Re: [ATM] Calculate Astigmatism [and: Interferometry]

[Aplanatic@aol.com]

Greetings,

Mike Peck writes:

> Let's cut ourselves some slack and multiply that by a factor of 4. So to
> measure primary astigmatism to even maximal tolerance we'd have to measure
> radius of curvature differences to ~0.05mm. That might not be so difficult
> *if* you measure two or more diameters without disturbing your apparatus.
> But when you do a zonal test on a single diameter, rotate your mirror, then
> fiddle the tester to relocate the light cone you're almost certainly
> throwing away the ability to make differential measurements to the required
> accuracy.
> 
> I think Dave Rowe made a couple of pretty good posts on precisely this
> subject on the Yahoo group ATM_Free last week. Alas for the innumerate
> among us, he used pretty much the same scary math as Jim.

Yikes!  I just re-read what I wrote.  It is, unfortunately, scary and hard to follow.
 
> This seems to be an ongoing source of confusion for ATM's and even some
> pros. I suspect it's because people don't (or can't) work through the
> arithmetic, and don't quite understand the distinction 
> between primary and
> higher order astigmatism.

Yes, the amateur TM community has this significant test problem.  As we make mirrors larger and thinner, primary astigmatism becomes a big issue.  We can inadvertently grind and/or polish it into the glass itself, or we can mount the mirror poorly and let gravity do it for us.  In either case, being able to understand and test for primary astigmatism is, I think, an important aspect in designing and fabricating large, lightweight telescopes.

So, I've recently completed a modified version of the Bath interferometer.  The common-path nature of this interferometer has significant advantages, I think, over the Fizeau and Twyman-Green types.  It is very easy to setup and use, the fringe contrast is always excellent and it works nicely for both coated and uncoated mirrors without the need for additional attenuation in the test beam.  Best of all, it works in white light.  No laser is necessary.  It has one disadvantage: the test-beam foci are not on the optical axis.  This creates test-induced astigmatism.  For most situations this effect is small and can easily and safely be removed in software.  See the postscript.

If you really want to measure and understand astigmatism I recommend that you make an interferometer.  Fizeau, Twyman-Green or Bath all work fine.  You can then use FringeXP or Mike Peck's RFringe to reduce the data.  It's a wonderful and rewarding project.  I've already learned strange and wonderful things that I'll share with you as my understanding and experience progresses.

Dave Rowe

PS  I've derived a formula for calculating the effect of the off-axis beams on the Zernike coefficient for astigmatism.  I'd like an independent analysis or two.  If you're interested please contact me.


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