What is the reason why a circle is not round

That looks more like mechanical slop than a calibration issue.
Go over your belts and pulleys first.
Are you using a very high speed? What are your feed rates ?

• Jack Wilborn

  : Speeds are not typically higher than 500 mm/min. I just touched the belts and to my feel no slack. Linear lines look good. But just did a run now with a corner radius and the tangent line is not perfect (not so bad). I will do another test run with a 50 mm circle now.

Primary item to check is the set (grub) screws. This link is for Sculpfun machines, but most of the information appliea to all diode lasers.

• Jack Wilborn

  : Thanks. FYI my 50 mm OD circle measures x = 50.3 mm and y = 49.3 mm.
• Abel

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  @Jack Wilborn

  : Image shows mechanical issue.