Yes simple rigs can give you a sphere, nature gives that one to us. You can 
do it by hand up to a meter or so in diameter. It took a few decades to develop 
optical tests and parabolizing strokes to take the sphere and grind it to a 
parabola, and nowdays, secondaries can be hyperbolas. A sphere does not make a 
good imager unless the focal length is huge compared to the diameter of the 
mirror. It's why old telescopes are long. But then f5 and greater system are 
still parabolic primaries. I don't think you can go spherical only until you 
start playing with f10 or greater. you could use a Dall Kirkam, but you need 
some image field correction still.

   The machine tools used in mirror grinding are not encoded to twice the limit 
required on the glass as called for by Mr Nyquist. All the optical grinders 
I've worked with are close to run open loop along these lines. There is a model 
by which glass is removed. Foccult testing and Hartmann testing give you the 
high and low points on a mirror. Strokes with a given grit are computed to 
remove the high surfaces, and then run on a machine that may only be encoded to 
0.010 inches/tick. You run the stroke, then run another optical test, then 
compute another stroke ..... You keep going until the error is within 
acceptable limits. Here's the machines I worked on.

http://mirrorlab.as.arizona.edu/

Andrew

> 
> Message: 1
> Date: Thu, 26 Aug 2010 17:22:15 -0400
> From: Przemek Klosowski <przemek.klosow...@gmail.com>
> Subject: Re: [Emc-users] Mirror Grinders.
> To: "Enhanced Machine Controller (EMC)"
>     <emc-users@lists.sourceforge.net>
> Message-ID:
>     <aanlktikupatkroy7vud0jajrrf560s3qa6v671ny0...@mail.gmail.com>
> Content-Type: text/plain; charset=ISO-8859-1
 
> Well, the beauty of the eccentric mirror polishers is that
> the
> kinematics of the polishing process make the mirror surface
> ideally
> spherical. It is possible to machine optical surfaces but
> you need
> subwavelength accuracy i.e. better than 500 nm.



      


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