher while 
completely ignoring slope errors. I think that's the route Jim Burrows
has 
advocated taking for some time.

On the other hand, I would have no trouble making an argument based on
wave 
optics that slope errors (or more precisely high spatial frequency
defects) 
do matter so you should certainly look at them. But, on the third hand I 
strongly suspect that given the limitations of the Foucault test and most

amateurs' skills the only real practical benefit of satisfying "M-L" is 
that it's more conservative than the "1/4 wave P-V" or "1/14 wave RMS" 
criterion.<

I haven't really pondered into it; more just a "fly-over" as usual. My
views come
more from logical thinking than studying the subject. So, don't hold me
responsible for 
typographical and other errors :) Potential problem I see with relying on
the slope error 
alone is that it doesn't necessarily reflect surface deformation with
sufficient accuracy, 
being difficult to detect when limited to narrow zones. In other words,
we can have 
nearly perfect slope  over 95% of the wavefront, and still have less
than negligible atlteration of wave interference in the focal zone, due
to 
slight radial (along r.o.c.) surface/wavefront displacements ocuppying
relatively 
significant area. But, then, that same difficulty would add to the
inability 
to obtain reliable RMS error from Foucault data. I wouldn't say there is
a way around it,
without resorting to some other method of determining surface/wavefront
profile.

Another good reason for the RTA standard to be more conservative than a
smooth 1/4 wave 
p-v error (other than compensating for measurement errors) seems to be
that  actual mirrors
are not likely to have it distributed quite smoothly, which requires
somewhat smaller error 
for nearly identical end result. Such profile of a realistic surface also
alters zonal geometric blur 
values vs. near-perfect conic, without it necessarily implying an
inferior surface performance-wise. 
In other words, it is probably easier, from the standpoint of actual
mirror making, to set a more conservative 
general blur standard for imperfect actual surfaces (vs. corresponding
near-perfect conic), 
than to set it according to a perfect conic and have to chase appropriate
near-perfect 
conic all the way through the parabolizing process. 

As you said, blur at the location of the circle of least confusion nearly
equal to the Airy disc implies 
0.046  waveront RMS error at the best focus, but only if the case of pure
spherical aberration. 
That is, only for a surface that is near-perfect conic. Actual mirrors
will likely be more or less deviant, 
which means that we can't count on that "best focus" anymore. Actual best
focus can be better, 
but chances are it will be worse than that. I don't know how Texereau
arrived at the RTA~1 or less standard, 
but him being so meticulous, it likely resulted from a number of
practical tests. That is exactly what we are
missing here, in order to come up with a specific conclusion on the
ralation - at least statisitical - between 
the RTA~1 standard and 1/4 wave criterion: results of analysis of a
number of actual mirrors with known Foucault 
test data and (reliable) RMS surface error.

Vlad

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