Re: [ATM] Foucault images

[Ken Hunter <atm_ken_hunter@yahoo.com>]

Mike,
   
  I'd try rotating the 3X telescope and then the slit itself to see which
  has an effect on the image. If it rotates with the slit, has to  be a 
  diffraction effect. If the rotation is with the 3x scope, possibly non-
  homogenous glass element???
   
  When you rotated the camera, did the lines line up in the same orientation 
  as the camera or the mirror? They should have rotated with the camera, i.e.
  if you rotated the camera, and they are in the camera, the lines should still
  align "top to bottom" in the photo as before and appear tilted on the glass. 
  If the lines stayed aligned "top to bottom" on the glass, they should have 
  appeared tilted in the photo and the problem is not generated in the camera.
   
  Seems kinda backwards until you think about it, it's my reason for asking.
   
  Ken Hunter

Mike Lockwood <melockwo@uiuc.edu> wrote:
  Hi,

First, for those interested, I tried tilting my digital camera to see
if the vertical artifacts tilted with it - they did NOT. So, I think
it is slit-related phenomena. Making the slit shorter vertically did
not affect it, from what I could see.

Also, I can notice the artifacts with my eye, but only if I hold it
VERY still. Any side-to-side movement causes the patter to appear to
move to rapidly to the side (when viewed through the 3x scope). The 
pattern is not enough to throw off readings, since my eye is not 
perfectly still when I take readings. Everything averages out. It is 
merely an annoyance when photographing smooth mirrors.

Stephen Koehler wrote:
> http://tinyurl.com/hp4cm
> There are some remarkable similarities
> between the two in the subtle features. Note how the outer bands
> get clearer in both. Note how the second band (from the middle)
> gets less distict as you go down. Note how the second, third, and
> fourth bands start to braid togther into an indistict mass.

Yes, that's a very good match. I checked the grating and it was
indeed my 133 lpi grating.

> One interesting note for the technically inclined is that I needed
> to use a pupil size of 1000 pixels wide. Combined with a padding
> of 1.2, I was doing 1200x1200 FFTs for the simulation. This was an
> unfortunate consequence of the mirror's large diameter and short
> focal ratio. These are the largest FFTs that I have had to use, to
> date.

Depending on software, a power-of-two-length FFT should be fastest
(1024, 2048), but I'm guessing you know that already.

> I don't know the thickness of this mirror, but I suspect that it is
> thinnish, and that it shows a fairly large amount of thest stand 
> astigmatism, oriented vertically. This is overlayed on the
> mirror's astigmatism in your composite Foucault in 12 orientations.
> When two astigmatisms are combined, the angle and strength of the
> composite varies.

Yes, it is ~2.25" thick, but you should also know that it has 3/16" of
wedge! The mirror is BVC.

That probably complicates the simulation too much to deal with, but
you should know it is there. Probably accounts for some of the
variation between my photos and your simulations.

> What I did was to experiment with the starting angle of the mirror 
> astigmatism (-70 degrees was best) and the strength of test stand 
> astigmatism (somewhere between .5 and 1 wave RMS) that made the 
> combination that most closely matched the 12-frame composite
> Foucault images. Here's the result, along with the original: 
> http://tinyurl.com/pj5s3 
> http://bi-staff.beckman.uiuc.edu/~melockwo/mirror_making/foc_hall/rotate_foc.jpg
> 
That is really excellent. Not a perfect match, but excellent
nonetheless, and the differences are probably explained by the wedge.

> The focus shift could be part of this. I took all the simulations
> at the same stage position, but I suspect that Mike was not able to
> control this as well. Also, test stand deformation often changes
> from one settiing of the mirror to another, which throws off the
> combined astigmatism.

Correct, I could not control the stage position precisely - I did not
try nulling a particular zone after rotating the mirror - I just did
it by eye. The bottom of the mirror was resting on a padded, radiused
block. It has a strange bevel, too.

> One thing I noted from the simulations is that the astigmatism
> should disappear at four evenly-spaced positions. Between each
> adjacent pair of these four, the astigmatism should switch back and
> forth (left lean, versus, right lean).

Yes, that's exactly what I expected when we did the testing, and this
is why we only rotated 30 degrees at a time. We weren't trying to
find exactly the four rotations where it disappeared, but we did want 
to see the pattern changing back and forth, and we saw that, as the 
photos show.

> Thanks for the interesting puzzle. I'm wondering if anyone else
> has an estimate, and whether different means were used to achieve
> it.

Thank you for your effort!

Mike Lockwood

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