Fwd: [ATM] how accurate is the foucault test

[Mark Holm <mdholm@telerama.com>]

I agree with Matthew Brown's reply on this topic, but I want to add one 
slight clarification.

Matthew wrote:

>  It turns out that the absolute radius of curvature isn't as important as 
>the differences between the radii of curvature of different parts of the 
>mirror. 

I would say, "precise knowledge of the absolute radius of curvature isn't as important".

In the usual Foucault test analysis (the math part) we subtract the reading for the innermost zone from itself and all the other readings.  This means that, instead of measuring the absolute radius of curvature at each zone, we are reading the difference between zones.  It is analogous to taking the first derivative of the radius of curvature formula.  The technique used to reconstruct the mirror surface from the Foucault readings is analogous to integrating that first derivative back to get the base function.  The integration constant then turns out to be related to the absolute radius of curvature.  It turns out that measuring it to tape measure accuracy is usually good enough.  I put a piece of masking tape over the end of my tape measure and have my assistant (usually one of my sons) hold the taped end to the center of the mirror while I read the KE position.  I have seen pictures of a test bench where the tape measure is built right into the bench, eliminating the need for a son.

In principle, it would be possible to do the Foucault test as a measurement of the absolute radii of curvature.  The problem is measuring that knife edge/source to mirror distance to the same high accuracy as the zonal shifts.  If one could overcome that, then the analysis could be done without the differentiation/integration process.  You still might have to do some curve fitting though, because of limited measurement precision, and because, what you usually want to know is the difference between your mirror's surface and a reference shape, usually a paraboloid.

The Couder mask is an aid to help with the fact that the human eye-brain is not good at making the Foucault shadow measurements without it.  Another technique is the Everest pin stick.  There have been hot debates between devotees of the two methods over which is better.  It seems to depend somewhat on the eye-brain combination you happen to be blessed with.

There are a few truly blessed souls who can read Foucault tests accurately without either.  Some of these have become saints in the atm pantheon.  Alika Herring comes to mind.

Mark Holm
mdholm@telerama.com


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