To: atm{at}shore.net
From: "Matthew L. Brown" 
Reply-To: "Matthew L. Brown" 



>
>Dr. Giuseppe,

  A parabola is a shape whose radius of curvature is smallest in the center
and increases outward.  So from the perspective of a sphere with the same
radius of curvature as the center of the parabola, the outer edges are
indeed flatter.  In fact, this is one method for parabolization.  However
consider a sphere tangent to the outer edges of a parabola.  The center of
the parabola, in this case, is deeper than the sphere.  So you can go to a
different parabola (one with a shorter focal length) by digging a hole in
the center.  This is easier to control than wearing down the edges, which
is easy to overdo, leading to turned-down-edge (TDE) which can require
removing lots of glass to correct.

=Matt


>Even if I've a PhD in Astronomy and reasonable knowledge in optics, I'm
>puzzled by something which will be certainly solved by somebody in the list.
>
>Textbooks on mirror making say that, in order to "parabolize" a concave
>spherical mirror, one should dig into the center of the surface;
>conversely, in order to "hyperbolize" a convex spherical mirror, one
>should depress the outer zones of the surface. To me, both those action
>lead straight to an ellipsoidal figure. In fact, in the case of a concave
>surface, a paraboloid results from flattening the outer zones with respect
>to the center, and even more so in the case of an hyperboloid.
>
>Where's the trick? Thank you all in advance.
>
>Dr. Giuseppe Bianco
>Centro di Geodesia Spaziale "G. Colombo"
>Agenzia Spaziale Italiana
>75100 Matera (MT), Italy
>phone:+39-0835-377209
>fax:     +39-0835-339005
>e-mail: giuseppe.bianco{at}asi.it

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