Re: [ATM] Looking for information on a telescope design

["vladimir sacek" <vla@toast.net>]

Clyde Bone wrote:

> I do not know where " This means that the imaging element in the Mersenne 
> arrangement will have four times more coma and sixteen times more 
> astigmatism than it would have if used alone" comes from, but it is 
> totally in error.  There is no coma or astigmatism to the edge of the 
> power field.<

Then you need to read again my post: it says exactly where it comes from. 
Btw. this is for the minimum secondary size of D/4; for other secondary 
sizes it will differ accordingly.

If you don't see the aberrations, that doesn't seem they are not there.
Most people won't "see" coma in an f/6paraboloid at 12mm off-axis.
Yet it is about 2 waves, or nearly 8 times the Airy disc diameter,
or 0.06mm (full blur; sagittal coma is 1/3 as large). Low magnification
hides most of it when looking at star images, but it does affect image
quality, smears the energy, lowers resolution and limiting magnitude.

Even without any telescope aberrations, this far off at f/6, a conventional
eyepiece would have 6-7 waves of astigmatism, forming nearly 1/4 degree
blur. Most people don't find it particularly objectionable. Even Nagler-like
eyepiece is likely to have over 1 wave of astigmatism and  nearly 1/10
degree blur that far off, at f/6. Would the Nagler field look better if the
blur wouldn't exceed 1 arc minute, which is the center-field quality limit?
You bet.

If you'd specify minimum secondary size of your Mersenne, imaging instrument
and field size, we might be able to figure out what is the magnitude of its 
off-axis
aberrations. Most modern lens objectives are corrected for coma, with 
relatively
low astigmatism remaining. In the Mersenne, this astigmatism will be 
multiplied
by a factor (1/k)^2, as mentioned. What it will come to depends primarily on
the field size. You don't seem to be going much over 1/3 degree radius, or 
so.
Typical small f/6 refractor has about 1/5 wave of astigmatism (approximately
1/8 wave of spherical aberration level) that far off axis. If your k~0.25, 
the
astigmatism is 16 times larger due to the angle projected from the 
secondary,
which would come to  over 3 waves, or about 5 times the Airy disc diameter
blur-wise.

Assuming that your system is a 20" f/6, 1/3 degree is some 17mm off axis
(actual linear height may vary somewhat, depending on the secondary-to-focal
plane distance), which means that the eyepiece astigmatism is by far 
dominant
for the conventional eyepiece, and roughly at the level of astigmatism of a 
Nagler.
(angular blur for the telescope astigmatism in a 20mm eyepiece at 17mm 
of-axis
is nearly 7 arc minutes; this would go as a better than average field 
definition,
not much over acceptable limit for the field edge of ~5 arc minutes).

But that is not the only Mersenne configuration possible. If we take, say, 
10" with
0.8 degree field radius and all else equal, the arrangement produces nearly 
six
times as much astigmatism at the field edge, or well over half degree blur 
diameter
(~0.14mm). This approaches level of astigmatism of a conventional eyepiece,
and is all but negligible. While the error would probably partly offset in 
combination
with conventional eyepieces, it would prevent it from using most of the 
advantage
offered by Nagler-type eyepieces.

Vlad

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