Re: [ATM] FigureXP - an apparent discrepancy in the centerzone effective radii.. II

[Jim Burrows <burrjaw@earthlink.net>]

At 2004-08-18 23:59 -0700, Mark Cowan wrote:

>I've run data from mirrors with excellent corrections
>through FigureXP under both Tex's z^2/2R arithmetic
>effective radii and Nil's (z^2+h^2/2)/2R and though
>usually the difference in reduced wavefront is minor,
>for slow mirrors it becomes high, and yet the
>diffractive effects on the latter would seem less,
>thus leading me to suspect the correction itself.

As Nils Olof says, this is a subjective issue - when would most users say 
the shadows are balanced?  Incidentally, I don't think your expressions are 
right:  1) there's no R in there, 2) assuming the quantity being divided by 
2R is the effective radiusē, it doesn't equal the square of Nils Olof's 
expression ave( ave, RMS).

You can do some simulation experiments with diffraction in there.  Download

         http://home.earthlink.net/~burrjaw/public/diffract.zip

and compare the Couder/Foucault readings (for a perfect parabola) when the 
right-left contrast difference is zero with the effective radii 
formulas.  I've done this and in most cases, Nils Olof wins, but it would 
be fun to try it for a slow mirror - I don't remember if this was one of my 
trial cases.

         -- Jim Burrows
         -- mailto://burrjaw@earthlink.net
         -- http://home.earthlink.net/~burrjaw
         -- Seattle N47.4723 W122.3662 (WGS84) 

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