To: atm{at}shore.net
From: Jim Burrows 
Reply-To: Jim Burrows 


At 18:31 2003-04-24 -0700, Matthew L. Brown wrote:

>There's more 'allowable' range to the readings than you expect.  Programs
>like Tex or Sixtests will help you by fitting a parabola to the readings
>and accounting for the area that each reading represents.
>As others have mentioned, the central region is less important, because it
>is shadowed by the secondary, so don't worry so much about features there
>and concentrate on the middle and outer regions.

Tex doesn't "account for the area" (old fashioned ). 
Sixtests and Figure45 do.  On the other hand, if Tex says it's 1/4 wave,
it's probably passing (Strehl > .8) - there's only a few 1/4 wave
mirrors that don't pass.  On the third hand, there's 1 wave mirrors with
errors in the central zones that do pass, even without obstruction.

>How to respherize?  If you draw your current figure -- try to draw
>something with a tighter radius of curvature in the center than at the
>edges -- it'll look somewhat like an hyperbola from your high school math
>course -- and draw a somewhat flatter sphere (same radius of curvature
>everywhere), below your surface everywhere (since you can only remove
>material, not add any).  The closest sphere will be tangent in the center
>and at the very edge.  The parabola you want is somewhere in between, but
>still tangent at the center and the very edge.  So you need to remove more
>material in the mid and outer zones than in the center.

It's simpler than that - a 1/3 CoC stroke will move the mirror toward the
sphere (in fact, I think, but not sure, that any CoC stroke
under-corrects), and even beyond - that's why Texereau's "normal
stroke" (p. 41) adds a 1/4 W to the 1/3 CoC stroke to keep the mirror
hovering around a sphere.

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

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