RE: [ATM] Astigmatism in round robin mirror C with Foucault.

["Scott Milligan" <starzkey@charter.net>]

There's been a number of questions and comments on this list about the 
ability to measure astigmatism using foucault.  I think the consensus is 
that, since it can't be seen in the test, it can't be measured.  There 
have been some dissenting views on this, sometimes from the same people 
making the statement in the first place (myself inculded)!!!  


On the subject of measuring astigmatism using the Foucault test, my two
cents worth is to say that any test that doesn't preserve a common distance
from the knife to the mirror between separate scans cannot hope to measure
third order astigmatism (i.e. cylinder error).

Measuring the difference between fit values of the conic constant taken
across orthogonal diameters does not quantify low order astigmatism; rather,
this evaluation describes the azimuth variation of spherical aberration and
other "symmetric" error terms.  This is almost always a minor, higher order
affect (at least among experienced mirror makers), whereas low order
astigmatism can be quite a bit larger, in both amplitude and in terms of the
percentage of the aperture affected.

To get a quick feel for what the tolerance on preserving the common ROC
between scans has to be to measure astigmatism, calculate the 1/4 wave depth
of focus for whatever mirror you are considering.  Example; an F/4 mirror
tested at ROC has a quarter wave DOF = 2*lambda*F/#^2.  Here, F/# = 8 (test
at ROC), lambda = 0.5 microns, so DOF = 64 microns, which is about 0.0025
inches.  If you can't hold the ROC reference tighter than that, than your
measurement will be meaningless.

Scott Milligan

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