An optical component has a substrate, on which at least one curved substrate surface is formed that defines an optical axis of the optical component, wherein the substrate surface is coated with a multilayer coating that is active in the ultraviolet region at a design wavelength λ0 and includes a first layer, applied to the substrate surface, made from a first dielectric material and at least one second layer, applied to the first layer, made from a second dielectric material. The substrate consists essentially of a crystal material that has an axially parallel crystal direction, running parallel to the optical axis, and edge crystal directions perpendicular to edge regions of the curved substrate surface. An angle between the axially parallel crystal direction and the edge crystal directions is at least 17°, and the first layer has an essentially untextured layer structure. An anisotropy, caused by the substrate structure, in the optical properties of the multilayer coating can thereby be avoided.