Abstract: The invention relates to a device (10, 32, 56) for cutting a workpiece (12) by means of a working laser beam (14), comprising a housing (16), through which a path is made for the working laser beam (14) and which has a focusing lens (18) for focusing the working laser beam (14) onto the workpiece (12) to be cut within a working area (48), a lighting device (44) with a light source (46) for the incoherent lighting of the working area (48) of the workpiece (12) to be cut, a camera (32), coupled coaxially into the path of the working laser beam, for observing the working area (48) of the workpiece (12) to be cut, wherein an optical filter, which is substantially opaque to the working laser beam (14), is arranged ahead of the camera (32) in the path of the observation beam (22), and comprising a processing unit (56), which is designed for processing image data from the camera (32), in order to determine the geometry and quality of a slit (50) produced in the workpiece (12) by the working laser beam (14), wherein