Re: [ATM] Calculate Astigmatism

[Michael Peck <mpeck1@ix.netcom.com>]

At 11:07 24-03-04 -0600, Stephen C. Koehler wrote:

> > 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 don't understand the need to not disturb the apparatus over a mirror
>rotation.  Couldn't you use the measurement of the center zone on each data
>set as a baseline, or at least make the assumption that your innermost zone
>is not much affected by astigmatism?  This would eliminate the need to
>maintain the test rig distance over a mirror rotation.
>

OK, I've posted some pictures that I hope will show why this doesn't work.

Here's the setup. I have a 16" (400mm) f/5 paraboloid with 25nm rms (on the 
surface) of primary astigmatism. That's about a half wave peak to peak on 
the wavefront, an unacceptable amount. I've oriented the astigmatism so the 
"X" and "Y" axes have the maximum departures from the nominal curve.

Figure 1 <http://home.netcom.com/~mpeck1/astro/temppix/fouc_astig.png> 
shows the moving source Foucault readings for the X and Y axes (green and 
red, respectively), measured as offsets from the nominal center of 
curvature. Notice at this scale the readings are simply offset from each 
other by a nearly constant amount, which in this case is slightly under 0.1mm.

This is shown at larger scale in Figure 2 
<http://home.netcom.com/~mpeck1/astro/temppix/fouc_offset_astig.png>, where 
I've subtracted the nominal readings for a perfect paraboloid. It's this 
essentially constant offset in the readings that contains whatever 
information your zonal test has about primary astigmatism. If you can't 
measure this, you aren't measuring astigmatism.

Suppose you do as Steve suggests, and anchor the measurements at the 
center. Figure 3 
<http://home.netcom.com/~mpeck1/astro/temppix/fouc_dev_astig.png> shows the 
deviations from ideal measurements, with the Y axis scale now in microns. I 
hope everyone realizes that 0.12 um difference at the edge is entirely 
negligible.

Measuring the constant offset of 0.1mm in Figures 1 and 2 should be 
feasible, provided - as Dave, Jim and I have suggested - you can measure 
multiple diameters in one test run somehow. Remember though this will give 
you a measurement of a ruinous amount of astigmatism.

Having recently joined the burgeoning ranks of amateur interferometrists 
myself I'd say that if you really think you have reason to suspect 
astigmatism in your optical products you should probably be thinking about 
doing interferometry (or some other whole mirror test). If I can assemble 
one anyone can.

Mike Peck

_________________

Michael Peck
email mpeck1@ix.netcom.com
Wildlife photography page http://home.netcom.com/~mpeck1/index.html
Amateur telescope making http://home.netcom.com/~mpeck1/astro/astro.html

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