ATM Re: R-C cass design.

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

Jim,

> ... one can
> set up the 2 DEs for the R-C cass expressing axial stigmatism and the sine
> condition with two parameters (say the mirror separation and primary-focus
> distance).  It's sort of like continuous ray tracing.  Once again,
> uniqueness says there's only one pair of surfaces satisfying those
> conditions, and with the sine condition introducing trig functions, it's
> unlikely it's a hyperbola.

Interesting approach. After consulting some of my books, I've
found following :

Any aplanatic equivalent of Cassegrain telescope is called Ritchey-Chretien.

(Popov, Aspheric surfaces in astronomical optics, Nauka 1980)

This is important implication, and shows that I was wrong in saying
that only conic section solution is called Ritchey-Chretien.  
There is even an example in the book of a system that has a planoid
secondary (whose surface is similar to Schmidt curve!), that is still
called Ritchey-Chretien. In fact, Maksutov calls it "a bordering design
of Ritchey-Chretien family".

In above mentioned book there is a generalized solution for any two
mirror system, unfortunately too long and complicated to be presented
here. But in short, it does state that for systems with ultra fast
primaries (like rentgen scopes, but also mentions Hubble as an example
because of very stringent 1/50 wave requirement), a conic section
primary & secondary CANNOT fully correct coma. Then it goes and later
gives eccentricities for Hubble's primary and secondary (as if they
both were ordinary hyperbolas) ! You figure it out ...

Cheers,
Bratislav