[ATM] Aplanatic Schmidt-Cassegrains with aspherical mirrors

[Michael Peck <mpeck1@ix.netcom.com>]

After slogging through the relevant section of Schroeder (8.1), who gives a 
more thorough discussion of SCT design than Wilson - and a more thorough 
discussion in the 2nd edition than the first of "Astronomical Optics," I 
think I more or less understand this.

In an ordinary Cassegrain (2 mirrors, no refractive elements) for any given 
geometry there an infinite number of ways to eliminate spherical aberration 
by adjusting the conics of the mirrors. There's one unique design that's 
aplanatic. That's what we know as the Ritchey-Chretien.

Add a thin aspheric plate at the front end and it now becomes possible to 
eliminate two out of the three most interesting Seidel aberrations with an 
infinite range of possible solutions. For any given geometry there's one 
unique design that's both aplanatic and anastigmatic. That's basically what 
Rick posted the other day -- it seems for "typical" SCT geometries similar 
to commercial systems both mirrors would have to be oblate.

At the other end of the scale if you make the mirrors with the parameters 
of a true RC the front "corrector" has nothing to do. The corrector CANNOT 
correct the astigmatism inherent in the design, and in fact the optimal 
corrector design is a plane parallel sheet (to 3rd order -- you could put a 
bit of 6th order correction on it to correct the higher order SA of the RC 
design).

In between, as I said, there are an infinite number of aplanatic designs 
with varying amounts of astigmatism. The only one that really seems 
interesting to possibly build is simply R&vanV's "optimized" compact SCT 
with a spherical primary and aspherical secondary.

There is a basic tradeoff in these designs. On the one hand astigmatism 
decreases as you go from the RC to the oblate mirror anastigmat-aplanat. At 
the same time spherochromatism increases because the corrector is being 
required to do more of the work of spherical aberration correction. Rick's 
design (and the similar one I came up with) looks not too attractive for 
that reason.

This still leaves me wondering what Meade is up to. Right now I'm guessing 
they figured out how to manufacture aspherical secondaries, tweaked the 
optical design including reducing the secondary magnification to flatten 
the field somewhat, and repackaged the mechanicals and electronics. If 
that's the case calling it a "Ritchey-Chretien" is a bit of a stretch.

Mike Peck

_________________

Michael Peck
email mpeck1@ix.netcom.com
Wildlife photography page http://home.netcom.com/~mpeck1/index.html
Amateur telescope making http://home.netcom.com/~mpeck1/astro/astro.html 

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