(ATM) Secondary Fab/Conic Sections/Bill's Compound Scope

[epabcc@epa.ericsson.se (Bratislav Curcic)]

A conic section is defined by Schwartzshild's constant and paraxial
radius of curvature ONLY. F/ratio doesn't matter. If you have good
ray-trace program, you can "create" a certain conical surface, and 
make it either concave or convex simply by changing the sign of
the radius. So, say you've optimized your Cassegrain with certain
conic constant and radius. Simply "remove" the primary, enlarge 
the secondary, change the sign of the "radius" column, and instead
of a parallel beam, shine a pencil of rays originating from a radius
of curvature onto it. They will come back not into the point (like in
case of sphere), but with certain longitudinal aberration. Pick 4
or 5 zones on the secondary, note down the longitudinal aberrations
needed, and you have a set of figures to work with ! Same as if you
are striving for a parabola, but instead y*y/R for each zone, use 
ray-trace progam provided figures as desired values (they will be 
something like K*y*y/R anyway, where K is a constant). 
After you've finished with a concave test plate, use inteference method
to make convex (I know, it's slow but I don't know of better method to
get a good secondary). If your hyperbola is not too strong, you MIGHT
get away with a spherical test piece, and look for certain interference
pattern (like in Texerau), but that seems a bit too "loose" to me.
Local retouching on a 2" secondary is almost impossible to do without
screwing up the smoothness (as all opticians at Meade and Celestron
know very well !)    :-)

Bratislav