"I see some refer to astigmatisms and "over corrections", and the like. How can I check for such anomalies? Additionally, while I understand how important mirror cooling to the ambient temperature is, perhaps I don't realize just how crucial that really is?"
A few quick tests when cooled and collimated in reasonably good seeing.
Try to evaluate the "snap" to the focus. If focus is fairly snappy, it's doing well. If it smashes through focus without any firm point where you know you're in focus, you likely have some spherical aberration. Spherical aberration does not have one focal point, it produces a small range of focus points from each zone.
So you get a set of "caustic" focus points instead of one focal points. As you focus through the caustic, the image seems to mush through them without really coming to one distinct focus. You cannot say how much SA, but you can tell if it's bad. However, with SA you will have a position of "best focus." If you can find that, it'll be kind of snappy and just fine.
Another clue for correction error is whether the defocused pattern is clearly defined on each side of focus. If it is or you are close, you're fine. If outside defocused pattern is more blurry, you have some undercorrection. If inside is blurry, you have some overcorrection. A little bit of undercorrection is not a bad thing, but overcorrection (like a turned edge) can be. So, if you see a difference in the sharpness of the pattern, it's better if it's outside focus.
Astigmatism you will get an elongated defocused pattern that flips 90 degrees on either side of focus. The amount of elongation is indicative of the amount of error. Defocus both sides not too far from focus and see. If it's slightly elongated, no worries. If it's noticeable, you have some problem.
Try to do your star testing close to focus with just a few rings, not the huge defocused pattern with the diagonal shadow in the center. Except, at this large defocus, you can check for zones and smoothness (in good seeing.)
Zones appear as brighter rings, brighter than the others (excluding the outer and inner most rings.) If you see a bright ring on one side of focus between the inner and outer ring, that's possibly a zone. Scroll to the other side of focus and see if that ring is darker than the rest. If so, you have a zone which may or may not be problematic.
A rough mirror, again in the best seeing you can get, will not be uniformly bright across the large defocus pattern with many rings and the secondary shadow. It'll actually look rough. The more uniform the larger defocused pattern is, the smoother it is.
None of these can quantify your mirror, just give you an idea of whether it's good, passable, or bad. Especially the snap to focus test. Try it on the moon, see if you can find a point on the moon you know you are in focus. If so, you're probably doing well. In the best moments of seeing, of course, and without seeing those "heat waves" if possible.
Edited by Asbytec, 01 February 2018 - 07:41 PM.