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@asi.it