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

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

Scot

> I've just now had the time to digest what you wrote regarding the off-axis
> performance to be expected from the Mersenne design, and have an 
> observation
> to add; given that the field of view in most telescopes will be limited by
> some linear format (i.e. eyepiece field stop or linear extent of CCD 
> chip),
> doesn't it follow that the off-axis contributions of the image-forming
> telescope (i.e. the last section in the optical design that sees the
> collimated output from the secondary)must remain fixed in magnitude?  The
> magnification added by M2 simply reduces the angular extent of the true
> field on the sky that can be imaged.  I do expect, however, that the issue
> of field curvature will be aggravated, since the imaging component must
> consist mostly of positive-powered elements, which are the wrong sign to
> compensate residual field curvature added by the convex M2.

>I've just now had the time to digest what you wrote regarding the off-axis
performance to be expected from the Mersenne design, and have an observation
to add; given that the field of view in most telescopes will be limited by
some linear format (i.e. eyepiece field stop or linear extent of CCD chip),
doesn't it follow that the off-axis contributions of the image-forming
telescope (i.e. the last section in the optical design that sees the
collimated output from the secondary)must remain fixed in magnitude? The
magnification added by M2 simply reduces the angular extent of the true
field on the sky that can be imaged. I do expect, however, that the issue
of field curvature will be aggravated, since the imaging component must
consist mostly of positive-powered elements, which are the wrong sign to
compensate residual field curvature added by the convex M2. <


Linear field size is irrelevant for the principle; incoming ray angle from 
the
secondary to any off-axis point in the final image of the Mersenne will be
1/k times larger than the incoming angle at the primary.

This is a consequence of the chief ray (the one reflected from the center of 
primary
mirror) for any off-axis point in the final image appearing as if coming 
from the
exit pupil formed by the secondary. Final image to exit pupil distance, in 
units
of primary's f.l. is given by p=(km^2)/(m+k-1), "k" being the height of 
marginal ray
at the secondary, and "m" the secondary magnification.

This defines the angle created by the secondary as h/p, "h" being the height 
in the
final image. At the same time, the actual incident angle is defined by h/f, 
"f" being
the system focal length. That makes the secondary angle f/p, or (m+k-1)/mk 
times
larger. For the infinite "m" of the Mersenne, the angle multiplication 
factor reduces to 1/k.

For two-mirror systems with finite secondary magnification, angle 
multiplication factor is
somewhat smaller for given "k". However, it can be greater for relay lens 
systems, due to
typically smaller value of "k".

You're right, field curvature in a Mersenne/refractor combination will be 
stronger than
in either of the two alone. Neglecting astigmatism, it would be given by 
1/R=(1/Rm)+(1/Rr),
with the Mersenne curvature (Rm) and that of the refractor (Rr) being of the 
same sign.

Vlad

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