ATM divergent collimator null idea

[Aart Olsen <aolsen@prairienet.org>]

I was reading Suiter's Star Testing book the other day when it made me
recall a variant of the Waineo null test that first occurred to me a few
years ago -- probably this isn't new.  I'm not clever enough to analyze it
or see if it is practical or possible, but no doubt the ATM list can
figure out the details:

To test a large mirror you point it at a finished 6 inch (e.g.) telescope
used as diverging "collimator".  Put an illuminated pinhole inside the
focus of this telescope and adjust the focuser so that beam spreads to
fill the aperture of the large optic under test.  This divergent beam will
be undercorrected because, while a hyperboloid is needed to produce a good
divergent wavefront, the telescope's mirror is a paraboloid.  On the
receiving end at the mirror under test the beam will appear to come from a
point at a finite distance and will come to focus outside the normal
infinity focus, farther away from the mirror.  At this finite focus a
parabolic mirror is overcorrected, because it's being focused as we
normally use a prolate ellipsoid.  So the questions are:

By positioning the foci can the undercorrection of the divergent
collimator be made to cancel the overcorrection of the near focused mirror
under test and create a null?  Is the sign even correct, i.e. might the
two correction errors add instead of cancel?  This is like the Waineo null
test but you're defocusing a parabola to produce SA instead of using a
sphere's inherent SA. I guess the amount of under- and overcorrection
depends on the half angle of the divergence, but I don't have a good feel
of how it relates to the f/ratios of the collimator and mirror.  If the
collimator is f/8 and needs to fill a larger f/4 aperture, at what
divergence does the undercorrection of the f/8 cancel the overcorrection
needed by the f/4?  It would be really sweet if some of this were
"automatic", e.g. if the under- and overcorrection cancel whenever the
divergent beam becomes congruent with the convergent beam of the mirror.

If it's possible, would it be practical?  In some respects it seems
handier than the Waineo test because most people don't have a perforated
test sphere but many do have a decent small telescope.  Pinhole and knife
edge placed in telescope focusers seems straightforward, although
mechanical errors and flaws in the secondary mirrors would confound the
test.  I can see making a dedicated collimator with the lighted pinhole
held in a spider hub near its prime (unfolded) focus, to get rid of
several potential errors.  At the other end, using the test mirror's
intended secondary allows you to correct the primary + secondary
combination (which has the interesting property of being simultaneously a
really good and a really bad idea!).  Are errors easy to spot?  You can
star test the mirror on the collimator's pinhole and that should reveal
many types.  Might testing be as simple as cutting a piece of ronchi film
in half, putting one piece in the collimator and the other piece at the
mirror under test, infocusing the collimator some amount, focusing the
mirror's ronchi so that its line count matches the collimator's, and if
the edges are straight your optic is good.  I'm not smart enough to pursue
this.  If the collimator is 1/10 wave is the null sensitive enough to see
a known fraction of this error on the test optic?

A good six inch mirror may not be available, but how about a lens and
monochromatic LED, i.e. a variant of the Dall test?

Thoughts?  My daughter points out that this is a bit like a wall eyed
person trying to make eye contact with a cross eyed person and, after
figuring it out, falling in love.  A very nice analogy, but it remains to
be seen whether it's a good match.

Aart Olsen
aolsen@prairienet.org