[ATM] Re: Foucault test limitations

[Vladimir Sacek <vladis.2@juno.com>]

Hi James,

>C) Finally, the Couder mask (or lack there of) can change the results of
a
test.  I think this is the point that Vladimir Sacek has been trying to
make.<

It did sort of digress to the mask, but my point was that the reading
accuracy requires defocus symmetry close enough to that of a perfect
conic; local surface irregularities can have it compromised.

I didn't try to summarize the main test limitations, but
detecting/quantifying astigmatism is certainly one of them. I believe
your results with it are valid, but it may not be the whole story. A
mirror with astigmatic surface deviation will likely have not only the
radius, but the conic varying with different diametral cross-sections as
well. Combination of  these two - astigmatic surface error (radius
variation), and conic variation - will determine reading results at the
c.o.c. One is possible to have either compensating or exaggerating effect
towards the other one in actual readings. In other words, it is possible
that relatively strong astigmatism can not be detected and, on the other
hand,  that moderate astigmatism shows its presence.

It is also possible that most of the diametral cross-sections have
near-identical conic, although the probability for that is small. If they
all would be, say, spherical, longitudinal (primary) astigmatism at the
infinity focus (given by wF^2/113.6, "w" being the wavefront error) would
double at the c.o.c. For an f/4.5 mirror that would come to 0.089mm
astigmatic defocus (sagittal to tangential) at the c.o.c. for 1/4 wave
wavefront of astigmatism. If the cross-sections are parabolic, the
astigmatic defocus would at the c.o.c. dissolve into spherical
overcorrection, whose longitudinal aberration is given by KD/8F, K being
the conic. A 16" f/4.5 mirror would have it over hundred times larger
than its astigmatic defocus. In order to detect this amount of
astigmatism from the readings, one needs to have reading accuracy
consistently better(significantly) than +/- 0.05mm. But this is the
simplest and the list probable scenario. Actual mirrors are all but
certain to be more complicated.

Vlad
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