On Beaming due to coherent inverse Compton scattering

We calculate the beaming of coherent emission by means of geometrical optics. When spherical elementary waves are phase-coupled in that way that constructive interference occurs along one axis, the intensity is lower for off-axis viewing angles. The spatial angle of constructive interference shrinks to a fraction of $4\pi$ when the length scale of the emission region is larger than the wavelength of the radiation. This leads to an amplification of the received radiation in addition to the relativistic beaming caused by the relativistic radial outflow which is thought to be important for the radio emission of pulsars. The effect will be calculated by numerical methods and can be approximated by a simple analytic expression.