An apparatus for coupling out radiation from an optical fiber, includes a housing, and a stop having a stop opening for delimiting an output coupling angle of radiation that is coupled out of an output end of the optical fiber to a maximum output coupling angle with respect to a central axis of the stop opening, wherein the stop is arranged in the housing. The stop has a stop body made from a transparent material, the stop body has a first total internal reflection face for reflecting radiation that is coupled out of the output end of the optical fiber with greater output coupling angles than the maximum output coupling angle, and the stop body has a second total internal reflection face for reflecting radiation that propagates opposite to the radiation coupled out of the output end and is reflected back by a workpiece.