Embodiments pertain measuring the weld penetration depth, particularly in welding, drilling or machining processes carried out by means of a working laser beam, wherein a measurement light beam of a sensor system is coupled into a processing beam path of the working laser beam in a laser machining head and bundled or focused into a measurement light spot on the surface of a workpiece by means of focusing optics of the processing beam path. The measurement light beam reflected on the surface of the workpiece is then returned to a measurement and evaluation unit of the sensor system in order to obtain information on the distance of the surface of the workpiece from the laser machining head. In order to obtain a surface profile of the workpiece in the region of the vapor capillary, from which the position of the vapor capillary relative to the point of incidence of the working laser beam can be determined, the position of the measurement light spot on the surface of the workpiece is guided over the vapor capillary in the welding direction, as well as transverse to the welding direction. The measurement light spot is during the subsequent laser machining process moved into the determined position of the vapor capillary in order to measure the weld penetration depth.