Device that illuminates a defined surface

An illumination device includes a radiation-emitting optoelectronic component and Fresnel optics including a Fresnel structure having annular ridges and annular grooves, wherein the ridges are configured as closed rings, the ridges and the grooves enclose an optical midaxis of the Fresnel structure, at least one first section of a ridge has a different shape in a predetermined angle range in relation to the midaxis than a second section of the ridge in a second angle range, and the ridges of the Fresnel structure include an inner face and an outer face in cross section through a plane of the midaxis, the inner face facing toward the midaxis in the radial direction, the outer face facing away from the midaxis in the radial direction, the outer face of at least one ridge having different angles in relation to the midaxis in two predetermined angle ranges in relation to the midaxis.