Ideally (for visual use) one wants a telescope that is/has: (a) such a small secondary that it is effectively unobstructed and (b) a wide field of view, i.e. corrected for coma and/or astigmatism and (c) a reasonable f-ratio, eg f.7 to f.12 to avoid very short focus eyepieces and (d) perfectly baffled so no extraneous sky light reaches the eyepiece, i.e. preferably not a Cassegrain (does it make any difference? I don't know). and (e) a fairly short tube for ease of mounting.
Suppose we take a short focus primary (eg f.3) and mount a barlow lens/coma corrector (designed for the purpose) on a small diagonal close inside the primary focus. The focal point would then be extended enough to come out the side of the tube, and we have several degrees of freedom in the design (eccentricity of the primary mirror as well as shape of the lenses) so it should in theory be possible to arrive at a coma-corrected design suitable for both wide angle or high power viewing, with a very small secondary, in a short tube.
I seem to remember a Newtonian with a barlow lens (let's call them "magnified Newtonians") in S & T but I don't think it managed to totally avoid coma. If one can buy coma correctors for dobs, though, it should be possible to make one with magnification, shouldn't it? Has anyone done it?
One could also consider an all reflecting version. If one tilts the secondary of a cassegrain (or preferably a Ritchey-Chretien) through, say, 30 degrees the eyepiece can be positioned in the side of the tube. I'd call this a "Tilted Secondary Ritchey Chretien". This reduces the secondary to focal plane distance (allowing a smaller secondary) and, for wide-field work, avoids the need for a large hole in the primary with its associated baffling problems. The shape of the secondary is defined (for ANY conic section primary, provided spherical abberation is not so large that rays intersect before reaching the secondary) as the intersection of a family of cones with a family of hyperboloids; and in the case with a parabolic primary, the secondary is an off-axis section of a hyperboloid with foci at the first and second focal points. So one can get a geometrically perfect image "on-axis" with a variety of primary conic sections; this then allows one to choose primary eccentricity (and secondary figuring to suit) to minimise coma or astigmatism, just as with an axi-symmetric Cassegrain. (So the primary mirror would be a figure of revolution just like in a Newtonian, though not necessarily a paraboloid).
Has anyone built (or raytraced) one of these? I suspect the secondary would not be very different to a convex toroid and would be figurable with a suitable null test. One could also consider catadioptric versions with a purely toroidal secondary and a figured corrector plate just before it.
Roger Moss