Scanning of sector and cosecant beams generated by a circular aperture

A method of scanning a one-dimensional shaped pattern generated by a circular aperture is presented. It is shown that the desired beam shape can be retained in the desired scan plane by superposing on the nonlinear phase distribution applied along and parallel to the meridian plane, a linear phase progression along the perpendicular direction. Analysis carried out using the stationary phase method of evaluating the integral reveals that the gradient of the linear phase progression is a function of position along the meridian plane of the aperture. Expressions for the phase functions are derived. Computed results on the phase distribution and the radiation pattern are presented.