According to a method for a depth measurement the depths of measuring points on a calibration surface are measured and correction values depending on differences between the measured values and known values are used and stored for a later correction. According to a method for the layer-wise production of a hollow the horizontal boundaries (xg, yg) for the removal of a layer (Si+1) depending on the hollow depth (z) were determined from the shape definition of the hollow. The measured values can be continuously stored and used for a later control of the laser processing device.