Re: [ATM] [atm_free] RE: data and musings on thin mirror

["Jerry" <wa4guu@verizon.net>]

Steve

That is neat. I like it. I will have to play with your method a bit more to
make sure I understand 100% correctly. It looks good so far. And for sure
the line number "difference" (and f# and grating line density) is the
answer. For a given f# and grating line density, the number of lines showing
indicates the distance to the COC. The line number "difference" indicates
the distance between COCs. In the case of the 16 inch ultra-thin each line
is worth .068 inch from COC.

I was using ratio because I started with the .15" COC to grating distance
that Dale gave. And then I figured the difference of center and edge COC by
ratio. I just quickly judged a 2:1 ratio and that meant .075" correction. 

Of the various estimates that I made, the closest was the one where I
calculated the distance the grating should have been for the number of lines
that the cone would illuminate on the grating. Using diameter 16" and radius
of curve 110.5" and a 100 lpi grating, I figured for Dale's image the
grating was .413 from COC. Using the 3 1/2 band to 6 band ratio (2.5 lines
difference), the one I took more care in counting, the correction then would
be .172 or 30%. And the 3 to 6 would be .207 or 35%.

That seems to match Dale's robo-foucault very well, but then not so well
with the interferometry. The mirror has astigmatism so there may be a
diameter that reasonably matches both interferometer and Foucault.

This particular mirror makes judging the center easy because it is very
spherical in the center. Just slightly oblate. A smoothly corrected mirror
would not be quite so easy in the center. The outer part is hard to judge on
this one and a smooth curve would probably be easier.

This also should work to determine the correction between any two locations
on the curve.

That is enough (too much) for one post. 

Jerry
 


-----Original Message-----
From: atm-bounces@atmlist.net [mailto:atm-bounces@atmlist.net] On Behalf Of
Stephen Koehler
Sent: Friday, February 10, 2006 10:24 AM
To: atm_free@yahoogroups.com; ATM list
Subject: Re: [ATM] [atm_free] RE: data and musings on thin mirror

Vladimir (and Jerry, later),

On 2/7/06, vladimir sacek <vla@toast.net> wrote:
>
> Stephen Koehler wrote:
>
> > I think the test for basic correction can be done without a need to
> > know the absolute distance inside or outside of focus that the Ronchi
> > image was taken, as long as you know the line spacing on the grating.
>
> I don't think that would work. Given everything else, line deformation is
> a function of both, nominal defocus (aberration) and nominal grating
> separation. Since any given pattern deformation can be result of an
> indefinite number of combinations of the two parameters, we need to
> know one in order to determine the other one.

I'm not sure I understand your argument, so let me explain my method,
and see if I can convince you.  This test may be impractical to
perform, but I think it works.

First, here is a simulation of a perfect 15.875" f/3.48 (sames as the
thin mirror) taken at various stage positions (top line).

http://www.visi.com/~mkoehler/eason_davis_misc/ronchi_f35.png

The stage positions were calculated to place 2 through 6 lines across
the Ronchi image.  At the bottom, I replaced the paraboloid with a
sphere of the same specs, so you can count how many lines would span
the image if you had extrapolated from the line spacing at the center
of the images above.  Note that as the stage moves out, as one line is
added to the full Ronchigram (outer zone), one line is also added to
extrapolated inner zone.  This will always happen when the stage is
outside the ROC of the outer zone, or inside the ROC of the inner
zone.  This fixed line difference is invariant.  In this example the
line difference is a little over 8 lines between the extrapolated
inner zone and the outer zone (8.14 to be exact).

This line diffrence can be used to calculate the focus shift from
inner to outer zone, if you know the mirror diameter, paraxial ROC,
and the spacing of the grating.

In this example, say you counted an eight line difference from any of
these images.  That means that if you were to slide the stage back
until the outer zone is nulled, there would be 8 lines in the
extrapolated inner zone.  8 lines at 100 lpi is 2.032 mm.  At f/3.48,
this corresponds to a focal shift of 7.07 mm (moving source), or 14.14
mm (fixed source).  This is reasonably close to the actual focal shift
of 7.24 mm.

As I said, I'm not sure it's easy to measure the line difference very
accurately.  I tried it on the simulation of Ronchi images from the
thin mirror, and got line differences of 1.79, 2.46, 3.0, and 2.56. 
It was easier to make the counts when there were a few more lines
spanning the images.  Assuming the first difference is an outlier, it
looks like the line difference is about 2.5.  This corresponds to a
focal shift of 2.21 mm.

Jerry,

what do you think of this way of performing the test?  I think it does
work to determine the focal shift without knowing the stage position. 
The trick is to use the line count DIFFERENCE, instead of the RATIO.

--
Steve Koehler
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