Problem with off set image

The 1st video is interesting. Are the shifted lines always associated with the werid laser head movement?
The 3rd video definitely points to missing steps.

Not clear if the issues shown in the 2 videos represent a single issue or multiple issues. I think the missing steps one should be more straightforward to address so suggest you start there and see if it changes the other behavior.

Have you done a thorough mechanical review of your laser? Good belt tension, no binding along the path, no debris in any travelling surfaces, no excessive backlash, etc. Try moving things by hand and feeling for any hitches or friction points, especially on the X-axis.

If you find nothing in that process take a look through this topic as it seems to be similar to what you’re seeing:
Closed shape multiple passes does not cut on same path - Hardware - LightBurn Software Forum
Bottom line reduce acceleration and speed and try to avoid resonance. Maybe try a test where you’ve significantly reduced these and see if you can reproduce the artifact. If not then start dialing up the settings until the issue manifests. Then you can determine your upper limit.

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