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Some kind of ellipsoidal shape mirror could reflect to a secondary mirror which is not in the way of the infalling light. Two advantages are immediately obvious. The primary mirror would not be partly shadowed by the secondary. And the support structure of the secondary would not cause diffraction spikes in point sources.

What are the reasons for why this is not only not the standard, but quite uncommon? Especially on the greatest telescopes, one would think that the additional production difficulties, if any, are not a relevant consideration given the budget and clever engineers behind them.

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  • $\begingroup$ It's easy enough to visualize the shape of the mirror. Take a mirror designed for a telescope and take a slice of 1/6 of it. From this section, trim the corners until you have an oval mirror. Now that we have computer control of the grinding, it is possible to make the mirror. Before computer control, it would have been nearly impossible to get the correct shape for the mirror. $\endgroup$ – LDC3 May 23 '15 at 5:06
  • $\begingroup$ Just a bit of background: telescope-optics.net/tilted2.htm $\endgroup$ – Wayfaring Stranger May 23 '15 at 12:21
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There is a 1.6 meter off-axis telescope for solar observation at Big Bear Observatory called the New Solar Telescope (NST). Off-axis is particularly helpful in solar observations because it reduces stray light and eliminates a rotating diffraction pattern which can be severe when the sun is the target. However, for most astronomical work the additional costs are just not worth it, yet. The extra mechanical costs may be greater than the extra costs for the optics. The total weight of optics and supporting structures of professional telescopes can be many tons. There is additional strain required to rotate and support an asymmetric structure like this, i.e. bigger motors are needed. Galaxies are not bright enough to produce diffraction patterns and the issue of stray light from nearby bright objects is far less of a problem than the foreground stars, zodiacal light, and night sky light actually in the line of sight. If a nearby star is producing a bothersome diffraction spike, one can usually rotate the field to avoid this. I am not saying that stray light or diffraction effects are never a problem, just that this is not a top problem and, if we need to trade down in size at all for an off-axis design, most astronomers would not accept it. Perhaps if relative costs for these telescopes come down in the future, they will be more common.

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Yes that does seem like the best possible scope design. They've been built by hobbyist astronomers (even with truss tubes holding the secondary/eyepiece section and a "tube" made out of cloth to block stray light).

I'm not sure if they did over 4 times the primary mirror grinding just to use an off-axis circle-ellipse that's less than a quarter the area of the mirror. That sounds like a lot of work and waste to get rid of diffraction spikes. Imagine grinding a mirror about a yard wide just to make a 12-16" telescope. Although you could cut and sell the rest of the mirror or use it to build an imaging scope for each CCD or something and still make a small regular scope from the middle. Maybe if you're really careful it'd be less work to grind the side of a parabola without grinding the rest of it. Especially if they sell off-axis mirror blanks now so you don't have to buy the costlier huge mirror blank, cut it and then be burdened with a mirror blank that has a circle cut out of it. I don't know, I know almost nothing about telescope making.

Other hobbyist telescope makers have built 1-vane secondary mirror supports cause they prefer fewer and worse spikes; and curved secondary mirror vanes, which have every possible angle somewhere along it in equal amounts instead of just orthogonal or triangular one so they spread out the spikes into a less bothersome halo.

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