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

["vladimir sacek" <vla@toast.net>]

Stephen Koehler

> I have, so far, demonstrated one example where this worked, at least
> for five positions of the grating.  If your contention is right, we
> should be able to find an example where the line counts do not result
> in the proper focal shift.  Assuming you want to pursue this, do you
> have a suggestion for what to try?

Try to induce variable (unknown) aberration. You are assuming a perfect
paraboloid, which itself would make the test purposless. Any of the
aberrated patterns (line-count-wise) given in your illustration for the
specified grating location could be duplicated with a number of different
aberration/location combinations. If we don't know actual grating location,
we can't possibly know the aberration.

The reason that the line count differential doesn't change in your model is
that the cone width differential between the sphere and parabola don't
change. But with the change of aberration (defocus) the cone width at the
grating location also changes, exposing more or fewer lines, depending on
the sign of aberration and side vs. defocus  (it also changes the pattern of
line deformation). In other words, it pretty much simulates the effect of
changing the grating location. Unless you know the actual grating location,
you can't tell what in the particular line count results from its location,
and what from the aberration. You need to know one in order to determine
the other one.

Vlad 

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