matt_d Therefore if my periodic error was a pure sine wave with no harmonic content I should expect no better than 0.105 arc-sec/sec as a reality check when measuring the slope on my graph.
Yep, that is correct, if there are no harmonics, you would expect that a guide star would move by 0.105 arcsec for every second that of your guide camera exposure time. With a 1 second exposure time, the guide star would have moved by 0.105 arc seconds by the time you finished the exposure (a small star trailing that causes a lag in the feedback loop).
Remember too that you are measuring the slopes where it is avaialble of that sheet of paper. What ZWO shows is the part of the curve where p-p error is worst, not where the slope is worst.
However, notice that the harmonics from your perfect sine wave are quite destructive, since the second harmonic's slope (look at the chain rule when taking the derivative) will cause 2x the ∆y/∆t for a given p-p amplitude, the 3rd harmonic will contribute 3x, etc... These are exactly what causes the curves not to look sinusoidal. The more wiggles or flat topping, the higher the harmonic content (for example, a perfectly flat top square wave would produce a slope that is equal to the slope from the fundamental, the slope of the fifth harmonic of a square wave is also equal to the slope of the fundamental, etc).
So, what you can hope for is that the harmonics die down rapidly, and there is no flat regions anywhere in the curve -- which is not true for many of the curves that we already see.
If you are using an ASIAIR, you will also find another limiting factor, not from the gears, but from how the ASIAIR computes the centroid for the multiple star case. For 10 to 12 stars, and exposures around 0.5 seconds, the limiting factor is in the region of 0.3" to 0.45" RMS (i.e., even if your mount can do better, the total (RA + declnation) long term autoguiding will be limited to the 0.5" RMS. If you add 20 dB of gain beyond 12 stars (to saturate the brighter stars so that they get excluded from the centroid averaging), you can do a bit better and get it down to the 0.25" region depending on the region of the sky that you are getting guide stars from (just for the RA or declination individually), and only if your mount's mechanical precision allows it.
All this is for guiding at the celestial equator. As you move closer to the pole, the RA error goes down (right at the pole, there is no RA error at all -- the RA error is just the centroid extimate error that I described above). Don't get fooled by "good numbers" that shills put out on YouTube when the image is taken within 45º of the pole.
Chen
