Re: [ATM] Re: Schmidt-Cassegrain

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

At 13mm off-axis ~35 micron only from field
curvature (~1200mm). But the field can be flattened
with a plano-convex lens with the curved surface radius
given by R=f(n-1)/n, with "f" being the mirror f.l. and
"n" the corrector refractive index. The price is introduction
of some spherical aberration.

If you are willing to go "long", you may consider Gregorian arrangement. In 
general, aplantic Gregorian
has somewhat better off-axis quality than a comparable
RC. Primary's conic is lower for lower secondary magnification and larger 
secondary relative size. Secondary conic is always low, about -0.2, give or 
take.
If you'd accept inaccessible image, secondary magnification can be bellow 2. 
The tube structure doesn't have to go all the way to the secondary, which 
can be
mounted as an extention. The nice thing about Gregorian
is that the light bundle diverges towards secondary, so that nearly entire 
interspace between the secondary and
the image location can be obscured by some sort of
cilindrical baffle - something that can't be done against
converging Cassegrain cone. The result is nearly perfect baffling in the 
Gregorian.

At certain combinations of secondary size and magnification, the astigmatic 
field in the Gregorian
has nearly flat median (best image) surface, so that no
flattener is necessary. Unfortunately, it requires rather
large secondary sizes. One with only mildely curved (~4300mm) best field 
surface and not too big secondary would look like this (with D=600mm f/2 
primary):

primary: R=-2400, K=-0.746, 1680mm to secondary
secondary: R=576mm, K=-0.177

Secondary minimum size is 0.4D and magnification is 1.5, for an f/3 system. 
The astigmatic blur is nearly 40 microns
11mm off-axis (gets bellow 25 microns at ~8.5mm off-axis). Assuming ~50% 
obstruction, allowed front detector
diameter in the light converging from the primary would be less than ~60mm.

With smaller secondaries and higher magnifications, placing the detector 
gets more comfortable, but a plano-convex lens is needed to flatten the 
field.

Vlad




> Vlad, thank you again for your analysis.
> With all those difficulties and limitations
> a Schmidt plate is beginning to look attractive  ;-)
> and i could mount the camera directly at the f/2 focus.
>
> One last question : with a flat detector 22.7 x 15.1mm,
> what would be the image blur size at the edge ?
>
> Jean-Guy
>
> ----- Original Message ----- 
> From: <vlad@copper.net>
> You are right, the three mirror systems,
>> especially with this fast primary, are sensitive
>> to anything one can think of. It is hard to
>> have them "synchronized" on the raytracing board,
>> let alone real telescope. After taking a closer look
>> at the (better) three mirror system showed that it
>> still have more than negligible astigmatism/field
>> curvature, although its performance is still good, nearly as described. I 
>> checked out simplified form of this arrangement:
>> two-mirror w/three reflections (concave secondary reflects back onto the 
>> primary, which then focuses
>> through the secondary). For a flat Petzval aplant,
>> required parameters are:
>>
>> primary/tertiary: R=-2400mm, K=-1.138, 828mm to secondary
>> secondary: R=-1200, K=-6.806
>>
>> Resulting system is an f/4.7, with 15 micron blur 12mm
>> off-axis on ~600mm curved astigmatic field. It is on par
>> with the comparable RC, with somewhat easier to make optics (K1~-1.3, 
>> K2~-10 for the RC). It may be possible to adjust
>> mirror radii so that the best image surface is nearly flat, which
>> would make it even more viable. It's sort of odd that this
>> variant hasn't been mentioned.
>>
>> But, after all the talk, there's still no "right" answer:
>> a wide-field corrected arangement with spherical or mildely
>> aspherized f/2 primary w/o full aperture corrector. As Robin Williams 
>> said on the "Actors Studio" interview: "We're
>> trying, we're trying..."
>>
>> Vlad
>>
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