In a grinding machine a measurement arrangement is provided for the monitoring of the processing of a work piece, especially to make tools. The measuring arrangement uses, preferably, combined transmitted-light and incident-light based techniques so that both the edges and surfaces and depressions on the work piece are detected precisely. The automatic measurements makes it possible to automatically adjust the process parameters for the grinding process so that changes due to temperature drift, mechanical imprecisions of the mechanical system of the grinding machine or wear on the grinding disks are automatically compensated. This makes possible production of relatively large batches within very close tolerances and with high precision.