RE: ATM Mirror Evaluation - Strehl Ratios vs. MTFs

["Bell, Andrew" <AMB2@pge.com>]

The glass that I push is usually hypothetical (rather than pyrex or plate),
but I like looking at the mathematical parts of this.  I think the point
Steve Steel made yesterday afternoon is a very good one -- there is no real
way of directly measuring the Strehl ratio or determining the MTF for a real
mirror.  In both instances, the best that we can do is fit a mathematical
model of the mirror surface to the test data, and then calculate a Strehl
ratio and/or determine the MTF for that specific "model" of the actual
surface.

The more zones that you measure (and the more individual measurements that
you make for each zone under different testing conditions), the better job
that you or the software will be able to do of developing an accurate model
to the real surface and also of estimating the uncertainty of that model.
To paraphrase oft-given advice ... better to "measure more" and "interpolate
less"!

Also, the MODEL surface is always going to be a very smooth one -- that's
just the nature of the mathematics that's being used.  So I would put more
weight on a good Strehl ratio estimate for a mirror that I was pretty sure
was itself smooth, in preference to the same estimate for a different mirror
that had been through a lot of mid-course corrections or unusual laps since
the last time it had been polished to a sphere (just because I'd have more
confidence in the accuracy and precision of my model surface for that first
mirror than I would for the second one).

I haven't seen any updates for a while on the progress of the round-robin
mirror tests that got underway a couple of months, and have forgotten who
was organizing them.  Is there any news to report?

-- Andrew Bell

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Date: Thu, 4 Oct 2001 14:26:45 -0400 
From: Stephen Steel <steve.steel@kvs.com>
Subject: RE: ATM Mirror Evaluation

When John uses the term Strehl ratio, he actually means the Strehl ratio AS
PREDICTED by a model of the mirrors surface made to fit the Foucault test
data.  The various Foucault analysis programs may use slightly methods of
estimating a model surface from the test data, but there will always be some
difference between the model surface (from which the predicted Strehl ratio
is calculated) and the actual surface.

So there is a second question here: "Given two mirrors, both with the same
predicted Strehl ratio from Foucault data, how much difference would we
expect in the actual measured Strehl ratio if one mirror's imperfection
consists mainly of a TDE and the other mirror has mainly random
imperfections".