The invention relates to the production of a scintillator system which comprises an Anti-Scatter-Grid (20) and an arrangement of scintillator cells. In a first processing step, a rectangular pattern of slots (11, 12) is cut into the top surface of a scintillator crystal (10). An Anti-Scatter-Grid (20) is then inserted with one end into said slots and fixed there with a glue. Finally, the top layer (thickness d) is separated from the scintillator crystal (10) yielding the desired scintillator system.