Hi Anders,
I started using an AF3 with my setup (TS 115 f/7 reduced to f/5.6 -> 645mm focal length, ASI1600MM-Pro) a couple of weeks ago only and I've had good results using the polynomial method.

I use the full frame with an annulus between 25% to 70%, exposures are 1 second long, binned 2x2 (I've setup an average of 3 images for exposure, but I'm not sure if this parameter is used in the full-frame mode). Autofocusing takes only 8 exposures and the solution falls consistently within my critical focus zone. The whole process takes approximately 140 seconds.

I'm curious, why does your target move that much during focusing?

I leave auto-guiding on during focusing (I guide a non-moded HEQ5 with a 60mm guidescope at f/11 with an old ASI120MM and my guiding is consistently around 0.5" RMS*), but even if off it will move very little if I've got my PA right. 

* that is, when the ASI120MM is not glitching... :(

Ricardo
 

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