Re: [ATM] Aplanatic Schmidt-Cassegrains with aspherical mirrors

["vladimir sacek" <vlad@copper.net>]

The only excuse (not a justification) for them to call
the design an RC would be if they use corrector and spherical primary to 
"simulate" hyperboloidal RC primary in regard to s.a. (over)correction in 
combination with appropriately aspherized secondary. But it doesn't seem to 
be working that way. For any given SCT configuration, there is only one 
conic of the secondary that corrects for coma. The  primary/corrector are 
adjusted accordingly, to correct for spherical and, if possible, 
astigmatism. I tried if it works the other way around (starting with an
appropriate RC hyperboloid), but couldn't get an aplant.
Looks like one possible "explanation" less..

Vlad

> 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
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