Re: ATM aargh! maybe

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

Mark Holm wrote:

> RMS is a better predictor of
> image formation.  As I understand it, RMS essentially weights the
magnitude
> (height) of a surface error by the amount of area that error covers.
So, if you
> have two zones of equal height above (or below) the best fit
parabola, the one
> that covers more area contributes more to the RMS error.  This also
corresponds
> to the amount of light reflected by each zone.

Yes, but there is more to the Root Mean Square than that. The
deviations are squared before they are "meaned" and twice the
deviation means four times the contribution (before "rooting"). Now,
using the second power here is no coincidence - what determines the
"irradiance at the Gaussian focus" is the integrated in-phase
contributions from each surface element, and since the cosine is
approx 1-x^2 where x is the phase error or wavefront deviation, the
mean squared error is a good indicator of the loss of coherence that
lowers the diffraction peak (I *believe* the sine terms cancel at best
focus). So if 400 square nanometers lowers the peak by 20%, 100 square
nanometers lower it by 5%, and so on - but for very large errors, this
approximate relationship breaks down (where fourth-order terms becoms
significant).
>
> The problem with RMS is that it doesn't give any guidance about
where you need
> to have polishing action.  When I am looking at a Foucault test
result plot and
> trying to decide what to do next, RMS and Strehl are good for
deciding whether
> to stop.  P-V, and, of course, the locations of the high or low
zones tell you
> about how much, and where you need to remove glass.

I can't see how the P-V value would be more helpful. Sixtests plots
the profile,  but Figure lets you move the focus to make the excess
glass appear at center or at the edge, for instance.

>  So, it is easy to think,
> "When I get that curve so it all lies within x nanometers, I'm
done."

I'd say it is as easy to think: when sixtests/figure says RMS less
than 10 nm, I can stop - unless of course the profile suggests I could
try do better (if you do, you will probably regret it  ;-)

> Sixtests
> will do a plot with the surface deviations scaled according to RMS.
It usually
> shows that errors near the edge are more important than ones near
the middle.
> That is useful guidance.
>
> I usually use 1 wavelength = 500nm.  According to what I have read,
500nm is
> very near the peak of the sensitivity curve for dark adapted human
vision.
> Daylight vision has its peak of sensitivity near 560nm.

Yes, but even if averted vision peaks near 500 nm, the resolution is
pretty low and diffraction is almost never an issue.
>
> http://www.atmsite.org/contrib/Holm/vissens.html
>
> Also, 500 is an easier number to remember and plug into a
calculator.  It is
> easier to remember the fractions of 500 too.  1/4 wave = 125nm.
1/10 wave = 50 nm.

YMMV. But evaluation programs that give results in fraction of
wavelength must necessarily assume a reference wavelength. Using
nanometers bypasses this completely.

Nils Olof