To: amul49{at}eth.net, atm{at}shore.net
From: mdholm{at}telerama.com
Reply-To: mdholm{at}telerama.com


Aditya,

If your Foucault readings, and my analysis are correct, you have a very
nearly perfect figure.  You should not even think about putting this mirror
back on a lap until considerably more thought and measurement have gone
into the decision.

Stage 1:  We need to verify that I got the correct numbers and information.
     I assumed that you used a fixed source tester.  That is, the light source
     does not move toward and away from the mirror as the knife edge does.
This
     is a critical point.  If I am wrong, then your mirror is overcorrected.
     rather than near perfect.

     I used Sixtests to analyze your Foucault readings.  Sixtests uses only
     millimeters, so I converted all of your measurements.  Here they are so
you
     can double check them.

     O.D. 200
     ROC  2825.75
     Sec Dia  38.1

hm (in)         1.487       2.468       3.139       3.688
hm (mm)         37.7698     62.6872     79.7306     93.6752

raw (in)        0           0.064       0.08        0.106
                0           0.046       0.07        0.101
                0           0.051       0.07        0.106
                0           0.048       0.063       0.102

avg (in)        0           0.05225     0.07075     0.10375
std (in)                    0.0070134   0.006057    0.0022776


avg (mm)        0           1.32715     1.79705     2.63525     geo mean std
std (mm)                    0.1781399   0.1538483   0.0578513   0.1166064

Since you obviously used Nils Olof Carlin's recommended zone radii, I
assigned the zone center radii (hm) according to Nils Olof's formula.

If I am right, then Sixtests says your mirror has a deviation from a parabola of
4.8 nM RMS.  This is very good, in fact, if further measurement confirms
it, it is excellent.  You are not likely to improve it by more work.  If
this result proves out, this will be an excellent mirror that, if teamed
with an excellent diagonal, and well mounted and aligned, will produce
images that will be difficult to impossible to tell from perfect.  Sixtests
also predicts a Strehl ratio of 0.988 for this mirror, also an excellent
result.  Sixtests also says the mirror is slightly undercorrected, with a
deformation constant of -0.922.
-1 is a parabola.  Do not let this difference worry you.  Sixtests has taken
that into account already in calculating the RMS error and Strehl ratios.

Stage 2:    You need to decide whether the mirror figure is good enough in
     qualitative ways.  Is it well polished?  Is it a smooth polish?  If it
     still has many pits, or the surface looks rough under the Foucault test,
     you may need to do more work.

Stage 3:    You need to take more Foucault measurements to confirm the result
of
     the measurements you have already made.  I suggest another Couder mask
with
     zones between the zones in the mask you are already using.  If you used my
     Couder Mask program, you can just use the "Intermediate Mask".  It is
     designed exactly for this situation.  This will give you a total of 7 or 8
     zones depending on whether you use the center zone.  This gives some
     redundancy to your measurements (a good thing at this stage), and also
     allows the Foucault test to begin to resolve some zonal errors.

     Mark 3 places equally spaced around the edge of the mirror.  Place the
     mirror on the test stand with mark 1 up.  Do a set of measurements.  Then
     measure with marks 2 and then 3 up.  Then do it again with marks 1, 2 and
3
     down instead of up.  This will give you six sets of measurements.  If
these
     measurements are in reasonable agreement, and still indicate a good
figure,
     and you decided the polish is good, then you are done.

I do not set my tester to 0 for the innermost zone.  Instead, I just read
whatever the indicator says when I have the innermost zone balanced.  The
analysis programs work fine with this form of data.  Also, then you can
calculate a standard deviation from these data points just like for the
others.
 It is useful in the statistical analysis of your data.

I will capture images of Sixtests results and post them at a web site.  I
will send another message when I have done that.

Mark Holm
mdholm{at}telerama.com

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