The graphic elements of a document are reproduced on the surface of a workpiece (5) that is machined by focussed electromagnetic radiation (11), in particular laser radiation. In an installation for scanning the document and for machining the surface of the workpiece (5), the document, for example a drawing, is first scanned by electromagnetic radiation and an electronic reproduction of the document is prepared in the control and memory unit (16) that controls the installation. The surface of the workpiece (5) that takes the place of the document is machined according to this electronic reproduction. The same radiation guiding (3, 4) and focussing means (2), controlled by the same programme, are used for scanning and for machining. The machining process can be repeated on a plurality of workpieces (5). Small errors in the reproduction of the optical elements used in the focussing means (2) do not affect the quality of the reproduction. Only simple programmes are required for electronically controlling the installation. It is possible to include various quality control means in this process and in the corresponding devices.