Implementations of the present disclosure include methods, systems, and computer-readable storage mediums for determining a deviation between an actual position and a desired position of a laser machining head of a laser machining machine. Implementations include actions of selecting at least two different machining positions of the laser machining head, in which a laser beam emitted by the laser machining head is directed onto a desired position of a workpiece, moving the laser machining head into a first selected machining position and forming a through-opening into the workpiece at or around the desired position by operation of the laser beam, moving the laser machining head into a second selected machining position and detecting radiation generated by an interaction between the laser beam and the workpiece, and determining whether there is a deviation between an actual position of the laser machining head and the desired position based on the detected radiation.