Laser beam welding of geometric figures using OCT seam tracking

A measuring device for monitoring a laser welding process that is connectable to a machining device for machining a workpiece by a high-energy processing beam that is displaceable on the workpiece along a main machining path that corresponds to a contour of a closed geometric figure. The measuring device includes an optical coherence tomography unit having a measuring beam source for generating an optical measuring beam that is displaceable on the workpiece by at least one movable deflection unit. The optical measuring beam is displaceable on the workpiece along a first discrete measuring line, along a second discrete measuring line, and along a third discrete measuring line, in each case transversely with respect to the main machining path and intersecting same. The measuring device is configured for determining characteristic features of the geometric figure represented by the main machining path, according to the collected measuring data.