Geometrical optics is used to analyze the propagation of high-frequency radiation emitted by a point source in a circular orbit in the equatorial plane of an extreme Kerr metric black hole. Both the apparent position and the energy flux of the brightest images as seen by certain distant observers are calculated as functions of time, taking into account the changing surface brightness of the image and its changing angular size. When the star's orbit is close to the black hole and the observer is close to the equatorial plane, the energy flux is sharply peaked in time. The correlation between direction of emission in the frame comoving with the source and the asymptotic direction of a beam of radiation gives the time-averaged energy flux as a function of polar angle. When the orbit of the source is close to the horizon in coordinate radius, most of the radiation comes out near the equatorial plane.