ATM 2-Diameter testing.

["James W. Burrows" <burrjaw@halcyon.com>]

I think we _can_ get a handle on astigmatism by testing on two 
diameters.  The main idea is that the (fixed-source) KE moves twice as far 
as a displacement of the mirror.  Using Texereau's example on p. 102, the 
difference between the averages of the D1 and D2 readings is .0035", so we 
deduce that the mirror shifted by .00175" when Tex rotated it.  Now if we 
bias the D1 and D2 readings so they have the same average as the D12 
readings, those become the readings we would have gotten if the mirror 
hadn't shifted.

We reduce three sets of data:  the D12 set to find the focal length of the 
mirror's best-fit parabola, then the shifted D1 and D2 sets relative to 
that focal length (I think Dave Rowe's Figure34 has that capability - the 
new version of sixtests will also have it).  I get the D1 set has a surface 
RMS of 6.2 nm, the D2 set 4.7 nm, for a combined RMS of 5.5 (including 
astigmatism!) slightly worse than the D12 set's 4.0.

        -- Jim Burrows  phone 206.244.2933, fax .0294
        --              mailto:burrjaw@halcyon.com
        --              http://www.halcyon.com/burrjaw/
        -- Seattle      N47.47233, W122.36620 (WGS84)