Actually the original rule of thumb for the AO-7 was 10/10/10. 10th mag star on a 10 inch scope could correct at 10Hz. And remember this was in 1997-8 with the TC-211 guide chip, hardly a QE barn burner. What a giant leap when the TC-237 came along!
In my notes from 2007, my tests with a C11f/10 + ST8XME guide chip (the TC-237): exp time=0.1 sec, SNR=16 for 10.1 mag star using 3x3 binning and autodark.
So this is close to the 10/10/10 rule, although I would say the rule was a bit optimistic since you would likely be using a guide star with SNR~3. Below what I would consider a robust choice (I set ACP's minimum automatic guide star finder SNR to at least 7). But then again 10th mag guide stars are not falling on to your small guide chip all the time!
As mentioned by Eden and others previously, I think the actual elephant in the room is the isoplanatic path. While I believe it is larger than a few arcseconds (IIRC on the order of arcminutes depending on the type of deformation), even the most serious pro system today cannot overcome it, no matter how many kHz or higher orders are corrected. The input information, the guide star motion/deformation, is not correlated to the main image motion/deformation. The only way around this is an artificial guide star (e.g. a laser), or a bright star as the target.
One thing that always bothered me with the AO implementation: the bump algorithm. When the AO mirror/plate thingy gets past a predetermined point in its range of travel (say 50%), the software activates the normal guider relays to push the star back towards the middle of the guider chip, so that the AO deflection can be reduced below the threshold. Sounds ok at first but...the original SBIG implementation, and the MaxIm one I did, did not bump smartly.
The bump would activate the one relay (of N/S/E/W) that would push the star in the direction closest to back in the middle, and the relay activation time was a configurable, but constant number of seconds, 100 msec the default IIRC? With the AO7 running at high speed this actually worked ok since you would get multiple AO corrections while the guide star was slewing from the mount motors, hence the guide star sorta holding steady on the chip while the deflection percent was being reduced. So you wouldn't notice it too much.
With the somewhat slower AO8/AOL, or with fainter guider stars, where you are stuck at <2Hz update rate, the bump is noticeable. Plus it happened in the same direction for most of the exposure (DEC drift or RA drift is fairly constant for <1hr exposures). Additionally if the drift was at 45 deg from the RA or DEC axis, you would get two bumps in short order.
If you picked a larger bump time, you would get fewer bigger bumps. A small bump time meant lots of little ones as the deflection percentage straddled the threshold. What was better? I never really figured that one out...
So ideally the bump would be in the exact direction and the correct magnitude to get to deflection 0%, and slow enough for the AO to compensate for the motion, call it a drift correction slew. Or to be really smart the AO software would know the bump is happening and correct simultaneously without waiting for guide star exposures - this last one might be too smart and make things worse due to backlash etc but it looks good on paper
Best,
EB