Re: ATM [Fwd: Re: Mirror Cells for Amateur Telescope Makers]

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

Mark Holm had a discussion with Jonathan Dietch, see below

My comments;

Jonathan: P-V isn't the real issue here, neither is slope (for the
reason Mark outlines). RMS is a truer measure of the light deviated
from the "Airy disc"- and Dave Lewis points out , rightly, that it is
the RMS error that you should minimize. You say "You can have a 1/60
P-V surface that gives horrible images because the surface is very
wavy and not smooth" - a bit surprising to me - what kind of error
would that be? When I joined the ATM list in -97, there was an
interesting thread about a "sawtooth"-shaped mirror - it could be fun
going to the archives to read it.

Mark: The 1/4 wave criterion is not quite arbitrary, and anyway what
Rayleigh claimed was that here (talking of pure low-order spherical
aberration) is where deviations are getting "prejudicial" - not where
they get noticeable, as often supposed. In the case of a sphere (but
not with other aberrations!) 1/4 wave P-V corresponds to approx 1/14
wave RMS - half of this would be very hard to notice, ever (what would
you compare to?).
As for the width of the diffraction peak it is not much changed by
surface errors - the scattered light largely fills the system of rings
around it, the smaller the irregularities, the wider the spread.

Nils Olof

Jonathan :

> > Correct me if I'm wrong but to me P-V error is not the key factor
in cell
> > design.  It's the maximum tolerable contour slope deviation that
is the
> > issue.  What I am looking for is a contour that does not cause the
reflect
> > ray to deviate from focus by more than a small fraction of a
wavelength.
> > You can have a 1/60 P-V surface that gives horrible images because
the
> > surface is very wavy and not smooth.  I am not a math or
engineering guy.
> > Perhaps you can run some numbers on this?

Mark:
> >
> > This ground has been gone over many times by people who are much
better at the
> > theory and math than I.  I will try to explain.
> > 1. The ray theory of light is not sufficient when you get down to
the level of
> > forming good images with resolution near the theoretical best.
Slopes only
> > work with ray theory.
> > 2.  In wave theory, it is path length that matters.  In
particular, for a good
> > image, it is the difference in path length between the "rays" that
traverse
> > one part of the mirror and another.  The Raleigh criterion says
that for a
> > good image, the difference in path length from one part of the
mirror to
> > another, as measured at the final image, should not exceed 1/4
wave.  Now the
> > choice of 1/4 wave was somewhat arbitrary.  Over the decades
(almost centuries
> > now) since, experienced astronomers and opticians have found that
it is
> > possible to detect improvements in image quality due to smaller
deviations,
> > when those deviations are eliminated.  1/8 wave at the image is
much closer to
> > the real limit where getting any better is not going to help much.
Seeing good
> > enough to make use of a better optical system doesn't happen too
often in all
> > but a few locations.  1/10 of a wave at the image is a good
shooting point for
> > perfectionist ATMs.  I think Mel Bartels has a discussion of this
at his web
> > site.
> >
> > 3.  The theoretically astute say that RMS is a better measure than
P-V because
> > RMS weights the deviations by the amount of light that is affected
by a
> > particular surface defect.  Values for "good" RMS surfaces start
around 1/100
> > wave and go down.  For smooth figure errors, RMS and P-V usually
change pretty
> > much together, though it is possible to find examples of shapes
where the
> > difference between the two is fairly significant.
> >
> > 4.  ATM's discussing mirror figure usually assume a smooth figure.
What happens
> > if the surface is wavy?  Theoretical and practical work shows that
small scale
> > irregularities, waviness, scatter light at larger angles outside
the principal
> > diffraction peak than smooth errors.  So, a smooth 1/20 wave
(surface) error
> > will scatter light from the principle diffraction peak a little to
the side,
> > effectively widening and lowering the peak just a little.  1/20
wave ripple will
> > send the light more broadly over a larger area.  The central peak
will be
> > lowered about the same, but not widened so much.  The light will
show up farther
> > out in a wide blur.  The amount of light scattered is roughly
proportional to
> > the area that is high or low.
> >
> > 5.  The standards I state on my mirror cell web site are actually
pretty
> > conservative.  In his Sky & Telescope article introducing Plop,
David Lewis used
> > a criterion of 1/120 wave RMS at the surface as about equivalent
to 1/20 wave
> > P-V at the surface, or 1/10 wave P-V at the image.  This was the
maximum error
> > he was willing to let a cell introduce.  I usually use 1/40 wave
P-V at the
> > surface or 1/20 wave at the image, roughly twice as rigorous.  My
thought is
> > that cell design is usually easier to control than mirror figure.
Adopting a
> > more complex flotation design is less difficult than polishing a
good figure.
> > One might as well do something that is reasonably easy to preserve
image quality
> > in the hope that one will be able to make or buy optics good
enough to warrant
> > it and enjoy seeing good enough to make use of it.  A good
flotation system
> > can't make a poor figure better (Well except for the special case
of deliberate
> > mirror flexing.) but a poor flotation can make a good mirror
perform poorly.
> >
> > Requiring that your cell introduce less than 1/40 wave P-V error
is almost
> > certainly fooling yourself.  A. The cell probably won't work that
well anyhow.
> > You get into construction tolerances and the approximations in
Plop's analysis.
> >   B. Not many opticians can make mirrors better than 1/20 wave
(1/10 wave
> > image).  And that 1/10 wave has to be made at the sum of the
primary, secondary
> > and eyepiece errors.  C. Tube currents and atmospheric seeing will
limit you to
> > this level or worse a lot of the time, unless you have access to a
specially
> > good observing site.  To deal with tube currents, you really need
to put a fan
> > blowing across the front of the mirror.  There are a couple of
good Sky &
> > Telescope articles about this.
> >
> > That is the reasoning as I know it.