Jan75 I use a 80 mm and 328 mm guide-scope from TS, for example, and a ASI ZWO 220 mini camera (4 µm pixels) this yields a resolution of 2.52"/pixel.
It is not just the focal length of the guide scope but the spot diagram (sort of the magnitude of the point spread function) all the way to the edge of the guide frame of the scope, since we need multi-star guiding when using short guide exposures.
I'd recommend taking an image from the guide system and look at the HFD of an average star in that image. If you use ASIAIR, just use the Detect Star utility, even though the numbers you get from ASIAIR are actually sky background dependent (another poor implementation by ZWO; everything in ASIAIR seems to be a copycat of real programs, without any understanding of the basic principles).
In my case, I use a guide scope with 55mm aperture and 250mm focal length (Borg 55FL objective), together with a TS flattener that is really meant for their 60mm- f/6 scope -- but appears to work well enough to get good stars across an ASI178MM frame. With that, I typically get an HFD or around 2.3 pixels. So quite close to critical sampling, by luck -- which could explain why I could get so many guide stars even with low camera gain, that some other folks could not.
Centroids are computed based on this star diameter (which is typically way larger than the Dawes limit, and gets worse with poorer optics). So I have been depending on actually measuring the HFD to determine whether it is under- or over-sampled, rather than the theoretical star size (usually based on the Dawes limit).
Being oversampled is not bad, but you do loose star brightness (and need more camera gain). But you do not ever want it to be under-sampled, since centroid estimation becomes increasingly inaccurate. Imagine a star that is so small that 90% of it completely inside a pixel (with very little energy outside that pixel). That star can move and the centroid estimate will not change (i.e., centroid remains at the centroid of the pixel). That may be the case with the ASI220 camera with its giant pixels. If the measured HFD of a star is smaller than 1.8, I suspect that it will be problematical since the true HFD is probably even smaller.
With my current guide system, I can actually see centroid estimation errors from ASIAIR as I change the camera gain. With 11 to 12 stars, and 0.5 second exposures, ASIAIR is producing an error (i.e., it will steer the mount the wrong way even when the mount has no error in that frame) of the order of 0.3" to 0.4" RMS! By adding 20 dB more gain (200 gain steps for ZWO camera, and correspond to an analog linear gain of 10), the centroid error falls to the 0.2" to 0.25" region. (With that I can actually guide my RST-135e to 0.35" RMS total when there is no wind.)
Now, if your mount has large errors (say 0.9" RMS), then the centroid error is not a problem -- the mount is the problem (i.e., focus on fixing or replacing the mount instead of the guide scope). However, if the mount itself is capable of guiding to better than 0.5" total RMS, then getting a good guide scope/camera match is worth the money (the Borg 55FL objective itself is twice the cost of a ZWO SeeStar :-).
An easy way to watch for the errors is to first do a good polar alignment so that there is very little declination drift (10" to 20" is good enough). First calibrate PHD2 with declination guiding turned on. Wait for it to start guiding, and turn it off. Then turn declination guiding off and start guiding. Since there is no declination drift, a perfect centroid estimation should also show no declination error. But if you watch the declination graph, you will see it moving. The ASIAIR is telling the mount to adjust the declination motors even when it should not be, had declination pulses been turned on. You can then try adjusting the gain of the guide camera and see if the declination guide graph becomes better. Anyway, all these observations should help you understand the guide process (even though with the ASIAIR, it is hidden inside a black box).
For what its worth, I am increasingly (like some of the Cloudy Nights folks) leaning toward the ZWO mounts having some fundamental flaws. I don't think guide scope/camera tweaks will or can solve that.
Only a proper study and redesign -- after understanding what causes the current problems -- can do that. But what do you do with the customers have already paid for the current mounts, and does ZWO even have the necessary mechanical engineering talents to achieve that? Right now, they appear to just be deer caught in headlamps. The recent attempt to increase the MinMo is very telling of how much they understand (or, more accurately, do not understand) the characteristics that are important with mounts with large error slopes.
Superficially copying someone else's product without doing serious engineering work will lead to problems -- I think you will remember episode where the tantalum capacitor leaks that rendered electronics to fail after a few years, and also the exploding lithium batteries more recently. In both cases, the chemicals used were missing some critical stabilizing material which the copycats' spies did not manage to copy.
Chen
