Re: ATM Ronchi and Figuring (Which Witch)

[Anthony Stillman <atmer@flash.net>]

Scott Rychnovsky wrote:
>If the tool never touches the edge of the mirror, but does work the
>central area, then the ROC of the center will get shorter while the
>ROC of the edge will be unchanged.


The subtle subtext of Scott's post is, usually for ATMs, any radius
paraboloid will do.  As long as it goes to the edge.  The very edge.  A
razor sharp edge.

I thought I would pointlessly elaborate.

Consider a paraboloidal mirror with osculating radius R1.  The derivative
of the profile (a parabola) of this mirror is a straight line with slope
1/R1.  Now, dig out the center of the mirror to the seventy percent.
Again, make this shape paraboloidal but with a shorter osculating radius
R2.  The derivative of this parabolic profile is also a straight line, but
with slope 1/R2.  The two curves are continuos, but the slopes, the first
derivatives, are discontinuous at the seventy percent zone.

Now lets look at this mirror under the ronchi or foucault(1).  Using the
outer zones as a guide shows, inner zones as over-corrected.  Using the
inner zones as a guide, shows the outer zones as under corrected (turned
down), just as Scott wrote.

It might be argued that such a discontinuous surface is not physical, that
it wouldn't happen.  Of course only a theoretical physicist would argue
this, and they would never be allowed to touch a mirror, as it would break
in their hands, likely at the
70.71067811865475244008443621048490392848359376884740 percent zone.
(Obviously, I had to round this off a bit.  Sorry)

So, what to do with this piece-wise piece of crap mirror.  Try working MOT
and continue to dig out the center, pushing the correction out to the edge.
This will "choose" the shorter osculating radius for the mirror.  And,
though someone else might have good luck doing this, if I did it, by the
time I had the edge properly corrected the center would be over-corrected.

I could use a sub-diameter star lap, TOT and work the ridge. This has the
interesting effect.  Assuming I feather the stroke properly(2), in addition
to pushing down the 70 percent ridge zone, I lengthen the osculating radius
of the center zone and shorten the osculating radius of the edge zone.
That is, by not working the edge, I turn it up.  And, the osculating radii
of the two zones are averaged.  A totally pointless objective.

Anthony


1) If these are slope tests as is so often said, how is it then that under
autocollimation or when using a plane wave, a paraboloidal mirror shows
straight ronchi lines and an evenly gray foucault?

2) As if I could.  In generally I end up with three zones and two ridges.
But, I can fix that.  All I have to do is use smaller tools ;-)