This paper discusses how to calculate the surface of a mirror for shaping a directional pattern represented by a vector function of a single argument. A general representation of a mirror surface for an arbitrary wave-front shape of an illuminating beam is obtained in the form of the envelope of a family of surfaces. Each surface of the family transforms the entrance pupil into a beam with a planar wave front having a designated direction. For a spherical illuminating beam, the equation of the mirror is represented in the form of the envelope of a family of paraboloids of rotation. © 2005 Optical Society of America

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