A method for producing a coated component consisting of transparent or opaque fused silica, the method comprising the following steps: (a) providing a substrate of transparent or of opaque fused silica that comprises a coating surface; (b) applying a SiO 2 granulation layer to the coating surface, said granulation layer having an inner portion adjoining the coating surface and having a first granulation fine fraction, and an outer portion adjoining the free surface of the granulation layer and having a second granulation fine fraction, wherein the second granulation fine fraction is higher than the first granulation fine fraction; (c) sintering the granulation layer so as to form a dense SiO 2 surface layer, characterized in that the supplying the SiO 2 granulation layer according to method step (b) comprises: providing a dispersion containing a dispersion liquid that comprises amorphous SiO 2 particles which form a coarse fraction with particle sizes ranging between 1 μm and 50 μm and a fine fraction of SiO 2 nanoparticles having particle sizes of less than 100 nm, wherein the solids content constitutes between 70 and 80 wt.-% of the dispersion, and wherein the SiO 2 nanoparticles constitute between 2 wt.-% and 15 wt.-% of the dispersion, applying the dispersion to the coating surface by casting or spraying it thereonto so as to form a slurry layer having a layer thickness of at least 0.3 mm; and drying the slurry layer by removing the dispersion liquid at a rate and in a direction such that the removing of the dispersion liquid enriches the fine fraction in the outer portion of the granulation layer, thereby a casting skin is formed. (a) providing a substrate of transparent or of opaque fused silica that comprises a coating surface; (b) applying a SiO 2 granulation layer to the coating surface, said granulation layer having an inner portion adjoining the coating surface and having a first granulation fine fraction, and an outer portion adjoining the free surface of the granulation layer and having a second granulation fine fraction, wherein the second granulation fine fraction is higher than the first granulation fine fraction; (c) sintering the granulation layer so as to form a dense SiO 2 surface layer, characterized in that the supplying the SiO 2 granulation layer according to method step (b) comprises: providing a dispersion containing a dispersion liquid that comprises amorphous SiO 2 particles which form a coarse fraction with particle sizes ranging between 1 μm and 50 μm and a fine fraction of SiO 2 nanoparticles having particle sizes of less than 100 nm, wherein the solids content constitutes between 70 and 80 wt.-% of the dispersion, and wherein the SiO 2 nanoparticles constitute between 2 wt.-% and 15 wt.-% of the dispersion, applying the dispersion to the coating surface by casting or spraying it thereonto so as to form a slurry layer having a layer thickness of at least 0.3 mm; and drying the slurry layer by removing the dispersion liquid at a rate and in a direction such that the removing of the dispersion liquid enriches the fine fraction in the outer portion of the granulation layer, thereby a casting skin is formed. providing a dispersion containing a dispersion liquid that comprises amorphous SiO 2 particles which form a coarse fraction with particle sizes ranging between 1 μm and 50 μm and a fine fraction of SiO 2 nanoparticles having particle sizes of less than 100 nm, wherein the solids content constitutes between 70 and 80 wt.-% of the dispersion, and wherein the SiO 2 nanoparticles constitute between 2 wt.-% and 15 wt.-% of the dispersion, applying the dispersion to the coating surface by casting or spraying it thereonto so as to form a slurry layer having a layer thickness of at least 0.3 mm; and drying the slurry layer by removing the dispersion liquid at a rate and in a direction such that the removing of the dispersion liquid enriches the fine fraction in the outer portion of the granulation layer, thereby a casting skin is formed.