@Ken, @Gnomus, thank you very much for feedback!
Yes Ken, I have read this instruction.
And yes Gnomus you are correct, my step size and the number of positions are not fitting 100% the advises from the manual. But also with bigger step sizes I get similar results and I do not believe my problem has to do with step sizes and/or backlash compensation settings for following reasons:
For clarification I would like first to distinguish between "stepper motor position" and "focuser position".
For me "stepper motor position" is the number reported in the GUI of SGPro and which would change on pushing the coarse buttons, also if the motor is not attached to the knob of a focuser. It only counts the movements of the motor.
The "focuser position" is the actual position of the camera sensor relativ to the optical relevant parts (e. g. lenses) of the telescope.
Your desire is to keep the stepper motor position and the focuser position synchronous.
To make it easy, let's say you have a system, that if it is working in a mode without backlash (or slipping) 1 step of the stepper motor causes the focuser to change its position by 1 µm. Further assume that the system has a backlash of 500 steps.
This means (as far I have understood) that, e. g. if the last movement was IN and you move the stepper motor 1000 OUT, the stepper motor needs 500 steps before the focuser position starts to change. In result the stepper motor is moved out 1000 steps, but the focuser position has only changed by 500 µm outwards. Every further step OUT causes the focus position to change by 1 µm, but the system remains 500 steps asynchronous.
If you now move IN again, say by 1000 steps the same happens in the other direction and because of the backlash the focuser position is only changed by 500 µm inwards.
As net result you have moved the stepper motor 1000 steps OUT and then 1000 steps IN, while the focuser position has changed first 500 µm outwards and then 500 µm inwards.
The backlash compensation of SGPro "only" helps that, if the last movement was IN and you move 1000 steps out, the focus position is actualy changed by 1000 µm, (the system remains synchronous, after a single direction change)
For me that means, that even if you have the backlash compensation disabled you should achieve the focus position always at the same stepper motor position ± backlash of the system in steps.
But unfortunately my system behaves not like this.
The autofocus first moves IN (e.g. 100 step wise) to figure out the stepper motor position of the lowest HFR. It is moving inwards until the HFR starts getting higher for a while. Then the autofocus has to move out again to get this "lowest HFR position". But every time this position is too far out, and I have to move IN again manually to get the actual lowest HFR position, which always results into a lower stepper motor position than originally estimated.
As I have started a few days ago, I achieved the best HFR position at around 32000, in the meantime my best HFR position is around 16000.
That means in average the IN stepper motor movements are resulting less focuser movements than the corresponding OUT movements. Or in other words: to achieve the same focuser movement inwards and outwards, more stepper motor steps are required for the IN movement.
But what might the reason for this?
So far I have following hypotheses:
Slipping of the focuser or the stepper motor as the equipment is to heavy.
Counterargument: I think I should have observed more erratic changes of the HFR on moving the stepper motor
I have backslash only on moving inwards (on every single move)
Counterargument: I can observe continiously HFR changes on moving the stepper motor 20 step wise inwards. And if this sort of backlash is very small, it would not affect the auto focus routine at a single run.
Sorry for that long post and thanks a lot in advance for help with my problem.
Have a happy new year!