The present invention provides a method of and apparatus for marking or inscribing a workpiece (3) with high-energy radiation, more particularly with a laser beam (1), the workpiece (3) having a light-scattering surface (9) and the material of the workpiece (3) being transparent for the radiation wavelength, and a polymer matrix (7) being disposed on the workpiece (3) in such a way that the radiation passes through the workpiece (3) and its light-scattering surface (9) before impinging on the polymer matrix (7), characterized in that the light-scattering surface (9) of the workpiece (3) is wetted with a liquid or viscoelastic medium (11).