ATM Rumak Fabrication Tolerances (long)

[Aplanatic@aol.com]

I have taken a look at the Rumak design given in "Telescope Optics" by Rutten
and van Venrooij.  Of particular interest to me is the required accuracy of
fabrication of the various components, especially the corrector meniscus, and
methods of achieving these required accuracies.  The Rumak design in R and vV
is an 8" f/15 and has about 9.5" of back focal length (BFL).

First, as a side note, the Rumak performs very well indeed at its designed
f/ratio of 15, and all surfaces are spherical, which I consider a significant
fabrication advantage.  I tried varying the f/ratio of the telescope while
maintaining the same BFL and found that designs down to about f/10 can be
implemented with diffraction limited performance by tweaking the meniscus
thickness and radius of curvature (RoC) of the two meniscus surfaces, always
keeping them spherical.  Chromatic aberration remains very small for designs
in the f/10 to f/15 range.  Images to the edge of a 35mm film frame are
essentially diffraction limited in this f/ratio range.

I then intentionally varied the RoC of one of the meniscus surfaces.  The
tolerance on each of meniscus surfaces, individually, is about 0.03% to
maintain diffraction limited performance, for designs from f/10 to f/15.  If
both surfaces vary together, with the same percentage change, then the RoC can
vary as much as 2%.  In other words, making a small scaling error, in a
spherometer for instance, is not a disaster, per se, as long as the error is
in scaling and is consistent between the convex and concave surfaces.

I then varied the thickness of the meniscus, and found that the tolerance is
about 0.2 mm.

In each case above, the problem introduced by inexact meniscus fabrication is
an increase in the spherical aberration of the system, with little or no
change in the off-axis performance.  This suggests that the optical system can
be "tuned" by on-axis measurements in the final figuring steps.  Indeed, when
the RoC or thickness of the meniscus is intentionally varied from ideal, then
corrective measures can be taken by 1) changing the RoC of either surface of
the meniscus, or 2) aspherizing the secondary.  Apherizing the primary is not
recommended because of its large effect on the off-axis performance.  In fact,
the primary must be quite spherical for excellent off-axis images.

The 0.03% tolerance on the RoC of the meniscus appears to be the most
difficult part.  Other fabrication errors can be compensated for, to a large
degree, by a "tweak as you go" plan.  In other words, I would make the primary
and secondary mirrors and measure the RoC of these components before making
the meniscus.  Then, a final design of the meniscus can be made.  During
meniscus fabrication, the center thickness can be monitored and slight tweaks
to the RoC of the meniscus surfaces can be made in real time, determined by
the final measured meniscus thickness.  This is probably best done at
something like 400 grit with some compensation made for the material expected
to be removed in final grinding and polishing.

This leaves the meniscus RoC as the final problem.  If RoC measurements can be
accurately made, then it's only a matter of a great deal of patience in
achieving the desired RoC of each surface.  However, I fear that the accuracy
of the RoC measurement will be the limiting factor even with a decent,
machined spherometer.  Why?  I have looked into the accuracy of various linear
measuring devices such as dial indicators and micrometer screws.  Without
getting into the complexity of an optical micrometer, the accuracy of these
mechanical devices is on the order of +/-200 to +/-400 microinches over a
travel of about 0.5".  Since the sagitta of the meniscus is about 0.6" for the
8" aperture telescope, a sagittal measurement error of 300 microinches
corresponds to a 0.05% error in the RoC of the surface.  Since systematic
errors are expected to be on the order of several hundred microinches, the
total expected error for each surface may well be as much as 0.08%.  Since the
RoC measurement error of the second surface can deviate in the wrong direction
from the first surface, one must allow for as much as 0.16% total error,
differentially, between the two surfaces.  This is, of course, a disaster.
Spherical aberration will be enormous with this much error.

So, the optician, I believe, is faced with a figuring problem.  The telescope
can be assembled and tested and the final meniscus surface (or perhaps the
secondary) can be "tuned" for performance.  There are two problems with this.
First, it requires a test method.  Autocollimation null testing would be the
prefered approach but then an optical flat of some kind is required.  Perhaps
a Mercury/oil flat would do.  Star testing is a possibility but has
atmospheric turbulence involved and is quite inconvenient.  Interestingly, a
distant point source is a possibility, as the required distance to the source
for an 8" f/15 scope is only about 10 meters for 1/8 wave accuracy and 30
meters for a f/10 scope.  Secondly, if the RoC of the final surface needs to
be changed by 0.16%, a lot of glass must be removed, requiring, I think, a
retreat to fine grinding.

Dave Rowe
Torrance, CA