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Light in a tapered thin-film optical waveguide radiates into the substrate because the waveguide mode in the taper becomes cut off. Our measurement of the radiation pattern shows that the light emerges from the taper as a narrow beam with an angular width of only 2°-4°. We have studied the problem based on ray optics and based on a wave theory of radiation modes. We also have demonstrated a film-to-fiber coupler in which an optical fiber collects all the light emerging from the taper.