minou14chat quite regularly this error is at 0.7" despite multistar guiding.
OK, multi-star guiding needs some explanation (the DONUTS paper that I linked to also uses multi-star guiding since it applies a Fourer Transform to the entire image to detect centroids).
Multi-star centroid guiding should be very good, as long as you understand how it works, and what are the pitfalls, and how to avoid those pitfalls (probably need to brew your own guide software to avoid all the pitfalls completely).
Multi-star guiding depends on the fact that even through the same atmosphere, each star scintillates and distort independently. I.e., the stars (even though they are in the same guide frame), are distorted by different pockets of atmospheric turbulence. Furthermore, the statistics are stationary and ergodic (most physical phenomenon are, but mathematicians like to be more general :-), which means that the error from time averaging of a single star is the same as the ensemble average of multiple stars. And further, it does not matter if you measure now, or one second from now ("stationarity").
What this means is that measuring the centroid for 1 second is statistically the same as measuring the centroid of the star in the next second. And measuring the star for 2 seconds is the same as averaging the centroid from two 1-second measurements. Each time you double the time, the variance (handwavingly, the square of the RMS value) halves. In otherwords, each time you double the exposure time of a guide frame, the RMS error falls by a factor of 1.414 (i.e., square root of 2). This is how you average out the atmospheric turbulence.
The problem is that for some mounts, you simply cannot afford to expose at a frame rate of 0.5 FPS. The guide star would have move substantially in that 2 second period.
This is where ergodicity comes in.
What ergodicity tells is that measuring two different stars for 1 second each will provide the same variance reduction as measuring 1 star for a total of 2 seconds. So, if you can measure two stars in a 1 second frame, it gives the same accuracy as measuring one star for 2 seconds. And, measuring 4 stars for 0.5 seconds is also equal to measuring 1 star for 2 seconds, etc. Every doubling of stars will half the varaiance, exactly like doubling the exposure time. Ergodicity at work.
Now, the problem with todays software is that the centroid averaging for multiple stars are weighted by their signal to noise ratio. This is wrong. What happends is that if there is a very bright star in the ensemble, the multiple star case falls back to just the error that is caused by atmospheric turbulence of a single star again, since its SNR is way higher that all the SNR of the other stars combined. I had descibed this and showed stellar SNR distribution in a posting here perhaps a month or two ago using stellar magnitude data from the Hipparchos catalog.
So, even when you perform multi-star centroid averaging for 12 stars, you often (because of the SNR weighting) only result in improving the variance by the equivalent of the improvement from using 2 to 3 stars, which is crap.
Because of stellar brightness distribution, you can improve the situation substantially by making the star selection not pick the two or three brightest stars in the field. If the guide algorithm does not do this for you, you can often force it by purposely applying enough gain so that the brighter stars become saturated and by default, they do not get selected by pretty much all guiding software I am aware of (since you cannot guide on saturated stars).
Better weighting function needs to be found and used. I actually have collected some data on centroid noise vs stellar magnitude (to use as the weights) a couple of months ago, but haven't had time to analyze what a good weighting function is. Ideally, the weights should be dependent on centroid accuracy and not stellar SNR.
The DONUTS multi-star guiding, for example, by the nature of extracting centroids using a Fourier Transform, uses the equivalent of uniform weights on hundreds, if not thousands of stars.
Incidentally, INDIGO includes a DONUTS algorithm in their library; but apparently requires large guide scopes to work well (at least according to an email from Peter Polakovic). I have not tried it myself. You can check GitHub to see the code -- probably the first multi-star guiding that is implemented for hobbyists.
Chen
