Re: [ATM] Calculate Astigmatism

["David Harbour" <scarab2@cox.net>]

This is what I was trying to remember; now I remember it.

Professor Schwartz, Jack of all trades, has reached back into the infinite
recesses of his massive cranium, again, and surprised at least me (or
rather, I guess, has not surprised me), with some very lucid and wonderful
stuff, here. Well done, Doktor- the DEFINITIVE ANSWER to the entire
question.

Davey

----- Original Message -----
From: "Richard Schwartz" <richas@earthlink.net>
To: "Michael Peck" <mpeck1@ix.netcom.com>; <atm@atmlist.net>
Sent: Thursday, March 25, 2004 5:17 PM
Subject: 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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>
>
>
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