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

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

At 21:50 1/12/05, vladimir sacek wrote:
>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.

Oh, there are infinitely many ways to create an aplanatic SCT if you make 
the primary conic an adjustable parameter. The "easy" way to see that is to 
notice that for a specified layout and ignoring curvature and higher order 
terms on the Schmidt plate you've got three variables left - the conics on 
the two mirrors and the 4th order aspherical term on the plate. There are 
three Seidel aberrations of interest - astigmatism, coma, and spherical 
aberration. The geometry determines field curvature, so you can't do 
anything about that and you don't care about distortion. In general then 
you'll have a single unique solution for an aplanatic, anastigmatic design. 
If you drop the requirement for anastigmatism you still have three 
variables but only two equations to solve. Therefore infinitely many 
combinations are possible. If I get a chance I'll post some design 
variations later.

I don't want to get scolded by list management for discussing commercial 
telescopes too much, so I'll mention Meade just one more time. On one of 
the Yahoo chat groups that sprang up to hype these things a dealer who 
probably knows more than he's allowed to say assured me that their new line 
of Ritchey-Chretiens *do* have two hyperboloidal mirrors. Since that's a 
readily verifiable fact (at least when they become available to people who 
aren't constrained by nondisclosure agreements) I have to assume he's 
telling the truth. That means they're true RC designs. The one thing that 
still puzzles me a bit is that if the mirrors have the conics of an RC the 
corrector plate has nothing to do except hold the secondary assembly. 
That's fine if you don't mind having a thin piece of glass at the front end 
of your telescope, but they also claim to be using it to "minimize" 
astigmatism. The only way I see to affect astigmatism given two 
hyperboloidal mirrors is to tweak the conics of the mirrors a little bit 
and add some correction to the corrector. That will affect the astigmatism 
a little bit in the right direction, but only to a very limited extent.

Mike Peck


------
Michael Peck
mpeck1@ix.netcom.com

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