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Re: [ATM] Calculate Astigmatism
I guess nobody gets it about the tilted mask with apertures that look like
O
O
where the foucault tester is zeroed, and then
O
O
where the reading is taken. (Sorry for the ascii art here.)
This provides the radius of curvature across two perpendicular axes of the
mirror. If the two readings are the same, there is no astigmatism in
those axes.
I'm not smart enough for all that complicated Zernikie stuff, but I fugger
that if the sagitta of a mirror is within 1/20 wave, you are probably OK.
>From my ham radio days, I remember a formula for the range of a UHF radio,
r = sqrt(2*s*R), where s is the height of the antenna above the earth, and
R is the radius of curvature of the earth.
Lesseeee... using that same formuler gives R = .5*r^2/s. So how much
change is there in R if s changes by about a micro-inch?
Differentiating, I get dR/ds = -.5*(r/s)^2. (Assuming a vertical knife
edge) r is the horizontal distance of the mask aperture from the mirror
center.
Example: you have a 13" f/5 mirror. Then R is 130". Suppose you have
1" mask holes at the edge zone of the mirror-- then the center of holes is
about 6" from the center of the mirror, and the horizontal distance is
6/sqrt(2) = 4.24". The corresponding sagitta is .5*4.24^2/130 = .069".
Prugging this into the above formula for dR/ds gives -1875 for the
derivative. And multiplying this by ds = .000001" gives a dR = .0018". I
leave it to the community's judgment if .0018" is measurable on a foucault
tester; for some of you it may be pushing your luck or imagination, but
some of you are magicians who can see the legendary dusky markings on Io.
However, one thing is for sure: you must not disturb the mirror or the
tester when you rotate the mask 90 degrees. This can be easily done with
a test setup wherein the mask is not contacting the mirror or its test
stand.
Note that this measures only one of two components of astig. To measure
the other component, you must rotate the mirror 45 degrees in its test
stand and repeat the test. The overall astig is the root-sum-square of
the two components.
. . . Richard
> [Original Message]
> From: Michael Peck <mpeck1@ix.netcom.com>
> To: <atm@atmlist.net>
> Date: 3/25/2004 9:25:29 AM
> Subject: Re: [ATM] Calculate Astigmatism
>
> 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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